The Field Substellar Mass Function Based on the Full-sky 20-pc Census of 525 L, T, and Y Dwarfs

We present final Spitzer trigonometric parallaxes for 361 L, T, and Y dwarfs. We combine these with prior studies to build a list of 525 known L, T, and Y dwarfs within 20 pc of the Sun, 38 of which are presented here for the first time. Using published photometry and spectroscopy as well as our own follow-up, we present an array of color-magnitude and color-color diagrams to further characterize census members, and we provide polynomial fits to the bulk trends. Using these characterizations, we assign each object a $T_{\rm eff}$ value and judge sample completeness over bins of $T_{\rm eff}$ and spectral type. Except for types $\ge$ T8 and $T_{\rm eff}<$ 600K, our census is statistically complete to the 20-pc limit. We compare our measured space densities to simulated density distributions and find that the best fit is a power law ($dN/dM \propto M^{-\alpha}$) with $\alpha = 0.6{\pm}0.1$. We find that the evolutionary models of Saumon&Marley correctly predict the observed magnitude of the space density spike seen at 1200K $<T_{\rm eff}<$ 1350K, believed to be caused by an increase in the cooling timescale across the L/T transition. Defining the low-mass terminus using this sample requires a more statistically robust and complete sample of dwarfs $\ge$Y0.5 and with $T_{\rm eff}<$ 400K. We conclude that such frigid objects must exist in substantial numbers, despite the fact that few have so far been identified, and we discuss possible reasons why they have largely eluded detection.


INTRODUCTION
We now find ourselves at a moment in history where selecting parallax-based censuses of nearby objects from the hottest O stars to the coldest Y dwarfs is almost a reality. With the release of Gaia Data Release 2 (DR2; Gaia Collaboration et al. 2018) and Data Release 3 (scheduled for the first half of 2022), the astronomical community can begin extracting complete, volume-limited samples out to distances which provide exquisite statistics on the distribution of stellar types. As a result of operating at wavelengths <1 µm and selecting a conservative detection threshold, Gaia provides complete astrometry only for L5 dwarfs out to ∼24 pc (Smart et al. 2017). Extending this census to colder types, though, is more easily accomplished by ground-based or space-based astrometric monitoring at longer wavelengths, where late-L, T, and Y dwarfs are brightest. A complete, volume-limited census across all stellar and substellar types is extremely useful in a variety of investigations, including: (1) analysis of the mass function, (2) determining the frequency of binaries across all types, (3) providing a catalog of host stars around which the nearest habitable planets to our own Solar System can be searched, and (4) establishing correlations among colors, absolute magnitudes, spectral types, effective temperatures, etc. that can be applied to other samples whose parallaxes are unknown or not so easily measured.
In this paper we provide the cold dwarf complement to the complete, nearby samples being extracted from Gaia. Our contribution is twofold. One, we present analysis on a flurry of new discovereies by the Backyard Worlds: Planet 9 (hereafter, "Backyard Worlds") and CatWISE teams that in the last several months have helped to identify even more previously hidden members of the 20-pc census. Two, we present a set of 361 parallaxes measured by the Spitzer Space Telescope (hereafter, Spitzer) that, when combined with astrometric monitoring of other objects by the astronomical com-munity, establishes a complete, full-sky, volume-limited census of L, T and Y dwarfs out to 20 pc. We use this census to establish the shape and functional form of the mass function in the substellar regime.
This paper is organized as follows. In section 2 we provide motivation for studying the mass function and describe what can be learned from the results. In section 3 we build the seed list of targets for the 20-pc L, T, and Y census and describe how this parallels historical efforts to catalog nearby stars of types M and earlier. In section 4 we discuss our Spitzer data acquisition and the subsequent astrometric reductions, and we compare our results to other published parallaxes for objects with independent measurements. In section 5 we discuss photometric and spectroscopic follow-up in support of the 20-pc seed list. In section 6 we construct the final 20pc census, and in section 7 we examine outliers on various color-color and color-magnitude diagrams in order to more carefully characterize objects in the census. In section 8 we assign values of T eff to each object, then calculate space densities as a function of T eff , once we have determined completeness limits and completeness corrections. In section 9 we provide the best fits of these measured space densities to predictions. These predictions simulate space densities for various forms of the mass function passed through two different sets of evolutionary models. We also discuss the value of the low-mass cutoff and ponder why so few brown dwarfs with T eff < 400K have been uncovered to date. We conclude with future avenues of exploration in section 10.
The two main, competing forms for the stellar mass function are the power law and the log-normal. At a fundamental level, a power law would inform us that the physical process is scale-free, meaning that the mass of the natal cloud has no bearing on the final stellar mass distribution, only on the total number of objects formed. That is, the relative distribution of masses formed from a small cloud will be the same as that from a much more massive cloud. A power law functional form would therefore imply a single physical process reigning over all of star production. If a universal power law is the correct form, then averaging results over many different star formation sites -as we do when looking at an older, well mixed, volume-limited sample near the Sun -should still result in a mass distribution with a power law form.
Even if a power law form describes the observed data, it is common in Nature to find that it applies only above some minimum value. For example, in investigations such as the peak intensity of solar flares or the magnitudes of earthquakes, a power law fits the data well only if a minimum value is imposed (Clauset et al. 2009). To employ a reductio ad absurdum of our own, there must be a minimum value for the cut-off mass of star formation because Nature cannot create a star containing only one atom.
The log-normal form, on the other hand, is the result expected when there are many processes that contribute multiplicatively to the result. (Contrast this to a normal distribution, which is the result of processes that contribute additively.) As Kapteyn (1903) elegantly argued, even if some physical processes, like the swelling in diameter of a growing blueberry (or a stellar embryo), appear to be normally distributed -i.e., a symmetric distribution centered on some mean value -other quantities, such as the growing volumes of those blueberries (or stars), would necessarily have skewed distributions. He argued that skewed forms are, in fact, favored over symmetrical ones. Many of Nature's skewed distributions are well characterized by a log-normal form (Limpert et al. 2001), again implying that several independent processes are working together to produce the final outcome (Miller & Scalo 1979).
If a single functional form fails to describe the observed distribution over the entire mass range from O stars to Y dwarfs -and it is well known that there is a break in the shape of the mass function below 1 M (see Figure 2 of Bastian et al. 2010, who give an overview of the stellar initial mass function) -then the inflection in the shape of the mass function roughly corresponds to the mass at which a new set of physical processes is becoming dominant. In fact, the mass function may have several inflection points, indicating that separate sets dominate in different mass regimes.
Even with solid knowledge of the mass function's shape across the entire mass spectrum of interest -in our case, over the entirety of the brown dwarf masses -divining the physical causes responsible for that shape will be difficult. Nonetheless, knowing the shape enables a semi-empirical determination of the low-mass cutoff and allows us to build simulations that better reflect true space densities across all spectral types.

BUILDING THE TARGET LIST
Since the 1988 discovery of GD 165B (Becklin & Zuckerman 1988), large swaths of the astronomical community have contributed to uncovering hidden L, T and Y dwarfs in the immediate solar vicinity. New members of the 20-pc census have been announced not only by brown dwarf researchers specifically looking for examples (e.g., Kendall, et al. 2004), but also by researchers in unassociated fields who have serendipitously found others (e.g., Hall 2002, Thorstensen & Kirkpatrick 2003. New additions to the sample have been published as single-object papers (e.g., Ruiz et al. 1997, Folkes, et al. 2007); as part of large photometric (e.g., Delfosse et al. 1997, spectroscopic (e.g., Schmidt, et al. 2010), proper motion (e.g., Smith et al. 2014, Meisner et al. 2020a, or parallax surveys (e.g., from Gaia: Reylé 2018, Scholz 2020; or as the result of dedicated searches for companions around higher mass stars (e.g., Thalmann et al. 2009, Freed et al. 2003 or around other brown dwarfs (e.g., Volk et al. 2003. Construction of the census of the closest L, T, and Y dwarfs has been the effort of many dozens of lead authors presenting results in hundreds of publications.

A Nearby Census in its Historical Context
Compiling these results into a volume-limited data set is a difficult task. To place this in historical context, consider that the first parallax -that of the 3.5-pc distant 61 Cygni AB -was obtained in 1838 by Bessel (1838). Few stars were bright enough and near enough to the Sun to have accurate astrometry measured, but there was enough information seven decades later for Hertzsprung (1907) to compile what may have been the first list of nearby stars (see Batten 1998). It was not until 1913-1914 that the first M dwarfs with both a parallax and a measured spectral type were published -Groombridge 34 (Adams 1913) and Lalande 21185 (Adams & Kohlschütter 1914). This prompted Hertzsprung (1922) to update his previous paper, the new list having just under thirty stars confirmed to lie within 5 pc of the Sun. Just four years later, nearly a hundred nearby M dwarfs had been identified (Adams et al. 1926). Occasional updates on the 5.2-pc sample were made for years thereafter by van de Kamp (1930van de Kamp ( , 1940van de Kamp ( , 1945van de Kamp ( , 1953van de Kamp ( , 1955van de Kamp ( , 1969van de Kamp ( , 1971, the last update containing a total of sixty stars, including the Sun. Kuiper (1942) published a larger list, pushing out to 10.5 pc, that contained 254 individual objects. In more recent times, similar lists have appeared, such as the online list 1 of the top one hundred closest systems -which as of the last update in 2012 extends to a radius of 6.95 pc from the Sun -by the Research Consortium On Nearby Stars (RECONS) team, or the 8-pc census presented by Kirkpatrick et al. (2012) that contained 243 individual objects.
The above lists, however, have inadequate statistics with which to perform any meaningful analysis of the mass func-tion. Other lists, covering a more substantial volume, are clearly needed for this work, and such compilations were amassed in the latter half of the twentieth century. The 20pc catalog of Gliese (1957) contained 1,097 individual objects, and a second catalog was produced over a decade later (Gliese 1969) to update that number to 1,890. A supplement to the second catalog was published by Gliese & Jahreiß (1979) and listed an additional 462 objects. A third catalog, produced on CD-ROM (Gliese & Jahreiß 1991) but never published in a refereed journal, contained over 3,800 entries within 25 pc. A fourth catalog, promised around 1999 2 , never materialized. These catalogs have now been superseded by Gaia.
The list of nearby L, T, and Y dwarfs, on the other hand, has not been superseded, because Gaia can acquire accurate astrometry for L5 dwarfs out to only ∼24 pc, T0 dwarfs to only ∼12 pc, T5 dwarfs to only ∼10 pc, and T9 dwarfs to only ∼2 pc (Smart et al. 2017). As argued in , a 20-pc census provides adequate statistics for determining the mass function in the L, T, and Y dwarf regime, and 20 pc is also the maximum distance 3 at which a census of Y0 dwarfs can be constructed, given the sensitivity limits of Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) data. Best et al. (2020) have argued for a partialsky 25-pc census for low-mass mass function studies; however, their desire to perform astrometric follow-up from the United Kingdom Infrared Telescope (UKIRT) restricts them to −30 • < δ < +60 • , so their increase in volume over a fullsky 20-pc census is only ∼33%.
In order to construct a census of nearby, low-mass dwarfs, we began constructing an archive in 2003  to amass published discoveries of all L and T dwarfs along with their near-infrared photometry and spectral types. At the time the catalog was begun, the list of L and T dwarfs contained 277 objects. Shortly thereafter, the list had grown into a publicly available online database 4 listing 470 L and T dwarfs (Gelino et al. 2004). By 2009 this number had grown to over 650 L and T dwarfs (Gelino et al. 2009), and by late 2012, which was the last online update, the list had grown to 1,281 L, T, and Y dwarfs. Other researchers provided their own post-2012 updates; the Mace (2014) list had 1,565 entries and the List of UltraCool Dwarfs 5 had 1,773, although neither of those has been updated in the last 5+ years. One of us (CRG) maintains an in-house spreadsheet that captures new discoveries from the literature, and at its last update in Oct 2019, it contained 2,513 L, T and Y dwarfs.

Building a List of Probable 20-pc L, T, and Y Dwarfs
The efforts above provided the cornerstones for the building of a volume-limited census needed for this paper. For each of the known L, T, and Y dwarfs, the object's spectral type and magnitudes in the WISE W2 band and in H band, the latter of which is invariant between the 2MASS and MKO filter systems (see , were tabulated. Using the color/spectral type to absolute magnitude relations presented in Kirkpatrick et al. (2012) and Looper et al. (2008a), we calculated spectrophotometric distance estimates and retained all objects having d < 23 pc. Separately, we combed the literature in search of published trigonometric parallaxes for each of the known L, T, and Y dwarfs, many of which were already compiled in the CRG spreadsheet noted above. Objects with trigonometric parallaxes measured to better than 10% accuracy and falling within 20 pc were kept in our official nearby census, and those lacking a parallax with 10% accuracy or lacking astrometric follow-up entirely but having distance estimates within 23 pc were retained for further astrometric monitoring with Spitzer. This limit was chosen to account for margin of error in the distance estimates, the expectation being that most objects truly within 20 pc would have estimates placing them within 23 pc.
In , we used the Infrared Array Camera (IRAC; Fazio et al. 2004) to measure preliminary trigonometric parallaxes for those objects having spectral types of T6 and later. These results were based on data from Spitzer programs 70062, 80109, 90007, 11059, and the first year's data from 13012 (all with Kirkpatrick as PI). This left a gap in the L and T dwarf sequence between T6 and the latest type for which Gaia has complete coverage (∼L5). The aim of Spitzer program 14000 (Kirkpatrick, PI) was to astrometrically monitor those objects in the gap that lacked published parallaxes of high quality but were believed to fall within 23 pc. An extension to provide additional data points for these objects at the end of the Spitzer mission was further approved as program 14326 (Kirkpatrick, PI).
Meanwhile, old WISE data and newer Near Earth Object WISE (NEOWISE; Mainzer et al. 2014) data were being continually processed, searched, re-processed, and re-searched in hopes of uncovering new objects at the coldest types, since  found that the targets in that paper were not complete to 20 pc for any of the late-T or Y dwarf types. Specifically, their measured completeness limits ranged from 19 pc at T6 to only 8 pc at Y0. Both the Backyard Worlds (Kuchner et al. 2017) and CatWISE (Eisenhardt et al. 2020) teams were continuing to identify new candidate late-T and Y dwarfs from WISE data as Spitzer hurled toward its assigned decommissioning date in late-Jan 2020. As chronicled in Meisner et al. (2020a,b), candidates lacking extant Spitzer photometry were added to Spitzer photometric programs 14034 (Meisner, PI), 14076 (Faherty, PI), and 14299 (Faherty, PI). As these new IRAC data became available, we used the new Spitzer photometry to predict a distance to each candidate using the M ch2 vs. ch1−ch2 color 6 relation of . Such objects with spectrophotometric distance estimates <23 pc were the subject of yet another Spitzer astrometric follow-up program (14224; Kirkpatrick, PI).
Not all of the late-type candidates were included in programs 14034, 14076, or 14299, however, either because ch1−ch2 data already existed in the Spitzer Heritage Archive, mainly from our own, earlier programs (70062, 80109, or 11059), or because their discoveries occurred after the end of the Spitzer mission. These objects, which were selected by the community scientists of Backyard Worlds, team members of CatWISE, or both were uncovered via the same selection criteria discussed in Meisner et al. (2020a,b) and are listed in Table 1. Also included in this table are additional late-T and Y dwarf candidates, observed as part of Spitzer photometric program 14329 (Marocco, PI), that were discovered as part of the CatWISE2020 effort (Marocco et al. 2020b) and have not previously been published.  Table 1 continued 6 For brevity, we refer to IRAC's two short wavelength bands as ch1 for the 3.6 µm band and as ch2 for the 4.5 µm band.  Sometime after Spitzer program 14224 was selected for 246.5 hours of data collection, we were informed that, for unforeseen logistical reasons at the Spitzer Science Center, the originally planned 2019 Apr 15 start date of our observations would have to be moved to 2019 Jun 16 and that our allotted time would be halved. This had two ramifications for the intended science: (1) In order to get enough astrometric data points for a meaningful parallactic solution, we had to remove many of the original targets in the program, and (2) the later start date meant that we would only be able to obtain observations at one additional epoch for those targets with a visibility window that closed between Apr 15 and Jun 16, which was roughly one-third of the targets. As a result, we dropped most of the objects in our program with spectrophotometric distance estimates between 20 and 23 pc, along with some of those with the earliest types (around T6). We were also forced to rely more heavily on outside astrometry since our Spitzer data would now cover an insufficient time baseline to disentangle the effects of parallax and proper motion. More discussion of this can be found in section 4. Table 2 lists all 361 targets that were eventually observed in one of our Spitzer parallax programs. In total, 98.7% of the Astronomical Observation Requests 7 (AORs) in the table were from programs proposed by various WISE, CatWISE, and Backyard Worlds team members. We used the Spitzer Heritage Archive to supplement our 5,041 AORs with another 66 from other researchers, which primarily enabled us to extend the time baseline of the Spitzer data set. Table 3 lists the individual Spitzer programs whose data were used. Of these 66 supplementary observations, fifteen were taken during the original Spitzer cryogenic mission and were reduced using software applicable to that mission phase, as described in more detail in section 4.  (14), 13012 (12) a Full object designations can be found in Table A1.
b The units are Earth-based years. To translate into the number of Spitzer orbits of the Sun, multiply these values by ∼0.98.
NOTE-(This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.)

ASTROMETRIC DATA ACQUISITION AND REDUCTION
The reduction of the Spitzer astrometry used the same methodology as that outlined in section 5.2 of , with the following exceptions. First, the list of possible re-registration stars was paired not against Gaia Data Release 1 (DR1) but with the newer Gaia DR2 instead, as the latter contains five-parameter (α 0 , δ 0 , ϖ abs , µ α , and µ δ ) solutions for ∼70% of cataloged objects. Second, we used these full astrometric solutions to predict the perepoch positions of each re-registration star at the observation date of each AOR, thereby enabling us to measure absolute parallaxes and proper motions of the Spitzer targets directly 8 . Third, to assure that we had a sufficient number of five-parameter Gaia DR2 re-registration stars per frame, we set the signal-to-noise (S/N) requirement to S/N ≥ 30 per frame 9 ; in , we used S/N ≥ 30 only when the field for that target was starved of S/N ≥ 100 background stars. As stated in that paper, however, the inclusion of re-registration stars with 30 < S/N < 100 does not generally degrade the χ 2 values of the final parallax and proper motion solution compared to solutions using S/N ≥ 100 stars only. Fourth, one small modification to the astrometric solution was included for these new reductions. In , the mean epoch for all solutions was set to 2014.0 because the time span for each of the objects was similar. The time coverage of the new data set, however, varies greatly from object to object (see Table 2), so we have chosen to compute and report the mean epoch of each object separately. For those AORs in Table 3 that came from the cryogenic portion 10 of the Spitzer mission, we modified our reductions slightly. During the single-frame reduction step detailed in section 5.2.2 of , we ran the MOPEX/APEX software so that the Point Response Function (PRF) fitting made use of the PRF maps measured for cryogenic data. All data from the warm mission were, as before, reduced using PRF maps applicable to the warm phase.
As stated in section 3.2, some of our Spitzer astrometry from Cycle 14 lacked a sufficient time baseline with which to disentangle proper motion and parallax, so we supplemented the Spitzer data with positions derived from the un-WISE (Lang 2014) "time-resolved" coadds of Meisner et al. (2018a,b). The methodology is the same as that described in section 8.3 of Meisner et al. (2020a), which measures the positions of our sources on the time-resolved unWISE coadds whose astrometry has been re-registered to the Gaia DR2 reference frame. The unWISE measurements used here are the NEO5 version of the time-resolved coadds, covering early 2010 through late 2018. For this current work, however, the coadds were produced on an epochal basis; that is, because we needed a clearly defined time stamp, positions were not combined across differing time-resolved sets (usually spaced by six months), as was done in Meisner et al. (2020a) to increase the S/N of the final detection.
Because our planned observations between 2019 Apr 15 and 2019 Jun 16 never materialized (see section 3.2), thirteen of our 361 sources had Spitzer observations sampling only one side of the parallactic ellipse and thus, only a proper 8 For the twenty-five targets having full five-parameter solutions themselves in Gaia DR2, special care was taken to remove the target from the list of re-registration stars. 9 Source crowding in a few Galactic Plane fields, such as that for WISE 2000+3629, forced us to impose higher S/N cuts. 10 Cryogenic data, which are those prior to mid-2009, currently have a CRE-ATOR software processing tag with prefix of "S18" in their FITS headers, whereas data from the warm mission have "S19." Also, the Astronomical Observation Template type (AOT_TYPE) in the header will be tagged with a suffix of "PC" (post-cryogenic) for warm data but will lack this tag for cryogenic data. motion measurement was possible. For these cases, the same fitting procedure outlined above was used except that the parallax term was set to zero. For each target, a listing of all of the measured positions from our Spitzer reductions-and from the unWISE reductions, if applicable -is given in Table 4. Per the above discussion, all positions are re-registered to the Gaia DR2 reference frame and have uncertainties and time stamps attached. Additional information regarding registration of the unWISE astrometry can be found in section 8.3 of Meisner et al. (2020a).
Because the two sets of astrometry are taken from different positions within our Solar System -one from the Earthorbiting WISE spacecraft and the other from the Sun-orbiting Spitzer spacecraft -all observations were tagged with the XY Z positions within the Solar System corresponding to the Modified Julian Date (MJD) of the data. For Spitzer observations, these XY Z positions are tabulated by the Spitzer Science Center in the FITS image headers; for the unWISE epochs, we used the mean MJD of each epochal coadd and assigned to them the XY Z of the Earth at that time, using data available through the JPL Horizons website 11 . Note that the use of the Earth's position is sufficient since the unWISE epochal data themselves are an average over a few days of WISE observations near that mean epoch. Even with the inclusion of non-Spitzer astrometry into the astrometric solutions, no special modifications to the fitting routine employed in section 5.2.3 of  were needed. It should be noted that, with the exception of a very small number of confused observations noted in Table 2, all astrometric data points were used in the fits since no sigma clipping and refitting were performed.
In principle, the unWISE epochal astrometry was needed only for those Spitzer data sets that had observations covering fewer than three Spitzer visibility windows. In practice, however, we included unWISE data into the astrometric solutions for all objects in programs 14000, 14224, and 14326; the only exceptions were objects in common to program 13012, as these already had Spitzer observations spanning multiple years.
Plots of our astrometric measurements and their best fits are shown in Figure   Our astrometric results are summarized in Tables 5, 6, and 7. For each object, the RA and Dec position (in deg) with their uncertainties (in mas) are quoted at the mean epoch, t 0 , along with the absolute parallax (ϖ abs ) and absolute proper motions (µ RA and µ Dec ) and their uncertainties. Also listed are the chi-squared value of the best fit (χ 2 ), the number of degrees of freedom in the fit (ν), and the reduced chi-squared value (χ 2 ν ), along with the number of Spitzer (# Spitzer ) and WISE (# W ISE ) astrometric epochs and the number of Gaia DR2 five-parameter re-registration stars used (# Gaia ). The two values listed in the # W ISE column refer to the number of astrometric epochs in bands W1 (3.4 µm) and W2 (4.6 µm), respectively. We find that the median χ 2 ν value across all of our solutions in Tables 5, 6, and 7 is 1.03, indicating that our uncertainties are properly measured.
Given the wide range of parallax uncertainties found in our final astrometry, we should determine at what point the uncertainty is too large to give a credible result. Lutz & Kelker (1973) looked at populations of objects with differing parallax uncertainties to see at which values these uncertainties become so large that characterizing the true absolute magnitude of the population becomes impossible. For parallax uncertainties of 5%, the distribution of the ratio of the true parallax to the measured one resembles a Gaussian with a tight variance, but the central value is slightly less than one. This effect is predictable and thus correctable. When the astrometric uncertainty of the population reaches 15%, the effect is still correctable, but the distribution of true-to-measured parallaxes is broader and centered considerably further from unity than for the case of 5% uncertainties. Francis (2014) improves (and corrects) the formalism of Lutz & Kelker (1973), showing that the predicted absolute magnitude error is 0.1 mag for an astrometric uncertainty of ∼12.5%. (Lutz & Kelker 1973 state that for a magnitude error this small, an astrometric uncertainty of <10% is required.) Francis (2014) further demonstrates that the effect becomes uncorrectable at astrometric uncertainties between 17.5% and 20.0%. With these values in mind, we have chosen "high quality" parallaxes to be those with uncertainties ≤12.5%, "low quality" to be those with 12.5-17.5% uncertainties, and "poor quality (suspect)" to be those with ≥17.5% uncertainties. Table 5 lists 296 targets for which the uncertainty in the parallax is ≤12.5%. Results in this table can be considered robust. Table 6 lists 18 targets for which the parallax uncertainty falls between 12.5% and 17.5%. Results from this table should be used with caution, as additional monitoring is needed to drive these uncertainties lower. Finally, Table 7 lists 47 targets for which the parallax uncertainties are ≥17.5%. For most of these objects, the > 3σ detection of a parallax and/or proper motion proves that they are nearby, but derived distances and absolute magnitudes should be regarded as suspect. For these, additional astrometric observations from post-Spitzer resources are needed to establish credible values.   Figure 1b. Example of a target whose astrometric fit uses both Spitzer and unWISE data. (Upper left) A square patch of sky showing the measured astrometry and its uncertainty at each epoch (black points with error bars) plotted in RA vs. Dec. Points with small error bars are the Spitzer ch2 measurements; those with larger error bars are the WISE W1 and W2 measurements. The blue curve shows the best fit from the vantage point of Spitzer, and the orange curve shows this same fit as seen from the vantage point of WISE. Red lines connect each observation to its corresponding time point along the best-fit curve. (Upper right) A square patch of sky centered at the mean equatorial position of the target. The green curve is the parallactic fit, which is just the blue curve in the previous panel with the proper motion vector removed. For clarity, only the Spitzer astrometric points are shown, again with red lines connecting the time of the observation with its prediction. In the background is the ecliptic coordinate grid, with lines of constant β shown in solid pale purple and lines of constant λ shown in dashed pale purple. Grid lines are shown at 0. 1 spacing. (Lower left) The change in RA and Dec as a function of time with the proper motion component removed. The parallactic fit is again shown in green and only the Spitzer astrometry is shown. (Lower right) The RA and Dec residuals from the fit as a function of time. As with the lower left panel, only the Spitzer data are shown. Figure 1c. Example of a target whose astrometric fit uses both Spitzer and unWISE data but for which a parallactic fit could not be attempted. (Left) A square patch of sky showing the measured astrometry and its uncertainty at each epoch (black points with error bars) plotted in RA vs. Dec. Points with small error bars are the Spitzer ch2 measurements; those with larger error bars are the WISE W1 and W2 measurements. The blue curve shows the best proper motion fit. Red lines connect each observation to its corresponding time point along the best-fit curve. (Right) The RA and Dec residuals from the fit as a function of time. Only the Spitzer data are shown since the error bars of the WISE points would otherwise dominate the plot.   Table 5 continued           All 142 Spitzer targets from  have new measurements in this paper. A comparison between the measured astrometry for these objects is shown in Figure 2. No bias in the measured parallaxes is seen between the two sets of results, as shown in the top panel of the figure.
Biases are evident in the measured proper motions, however, in both Right Ascension (middle panel) and Declination (bottom panel). These differences are small; the offset (dotted red line) in the lower panel of Figure 2, for example, corresponds to a motion difference in Declination of −4.6 mas yr −1 . Other than the longer time baseline, the only difference between our new results and those of  is the methodology for calculating absolute parallaxes. In , a correction from relative to absolute was applied after the fact, whereas in this paper the Gaia DR2 parallax and motion values of the re-registration stars were used to measure the absolute astrometry of target objects directly. In , the post facto corrections were applied only to the parallaxes. Therefore, the differences in motion values between the two papers are just a reflection of the fact that the  motions were deliberately reported as relative whereas the ones in this paper are absolute.
We can illustrate this as follows. By not correcting the proper motions to absolute, the solar motion is imprinted on the values reported in , and this is reflected in the way the differences between the Kirkpatrick et al. (2019) relative motions and this paper's absolute motions behave around the celestial sphere. If we were to invent a coordinate system having the solar apex and antapex as its poles, then the difference between relative and absolute motions would be smallest toward the poles and largest at locations on the sphere 90 • away from the poles -i.e., along this coordinate system's equator, where the solar motion is reflected in an apparent "streaming" motion of the background stars. The solar apex is located toward (RA, Dec) = (18 h 28 m , +30 • ), meaning that this invented coordinate system is within 30 • of orthogonal to the equatorial system. This means that the differences between relative and absolute motions will be near zero at the apex (RA ≈ 277 • ) and antapex (RA ≈ 97 • ). Likewise, the relative proper motions will be maximally too high relative to the absolute ones near RA = 7 • (where the true motion and reflex solar motion add constructively) and maximally too low near RA = 187 • (where they add destructively). This is the same qualitative behavior exhibited in the middle panel of Figure 2. The uncorrected solar reflex motion itself will be a more constant offset along Declination, and the difference between relative and absolute motions in Declination will be negative since the solar apex lies north of the celestial equator. The bottom panel in Figure 2 qualitatively shows this behavior, too.

Comparison to Gaia Results
At the time objects were chosen for Spitzer program 14000, Gaia DR2 had not yet been released and the magnitude limit at which Gaia astrometry could be reliably measured was still unclear. Making a conservative guess resulted in an overlap of twenty-five objects that, fortunately, now enables a direct comparison to Gaia ( Figure 3). As all three panels of the figure illustrate, the differences between our measured absolute astrometry and that of Gaia are only marginally significant, those differences falling at the 0.8σ (where σ refers to the combined value; ∆ϖ abs = 2.8 mas), 0.9σ (∆µ α = 2.7 mas yr −1 ), and 0.6σ (∆µ δ = −1.9 mas yr −1 ) levels for the top, middle, and bottom panels, respectively. These values of the significance would shrink even further if, for example, it were found that the Gaia astrometric uncertainties for objects this faint were underestimated. For reference, these twenty-five targets have Gaia G-band values between 19.1 and 20.9 mag and quoted parallax uncertainties between 0.4 and 2.1 mas, the latter of which are typically only 3-4× smaller than those we measure with Spitzer.
The objects whose Gaia parallaxes we are using for comparison in Figure 3 are among the reddest and faintest objects that Gaia can detect. We can test whether the offsets seen between Gaia and our Spitzer results are pointing to an issue with the Gaia parallaxes themselves by comparing other Gaia parallaxes to independent literature values. Figure 4 illustrates this using parallaxes from Dahn et al. (2002), Dieterich et al. (2014), Winters et al. (2015), and Bartlett et al. (2017). Most of these parallaxes were measured by groundbased CCD programs, with the exception of those from Winters et al. (2015), who presented weighted parallax results using ground-based astrometry measured from photographic plates, CCDs, and infrared arrays as well as astrometry from Hipparcos 12 . In our figure, care was taken not to double count results, so any data from Winters et al. (2015) that were included in the other references were removed.
These astrometric offsets with respect to Gaia are plotted as a function of apparent G RP magnitude in the top panel of Figure 4. As G BP is known to be systematically underestimated for the reddest objects in Gaia )which in turn affects the G BP − G RP color -we instead use absolute Gaia G-band magnitude in the bottom panel as a proxy for color. Colors like B−R directly correlate with M G (or M V ) magnitudes across M and L dwarf spectral types (Pecaut & Mamajek 2013;Dieterich et al. 2014). The two panels also show a small bias between these published parallax values and those of Gaia, and the bias has the same sign as that seen in the Spitzer-to-Gaia comparison in Figure 3. Moreover, the two panels in Figure 4 suggest that there is a tendency for 12 We retained only those Winters et al. (2015) parallaxes built on absolute parallax values so that no additional relative-to-absolute bias would be introduced  Figure 3. Comparison of the astrometric results from this paper to those presented in Gaia DR2 for the twenty-five objects (blue stars) in common. Mean offsets along the y-axis are shown by the dotted blue line; the dashed black lines show 3σ excursions. Objects with χ 2 ν values of 1.5 or greater are marked by squares and are not included in the computation of the mean. this bias to increase with fainter apparent magnitude and/or redder color.
The cause for this bias, and whether it highlights an unknown issue with the faintest Gaia astrometry, is unknown. Smart et al. (2019) compared a larger list of previously published parallaxes to those of Gaia DR2 and also found a difference. They concluded that the discrepancy could be reconciled if either the uncertainties in the (heterogeneous) ground-based parallaxes or the Gaia uncertainties themselves were increased. Given that our new set of homogeneous Spitzer astrometry shows a similar discrepancy as previous ground-based measurements suggests that the Gaia uncertainties are underestimated.

Comparison of Spitzer+unWISE to Pure-Spitzer Results
Above, we hypothesized that the small offset seen in the parallax differences with respect to Gaia would shrink if the Gaia uncertainties were found to be underestimated. Another possibility, which we will dispel here, is that our own measurement technique has introduced a small bias.
The Spitzer parallax measurements used in Figure 3 were supplemented with data from unWISE in order to extend the astrometric time baseline. These objects, although they are among the faintest that Gaia can measure, are the brightest objects in the Spitzer program. For this reason, their high-S/N Spitzer data alone are sufficient to obtain quality parallaxes, so we have performed a special "Spitzer only" reduction to ascertain whether or not the inclusion of the un-WISE data has led to a bias. A comparison of the reductions with and without the unWISE data is shown in Figure 5. As expected, no significant difference is present, a bias having been detected only at the 0.2σ level. Best et al. (2020) As this paper was being written, the parallax compilation of Best et al. (2020) became available, allowing us to do a comparison of our Spitzer results to another independent set of astrometry. This comparison is shown in Figure 6. The offsets seen are at the 0.8σ (∆ϖ abs = 4.3 mas), 0.5σ (∆µ α = 1.6 mas yr −1 ), and 0.4σ (∆µ δ = 1.1 mas yr −1 ) levels for the top, middle, and bottom panels, respectively. Whereas our Spitzer parallaxes are slightly larger (by 0.8σ) than those of Gaia, Best et al. (2020) find that their UKIRT parallaxes are slightly smaller (by 1.6σ) than those of Gaia. Curiously, Best et al. (2020) also conclude that either their parallax uncertainties or those of Gaia are underestimated, at least the third such case in the recent literature to suggest that Gaia astrometric uncertainties may be too small for L and T dwarfs. 5. SUPPORTING DATA Distance is only one of the important quantities needed when characterizing sources for the mass function analysis. Photometry across the optical through mid-infrared bands is needed to better assess the temperature of each source, which is needed when building a mass function that is tied to T eff as   the "observable" parameter. Spectroscopy is another powerful tool, and the most reliable one when assessing the small fraction of sources that have unusual features. These oddities complicate our ability to assign objects to the correct T eff bins because their colors and spectral types follow relations that are different from the bulk of normal, single objects. For example, one oddity identifiable through spectroscopy is low metallicity, which may indicate an older subdwarf (e.g., Zhang et al. 2017). Another is low-gravity, which may indicate that the object is unusually young since it has yet to contract to its final, equilibrium radius (e.g., Faherty et al. 2016).   Yet another is unresolved binarity, particularly at the L/T transition where spectroscopic blending of features makes composite spectra easier to distinguish (e.g., Burgasser, et al. 2010b). In the subsections that follow, we describe the data acquisition and reduction implemented for our photometric and spectroscopic follow-up campaigns. A compilation of our photometric, spectroscopic, and astrometric data is listed in Table A1, which is described in the Appendix.

Facilities with 1-2.5 Micron Capability
The large-area archives searched for existing data were the Two Micron All-Sky Survey (2MASS; Skrutskie et al. 2006), the various UKIRT-based surveys being done with the Wide-field Camera (WFCAM; Casali et al. 2007) as part of the UKIRT Infrared Deep Sky Survey (UKIDSS; Lawrence et al. 2007), and the various surveys being done with the Visible and Infrared Survey Telescope for Astronomy (VISTA; Emerson et al. 2006) (B20) )/( 2 µ (this work) + 2 µ (B20) ) 0.5 Figure 6. Comparison of the astrometric results from this paper to those from Best et al. (2020), for the 124 objects (green points) in common. Mean offsets along the y-axis are shown by the dotted green line; the dashed black lines show 3σ excursions. Objects with χ 2 ν values of 1.5 or greater in either work are marked by squares and are not included in the computation of the mean. 2010). Data were examined using the online WFCAM Science Archive 13 and VISTA Science Archive 14 .
Given the complex spectral energy distributions of L, T, and Y dwarfs, care needs to be taken with regards to filter systems. The two filter systems employed by these nearinfrared surveys are those of 2MASS 15 and the Maunakea Observatories (MKO; Tokunaga et al. 2002). Because of bandpass differences between these systems, the magnitude measured in, for example, the 2MASS J filter may differ appreciably from the magnitude of the same L, T, or Y dwarf measured in MKO J. As a result, we report J magnitudes in both. The H-band filter bandpasses are essentially identical between 2MASS and MKO, so a single H-band magnitude is reported. The 2MASS K S -band and MKO K band are also reported separately. (Note that none of these large-area surveys uses the MKO version of the K S filter.) Per the recommendations given at http://horus.roe.ac.uk/vsa/ dboverview.html, we selected magnitudes with the string AperMag3 from both the WFCAM and VISTA Science Archives. For merged catalogs with multiple data sets per band, we chose the individual-epoch AperMag3 magnitude with the smallest uncertainty. Magnitudes combined over multiple epochs were avoided; because most of our objects have high motions, these combined magnitudes are generally incorrect because one epoch of blank sky has been averaged into the combined magnitude. That is, the catalog's crossmatching between epochs is done purely on position, not on source identification.
For sources not covered or detected by these large-area surveys, we obtained follow-up photometry using the 2MASS camera (Milligan et al. 1996)

Facilities with 3-5 Micron Capability
In Table A1, we have used the CatWISE2020 Catalog and Reject Table ) as the primary source of photometry in the 3-5 µm range. Specifically, we used the W1 and W2 magnitudes computed by the moving solutions (w1mpro_pm and w2mpro_pm) because these should be more accurate than photometry from the stationary solution given the high motions of our objects and the long, eight-year time baseline covered by the CatWISE2020 data. For comparison, we have also listed photometry (including W3) from the AllWISE Source Catalog and Reject Table. For AllWISE, we selected values from the stationary solution since these should be more stable than the moving solutions, as these were based on fragile motions measured over only a six-month time baseline. (For objects lacking AllWISE detections, the stationary solution from CatWISE2020 was used instead, as noted in the table.) Table A1 also contains Spitzer/IRAC photometry in ch1 and ch2. Data from both our photometric follow-up and astrometric monitoring programs were used. For the latter programs, which had many epochs of ch2 data, the PRF-fit photometry from each individual epoch was used; the reported magnitude is that resulting from the weighted mean flux. We also searched for ancillary data in the Spitzer Heritage Archive to further supplement our ch1 and ch2 measurements. Those ancillary data sets are listed in Table 8. We have reduced those data using the same mosaic portion of our astrometric pipeline, and report the resulting PRF-fit magnitudes in Table A1. In these reductions, we used the PRF suite applicable to the phase of the mission, either cryogenic or warm, during which the data were taken. For targets in campaigns using IRAC's "sweet spot" (Ingalls et al. 2012), we took only a portion of the resulting AORs since there is an enormous amount of data available; specfically, we selected a set of nine consecutive AORs toward the beginning of the campaign, another nine toward the middle, and another nine toward the end, and used those to build the mosaic needed for our pipeline.  Table 8 continued   NOTE-Program numbers followed by an asterisk were part of the Spitzer cryogenic mission and those with a suffix of "ss" used the IRAC "sweet spot".

Spectroscopy
We have obtained near-infrared spectra of some of the objects believed to lie within the 20-pc volume that lacked spectral types in the literature. These are listed in Table 9. Details on the observing runs and data reduction methods are given in the subsections below.

LDT/NIHTS
Two objects were observed on 2019 Nov 13 (UT) using the Near-Infrared High Throughput Spectrograph (NIHTS; Gustafsson et al. 2019) at the 4.3-meter Lowell Discovery Telescope (LDT) at Happy Jack, Arizona. The 1. 34-wide slit was used providing an average resolving power of 62 over the 0.9-2.5 µm wavelength range. A series of ten 120s exposures was obtained of both WISE 0613+4808 and WISE 2012+7017 at two different positions along the 10 -long slit. Flats and xenon arcs exposures were taken at the beginning of the night and the A0 V stars, HD 45105 and HD 207646, respectively, were obtained for telluric correction purposes. The data were reduced using the Spextool data reduction package , and telluric correction and flux calibration were achieved following the technique described in Vacca et al. (2003).

Keck/NIRES
Four objects were observed over the nights of 2018 Sep 01, Oct 27, and Nov 17, and 2019 Oct 28 and Dec 19 (UT) using the Near-Infrared Echellette Spectrometer (NIRES; see, e.g., Wilson et al. 2004) at the W.M. Keck II telescope on Maunakea, Hawaii. Setup and reductions were identical to those described in Meisner et al. (2020b) and covered a spectral range of 0.94-2.45 µm at a resolving power of ∼2700. Note that the spectra for Gaia 0412−0734 were combined across nights.

CTIO/ARCoIRIS
Eight objects were observed over the nights of 2018 Apr 01-03 and 2019 Jun 19 (UT) using the Astronomy Research using the Cornell Infra Red Imaging Spectrograph (AR-CoIRIS) at the Victor Blanco 4m telescope at the Cerro Tololo Inter-American Observatory (CTIO), Chile. Instrument setup and data reductions are identical to those detailed in Greco et al. (2019) and covered a spectral range of 0.8-2.4 µm at a resolving power of ∼3500.

IRTF/SpeX
Ten objects were observed over the nights of 2018 Jun 16, Nov 25, and 2019 Jan 22/23 and Mar 16 (UT) using SpeX  at the NASA Infrared Telescope Facility (IRTF) on Maunakea, Hawaii. SpeX was used in prism mode with a 0. 8-wide slit to achieve a resolving power of R = 100-500 over the range 0.8-2.5µm. All data were reduced using Spextool ). A0 stars were used for the telluric correction and flux calibration steps following the technique described in Vacca et al. (2003). (UT) using the Folded-port Infrared Echellette (FIRE; Simcoe et al. 2008Simcoe et al. , 2010 at the 6.5m Walter Baade (Magellan I) telescope at Las Campanas Observatory, Chile. Observations were done in high-throughput prism mode with the 0. 6 slit, which gives a resolving power of R≈450 covering 0.8-2.45 µm. Reductions followed the steps described in Meisner et al. (2020b).

Spectral Classification
The spectra were classified as follows. For the single optical spectrum of WISE 2126+2530 in Figure 7, we overplotted spectral standards from Kirkpatrick et al. (1997), which are based on the optical classification system of Kirkpatrick et al. (1991) and looked for the best match over the entirety of the spectral range. For near-infrared spectra in Figures 8  and 9, we also performed a best by-eye fit, but using the nearinfrared standards established by Kirkpatrick et al. (2010) for the L dwarfs,  for early-T through late-T, and Cushing et al. (2011) for late-T through early-Y. In total, we classify four objects as M dwarfs, eight as L dwarfs, and 38 as T dwarfs.
6. BUILDING THE 20-PC CENSUS 6.1. Objects to consider The newly reduced Spitzer astrometry, along with published literature values, now enables a refinement of the 20pc census. If an object has a trigonometric parallax measurement with an uncertainty ≤12.5%, we take that parallax at face value and retain the object if ϖ obs ≥ 50 mas. In this group there are a few objects that are worthy of special mention:  Figure 8. Spectra of M-and L-type dwarfs compared to the spectrum of the standard nearest in type. These near-infrared standards are taken from Kirkpatrick et al. (2010). The flux of all objects is normalized to one at 1.28 µm and offset by integral increments to ease comparison. Spectra of the target objects are in black and those of the standards in other colors. Our spectral classification of each target object is also shown in black and that of the nearest standard in other colors. Smoothing has been applied for some of the noisier target spectra.
• CWISE 0536−3055: Based on the data available to Meisner et al. (2020a), those authors were unable to confirm the motion of this candidate. Using the Spitzer ch1 and ch2 magnitudes and color, our type and distance estimates suggest a [T9.5] 16 dwarf at ∼17.4 pc. Our Spitzer astrometry from Table 5 gives a total proper motion of 37.4±13.7 mas yr −1 , which is different from zero only at the 2.7σ level. More telling, however, is the high-quality absolute parallax, which is 78.1±3.8 mas (only 5% uncertainty; Table 5) based on Spitzer astrometric sampling with good coverage over the parallactic ellipse ( Figure Set 1). CWISE 0536−3055 is therefore confirmed to be nearby and to fall within 20 pc of the Sun. This object represents a rare case in which the six-month parallactic motion (156.2 mas) is far (8.4×) larger than the six-  T7   T7   T8   T8   T8   T8   T8   T8   T9   T9   T9 T9 T9 Figure 9. Spectra of WISE-selected objects compared to the spectrum of the standard nearest in type. These near-infrared standards are taken from  and Cushing et al. (2011). See the caption to Figure 8 for other details.
month proper motion (18.7 mas). Obtaining a radial velocity of this object would inform us whether CWISE 0536−3055 is coming toward our Solar System or away, and how that translates into a closest approach distance.
• WISE 0546−0959: As with CWISE 0536−3055 above, this T5 dwarf has an exceptionally small proper motion of 11.8±3.5 mas yr −1 according to Best et al. (2020) or 10.3±2.5 mas yr −1 according to our Spitzer astrometry, despite its large parallax of 50.4±3.6 (Best et al. 2020) or 57.5±3.9 mas (our Spitzer measurement). In this case, the six-month parallactic motion is ∼20× larger than the six-month proper motion. In addition to objects with well measured parallaxes, there is another set of potential 20-pc members with poorer or nonexistent parallax measurements that need additional scrutiny. The objects are listed in Table 10 and are (a) pulled from Table 1 or Tables 6-7, (b) are objects originally included in Spitzer program 14224 but dropped because of time restrictions, or (c) are previously published objects rediscovered by the CatWISE or Backyard Worlds teams for which initial estimates indicated distances within 23 pc of the Sun. We use a combination of photometric and spectrophotometric distance estimates to determine whether each object should be included in the 20-pc census. Namely, we use data from 20-pc census members with robust parallax measurements (uncertainties ≤ 12.5%) to construct three independent relations of M J vs. J−W2 (valid for J−W2 ≥ 4.0 mag, or for 2.0 ≤ J−W2 < 4 mag if W1−W2 ≥ 2.2 mag), M H vs. near-infrared spectral type (valid for all L, T, and Y spectral types), and M ch2 vs. ch1−ch2 (valid for ch1−ch2 ≥ 0.4 mag). Using data provided in Table A1, we use the apparent magnitudes and colors of each object in Table 10 to estimate a distance from each relation, and then average the results to provide a final distance estimate. For some objects, there is not sufficient observational data for any of these relations -or the object has colors outside the range for which the relations are valid -so instead we use a M W 2 vs. W1−W2 relation (valid for W1−W2 ≥ 0.5 mag), also constructed from 20-pc members with robust parallax measurements, to provide a distance estimate. a This object is excluded for our 20-pc L, T, and Y dwarf census because its type is earlier than L0. We also provide spectral types in Table 10. For objects without measured spectral types, we provide type estimates by using the final distance estimate in the table combined with the object's ch2 magnitude to provide an estimate of M ch2 . We then take data from 20-pc census members having robust parallax measurement (uncertainties ≤ 12.5%) to construct a relation of spectral type vs. M ch2 (valid over the entire range needed, 10.5 < M ch2 < 16.0 mag), and use this to predict the type. (A value of M W 2 is used as a proxy for M ch2 when no ch2 magnitude is available.) These estimated types are enclosed within brackets in the table.
Several objects requiring special consideration are noted by "see text" under the Remarks column in Table 10. Those objects are discussed below: • 2MASS 0103+1935: This optical L6 dwarf  has two independent parallax measurements, both low quality, of 35.9±5.7 mas (Table 6) and 46.9±7.6 mas . Given that both measures suggest a parallax below 50 mas, we consider this object to fall outside of 20 pc.
• CWISE 0212+0531: This object was announced in Meisner et al. (2020a), although those authors were not able to confirm the object's motion. Based on the Spitzer ch1 and ch2 magnitudes and color, our spectral type and distance estimates suggest [≥Y1] at <13.3 pc. Our Spitzer astrometry from Table 7 gives a total proper motion of 82.6±52.7 mas yr −1 , which is different from zero at only the 1.6σ level. The resulting parallax is 24.7±16.3 mas, with one parallax factor being represented by only a single Spitzer data point ( Figure  Set 1). Because both the motion and parallax are insignificantly different from zero, and because the measured parallax is much smaller than the expected value, we consider this to be a background object.
• CWISE 0423−4019: Our Spitzer photometry suggests a [T9] dwarf at ∼16.5 pc. Our Spitzer parallax measurement of −11.7±6.9 mas and total proper motion of 3.8±3.3 mas yr −1 , however, show that this is a background object and not a nearby brown dwarf.
• CWISE 0424+0002: This object was announced in Meisner et al. (2020a), although those authors were not able to confirm the object's motion. Our Spitzer astrometry from Table 7 gives a total proper motion of 208.7±35.0 mas yr −1 , which is different from zero at the 6.0σ level. The resulting parallax is 37.4±11.7 mas, representing a 31% uncertainty, and there is only a single Spitzer data point at one of the maximum parallax factors (Figure Set 1). Our spectrum from Figure 8 confirms that it is nearby. Because the motion is confirmed but the trigonometric parallax is not yet credible, we use our (spectro)photometric distance estimates to place this object within 20 pc.
• CWISE 0442−3855: Our Spitzer photometry suggests a [T8.5] dwarf at ∼16.8 pc. Our Spitzer parallax measurement of −12.4±4.9 mas and total proper motion of 3.6±2.6 mas yr −1 , however, show that this is a background object and not a nearby brown dwarf.
• CWISE 0617+1945: Using the colors of this object in Table A1, we are unable to provide a distance estimate using any of our four preferred absolute magnitude relations. Using the MKO-based JHK magnitudes from Table A1, the color-color plots presented in section 7.4 suggest that this is a late-L dwarf, which would indicate M H = 13.8 mag and a distance of ∼7.5 pc. As further discussed in section 7.3, the object appears to have a co-moving companion to its north-east, which is faint enough that it does not strongly affect the distance estimate. We consider this pair to fall within 20 pc.
• ULAS 0745+2332: This object, discovered by Burningham et al. (2013), lies in very close proximity to a background star that complicated our Spitzer astrometric measurements, leading to a false, negative parallax (Table 7). This object is not detected in any of the various WISE catalogs consulted for Table A1. The discovery paper lists a T8.5 spectral type and estimated distance of <19.4 pc, so we include this object in the 20-pc census.
• WISE 0830+2837: This candidate Y dwarf from Bardalez Gagliuffi et al. (2020) is sufficiently red in its Spitzer colors to be a possible bridge source in T e f f between spectroscopically verified early-Y dwarfs and WISE 0855−0714. Given its estimated distance of ∼8.2 pc and our low-quality parallax of 90.6±13.7 mas, we consider this object to be well within 20 pc.
• CWISE 1008+2031: This object was announced in Meisner et al. (2020a), although those authors were not able to confirm the object's motion. Our Spitzer astrometry from Table 7 gives a total proper motion of 215.3±51.5 mas yr −1 , which is different from zero at the 4.2σ level. The resulting parallax is 37.1±15.1 mas, representing a 41% uncertainty, with the Spitzer astrometric sampling providing only a single point at one of the maximum parallax factors ( Figure Set 1).
Because the motion of this object confirms it as being nearby and our photometric distance estimates place it within 20 pc, we include it in the 20-pc census.
• WISE 1040+4503: This object was announced in Meisner et al. (2020a), although those authors were not able to confirm the object's motion. Our Spitzer astrometry from Table 7 gives a total proper motion of 91.7±32.3 mas yr −1 , which is different from zero at the 2.8σ level. The resulting parallax is 18.8±9.8 mas, representing a 52% uncertainty, with the Spitzer astrometric sampling providing only a single point at one of the maximum parallax factors ( Figure Set 1). Given that the photometric distance estimate is outside of 20 pc and that a distance within 20 pc is not suggested by the available astrometry, we exclude this object from the 20-pc census. It may, in fact, be a background object.
• CWISE 1047+5457: Meisner et al. (2020a) estimated that this is a [Y0] dwarf at ∼21.7 pc. Our low-quality parallax value of 75.2±12.8 suggests that it is closer. One of the maximum parallax factors is sampled with only one Spitzer data point ( Figure Set 1), but this together with the other data samples strongly suggest a parallax >50 mas. We consider this object to lie within 20 pc, although higher quality astrometry is clearly needed.
• CFBDS 1118−0640: This object, which is a common proper motion companion to the mid-M dwarf 2MASS J11180698−0640078, was included in our Spitzer parallax program through a mistake. Its spectral type of T2 was paired up incorrectly with the WISE magnitudes of the primary, resulting in a photometric distance of <20 pc. The Gaia DR parallax of the primary is 9.90±0.15 mas, and our Spitzer parallax of the companion T dwarf is 1.4±5.2 mas. This object is therefore excluded from the 20-pc census.
• CWISE 1130−1158: This object has wildly discrepant distance estimates, with those using colors predicting a value within 20 pc and the one using spectral type indicating a value well outside 20 pc. Our spectroscopic follow-up from section 5.2 suggests that this object has a peculiar spectrum, particularly a depressed K-band spectrum similar to that seen in other T-type subdwarfs (e.g., Pinfield et al. 2014a). We therefore classify this object as an sdT5?. Given its possible subdwarf status, neither the color-based nor type-based relations may be accurate. For now, we consider this object to fall outside 20 pc, but additional astrometry is needed.
• 2MASS 1158+0435: This is an optical and nearinfrared sdL7 ) placed on the parallax program because distance estimates for L subdwarfs are not yet well established. Our Spitzer parallax value of 39.2±6.2 mas is based on a well-sampled parallactic ellipse ( Figure Set 1), so we consider this object to lie outside of 20 pc.
• ULAS 1319+1209: Burningham et al. (2010) classify this object as T5 pec based on a T5 fit in the J band and a T3 fit in the H band. In preparing our list of target objects for the Spitzer parallax program, we mistook this object to be the bright proper motion star immediately to its north, which has an AllWISE value of W2 = 12.56±0.03 mag. This led to an incorrect distance estimate of ∼9 pc. Our Spitzer parallax (7.8±6.5 mas) was measured for this brighter star, Gaia DR2 3739496602924096000, not of the T dwarf 17 . Investigating this further, we find that the Gaia star, which is not listed in SIMBAD, has a Gaia DR2 parallax of 9.22±0.11 mas and motions of µ RA = −135.2±0.2 mas yr −1 and µ Dec = 3.8±0.2 mas yr −1 . The motion measured by Burningham et al. (2013) for the T dwarf is µ RA = −120.9±16.0 mas yr −1 and µ Dec = −22.9±14.6 mas yr −1 which is consistent within the uncertainties to those of the Gaia star. Murray et al. (2011) estimate the distance of ULAS 1319+1209 to be 75±12 pc and note that it might be a halo T dwarf, although Liu et al. (2011) contend that thick disk membership is more likely. Burningham et al. (2013) estimate that the T dwarf falls between 58.6 and 99.1 pc if it is a single object, and could be as distant as 140.0 pc if a binary. These higher values are consistent with the distance to the Gaia object at 108.5 pc. The Gaia star has teff_val = 3974K, which would correspond to a late-K dwarf, whose metallicity should be easily measurable. We believe that this may be a new benchmark system and a particularly valuable one since the T dwarf shows peculiarities that may or may not be linked to a lower metallicity.
• Gaia 1331−6513: This is another object, like CWISE 0536−3055 discussed above, that has a very low motion value given its proximity to the Sun (∼16.0 pc). The total motion from Gaia DR2 is 21.2±0.3 mas yr −1 , meaning that the parallactic motion over six months is twelve times larger than the proper motion. A 17 Because our measurements are not of a brown dwarf or even of an object within 20 pc, we have excluded this source from Table A1. measurement of the radial velocity would inform us whether this object is coming toward the Sun or away from it and the timescale for closest approach to the Solar System.
• WISE 1355−8258: This object was announced in Schneider et al. (2016), and Kirkpatrick et al. (2016) noted its unusual near-infrared spectrum, which they tentatively interpreted to be an sdL5. Bardalez  attempted to explain the spectrum as that of an unresolved binary but were unable to find a binary fit that provided a convincing explanation. They noted, however, a possible kinematic association with the AB Doradus Moving Group, despite finding no spectroscopic evidence of low-gravity. Their best guess for the distance is 27-33 pc. Using WISE astrometry, Theissen et al. (2020) measure a fragile parallax of 60±19 mas (32% error). Using a combination of 2MASS and WISE astrometry, E. L. Wright (priv. comm.) finds a still fragile parallax of 73±16 mas (22% error). For now, we consider this object to lie outside of 20 pc but encourage future astrometric monitoring in an effort to better understanding this intriguing object.
• CWISE 1446−2317: Marocco et al. (2020) show that the Spitzer colors of this object place it among the coldest Y dwarfs currently known. Our Spitzer parallax measurements of 95.6±13.9 mas, though somewhat fragile based on its poorly sampled parallactic ellipse ( Figure Set 1), nonetheless strongly suggests proximity to the Sun. We include this object within the 20 pc census.
• CWISE 1458+1734: This object is from Meisner et al. (2020a), who suggest a spectral type of [T8] and distance of ∼21.6 pc. Our Spitzer parallax measurement of 1.3±7.2 mas (Table 7) is based on a fit to a wellsampled parallactic ellipse. The proper motion of this source is measured at high significance, 503.6±26.1 mas yr −1 (Table 7), so the lack of a measurable parallax is puzzling. We have compared the UHS J-band image from 2013 May to our own J-band image taken from Palomar/WIRC in 2020 Jul ( Figure 10) and confirm a motion along nearly the same position angle indicated by our astrometric fit in Figure Set 1. We note, however that the position angle of the motion vector is almost perfectly aligned with the major axis of the parallactic ellipse, meaning that an incorrect motion magnitude could easily erase the parallactic signature. We have performed a test of this hypothesis by determining what value of the total motion is needed to create a parallactic signature matching the distance estimate in Table 10 while also assuming that the motion direction measured by our Spitzer+unWISE astrometry is correct. We get the correct result if the total proper motion is reduced from 504 mas yr −1 to ∼300 mas yr −1 . This hypothesis is supported by the fact that CWISE 1458+1734 is moving between -and is bracketed by -two background objects that themselves fall along nearly the same position angle as the proper motion, and it is thus conceivable the unWISE astrometry of the T dwarf is pulled southeastward at early epochs by blending from the southeast source and northwestward at later epochs by blending from the northwest source, thereby inflating the true motion value. Crude measurements of the astrometry from the images in Figure 10 give a proper motion of ∼305 mas yr −1 , confirming our hypothesis. Nevertheless, the photometric distance of this source places it just outside 20 pc, so it is not included in our 20-pc census.
• WISE 1534−1043: This object is from Meisner et al. (2020a), who note that its placement on the J−ch2 vs. ch1−ch2 color plot suggest it is a mid-to late-T subdwarf. As such, deriving a photometric distance estimate from relations that assume solar metallicity is useless. Too few late-T subdwarfs are known to enable a better distance estimate, particularly since we do not know if the object's metallicity is similar to or more extreme than known T subdwarfs, so our Spitzer trigonometric distance measurement of 47.8±14.3 mas (Table 7) is the best current indicator, despite the large relative uncertainty of 30%. The object's high proper motion, 2772.7±57.3 mas yr −1 , also points to an old, kinematically heated object. (At 20 pc, this would correspond to a tangential velocity of 263 km s −1 .) The <50mas parallax suggests that we exclude this object from the 20-pc census as we await additional astrometric measurements.
• WISE 1619+1347: This object was announced in Meisner et al. (2020b), although those authors were not able to confirm the object's motion. Our Spitzer astrometry from Table 7 gives a total proper motion of 29.1±16.6 mas yr −1 , which is different from zero at only the 1.8σ level. The resulting, negative parallax of −9.1±4.3 mas, is based on Spitzer astrometric data that sample the parallactic ellipse well ( Figure Set 1). We therefore consider this to be a background object.
• CWISE 1827+5645: This object was re-discovered by high school student Justin Hong as part of the Summer Research Connection at Caltech in the summer of 2020. The object was first discovered during the original WISE mission and chosen for Spitzer follow-up in program 70062, where it was measured to have a ch1−ch2 color indicative of a late-T dwarf. Subsequent Palomar/WIRC J-band imaging indicated a magnitude of ∼19.0 mag, ruling out the possibility of its being a late-T dwarf. The object was rediscovered again by the Backyard Worlds team but was paired up with a J = 19.33±0.17 mag UHS object -the same object seen in the Palomar imaging -and believed to be a more distant early-T dwarf based on its implied J−W2 color. This J-band source is, however, an interloper in the field and not the brown dwarf candidate itself. (The same background object also contaminates the proper motion measure from CatWISE2020.) The Spitzer photometry from 2012 is clean; this color, together with clear evidence of motion through the epochal coverage of WISE and NEOWISE images, indicates a [T9.5] dwarf just outside of the 20-pc census.
• CWISE 2058−5134: We are unable to provide a distance estimate to this object using any of our four preferred absolute magnitude relations. Our spectroscopic follow-up (Table 9) shows that this is a T0 dwarf, which would indicate M JMKO = 14.5 mag using plots illustrated in the following section. This suggests a distance of ∼33.9 pc. We consider this object to fall outside of 20 pc.

The Resulting Census and Final Checks
Our final, full-sky census of L, T, and Y dwarfs within 20 pc of the Sun is presented in Table 11. This includes not only solivagant dwarfs within that distance but also all known L, T, and Y dwarf companions to earlier type stars within 20 pc. For objects confirmed or believed to be double or triple systems, each component that is an L, T, or Y dwarf is listed.
The table lists each object's discovery name, discovery reference, and optical and near-infrared spectral types (with reference), if measured. The table also lists the absolute parallax  from Table A1 and the total proper motion, along with a reference for the astrometry. For cases in which either a spectral type or parallax is estimated, the estimated value is shown in brackets. (For the T eff values listed in the penultimate col-umn, the reader is referred to section 8.1.) The last column of the table is reserved for special notes. If a note of "[]" is listed, then that object's listed parallax should be ignored in favor of the spectrophotometric estimate shown in brackets. If a note of "yng" or "sd" is listed, that object is discussed further in section 7.                        a The astrometry listed is for the primary star in the system.
b Values in brackets are estimates only.
c This object's parallax has been converted from relative to absolute by adding 0.9±0.3 mas, per the discussion in section 8 of .
d A "yng" entry indicates that the spectrum of this object suggests low gravity and youth. An "sd" entry indicates that the spectrum of this object suggests low metallicity and hence, old age. A value in brackets indicates that the value of the parallax in the ϖ abs column is uncertain and that our distance estimate from Table 10 suggests the bracketed value be considered as the parallax instead.
e Analysis in section 7.7 shows that this object is probably a late-M dwarf. It has been dropped from subsequent analysis and not considered a member of the L, T, and Y dwarf census.
f The Gaia DR2 identifications for these sources are given in Table A1  Having now compiled the census, it is instructive to look back to previous attempts at assembling lists of nearby L, T, and Y dwarfs. These comparisons show how quickly our knowledge of this sample has evolved in just over fifteen years. Kendall, et al. (2004) published a list of the sixteen nearest L dwarfs, out to ∼11 pc. Of those, fourteen appear in Table 11, the two exceptions being objects now considered to be late-M dwarfs: SDSS J143808.31+640836.3, which Cruz, et al. (2003) classify as M9.5 in the optical, and 2MASSW J2306292−050227 18 (aka TRAPPIST 1), which Gizis, et al. (2000) type as an optical M7.5. Looper et al. (2008a) published a list of L dwarfs believed to fall within 10 pc. All ten of those objects appear in Table 11. Reid et al. (2008) published a list of ninety-four L dwarf systems believed to lie within 20 pc. Eighty-four of these appear in Table 11 Kirkpatrick et al. (2012) published the full stellar census within 8 pc, using a combination of preliminary trigonometric parallaxes and spectrophotometric distance estimates for the L, T, and Y dwarfs. All thirty-three of those L, T, and Y dwarfs appear in Table 11.  gave a listing of 235 L0-L5.5 and T6-Y1+ dwarfs within 20 pc but missed a few objects, discovered prior to their paper, that this new census now includes. In the L0-L5.5 range, a handful of component objects in systems known to be binaries or triples Finally, there are two objects noted in Best et al. (2020) as falling within 20 pc that are nonetheless excluded from Table 11. 2MASS J05160945−0445499 has a parallax listed by Best et al. (2020) as 54.2±4.3 mas, but a more accurate parallax of 47.83±2.85 mas from NPARSEC (Smart, priv. comm.), places this object just outside of 20 pc. WISEA J055007.94+161051.9 has a Best et al. (2020) parallax of 53.9±2.8 mas, but a more accurate Gaia DR2 parallax of 49.1169±0.8467 places it beyond 20 pc.
The above checks are illustrative of the fact that our knowledge of the nearby census is constantly changing. New objects are still being discovered. Some objects already known within the census are found to be binary (or triple), and some higher mass stars within 20 pc are found to have L, T, or Y companions. Some objects originally thought to lie within the volume are found, once better astrometry is available, to fall outside. And objects are sometimes discovered then forgotten simply because there does not exist a living, publicly available database that adequately captures this information. Nonetheless, our knowledge -and our completeness -of this census is improving with time, thereby enabling a more robust look into the low-mass products of star formation. 7. CHARACTERIZING THE 20-PC CENSUS With the census of L, T, and Y dwarfs within 20 pc now compiled, we can begin to study the field mass function. As described in section 8 below, we must compute space densities binned by effective temperature so that we can compare the empirical data to mass function simulations. This requires us to calculate an effective temperature for each individual object. Most objects can be assigned temperatures using relations typical of old, solar-metallicity field objects, but some objects within the census are young or low metallicity. To handle these properly, we first need to identify which objects they are. Moreover, because we want to assign temperatures to individual objects, this means recognizing when objects are unresolved multiple systems, to the extent that our existing data can help to address that. In the next subsections we delve into this characterization of the census, as a prelude to determining the space densities we need.

Low-gravity (Young) Objects
Brown dwarfs with ages less than ∼100 Myr have not yet fully contracted to their final, equilibrium radius  and are identifiable through spectroscopic and photometric signatures that indicate a lower gravity than normal, old brown dwarfs that have fully contracted. These young brown dwarfs represent a challenge to determining the mass function via our methodology because the standard mapping of spectral type, absolute magnitude, or color into effective temperature does not apply to them . Young objects that fall within the 20-pc census need to be identified so that they can be placed into the correct bins of T e f f .
On the other hand, these same objects also represent an opportunity to probe the low-mass cutoff. Objects below a few Jupiter masses are generally very difficult to find if formed billions of years ago because of the intrinsic faintness resulting from their long cooling times. However, objects of similar mass can be much more easily detected when they are younger because they will be much warmer and brighter.
An isolated brown dwarf that shows signs of low gravity, if it can be associated kinematically to a moving group or young association of known age, can be placed on theoretical isochrones to produce a mass estimate. Although it was once believed that a large reservoir of rogue planets -objects that escaped their original protoplanetary disks -existed in the Milky Way (Sumi et al. 2011), microlensing results with more robust statistics have shown that the population of field objects having masses down to at least a few Jupiter masses appears to be drawn from the same population as higher-mass brown dwarfs and stars (Mróz et al. 2017). Thus, such young brown dwarfs can serve as independent probes of the lowmass cutoff value of star formation itself.
Spectroscopic signatures of youth have been noted in late-M, L, and even some T dwarfs (e.g., Cruz et al. 2009;, and classification systems have been developed to incorporate these. The most commonly used system (Kirkpatrick 2005) assigns a suffix of β, γ, or δ to the core type to indicate the degree to which lowgravity signatures are evident, with the infrequently used α suffix assigned to spectra with gravities typical of old field objects. Faherty et al. (2016) note that a fraction of objects assigned β designations seem not to belong to any known, young moving groups, and some young associations of presumably fixed age can contain objects with both β and γ designations. Sengupta & Marley (2010) point out that the rotation rates of some brown dwarfs can make them oblate, but non-sphericity in an old object seen equator-on is unlikely to produce the radius inflation needed to turn an α classification into a β classification, for example. The differences between the two classifications is thought to be around 0.5 dex in log(g) (see Figure 9 of Burrows et al. 1997), so a simple calculation shows that a radius increase of 10× would be needed to achieve the effect. Gonzales et al. (2019) has further noted that the late-M dwarf TRAPPIST-1, though presumably of field age, nonetheless has near-infrared spectral indices indicating an intermediate gravity. If this star's radius is truly inflated, it could be due to magnetic activity or to tidal interactions by the numerous planets in its solar system. (It has also been shown that low-gravity indices can some-times be incorrectly assigned in the near-infrared for subdwarfs [Aganze et al. 2016], although a more careful analysis of the overall spectral energy distribution can eliminate this problem.) For the remainder of our analysis, we will regard β designations to be true indicators of low gravity even if youth cannot confidently be assigned through moving group membership.
Several L, T, and Y dwarfs in the 20-pc census (Table 11) are known to have low-gravity features. Given that our Spitzer monitoring has improved the astrometry for many of these targets, we can now run analyses to determine if there are any objects found to be high-probability members of any known moving groups but lacking spectra or having spectra where gravity diagnostics are less clear. For this exercise, we consider only those objects in the 20-pc census having measured trigonometric parallaxes, and we use two separate tools that can assess membership probabilities based on the subset of kinematic data we have -positions, distances, and motions, but not radial velocities. The first tool is Banyan Σ , which uses Bayesian inference to compute the membership probabilities for twenty-nine different associations within 150 pc of the Sun. For our set of input parameters (RA, Dec, ϖ abs , µ α , µ δ ), Banyan Σ uses Bayes' theorem to marginalize over radial velocity, and the Bayesian priors are set so that a probability threshold of 90% will recover 82% of true members. The second tool is LACEwING , which determines the membership probabilities in 16 different young associations within 100 pc of the Sun. Unlike Banyan Σ, the LACEwING code takes a frequentist approach and works directly in observable space (proper motion, sky position, etc.) rather than in XY Z and UVW for its probability computations. Table 12 shows the results of our Banyan Σ and LACEwING runs. The table retains only those objects that have β or γ spectral classifications ("Sp.Type Opt" or "Sp.Type NIR", copied from Table 11) in the literature, have a Banyan Σ probability of ≥90% for young association membership, or have a non-zero LACEwING probability for membership. Other columns list the possible associations assigned by Banyan Σ and LACEwING. When there are multiple moving groups that match, the relative probabilities are listed for those groups having at least a 5% probability. The final columns list whether or not the spectrum shows lowgravity features ("Low-g?"), whether the results suggest possible membership in a moving group ("Assoc. Memb.?"), the published reference first noting the object's possible youth ("Youth Ref"), and the mass estimate and its published reference ("Mass" and "Mass Ref.") for any objects with established membership. Ref.
(1)  b By definition, this member of the AB Doradus multiple star system is a member of the AB Doradus Moving Group. Because this companion to the C component of the system has not been independently confirmed, it is not included in subsequent analysis.
Objects in Table 12 that have "yes" under the "Low-g?" column are ones for which a low-gravity classification exists. For these we assign their T e f f values using each object's measured near-infrared spectral type and the relation from spectral type to effective temperature applicable to young objects, as given in Table 19 of Faherty et al. (2016). For all other objects in the table, we assume that relations applicable to objects of normal gravity apply.
A number of objects in this table have full space motions available and have been confidently assigned membership in a young moving group. This has allowed researchers to identify several members of the 20-pc census that have masses below 25 M Jup . Presently, there are no young moving group members within 20 pc that push below 10 M Jup , although other members of lower mass have been identified at larger distances from the Sun.   Kirkpatrick et al. 2011 that is not noted for any peculiarities.) For these potentially young objects, obtaining radial velocities to determine robust membership may be quite difficult, but establishing new ultra-low-mass objects in the 20-pc census would provide extremely valuable knowledge.
Finally, we note that the Faherty et al. (2016) young relations show that young M9 and M9.5 dwarfs fall into the same 2100-2250 K bin as early-L dwarfs of normal gravity. This means that such objects need to be included in our present census so that this temperature bin is complete. The only known low-gravity dwarf in Faherty et al. (2016) that matches this criterion and falls within 20 pc is LP 944-20, but that object is believed to be somewhat older (475-650 Myr; Tinney 1998) than the low-gravity dwarfs needing special T e f f estimates and therefore is not considered further here.

Low-metallicity (Old Subdwarf) Objects
There is a sizable number of objects in the 20-pc L, T, Y dwarf census of Table 11 that have subdwarf spectral types or peculiar spectra whose features are attributed to low metallicity. See Zhang et al. (2017Zhang et al. ( , 2018Zhang et al. ( , 2019 for comprehensive lists of known sdL and sdT dwarfs. Because subdwarfs are generally older objects, it is no surprise that our volumelimited census has few subwarfs of type sdL (two) but many of type sdT (thirteen): unless the object is very near the stellar/substellar mass boundary, it will have cooled to later types given its long lifetime. These low-metallicity objects are listed below: • WISE 0448-1935: This T5 pec dwarf was discovered by Kirkpatrick et al. (2011), who noted an excess of flux at Y -band and a flux deficit at K-band relative to the T5 spectral standard. They note that such features are common to other known or suspected lowmetallicity T dwarfs.
• 2MASS 0645−6646: This object had the highest proper motion of all new discoveries listed in the 2MASS motion survey of Kirkpatrick et al. (2010), who classified it as an sdL8. It is one of only two Ltype subdwarfs within the 20-pc census. Likely due to its very southerly declination, it has received far less follow-up than many of the more distant L-type subdwarfs known.
• 2MASS 0729-3954: This T8 pec dwarf was discovered by Looper et al. (2007), who noted excess Y -band flux and depressed Hand K-band fluxes relative to the T8 standard. They noted that such features are seen in other T dwarfs suspected of low metallicity and/or high gravity.
• WISE 0833+0052: This object was discovered by Pinfield et al. (2014a), who classified it as a T9 with a suppressed K-band flux. They note that the blue Y − J color was not evident in the confirmation spectrum, but would otherwise point at a Y -band excess like that seen in other T dwarfs suspected of having a low metallicity.
• 2MASS 0937+2931: This T6 pec dwarf was discovered by Burgasser et al. (2002), who noted the highly suppressed K-band peak in its spectrum. Those authors argued that for a fixed effective temperature and composition, an older and more massive T dwarf would necessarily have a higher photospheric pressure than a younger object of lower mass, which would increase the relative importance of the collision induced absorption (CIA) by H 2 . Another possible hypothesis for the deficit of flux at K-band, they argued, is decreased metallicity, which also increases the relative importance of CIA H 2 . Of course, a combination of both effects -both a lower metallicity and an extreme age/high mass -could be contributing to the suppression of the K-band flux by CIA H 2 . We will also note here that theoretical models of CIA H 2 by Borysow et al. (1997) demonstrate that this absorption in T dwarf atmospheres is strong across the J, H, and K bands, although stronger at K than at H and stronger at H than at J. This would have the additional effect of enhancing the Y -band flux relative to J while flattening the K-band flux peak.
• 2MASS 0939-2448:  note a broader Y -band peak in this object along with a depressed K-band peak. Those authors found that the Kband depression is much greater than that allowed by models that cover a physical range of gravities, leading them to conclude that a lower metallicity was the primary cause.
• LHS 6176B (0950+0117): This object was discovered by Burningham et al. (2013), who established its companionship with the M dwarf LHS 6176A, which has a metallicity of [Fe/H] = −0.30±0.1 dex. The published near-infrared spectrum in that paper appears to show a depressed K-band and what may be a broader Y -band peak as well, although the spectrum only samples part of the Y -band itself.
• Gl 547B (1423+0116): Also known as BD+01 2920B, this T8 dwarf is the companion to an early-G dwarf. The discovery spectrum from Pinfield et al. (2012) shows a broader Y -band peak and more depressed Kband peak than the spectral standard of the same type. Those authors list the metallicity of the primary star as [Fe/H] = −0.38±0.06 dex, which directly links the Yand K-band peculiarities of this companion and other objects in this list to a lower metallicity cause.
• Gl 576B (1504+0537): Also known as HIP 73786B, this object was uncovered as a common-proper-motion companion by Scholz (2010). Murray et al. (2011) found that the primary star has a metallicity of [Fe/H] = −0.30±0.1 dex, and that the spectrum of the secondary has depressed Hand K-band peaks. (Their spectrum does not fully sample the Y -band peak.) Zhang et al. (2019) classify this companion as an sdT5.5.
• WISE 1523+3125:  discovered this object and noted that it has the same Y -and K-band peculiarities noted for known subdwarfs.
• WISE 2005+5424: This is an sdT8 from Mace et al. (2013b) and a companion to Wolf 1130A, whose • WISE 2134-7137: This object was discovered by Kirkpatrick et al. (2011). As they note, the spectrum of this object exhibits excess flux at Y and depressed flux at K, which could suggest lower metal content.
• WISE 2325-4105: This object, which was discovered by Kirkpatrick et al. (2011), has a spectrum exhibiting excess flux at Y and depressed flux at K. Both of these traits are common to most of the objects on this list.
A few other suspected subdwarfs within the 20-pc census are listed in section 7.6 below. A number of other L, T, and Y multiples in the 20-pc census are further discussed below. Each of these has likewise been confirmed via imaging and/or motion. (For systems with a suspected, but not confirmed, tertiary component, the component's suffix is shown in brackets.)

Confirmed L, T, and Y Multiples
• GJ 1001BC (0004-4044): Using multiple instruments on the Hubble Space Telescope (HST), Golimowski et al. (2004) discovered that the mid-L dwarf GJ 1001B was a binary. The multiple observations over different epochs confirmed that the binary is a common-propermotion pair.
• DENIS 0205−1159AB[C]: The host object in this system was discovered by Delfosse et al. (1997). The B component, which was discovered through Keck Observatory imaging by Koerner et al. (1999), was found by Bouy et al. (2005) through Hubble Space Telescope imaging to be elongated, leading to speculation that B is a close binary. It appears that the C component has never been independently verified.
• SDSS 0423−0414AB: The primary in this system was discovered by Geballe, et al. (2002). The companion was discovered by Burgasser et al. (2005) using imaging from the Hubble Space Telescope.
• CWISE 0617+1945AB: This object is new to this paper. Publicly available UGPS K-band images from 2010 Nov 16 UT and 2013 Apr 03 UT, which clearly show the source's motion to the WSW, also show a common-proper-motion companion 1. 3 arcsec to the NW ( Figure 11). The CatWISE2020 Catalog gives motions of µ α = −103.80±4.0 mas yr −1 and µ δ = −59.80±3.8 mas yr −1 for the A component. Only the A component is listed in Gaia DR2, but it has no parallax or proper motion measurements reported there. Null information in these columns is generally taken to mean that the five-parameter astrometric solution of position, parallax, and proper motion could not converge over the small time baseline of Gaia data available for DR2. This may be evidence that the source is an unresolved physical double whose orbital motion was confounding the Gaia fit. It is also possible that the A component is confused by an object in the background except that POSS-II F (red) and N (nearinfrared) plates from the mid-1990s do not show any comparably bright background source at the present position that would be compromising Gaia's astrometry. A plot of J MKO − K MKO vs. J MKO − W2 using the data presented in Table A1 shows that the A component falls squarely in the locus of other mid-to late-L dwarfs. Using an estimate of the J-band magnitude of B and assuming it is equidistant with A, we determine a spectral type for B of [T8:].
• 2MASS 0700+3157AB[C]: This system was discovered serendipitously by Thorstensen & Kirkpatrick (2003) when performing astrometric measurements of the unrelated nearby DC10 white dwarf LHS 1889. Using imaging observations with the Hubble Space Telescope, Reid, et al. (2006) discovered a faint companion.  have performed highresolution astrometric monitoring of the system and found that the L3: primary is marginally less massive (68.0±2.6 M Jup ) than the L6.5: secondary (73.3 +2.9 −3.0 M Jup ) despite the large difference in their luminosities. This led those authors to surmise that the B component was comprised of two lower-mass brown dwarfs, although they were unable to find a three-body solution in which theoretical evolutionary models could self consistently apportion the masses and luminosities at a single coeval age. For now, we consider the C component likely, but not confirmed.
• 2MASS 0746+2000AB: Based on its location on the color-magnitude diagram, 2MASS 0746 was suspected to be an unresolved binary by Reid, et al. (2000). Reid et al. (2001b) confirmed this hypothesis with imaging from HST and verified common proper motion of the components using earlier observations from the W. M. Keck Observatory.
• 2MASS 0915+0422AB: This object was discovered by Reid, et al. (2006), who also found it to be a binary using imaging from HST.
• WISE 1049−5319AB: This object, commonly referred to as Luhman 16AB, is the third closest system to the Sun and has been known as a binary since its discovery (Luhman 2013).
• Kelu-1AB (1305−2541): The overluminosity of this object relative to L dwarfs of similar spectral type had been noted after its trigonometric parallax was measured by Dahn et al. (2002) and Vrba et al. (2004). Liu & Leggett (2005) imaged the companion using the W. M. Keck Observatory and used earlier observations from HST to confirm common proper motion between the components.
• 2MASS 1315−2649AB: This highly active L dwarf was discovered serendipitously by Hall (2002) and identified as a binary via high-resolution imaging at the W. M. Keck Observatory by Burgasser et al. (2011b).
• Gl 564BC (1450+2354)  discovered this close pair as companion binary to the G2 V star Gl 564A using the Gemini North Telescope. Their subsequent observations at Gemini along with spectroscopy from the W. M. Keck Observatory confirmed the physical association of the L dwarf pair with the G dwarf primary.
• 2MASS 1520−4422AB: Observations of this object with the New Technology Telescope by Kendall et al. (2007) revealed that the object is a double and that the two components are both L dwarfs. The difference in magnitude between the objects matches expectations if two objects are equidistant.
• 2MASS 1534−2952AB: This mid-T dwarf was discovered by Burgasser et al. (2002) and found to be a binary through HST imaging by Burgasser et al. (2003c).
• 2MASS 2152+0937AB: This mid-L dwarf was discovered by Reid, et al. (2006), who also identified it as an equal-magnitude binary through HST imaging.
• Gl 845BC (2204−5646): This object is the companion to the nearby K dwarf Ind. It was discovered by Scholz et al. (2003) and further identified through imaging as a likely pair of T dwarfs by Volk et al. (2003). McCaughrean et al. (2004) acquired individual spectroscopy to confirm this as a physical pair of T dwarfs.
• DENIS 2252−1730AB: Kendall, et al. (2004) discovered this object, and it was identified as a binary system by Reid et al. (2006b) through HST/NICMOS imaging.
• 2MASS 2255−5713AB: This object was discovered by Kendall et al. (2007) and identified as a binary system through HST/NICMOS imaging by Reid, et al. (2008b).
Previously suspected multiple systems and new ones identified here for the first time are addressed in section 7.7.

Analysis of Color-Magnitude and Color-Color Plots
In order to identify other unresolved binaries or subdwarfs in the 20-pc census, we examine color-magnitude and colorcolor diagrams built from the photometric, astrometric, and spectroscopic data compiled in Table A1. On these we highlight known multiple systems, low-gravity objects, and lowmetallicity subdwarfs, as discussed above.
As mentioned in section 5.1.1, the data presented in Table A1 are drawn from a variety of sources, leading to heterogeneity, particularly in the photometric values. For example, although 2MASS covers the entire sky, it is not deep enough to detect many of the late-T and Y dwarfs. For those objects, the hemispheric surveys of UHS in the north and VHS in the south can provide deeper data. Although H-band filters are largely invariant across surveys, the same is not true of J and K. As shown in Figure 3 of González-Fernández et al. (2018), the 2MASS filters J 2MASS and K S are markedly different from the J MKO and K MKO filters used by WFCAM. Furthermore, although the VISTA employs the same J MKO as WFCAM, its K S filter is much closer to the K S filter used by 2MASS. Similarly, although WISE data in bands W1 and W2 cover the entire sky, deeper observations by Spitzer are done with complementary, though not identical, ch1 and ch2 filters, as shown in Figure 2 of Mainzer et al. (2011).
Ideally, transforming magnitudes in one filter to the complimentary filter in the other survey(s) would allow us to examine homogenized color-color and color-magnitude diagrams using as much data as has been currently collected for the 20-pc L, T, and Y dwarfs. Figure 12 shows the relation in absolute magnitude between J 2MASS and J MKO , K S and K MKO , W1 and ch1, W2 and ch2. Linear least squares fits to the trends are illustrated in the plots and listed in Table 13. The line of one-to-one correspondence is shown by the black dashed line on each panel.
Trends of colors with spectral type are illustrated in Figure 14(e-h). The two known L subdwarfs are much bluer than the mean trend in J MKO − ch2 and H − ch2 colors, though indistinguishable from the mean trend in ch1 − ch2 and W1 − W2. The T subdwarfs tend to lie redward of the mean trend in all four colors. Young L dwarfs are markedly redder than the trend in all four colors, whereas the few young T dwarfs known do not clearly differentiate themselves.
In Figure 15(a-h), we show these same plots as above, but with the axes flipped. This is to provide researchers with fits to convert absolute magnitudes or colors to a spectral type. As is illustrated in the plots, it is not always possible to provide simple polynomial fits over the entire range of absolute magnitude or color because of degeneracies. For example, a color of J MKO − ch2 = 3.0 mag corresponds to either a mid/late-L dwarf or a mid/late-T dwarf. Users are urged to check the notes in Table 13 to check the ranges over which these fits are valid.
In Figure 16(a-f), we illustrate trends of absolute magnitudes and colors as a function of ch1 − ch2 color. In the plots of absolute magnitude, multiples are seen as overluminous, as expected, and only the most metal poor T subdwarf, WISE 2005+5424 ([Fe/H] = −0.64±0.17) is well removed from the trend in M JMKO and M H . On the color plots, the T subdwarfs are redder in J MKO − ch2, H − ch2, and W1 − W2 at a fixed value of ch1 − ch2.
Plots of absolute magnitude and color as a function of W1− W2 color are shown in Figure 17(a-f). The same trends as those mentioned above in ch1 − ch2 color are seen.
Plots of absolute magnitude and color as a function of J MKO − ch2 and H − ch2 color are shown in Figure 18(a-e) and Figure 19(a-e). At a given absolute magnitude in M JMKO , M H , and M ch2 , young L dwarfs are shown to be redder than field objects, as are T subdwarfs, although L subdwarfs appear bluer. On the color-color plots, the reddest of the young L dwarfs are the reddest objects of all in J MKO − K MKO ; at their W1 − W2 colors, they are also the reddest objects in J MKO − ch2 and H − ch2.
Having established the locations of unusual objects on these diagrams, we examine the evidence for other, previously unrecognized (or, in some cases, previously suspected) young dwarfs, subdwarfs, and multiples in the 20-pc census. These are discussed in the next three subsections.

Potential Young Objects
No newly recognized young object candidates were identified from these diagrams.

Potential Subdwarfs
A number of objects, not discussed in section 7.2 above, appear to fall along the subdwarf locus in Figures 14 through  19. These are addressed below.
• WISE 0316+4307: This T8 dwarf falls along the locus of subdwarfs in the color-type plots shown in Figures 14e and f. It also appears as a color outlier on the color-color plot 17f.  acquired separate Jand H-band spectra of the object and did not note any peculiarities, although a spectrum across the full JHK wavelength range could elucidate whether the telltale K-band suppression seen in T subdwarfs is confirmed.
• WISE 0359−5401: This Y0 dwarf falls along the locus of subdwarfs in Figure 16d. No Y dwarfs have yet been classified as subdwarfs, but  found this object indeed falls in the part of the J − ch2 vs. ch1 − ch2 diagram where substellar models predict low-metallicity objects to fall. We consider this to be a normal Y dwarf in subsequent analysis, pending the empirical spectroscopic identification of other Y subdwarfs.
• WISE 0430+4633: This T8 dwarf falls along the locus of subdwarfs in the color-type plots of Figures 14e and f. It is also a color outlier on the color-type plot of Figure 14h and the color-color plot of Figure 16f. The spectral classification of this object is based on only a J-band spectrum by . As with WISE 0316+4307 above, a spectrum across the full JHK wavelength range is needed to confirm whether a subdwarf classification is warranted.
• UGPS 0521+3640: This T8.5 dwarf falls along the subdwarf locus in the absolute magnitude-color plot of Figure 16b. It is also an outlier on the color-color plot of Figure 16f. However, this source's photometry may be confused by the halo of a much brighter star. The near-infrared spectrum by Burningham et al. (2011) shows no peculiarities, so we think it is only the poor photometry that is causing this object to appear as an outlier.
• WISE 0751−7634: This T9 dwarf falls along the subdwarf locus in the absolute magnitude-color plots of Figures 16a,b and 17a,b, as well as in the color-color plot of Figure 17e. It is also an outlier on the colorcolor plot of Figure 17f. The near-infrared spectrum shown by Kirkpatrick et al. (2011) has low S/N in the K-band and may show the flux suppression typical of T subdwarfs, but an improved spectrum is needed to verify this.  notes that this object  Figure 14. Plots of various absolute magnitudes (a-d) and colors (e-h) as a function of near-infrared spectral type. Only members of the 20-pc census are shown, and plots a-d show only the subset of 20-pc objects having parallaxes measured to better than 12.5%. Plots of Mch2, JMKO − ch2, and H − ch2 are supplemented with W2 magnitudes when ch2 magnitudes are not available, as described in section 7.4. Polynomial fits that exclude known young objects (pink circles, section 7.1), subdwarfs (blue squares, section 7.2), and multiple systems (yellow diamonds, section 7.3) are shown in brown and described in Table 13. falls within the locus on the J − ch2 vs. ch1 − ch2 diagram where substellar models predict low-metallicity objects to fall. We await improved spectroscopic data before classifying this object as a subdwarf.
• WISE 1112−3857: This T9 dwarf falls along the subdwarf locus in the color-type plots of Figures 14e,f, and the color-color plot of Figure 16d. The near-infrared spectrum presented in  does not extend to the K-band but appears to show excess flux on the blueward side of Y -band, as seen in other T subdwarfs (see section 7.2). A more complete spectrum at higher S/N is needed to confirm the subdwarf hypothesis.
• WISE 1141−3326: This is a Y0 dwarf that falls along the subdwarf locus in the absolute magnitude-color plots of Figures 16a and 17a, and the color-color plots of Figure 16d and 17e. As noted in , however, these anomalies can likely be attributed to photometric contamination at earlier epochs when the source was passing in front of a background galaxy.
• WISE 1818−4701: A spectrum of this object has not yet been acquired, but it is believed to be a late-T dwarf. It falls along the subdwarf locus in the absolute magnitude-color plot of Figure 17a and colorcolor plot of Figure 17e. A spectrum is required to confirm or refute the subdwarf hypothesis.
• GJ 836.7B (2144+1446): This T3 dwarf, also known as HN Peg B, appears along the subdwarf sequence in the color-color plot of Figure 17f and is an outlier on the color-type plot of Figure 14h Figure 15. Plots identical to those of Figure 14, except that the x and y axes have been reversed. Polynomial fits to provide a translation from absolute magnitude or color into spectral type are shown in brown and described in Table 13. These fits exclude known young objects (pink circles, section 7.1), subdwarfs (blue squares, section 7.2), and multiple systems (yellow diamonds, section 7.3). of ∼300 Myr for the system, and Valenti & Fischer (2005) find that the primary has [M/H] ≈ −0.01. Since this object is obviously not a subdwarf, we suspect that the CatWISE2020 photometry may be corrupted due to the proximity of the bright primary itself. The All-WISE and CatWISE2020 photometry (Table A1) differ in both W1 and W2 by > 5σ, indicating that the the automated measurements are likely poor. Further evidence that the W1−W2 color may be suspect is the fact that similar plots with ch1 − ch2 color (Figures 14g and  16e) show this source falling along the locus of normal field dwarfs.
• GJ 1263B (2146−0010): This T8.5 dwarf, also known as Wolf 940B, lies along the subdwarf locus in Figures 17a,b. Burningham et al. (2009) find that the primary has an age of ∼3.5 Gyr and metallicity of [Fe/H] = −0.06±0.20, so the B component cannot be a subdwarf. As with GJ 836.7B above, the AllWISE and CatWISE2020 photometry (Table A1) differ in both W1 and W2, in this case by > 10σ and > 6σ, respectively. Further evidence that the W1 − W2 color may be suspect is the fact that similar plots with ch1 − ch2 color (Figures 16a,b) show this source to fall along the normal locus. We suspect that the bright primary has corrupted the WISE photometry of the secondary.

Potential Multiples
Several L, T and Y dwarfs within the 20-pc census have been previously published as suspected multiples and either remain unconfirmed or have subsequently been discounted. Several others are newly addressed here as suspected binary systems. Suspected companions are denoted by brackets ("[B]" or "[C]") around the suffix both in the text below and in Table 11.
• WISE 0309−5016A[B]: This T7 dwarf is an outlier on the absolute magnitude-type plot of Figure 14d and  Figure 16. Plots of various absolute magnitudes (a-c) and colors (d-f) as a function of ch1 − ch2 color. Only members of the 20-pc census are shown, and plots a-c show only the subset of 20-pc objects having parallaxes measured to better than 12.5%. Polynomial fits that exclude known young objects (pink circles, section 7.1), subdwarfs (blue squares, section 7.2), and multiple systems (yellow diamonds, section 7.3) are shown in brown and described in Table 13. Fits include only those points with ch1 − ch2 > 0.2 mag for panels a-e. on the absolute magnitude-color plots of Figure 16b ,c; 17a,b,c; 18a,b,c; and 19a,b,c. The consistent overluminosity of this object across colors and bands strongly points to its being an unresolved double with components of near-equal magnitude. As we did in , we consider it to be a two-body system in subsequent analysis.
• WISE 0350−5658: This Y1 dwarf falls well above the mean trend in Figure 16b. Oddities in absolute magnitude-type plots were also noted in . Few Y1 dwarfs are presently known, so it is unclear the extent to which this is just cosmic scatter for normal dwarfs of this spectral type. We consider this object to be single.  Figure 17. Plots of various absolute magnitudes (a-c) and colors (d-f) as a function of W1 − W2 color. Only members of the 20-pc census are shown, and plots a-c show only the subset of 20-pc objects having parallaxes measured to better than 12.5%. Polynomial fits that exclude known young objects (pink circles, section 7.1), subdwarfs (blue squares, section 7.2), and multiple systems (yellow diamonds, section 7.3) are shown in brown and described in Table 13. In panels a-c, the fits include only those points with W1 − W2 > 1.0 mag, and in panels e-f the fits include only those points with W1 − W2 > 0.8 mag  Figure 18. Plots of various absolute magnitudes (a-c) and colors (d-e) as a function of JMKO − ch2 color. Only members of the 20-pc census are shown, and plots a-c show only the subset of 20-pc objects having parallaxes measured to better than 12.5%. All five panels are supplemented with W2 magnitudes when ch2 is not available, as described in section 7.4. Polynomial fits that exclude known young objects (pink circles, section 7.1), subdwarfs (blue squares, section 7.2), and multiple systems (yellow diamonds, section 7.3) are shown in brown and described in Table 13 Figure 19. Plots of various absolute magnitudes (a-c) and colors (d-e) as a function of H − ch2 color. Only members of the 20-pc census are shown, and plots a-c show only the subset of 20-pc objects having parallaxes measured to better than 12.5%. All five panels are supplemented with W2 magnitudes when ch2 is not available, as described in section 7.4. Polynomial fits that exclude known young objects (pink circles, section 7.1), subdwarfs (blue squares, section 7.2), and multiple systems (yellow diamonds, section 7.3) are shown in brown and described in Table 13 • WISE 0535−7500: This ≥Y1: dwarf falls well above the mean trend on the absolute magnitude-type plot of Figure 14d and on the absolute magnitude-color plots of Figures 16c; 18a ,c; and 19a,b,c. This overluminosity was also noted by Tinney et al. (2014), , and . Opitz et al. (2016) used adaptive-optics imaging to rule any equal-magnitude companion at a separation greater than ∼1.9 AU. As with WISE 0350−5658 above, it is unclear the extent to which this may just be cosmic scatter for normal dwarfs of this spectral type, since few are known. We consider this object to be single.
• WISE 0546−0959: This T5 dwarf falls above the mean locus on the M H vs. ch1 − ch2 diagram of Figure 16b and the M H vs. W1 − W2 diagram of Figure 17b. Because it appears overluminous only in H-band, we consider this object to be single.
• 2MASS 0559−1404: This mid-T dwarf falls well above the mean locus on all of the plots based on absolute magnitude in Figures 14, 16, and 17. It is also an outlier on the M JMKO vs. J MKO − ch2 plot of Figure 18a. Two hypotheses have been proposed to explain the overluminosity, which was first noted by Dahn et al. (2002): (1) Burgasser (2001) suggested that the object was an equal-magnitude binary.
(2) Burgasser et al. (2003c) later proposed that the quick dissipation of clouds near the L-to-T dwarf transition could be responsible for the overluminosity, which is largest at J-band. However, both of these hypotheses have encountered problems in the intervening years. The cloud disruption theory was largely invoked to explain the J-band overluminosity (Tsuji & Nakajima 2003), but as our figures show, this overluminosity is present across all bands from J through W2. The binary theory has yet to be confirmed, either. High-resolution HST imaging by Burgasser et al. (2003c) showed no indication of a hidden companion down to a separation of 0. 09. Using radial velocity measurements covering a 4.4-yr period, Zapatero Osorio et al. (2007) found no velocity variations (to 1σ = 0.5 km s −1 ). Other radial velocity measurements by Prato et al. (2015) were able to rule out a companion with a period of a day or less, but these authors stress that there is still orbital parameter space between their sampled region and the 0. 09 (0.9 AU) limit by the HST imaging mentioned above. Given the inability of observers to confirm the binary hypothesis for this object, we will assume the object is a single dwarf in subsequent analysis.
• PSO 0652+4127: Best et al. (2013) label this object as a possible binary based on the fact that some nearinfrared spectral indices better match a L8+T2.5 composite that the single T0 type. Their single-object photometric distance suggests the object falls at 14.2±1.2 pc, whereas the binary hypothesis suggests 20.1±2.4 pc. Our Spitzer parallax gives a distance of 17.4±1.0 pc, which is intermediate between the two estimates.
In the absence of data confirming a companion, we consider this object to be single.
• SDSS 0758+3247: This early T dwarf was discovered by Knapp et al. (2004). It was identified by Burgasser et al. (2010) as a weak candidate for unresolved binarity due to its near-infrared spectral morphology. However, as stated in that paper, the single object spectral fit outperformed that of the best binary fit. Nonetheless, the spectral type listed in the SIMBAD database shows this as a composite type. Bardalez  list this system as a "visual spectral binary" but surmise that it is comprised of two components with types of T2.2±0.0 and T2.3±0.0 despite the fact that it is not possible to detect a binary comprised of identical components using low-resolution spectral morphology alone. Our plot of M H vs. near-infrared spectral type, for example, shows no overluminosity of this object compared to other early-T dwarfs, ruling out the equal-magnitude binary hypothesis. We thus consider this object to be a single brown dwarf.
• SDSS 0857+5708: This L8 dwarf falls above the mean trend on the plots of M ch1 and M ch2 vs. spectral type in Figures 14c,d. Given that there is no evidence of overluminosity in other diagrams and that there is no indication in the literature of binarity, we consider this to be a single object.
• WISE 0920+4538: Given that this L9 dwarf is labeled only as a weak binary candidate in  and that some of its peculiarities may be attributed to spectroscopic variations , we consider this to be a single object.
• 2MASS 0939−2448A[B]: This T8 dwarf has been considered an unresolved, equal-magnitude binary for many years based on its overluminosity, as discussed in . In section 7.2, we noted that the spectrum shows signs of low-metallicity as well. Thus, we consider this to be a T subdwarf binary.
• PSO 0956−1447: Best et al. (2015) list this late-L dwarf as a marginal spectral binary candidate. In the absence of any confirming high-resolution imaging, we consider this to be a single object.
• SDSS 1048+0111: This early-to mid-L dwarf falls above the mean locus on the plots of absolute magnitude vs. spectral type in Figures 14a,b. Reid, et al. (2006) did not find any evidence of binarity in highresolution HST imaging. Furthermore, we note that our perceived overluminosity vanishes if we plot against the optical spectral type of L1 instead of the nearinfrared type of L4 (Table 11). We consider this to be a single object.
• 2MASS 1231+0847: This T5.5 dwarf is overluminous for its ch1 − ch2 and W1 − W2 color on Figures 16a,b,c and 17a,b,c. The object was observed with high-resolution imaging on HST by Aberasturi et al. (2014), who found no companion with a separation > 0. 3 down to ∆J ≈ 2.5 mag (their Figure 7). As discussed in ,  proposed that this object's broad K I lines might indicate a higher gravity that is the consequence of lower metallicity. Given the uncertain cause of this object's peculiarities, we will consider it to be a single dwarf of normal metallicity in subsequent analysis.
• • ULAS 1416+1348: In , we considered this (sd)T7.5 to be an unresolved double based on its overluminosity with respect to normal late-T dwarfs and with respect to the few sdT dwarfs identified in that paper. However, it now appears that overluminosity with respect to normal T dwarfs of the same color or spectral type is a trait shared with a wider variety of low-metallicity T dwarfs. We therefore now consider this to be a single object.
• WISE 1627+3255A[B]: This mid-T dwarf is overluminous on the absolute magnitude-color plots of Figures 16a,b,c and 17a,b,c. Although Gelino et al. (2011) found no companion down to ∆H ≈ 5 mag at separations > 0. 2, we consider this object to nonetheless be a tight unresolved binary, just as  concluded.
• DENIS 1705−0516: Kendall, et al. (2004) discovered this early-L dwarf. Reid, et al. (2006), using HST/NICMOS imaging in 2005 Jun, found a faint source separated by 1. 36 and consistent with either a distant (1-2 kpc), unrelated mid-M dwarf or a physically related early-T dwarf. Our analysis of more recent imaging by HST/WFC3 (Program 13724; PI: T. Henry) as well as J and K S imaging by VHS show that the putative companion is a stationary background source, the motion of the early-L dwarf having increased the separation between the two objects to 2. 9 arcsec by 2015 Mar. We consider this L dwarf to be a single object.
• WISE 1804+3117: This late-T dwarf is overluminous only on the M ch1 vs. spectral type diagram of Figure 14c. This object has both an uncertain type of T9.5: and falls close to the Y dwarf regime where the identification of binarity has proven to be problematic. Therefore, as  also concluded, we will consider this object to be single in our subsequent analysis.
• Gaia 1831−0732: This object does not yet have a measured spectral type, but if a classification of L0 is verified, it is overluminous relative to other L0 dwarfs on the absolute magnitude vs. type plots of Figure 14a,c,d.
It is also overluminous on the absolute magnitude vs. color plots of Figure 16a,b,c, but this overluminosity would vanish if the object were actually a late-M dwarf. The fact that it is an outlier on the color-color plot of Figure 16e strongly suggests that it is, indeed, an M dwarf. Given the evidence that this object is earlier than L0, we exclude it from subsequent analyses.
• Gl 758B (1923+3313): This late-T dwarf companion was discovered using Subaru/HiCIAO by Thalmann et al. (2009), who also reported a possible third member of the system. Using the same instrument, Janson et al. (2011) confirmed that this purported Gl 758"C" was a background star based on data with a ∼1.5-yr baseline.
• 2MASS 2126+7617A [B]: This object appears overluminous on Figure 14b. Kirkpatrick et al. (2010) note that this object has peculiar spectra in both the optical and near-infrared, and the spectral types are discrepant between the two -L7 in the optical, and T0 pec in the near-infrared. These authors also found that a spectral binary comprised of an L7 dwarf and a T3.5 dwarf accounts for the main peculiarities in the near-infrared spectrum. Given that this is a strong case for a spectral binary, we tentatively include the B component in our subsequent analysis.
• 2MASS 2139+0220: This early-T dwarf was identified as a possible unresolved binary based on its near-infrared spectral morphology by Burgasser et al. (2010). Individual components of types L8.5 and T3.5 were suggested, although it was noted that the synthetic composite type still failed to reproduce important features in the observed spectrum. This object is now noted for its extreme variability (26% at J-band), leading Radigan et al. (2012) to conclude that the object's variations were caused either by multi-layered clouds or a cloud layer with holes. Bardalez  conjectures that some candidate spectral binaries may instead be single objects whose photospheres are comprised of multi-component cloud layers of differing temperatures. We consider 2MASS 2139+0220 to be a single object.

Other Outliers
• SDSS 0000+2554: This T4.5 dwarf is an outlier on the W1 − W2 vs. spectral type plot of Figure 14h, the W1 − W2 vs. ch1 − ch2 plot of Figure 16f, and the J MKO − K MKO vs. W1 − W2 plot of Figure 17d. Examination of the WISE images shows this object to be buried within the halo of the bright star Z Pegasi, which must be corrupting the WISE colors.
• WISE 0715−1145: This object appears as a color outlier on at least nine of the previous plots (Figures 14b,f;16e;17b,f;19a,b,c,e) but does not fall in the locus of known young objects, subdwarfs, or unresolved multiples. It is an L4 pec (blue) dwarf whose near-infrared spectrum is much bluer than the standard L4 dwarf but lacks indications of lowmetallicity , and it is one of just six blue L dwarfs known in the 20-pc census -the others being SIPS J0921−2104, 2MASS 1300+1912, 2MASS 1721+3344, VVV 1726−2738, WISE 2141−5118. Only three of these others (2MASS 1300+1912, 2MASS 1721+3344, VVV 1726−2738) appear as outliers on the previous plots, and these distinguish themselves only in Figure 14, which is based on spectral type. WISE 0715−1145 therefore appears to be the most extreme color outlier of the 20-pc blue L dwarfs. Faherty et al. (2009) noted that the general population of blue L dwarfs, despite not showing obvious signs of low metallicity, nonetheless have kinematics consistent with an old age.
• WISE 1828+2650: This Y dwarf is overluminous on Figures 14a ,b,c,d; 18b,c; and 19b,c. It also falls along the subdwarf locus in Figure 16d. This object was discussed in section 8.2.47 of . Compared to all other Y dwarfs with near-infrared spectra, this object has a unique spectrum that does not compare well with the known suite of theoretical models (Cushing et al., in prep.).

TEMPERATURES AND SPACE DENSITIES 8.1. Assigning Each Object to a T eff Bin
Finding the functional form of the mass function from our 20-pc census is not a straightforward exercise because mass is not an observable quantity. Moreover, since most of the objects in our L, T, and Y dwarf census are brown dwarfs, they continue to cool as they age, and as a result there is no direct mapping from spectral type to mass unless the age of the object is known. Only a small number of the objects within the census have age estimates -i.e., confirmed members of young moving groups and companions to higher mass stars whose ages are known through other means.
Because the bulk of our objects have no age estimates, we rely instead on simulating empirical distributions using various assumed forms of the mass function, an assumed star formation rate over the interval of interest, and theoretical models to evolve each object to the current epoch. This work is described in detail in sections 9.1 and 9.2 of . The evolutionary models allow us to transform the predictions into distributions of either effective temperature or bolometric luminosity. Both of these quantities have their own limitations, however. Effective temperature is not a directly observable quantity and requires either forward modeling (comparison to atmospheric models), inverse modeling ("retrieval" analysis), or calculation via the Stefan-Boltzmann Law. Measuring effective temperature via the Stefan-Boltzmann equation would require only a measurement of the bolometric luminosity and an assumption about the object's radius which, fortunately for most of these old brown dwarfs, can be assumed to be ∼1R Jup due to their electron degeneracy. However, if bolometric luminosities were already measured, we could forgo temperature determinations entirely and simply compare our observed luminosity distributions to the simulations. At present, however, we have insufficient data with which to compute accurate bolometric luminosities for most of these objects, although more complete spectral coverage over the bulk of these objects' spectral energy distribution will soon be obtainable using the Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer (SPHEREx; Doré et al. 2016Doré et al. , 2018, supplemented at longer wavelengths with data from WISE and the James Webb Space Telescope (JWST; Gardner et al. 2006).
For now, we are left to convert our sample into a distribution of effective temperature. Filippazzo, et al. (2015) calculated bolometric luminosities for a large number of late-M, L and T dwarfs, and used those to compute effective temperatures once a radius was deduced from model calculations. (These radii were very close to ∼1R Jup as expected, since most of these objects are old brown dwarfs that have contracted to their final equilibrium radius.) Those authors then plotted various observable parameters against the resulting effective temperature measurements and found that the relation with the smallest scatter was T eff vs. M H . For objects in our 20-pc sample that are thought to be old field objects, we can therefore use M H to transform into T eff . However, a few objects do not have H-band measurements, and for those we can use the measured spectral type (or its estimate) as the arbiter of effective temperature.
The relations presented in Filippazzo, et al. (2015) predate the release of Gaia DR2 and do not extend into the Y dwarf regime. Therefore, we have updated the data presented in that paper to include new Gaia parallaxes and improved parallaxes from Spitzer, and have also updated H-band values where more accurate photometry is now available from VHS or other follow-up surveys. Those results are given in Table 14. We have extended this list into the Y dwarf regime by including objects from Table 10 of  whose effective temperatures were calculated from published values computed using forward and inverse modeling techniques. a For objects also listed in Table A1, the abbreviated name is given; full designations can be found in Table A1 itself. For all other objects, the full name is presented.
b This is the (near-infrared) spectral type encoded as follows: c This is a four-character code that gives the reference for the spectral type, parallax, effective temperature, and H-band magnitude, respectively: These results are plotted in Figure 20 and the fitted relations given in Table 13. The plot in panel a shows that from early-L through mid-T (10.5 < M H < 15 mag), each 150K bin in T eff corresponds to a fairly narrow range of M H . However, at spectral types later than mid-T (M H > 15 mag), each 150K temperature bin encompasses a larger and larger range of M H values. In panel b we see the well-known result that objects in the L/T transition between types of late-L to mid-T span a very narrow range in T eff . Outside of this spectral type range, there is a monotonic trend of decreasing temperature with later spectral type.
For the 525 individual objects in the 20-pc census, we have assigned values of T eff as follows; these values can be found in column 10 of Table 11. For old field dwarfs of normal gravity, we take the measured values of T eff from Filippazzo, et al. (2015) if the object has a computed value there. Otherwise, we assign a T eff value using the relation in Figure 20a using the object's measured M H if an H-band magnitude exists and the parallax is known to better than 12.5%. If these conditions are not met, we use the spectral type contained in the SpAd column of Table A1 along with the relation shown in Figure 20b. The only exception is WISE 0855−0714, which is assigned a 250K value, as was done in .
For low-gravity (young) objects, we take the T eff value computed by Faherty et al. (2016) if the object has a value there; otherwise, we take the value from Filippazzo, et al. (2015). For other objects noted as young in column 11 of Table A1 but lacking measured values, we assign temperatures using an updated version (Faherty, priv. comm.) of the optical spectral type to T eff relation of Faherty et al. (2016). When no optical type is available, we use the near-infrared type as a proxy.
For low-metallicity (subdwarf) objects, we take T eff measurements directly from Filippazzo, et al. (2015), when available. However, no relation between absolute magnitude (or spectral type) and temperature exists for these subdwarfs. Three mild, and presumably single, subdwarfs in our sample have measurements in Filippazzo, et al. (2015): 2MASS 0729−3954 (752±69K), 2MASS 0937+2931 (881±74K), and ULAS 1416+1348 (656±54K). The field relation would suggest values of 749K, 858K, and 610K for these same three objects, respectively, showing that values from the field relation are consistent with the actual measurements. In fact, the most extreme subdwarf in the 20-pc sample, WISE 2005+5424, has a model fit temperature of 600-900K (Mace et al. 2013b), which is also roughly consistent with the field estimate of 574K. Thus, as was done for the old field objects above, we assign temperatures to the other subdwarfs using the field relations of Figure 20.

Space Densities vs. T eff and Spectral Type
To aid in comparison to our mass function simulations, we present our final space densities as a function of temperature. Specifically, these are shown as histograms binned in 150Kwide increments of T eff . To ease other empirical comparisons,  Table 14. Functional fits to the trends, shown by the white curves, can be found in Table 13. The colored bands on each plot depict each of the 150K-wide temperature bins into which the data will be sorted in the following section.
we also present space densities as a function of spectral type, binned via integral subtypes. Before computing these space densities, we must first determine whether the data contributing to each of these bins is complete to our target distance of 20 pc. For this, we use the V /V max test advocated by Schmidt (1968). The basis of this test is as follows. Consider a proposed completeness limit of d max . For each object i at distance d i within that distance, the test computes the ratio of the volume interior to that object's position, V i = (4/3)πd i 3 , to the total volume being considered, V max = (4/3)πd max 3 . The average of these ratios, V /V max = (1/n) × n i=0 (V i /V max ), should be ∼0.5 for a complete, isotropically distributed sample. Values that fall significantly below 0.5 indicate that there is incompleteness in the outer parts of the volume being considered. In other words, if the outer half-volume has significantly less than half of all objects within the total volume, the sample is likely incomplete to that distance.
We compute V /V max at half-parsec steps within each bin. The computation starts with the first half-parsec step falling just beyond the distance of the closest object in the bin and continuing out to d = 20 pc. These computations are graphically illustrated in Figure 21 for each bin in T eff and in Figure 22 for each bin in spectral type. Practically, though, what does "significantly below 0.5" mean for V /V max ?  proposed two ways to address this. First, a Poisson formalism was developed that establishes a 68% likelihood threshold (the equivalent of 1σ for a continuous distribution) that the V /V max is significantly different from 0.5, given the number of objects in the sample. These thresholds are shown as the light grey error bounds in Figure 21 and 22. Second, a run of 10,000 Monte Carlo simulations for a sample size of n objects was used to identify the range of V /V max around 0.5 that contains 68% of all simulated outcomes. Here, n is the number of objects in the most distant bin for which the Poisson formalism determined the sample to be complete. These simulated likelihoods are shown by the brown error bounds in the figures.
Using these methods, we find that our sample is likely complete 19 to 20 pc for all bins between 600 and 2250K in T eff . For cooler bins the completeness limit drops to 15 pc for 450-600K and to 11 pc for 300-450K. (The coolest bin with data, 150-300K, has only one object in it, WISE 0855−0714, so the completeness cannot be computed.) We note, however, that the 300-450K bin is likely complete over only a fraction of its 150K interval because the coldest assigned T eff for any object in this bin is 367K. We further note that two sources within the 525-object L, T, and Y dwarf 20-pc census -G 239-25B (1442+6603) and LSPM J1735+2634Bhave assigned T eff values (Table 11) that are hotter than the hottest temperature bin considered here. Finally, our measured space density in the 2100-2250K bin should be considered as a lower limit, too, because if we were to have included late-M dwarfs in our 20-pc census some fraction of them would have populated this bin. These results are shown in the first three columns of the upper portion of Table 15.
Bins of integral spectral subtype, which generally have poorer statistics can, by extension, be assumed complete out to 20 pc for types warmer than 600K, which is roughly late-T (Figure 20b). A close look at Figure 22 shows that the census appears to be complete for spectral types from L0 through T7.5. The completeness limit drops to ∼17 pc for types T8-T9.5 and to ∼13 pc for types Y0-Y1.5. Later types than this have only one representative per bin -WISE 1828+2650 at Y2 and WISE 0855−0714 at a type presumably later than that -so completeness limits cannot yet be determined. Results   1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1   Figure 21. The average V /Vmax value in 0.5-pc intervals for fourteen 150-K bins encompassing our 20-pc L, T, and Y dwarf census. Blue dots represent our empirical sample. Red labels mark the number of objects in the computation at each 0.5-pc interval. The black dashed line shows the V /Vmax = 0.5 level indicating a complete sample. The grey error bars show the approximate 1σ range around V /Vmax = 0.5 that a complete sample of the size indicated by the red number would exhibit, given random statistics. The brown error bars, offset by +0.05 pc from the grey error bars for clarity, show the 1σ variation around 0.5 obtained by 10,000 Monte Carlo simulations having the number of objects and completeness limit listed in Table 15.  Table 15.
The bins in our T eff and spectral type histograms are fixed, but our confidence in placing an object in a particular bin is directly related to the uncertainties in these quantities. For example, some of our objects have errors on T eff that are comparable to our 150K bin size, and the errors on some of our spectral types are also comparable to the integral spectral type bin size used. The lack of precision in these values is our biggest uncertainty in fixing the space densities in each bin. To address what the size of this uncertainty should be, we have run 10,000 Monte Carlo simulations for both the T eff and spectral type distributions. For T eff we have taken the error bars listed in Table 11, which were taken either from literature values (see Table 14) or assigned via the root-mean-square scatter from whichever relation in Table 13 was used for the T eff estimate. For spectral type, we have assigned the standard 0.5-subclass uncertainty to all types except those with uncertainties already specified explicitly or for those with brackets or colons, for which we have assigned 1.0-subclass uncertainties. For each simulation, we take the T eff or spectral type uncertainty, and multiply it by a random value generated from a normal distribution having a mean of 0 and a standard deviation of 1. We add this uncertainty onto the measured value, and then rebin. We then compute the means and standard deviations across all 10,000 simulations and report these in column 4 of Table 15.
These simulations have a drawback, however, because the T eff bins at either end of our 150-2250K range are incomplete. Firstly, the 1950-2100K bin will contain objects that scatter into the 2100-2250K bin, but this loss in the cooler bin will not be mitigated by a concomitant gain from the warmer bin because the object count in that latter bin is incomplete. Secondly, over the 300-750K range, we encounter differing completeness limits in distance across the three bins that span this range as well as having an incompleteness in temperature in the 300-450K bin. For example, objects that scatter from the 600-750K bin into the 450-600K bin will be lost if they have a distance larger than the completeness limit of that colder bin. Objects scattering in the other direction will not be similarly lost. The same is true of objects scattering between the 450-600K bin and the 300-450K bin. Given these biases, we adopt a methodology whereby we use the raw number counts in each bin to set the space density, but we use the uncertainties from the simulations to set a conservative limit on their 1σ errors.
Although most of our bins pass the V /V max completeness test to 20 pc, this does not address whether there are inhomogeneities in the all-sky distribution.  found an inhomogeneity in the T and Y dwarf counts toward the Galactic Plane, in which source confusion limits our ability to select objects in the faintest, coldest bins. We re-investigate this here. Plots of our all-sky distributions broken down by broad spectral class are shown in Figures 23  and 24. The plot of T dwarfs appears to show a thinner area of coverage around and just south of the Galactic Plane in Figure 24c. · · · 1 · · · · · · · · · ≥Y3 · · · 1 · · · · · · · · · a The SpAd spectral type from Table A1, which defaults to near-infrared types, is used here.
c This bin is complete only for its L dwarf complement. Since late-M dwarfs are also expected to populate this bin, the derived space density is considered to be a lower limit.
(a) 20-pc census -All L, T, and Y Dwarfs  Figure 23. Plots of the 20-pc L, T, and Y dwarf sample in equatorial coordinates. The four panels display the sample in its entirety (black), only the L dwarfs (blue), only the T dwarfs (green), and only the Y dwarfs (red). We address this further by dividing objects in our 20-pc census into two sectors, one for the objects having an absolute Galactic latitude (|glat|) < 14. • 48 (the "Plane" sector) and the second for objects having |glat| ≥ 14. • 48. This cut on glat was selected so that the first sector covers one quarter of the sky and the second covers the other three quarters. For each temperature and spectral type bin, we can therefore determine if the numbers in the Plane sector, when tripled, appear to be significantly lower than those found in the second sector. Using the complete samples as defined in Table 15, we find 27 Y0-Y1.5 dwarfs. Of these, 23 lie outside of the Plane sector, meaning that we would expect 23/3 ≈ 8 similar objects to lie in the Plane sector itself. However, only 4 are found there, for a shortfall of 4, or 15% of the total sample. Using the same methodology and combining spectral bins to increase the statistical significance of each binned population, we find shortfalls of 13% for T8-T9.5 (96 objects total), 10% for T6-T7.5 (88 objects total), 14% for T4-T5.5 (49 objects total), 12% for T0-T3.5 (35 objects total), 5% for L6-L9.5 (75 objects total), and 5% for L0-L5.5 (96 objects total). We thus apply an adjustment factor of 1.05 across the L dwarf densities and 1.13 across the T and Y dwarf densities. We apply these same factors to the T eff -based densities, and use an average adjustment factor of 1.09 to the 1050-1350K bins that cross the L/T transition. These factors are listed in the fourth column of Table 15. To compute the space densities, we used the formulae given in the footnotes of Table 15. These final values are given in column 6 and are represented graphically in Figure 25.
We  2019) results are consistently a factor of ∼1.9 higher. However, Bardalez Gagliuffi (priv. comm.) find that their published densities included a pessimistic set of assumptions in their completeness calculation. Our Table 15 values compare favorably to the T effbinned values of , the biggest deviations being a 1.2σ variation (difference factor of 0.84 between  and this paper) in the 750-900K bin and a 1.4σ variation in the opposite direction (difference factor of 1.27) in the adjacent 600-750K bin. 9. DETERMINING THE MASS FUNCTION In  we developed a formalism for translating various forms of the mass function into the observational domain, since mass is not an observable quantity for most objects within the 20-pc census. There are several steps in doing this, which we summarize below.
First, we considered a variety of functional forms of the mass function that have been proposed in the literature. These include power laws (dN/dM ∝ M −α ) with α values ranging from −1.0 to 1.5, the log-normal distribution   (dN/dM ∝ e −(ln(M)−µ) 2 /2σ 2 ) with values of the mean (µ) and standard deviation (σ) taken from Chabrier (2001), Chabrier (2003a), andChabrier (2003b), and a bi-partite power law favored by Kroupa et al. (2013). These forms determine the distribution of masses produced.
Second, a stellar birthrate that has remained constant in time over the past 10 Gyr was assumed.  found that the stellar luminosity function for T dwarfs is largely invariant to the birthrate assumed, although the L dwarf regime can still bear an imprint from recent events if star formation is more episodic. Allen et al. (2005) explored this further and found that changes in the luminosity function produced by the underlying mass function were much larger than those produced by variations in the birthrate.
Third, because most of the objects in our simulations are brown dwarfs, the observable quantity we use for the empirical determinations (T eff ) changes with time as the brown dwarf ages and cools. Hence, we tie each simulated object to an evolutionary path applicable to its mass, so that we can determine its current T eff . Two sets of evolutionary models were employed for this, resulting in two different sets of simulated T eff distributions. The first were the solar-metallicity COND models from Baraffe et al. (2003) that, because they neglect dust opacity, are most applicable to mid-M dwarfs and mid-to late-T dwarfs believed to be free of photospheric clouds. These model grids are sampled at five different ages (0.1, 0.5, 1, 5, and 10 Gyr) and sample the temperature range 125K T eff 2800K, which corresponds to masses around 0.01M < M < 0.10M . The second set of models were the hybrid suite of solar-metallicity models from Saumon & Marley (2008) that assume cloud-free atmospheres only in the late-M and late-T zones but account for cloud growth and subsequent clearing in and around the transition from L dwarfs to T dwarfs. The evolutionary model grids are sampled at twenty-six different ages in the 3 Myr < age < 10 Gyr range and cover the range 300K T eff 2400K, which corresponds to the mass range 0.002M < M < 0.085M .
Fourth, we used the inverse transform sampling method to turn the various forms of the mass function into space densities binned in T eff . The process is as follows. Each normalized mass function can be used as a probability density function, which gives the likelihood of drawing at random an object of a certain mass from within that distribution. In a practical sense, this random drawing is done by integrating under the probability density function to produce a cumulative distribution function, reversing the dependent and independent variables, and re-solving for the dependent variable, thus creating the inverse cumulative distribution function which then provides a mapping from the a random seed to an actual mass. The seed is produced via a random sampling of a uniform distribution over the range zero to one.
Fifth, we performed the simulations by creating 3×10 6 random seeds, each of which was assigned an age according to its order of selection. These ages were distributed uniformly over the subset of 0-10 Gyr interval over which each evolutionary model is valid. The seed was then passed through the inverse cumulative distribution function to assign its mass, then the assigned age and mass were passed through the evolutionary models to get the current T eff . Because the evolutionary models are sampled only on a sparse grid, bilinear interpolation between neighboring points was used to assign the temperature.
Finally, simulations were produced for each of the twelve assumed functional forms of the mass function, each of which was run through the two different evolutionary model grids. Furthermore, each simulation was run with three different values of a cutoff mass (10M Jup , 5M Jup , or 1M Jup ,), which is the lowest mass product that can be created. This resulted in a grid of seventy-two simulated T eff distributions.

Mass Function Fits
Here, we have compared our measured space densities to these seventy-two simulations. To determine the simulation that fits best, we have used the IDL routine mpfit (Mark-wardt 2009) to perform a weighted least-squares fit between the data and the simulations, where the only adjustable parameter is the scaling between the arbitrary number counts in the models and our measured space densities. For the calculation, we use only the eleven values in the upper portion of Table 15 that cover the range 450-2100K, as the other values are lower limits only. The best fit to each model produces a reduced χ 2 value. Figure 26 shows the fits for which this value is minimized. These best fits are identical to the best fits found by , and involved the single power law and log-normal forms. For each evolutionary model, the power law form is slightly favored over the log-normal based on the best-fit χ 2 minimization values. In contrast to the results of , we now find that the evolutionary code of Saumon & Marley (2008) is highly favored over that of Baraffe et al. (2003), and the reason for this is the inclusion in this paper of space density measurements over the cloudyto-clear transition that the Saumon & Marley (2008) models were designed to address. Specifically, the space density spike in the 1200-1350K bin of Figure 26 is well produced by simulations incorporating the Saumon & Marley (2008) models, and this bin is the one covering spectral types from ∼L8 to ∼T3 (the yellow zone in Figure 20b) over which cloud building and subsequent break-up have been hypothesized. These models not only predict the position of the spike but also correctly predict its magnitude. Furthermore, they also predict the magnitude of the drop-off and recovery at cooler types once clouds have cleared and cooling once again proceeds as normal.
The best fits across the coarse grid of 72 models are those with the single power law of α = 0.5. Figure 27 illustrates a few supplemental simulations to show that the minimum χ 2 value across a finer grid of models is actually reached at α = 0.6, which was the same conclusion found by . There is however, no significant difference between the χ 2 values of the α = 0.5, 0.6, and 0.7 models. Obtaining a more accurate space density in the 450-600K bin is critical to pinning down the true value of α.
As a closer look at Figure 27 reveals, the preferred value of α rests largely with the steepness of the curve over the 1200-450K region, and most of the power falls in that region's final bin (450-600K), for which the space density is the highest. If we use the densities implied by our temperature randomizations (column 4 of Table 15), we find a best fit of α = 0.4, although, as discussed earlier, the density for that bin is likely biased low. This leads us to conclude that our measurements of the space density support a value of α = 0.6±0.1.

The Low-mass Cutoff
Whereas the 450-600K bin is critical in determining the value of the power law's exponent, the next cooler bins are critical in determining the cutoff mass. The best fits to our observed space densities currently do not have a strong dependence on the low-mass cutoff. As the plots in Figure 27 show, this is because the lower limit to the density in the 300-450K bin is consistent with all three values of the cutoff mass   Figure 26. The best fits between the simulations and our measured space densities. Of the simulations that use the evolutionary tracks of Baraffe et al. (2003), the two with the smallest reduced χ 2 values are shown in the top two rows. Of the simulations that use the evolutionary tracks of Saumon & Marley (2008), the two that provide the best fits are show in the two bottom rows. "Model D" refers to the power law with α = 0.5, and "Model H" refers to the single-object log-normal form of Chabrier (2001). See  for additional information on these simulations. Each row shows the same model with a different low-mass cutoff: 10MJup (blue) in the left panel, 5MJup (dark green) in the middle panel, and 1MJup (red) in the right panel. Our measured space densities and their uncertainties are shown in black. Grey zones denote areas not covered by the simulations. (10, 5, and 1 M Jup ). An increase of just 40% in the value of this lower limit would enable us to confidently claim a cutoff mass below 10M Jup . (In  we had claimed to push the cutoff mass below 5M Jup , but this was based on a number of objects in the 300-450K bin that was half as large as the sample we are now using.) This bin is comprised mostly of Y0.5 to Y2 dwarfs (Figure 20b), which are challenging objects to uncover given their faint absolute magnitudes (M J ≈ M H > 23 mag, M W 2 = M ch2 > 15 mag; Figure 14). Even more critical to defining the low-mass cutoff is the next cooler bin, 150-300K, which presently has only one known object in it, WISE 0855−0714. Finding more representative objects in this bin would even more readily determine the cutoff mass, as the top row of Figure 26 shows. For the α = 0.5 model, the space density values in this bin vary wildly -from ∼0.2×10 −3 pc −3 for a 10M Jup cutoff, to ∼2.2×10 −3 pc −3 for a 5M Jup cutoff, to ∼4.5×10 −3 pc −3 for a 1M Jup cutoff. Finding objects in this bin is an even more challenging proposition, as WISE 0855−0714 itself has absolute magnitudes of M J ≈ 28 mag, M H ≈ 27 mag, and M W 2 = M ch2 ≈ 17 mag.
Nonetheless, we can use objects of known mass within the 20-pc census to help further refine the cutoff value. Most notably, a number of census members are known to belong to young moving groups and associations (section 7.1), and these objects will have hotter temperatures and earlier spectral types than older counterparts in the field of the same mass. Hence, finding an object of exceedingly low mass is a far less daunting challenge if is it younger and brighter. Young members of the 20-pc census are listed along with their assigned T eff values and published masses in Table 16.
Before exploring these masses, though, we note that such determinations are direct comparisons to evolutionary models and thus fail to provide an independent check of the theory. Are the masses coming from the evolutionary models trustworthy? To answer this, we have also listed in Table 16 those multiple systems within the 20-pc census whose masses have been measured dynamically. These objects are identified with their corresponding T eff bin and indicated in Figure 28. This figure shows, for both the Saumon & Marley (2008) and Baraffe et al. (2003) evolutionary tracks, the expected mass distributions from our simulations for each of our 150K bins. The simulations show a tight distribution of masses for the hotter bins, but the range of masses quickly expands for the colder bins. In the Saumon & Marley (2008) models, a wide range of masses is expected to inhabit each of the temperature bins from 750K to 1500K. At colder temperatures, though, the mass range reduces dramatically, with the 300-450K bin containing only objects with masses below ∼ 30M Jup . (Using the Baraffe et al. 2003 models, which explore even colder temperatures, we find that the mass range shrinks to < 15M Jup for the 150-300K bin.) For the warm bins with the narrowest mass distributions (2100-2250K and 1950-2100K), the two objects in Table 16 with dynamical measures have masses in accordance with the model predictions. Good agreement is seen at cooler bins as well. The only objects with measures that may be discrepant with expectations are the four objects in the 1650-1950K range (Gl 584B and C, DENIS 2252+1730A, 2MASS 0700+3157A) in panel (a), the highest mass object in the 1200-1350K bin (Gl 845B) along with the two objects in the 900-1050K bin (Gl 229B and Gl 845C) of both panels, and the three lowest mass objects (SDSS 0423−0414B and WISE 1049−5319AB) in the 1200-1350K bin of panel (b). These latter three objects can be explained as the inability of the older Baraffe et al. (2003) models to account for clouds in this range, since these objects do not appear unusual when compared to the expectations from Saumon & Marley (2008).
The other objects deserve closer scrutiny: • Gl 564BC: This pair has masses lower than 85% of objects in the 1650-1800K bin. Objects of this mass, according to our simulations, would have a relatively young age of ∼580±67 Myr. Potter, et al. (2002) note that the primary in this system, the G2 dwarf Gl 564A, is chromospherically active, a fast rotator, and an object of high lithium abundance, which places its age at <800 Myr. After a more careful analysis, Dupuy et al. (2009) adopt an age for the primary of 790 +220

−150
Myr, which accords with the young age expected by our simulations.
• DENIS 2252−1730A: The is the third other object in the 1650-1800K bin. It has a dynamical mass intermediate between Gl 564B and Gl 564C and would thus be expected from our simulations to have a similarly young age. However, there does not appear to be independent verification of a young age in the literature, such as a measurement of lithium absorption in the A component ).
• 2MASS 0700+3157A: This object falls in the 1800-1950K bin. Our simulations find that it has a mass lower than 85% of objects in its temperature bin, implying another relatively young age of 755±101 Myr. There is no independent assessment of age for this object, although  also note the model-implied young age for the primary. As stated in that work, Thorstensen & Kirkpatrick (2003) report no lithium in the joint spectrum of the AB pair, which would likely mean only that the age is >200 Myr.
• Gl 845BC: The masses of both components are surprisingly high for their respective temperature bins. In our simulations that use the Saumon & Marley (2008) evolutionary models, we find ∼250,000 objects in our 3-million-object simulation that fall in the 1200-1350K bin inhabited by Gl 845B but none of these simulated objects has a mass as high as Gl 845B. Likewise, of our ∼190,000 simulated objects in the 900-1050K bin, none has a mass as high as Gl 845C. This system is not believed to be exceptionally old, either (see , which might partly explain the ultra-high masses. Switching to the Baraffe et al. (2003) evolutionary code instead gives a similar result. The published mass measurements for this system are completely at odds with theoretical expectations.
• Gl 229B: This object has an ultra-high mass for its effective temperature. Its measured mass is almost identical to that of Gl 845C, so the arguments for Gl 845C above also apply to Gl 229B. Brandt et al. (2020) note that an exceptionally old age for the Gl 229 system is disfavored, making Gl 229B another T dwarf whose mass measurement is at odds with expectations.
In summary, then, the masses expected from our simulations are consistent with the measured dynamical masses in Table 16 for most objects for which direct comparisons can be done. The exceptions are Gl 229B and Gl 845BC, which remain puzzles.
The consistency between most of the measurements and the expected values at higher masses gives us a cautious confidence -but not independent confirmation -in trusting model-implied values at lower masses. Of the 20-pc moving group members listed in Table 16, the ones of lowest mass are between 10 to 12 M Jup . So, within the 20-pc census, we are not able to push the cutoff mass below 10 M Jup through either a critical analysis of the entire L, T, and Y sample or through an analysis of the subset with moving group membership. Despite this limitation, we can look at the young moving group members in a larger sample volume, which strongly hint at a low-mass cutoff substantially below 10 M Jup . As discussed in section 7.1, PSO J318.5338−22.8603, 2MASSW J1207334−393254b, and 2MASS J11193254−1137466AB are believed to have masses in the 4-7 M Jup range, and other objects identified in Table 12 could possibly lower the limit within the 20-pc census itself.

The Age Distribution
We can also compare the expected age distributions with our limited knowledge of the ages for objects in the census. Figure 29 shows plots analogous to the mass distributions shown in Figure 28. For the Saumon & Marley (2008) evolutionary tracks in the 900-2250K regime, the age distributions cover the entire range of 0-10 Gyr ages but with a skew toward young ages. The age distribution then flattens across the 600-900K range, although the youngest ages (<0.5 Gyr) start to disappear. A skew toward old ages appears below 600K, with the skew becoming more severe with higher cutoff mass. The Baraffe et al. (2003) evolutionary tracks show that this skew toward old ages is exacerbated in the coldest bin (150-300K). Here, a 10 M Jup cutoff mass would imply no objects with ages <7 Gyr, whereas a 1 M Jup cutoff would give a much more uniform age distribution, albeit with few objects having ages below 1 Gyr.
Most of the objects in the 20-pc L, T, and Y dwarf census lack age information, but we can examine this using tangential velocities as proxies of dynamical heating. Figure 30 shows the census' total proper motion and tangential velocity distributions. A total of 2% of the objects -  Table 16 that have dynamically measured masses (filled black stars) are plotted in their Teff bins at the x location corresponding to their mass; their y positions are arbitrary. NOTE-Legend for method: MovGp = mass comes from evolutionary models combined with the known age of the moving group or young association with which this object is a member; dynam = mass is measured dynamically.  Figure 30. Histograms of the total proper motion and vtan for the L, T, and Y dwarfs in the 20-pc census. In the upper diagram, the total motion is shown for all systems in the census. In the lower diagram, the tangential velocity is shown only for those systems having parallax measures with uncertainties below 12.5%. The median vtan value for objects in the lower panel is 30.8 km s −1 .
For the entire 20-pc census, we can check whether the expected inflation of the velocities at older ages is seen in our empirical data. To accomplish this, we compare the median ages expected from our simulations to the median v tan values from our actual measurements. In Figure 29 we illustrate the median age at each 150K bin for our α = 0.5 power law simulation. We also plot the measured tangential velocity against effective temperature in Figure 31, along with the median tangential velocity value in each of the 150K bins. In Figure 29, we see that the median age shifts to younger values from 2250K down to 1500K and reaches a minimum in the 1350-1500K bin before reversing course and trending to increasingly older values for increasingly cooler bins. Our measured v tan values in Figure 31 show only a little variation across the 500-2250K regime but increase substantially in the 300-450K bin.
Although the agreement is qualitatively the same -in the sense that the colder, older objects have higher velocities indicative of dynamical heating -the coldest portion of our sample may be biased toward higher velocities anyway. Objects in the coldest bins are Y dwarfs that are uncovered almost exclusively with WISE data and should have very red colors of W1−W2 > 4 mag. However, given their intrinsic faintness, they are usually not detected at W1, leading to W1−W2 color limits only. As the W2 mags themselves grow fainter, this color limit becomes less useful, and thus a detection of proper motion is the best way to discern W2-only Y dwarfs from background chaff. This reliance on a proper motion signature -which at faint magnitudes is itself only reliable if the motion is large -leads to a kinematic bias. Thus, the larger median velocity in the 300-450K bin may be a consequence of relying more heavily on motion as a selection criterion. 9.4. Where are the WISE 0855−0714 Analogs?
In the next fainter bin, 150-300K, WISE 0855−0714 is the only object recognized despite concentrated efforts to find other examples by both the Backyard Worlds and CatWISE teams. (With additional follow-up, WISE 0830+2837 from Bardalez Gagliuffi et al. 2020 may prove to be the second known member of this T eff bin.) As Figure 29b demonstrates, objects in this bin should be heavily skewed old unless the low-mass cutoff is substantially less than 1M Jup . Such a heavy skew to old ages also implies that such objects will be on average more metal poor than the Sun.
It is possible that analogs to WISE 0855−0714 have already been cataloged in the thousands of faint motion candidates already identified by the Backyard Worlds and Cat-WISE teams but remain unrecognized? After all, many of the objects have W1−W2 color limits only and were never imaged by Spitzer to provide more diagnostic ch1−ch2 colors. The answer is almost certainly "no," for the following reason. One of the criteria used to prioritize follow-up observations is the reduced proper motion, H W 2 = W 2 + 5 log µ tot + 5, which is a crude measure of the object's intrinsic faintness based on its apparent magnitude and the size of its transverse motion. If any of the motion candidates lacking solid color had distinguished themselves with an exceptionally faint H W 2 value -WISE 0855−0714 has H W 2 = 23.4 mag (Figure 1 of Bardalez Gagliuffi et al. 2020) -it would certainly have been noticed. WISE 0830+2837 from Bardalez , with H W 2 = 22.6 mag, is the nearest contender now known.
Four possible scenarios to explain our lack of success in finding additional objects in the 150-300K bin are (1) they are exceedingly rare, (2) their intrinsic faintness places them too close to the W2 detection limit of WISE for motion searches to identify them confidently, (3) their motions are so high that coadds cannot be used to push the WISE detection limits deeper, and (4) their colors and magnitudes differ significantly from expectations. We discuss each of these scenarios below: (1) The coldest objects are rare: Our result that the mass function is best fit with a power law of α = 0.6 and that the cutoff mass is likely at or below 5M Jup would imply a distribution of objects in the 150-300K bin like that shown in the green curve in the lower right panel of Figure 29b. This implies a space density of at least 2×10 −3 pc −3 , which makes objects in this bin as common as T6 or T7 dwarfs. It is thus hard to reconcile these results with the hypothesis that such cold objects are extremely rare. Furthermore, it would be an unbelievable stroke of luck 20 that our Sun falls a mere 2.3 pc from such an extremely rare, cold object, as it does with WISE 0855−0714. So we reject rarity as a possible cause.
(2) WISE is too shallow: History has shown us that allsky surveys can lead to curious results when researchers push those surveys near their limits. The bottom of the main sequence in the 1980s appeared to fall at late-M (Probst & Liebert 1983;Reid 1987) based on the dominant discovery engine of its time, the Palomar Observatory Sky Survey (Minkowski & Abell 1963;Reid et al. 1991). We now know, of course, that the reason for this is the low space density of early-L dwarfs (see Figure 27) and the fact that the POSS-I and POSS-II B and R plates failed to survey enough volume to detect all but the nearest L dwarf examples. The L/T pair WISE 1049−5319 is present on the southern UK Schmidt photographic plates but was not selected as a motion source (Luhman 2013); we find that Willem Luyten, despite having cataloged over 58,000 proper motion stars using photographic data (Luyten 1979), failed to catalog any of the 20-pc L dwarfs in Table 11. In the case of WISE, Wright et al. (2014) have used the relatively bright W2 magnitude of WISE 0855−0714 (W2 = 13.82 mag), its distance (2.3 pc), and the fact that it lies ∼2 magnitudes above the limit of the AllWISE Catalog to argue that there should be another 4 to 35 similar objects already detected in AllWISE itself. The CatWISE and CatWISE2020 Catalogs (see below) have increased the sensitivity to lower motions at fainter magnitudes, thus making the identification of these detected objects even easier. Hence, it is unlikely that the survey that found WISE 0855−0714 is too shallow to find other analogs.
(3) High motions confound deeper searches: The data sets using the longest time baseline of WISE data are CatWISE Preliminary (Eisenhardt et al. 2020) and CatWISE2020 (Marocco et al. 2020b). Most points on the celestial sphere are visited by WISE during a several-day window every six months. Both the CatWISE Preliminary and CatWISE2020 processing leveraged these repeats to measure proper motions of all sources. Full-depth coadditions, which took all of the available data to create a single, deep image, were used for source detection. Those source detections were then characterized through the stack of epochal coadds (from each sixmonth window) to measure photometry and astrometry for each source. Sources with significant proper motions could then be selected from the resulting source tables. Sources that fail to move a significant portion of a full-depth coadd's W2 FWHM (∼6 ; Meisner et al. 2019) benefit from the coaddition, as their S/N increases by roughly the square root of the number of epochs. However, sources with higher motions do not see this benefit; a very high motion source will appear as a tracklet of separate sources in the full-depth coadd, and each separate apparition contains the background noise component from all epochs but the source signal from only one. Therefore, faint, high-motion sources can be lost in this process. If many of the coldest brown dwarfs are older kinematically, as Figure 29a and b suggest, their concomitant high proper motions may quash their identification by the Cat-WISE pipeline.
(4) Cold objects have unexpected colors or magnitudes: The analysis from Wright et al. (2014) inherently assumed that WISE 0855−0714 is a representative member of the Y dwarfs populating the 150-300K bin. What if WISE 0855−0714 is atypical? It has v tan = 88.0 km s −1 , which, although in the highest 4% of all v tan values in Figure 31, is not exceptional. If the majority of objects in the 150-300K bin are much older and have higher kinematics, then their high motions may suggest that point (3) above is a contributing cause. In addition, however, their older ages would also suggest a somewhat lower metallicity in general. If we look at the 20-pc T subdwarfs (section 7.2) that have metallicity measurements, we find that values as low as [M/H] = −0.3 dex produce noticeable changes in the spectra of mid-to late-T dwarfs. Values of [M/H] = −0.6 dex begin to move objects into unfamiliar loci on color-magnitude diagrams. Inasmuch as molecular absorption strengths dictate the overall spectral energy distribution of Y dwarfs (Figure 15 of Doré et al. 2016), slight changes in metallicity could affect the relative importance of these bands and dramatically alter Y dwarf spectra and colors. Recent discoveries at early-T from Schneider et al. (2020) and Meisner et al. (2021) underscore the point that warmer brown dwarfs with presumably lower metallicity ([Fe/H] ≤ −1 dex) exist; their spectra are vastly different, at least in the near-infrared, from those of solarmetallicity T dwarfs. These may be harbingers of the photometric and spectroscopic bizarreness we can expect from the majority of later Y dwarfs, even if these Y dwarfs in general have less extreme metallicities. In summary, other nearby objects with temperatures comparable to WISE 0855−0714 must exist, based on evidence from the mass function shape and knowledge of its low-mass cutoff. However, the expected higher motions and lower metallicities of objects in this 150-300K bin, may make them a challenge to identify, especially when coupled with their intrinsic faintness.
10. CONCLUSIONS Our results, which use the final trigonometric parallaxes we have measured using Spitzer, confirm the result of  that the 20-pc brown dwarf portion of the mass function, which is based here on 525 L through Y dwarfs, can be best described as a power law with an exponent of α = 0.6±0.1. We have not yet, however, extended this analysis to higher masses to investigate how the mass function behaves over the entire mass range within 20 pc. Earlier analyses have indicated that the higher mass portion can be described as a two-part power law (Kroupa et al. 2013) or log-normal form (Chabrier 2003b). New data, particularly data from Gaia DR2 and subsequent releases can be used to refine our knowledge of the A through M dwarfs (and white dwarfs) with the 20-pc census as well as providing important astrometric information to help identify companions to those stars. Developing a database containing all knowledge of our stellar and substellar neighbors within this volume will enable us to explore the individual-object mass function with unprecedented detail.
Our results have also shown that the cutoff mass for star formation, is constrained to be lower than ∼10M Jup and that analysis of young moving group members over a wider sample likely constrains this value to ∼5M Jup . Obtaining a more solid value for the cutoff mass requires volume-complete subsets of a substantial number of Y dwarfs colder than 450K, and particularly below ∼350K, a regime in which we have only one confirmed Y dwarf. Although WISE has provided a trove of Y dwarf discoveries, probing a substantial volume colder than ∼350K may require other resources. One such resource currently being planned is the Near Earth Object Surveyor (formerly called NEOCam) that is due to launch in 2025. As discussed in Kirkpatrick et al. (2019b), NEO Surveyor will cover 64% of the celestial sphere in two bands, NC1 and NC2, that cover wavelengths of 4.0-5.2 µm and 6.0-10.0 µm. Portions of the sky will be repeatedly scanned during their 75-day visibility windows then scanned again roughly 215 days later when the next visibility window opens. The mission, although planned for five years, has a design lifetime of twelve years.
The absolute NC1 fluxes of 350K Y dwarf and a 250K Y dwarf are 103 µJy and 26 µJy, respectively. The use of image differencing for high-motion objects in NEO Surveyor data will theoretically allow us to achieve single-epoch S/N=5 sensitivities of ∼4 µJy at NC1, thereby greatly increasing the distances to which we can detect these coldest brown dwarfs. However, NEO Surveyor is run through NASA's Planetary Defense Coordination Office, so no funding is being provided for the additional processing needed for astrophysical studies. For a relatively small investment, NASA Astrophysics could realize the full potential of NEO Surveyor data for stellar astrophysical research, of which cold brown dwarf discovery would be a major beneficiary.  Tables 5, 6 , 7, 8, 9, 10, and 11, we have collected spectroscopic, astrometric, and photometric data from both this paper and the literature. These data are listed in Table A1. The various sections of the table are described in detail below. Close binaries are generally entered as a single entry with joint photometry unless there are components of the multiple with spectral types earlier than L0. For a full accounting of individual L, T, and Y components within the 20-pc census, refer to Table 11. A.1. Origin and Name Column T indicates the table(s) from which the source originates. Objects in the 20-pc census (Table 11) are indicated by "T". Users are encouraged to use this column rather than the parallax column if they wish to select the same set of objects that we included in our 20-pc census. Objects that are not listed in our 20-pc census (Table 11) but were nonetheless part of our Spitzer parallax program (Tables 5-7) are indicated by "P". Objects that are not from any of these tables but were part of our photometric or spectroscopic follow-up campaigns (Tables 8 and 9) are indicated by "F". Objects considered for the 20-pc census but ultimately not included (Table 10) are indicated by "C".
Column ShortName gives the abbreviated prefix and suffix of the full source name. This prefix is generally the survey of origin, and the abbreviated suffix is the sexagesimal RA and Dec of the source in the form hhmm±ddmm. As examples, CWISEP J193518.59−154620.3 is denoted as CWISE 1935−1546, and PSO J149.0341−14.7857 is denoted as PSO 0956−1447. Exceptions are made for objects with common names like Gl 570D and LHS 2397aB, whose full names are used instead.

A.2. Spectral Types
Columns SpO and SpIR list the optical and near-infrared spectral types, respectively, if known. These are converted to a decimal scale, and any qualifying criteria such as "pec", "β", and "sd" are dropped. The convention for the decimal scale is L0 = 0.0, T0 = 10.0, and Y0 = 20.0. As examples, an object with a spectral type of sdT8 is given as 18.0, and one with a type of L7: VL-G is given as 7.0. The two objects listed in Table 11 with types of "extremely red" in  are given in this table as 9.5. Column SpAd is the adopted spectral type, which is the same as SpIR if that value is not null; otherwise, it is the same as SpO. If both of those quantities are null, a spectral type estimate is given. A few objects, however, have null values for SpAd, and these are objects believed to be background interlopers and not brown dwarfs.
The source of the spectral type is given in column OI. An explanation of the double-letter code for this column can be found in the table comments.

A.3. Astrometric Data
Columns ϖ abs , µ α , and µ δ list the best measured trigonometric parallax and proper motion values in RA and Dec. The "best" astrometry is simply that data set with the smallest quoted uncertainty in the parallax or, for objects lacking a parallax measurement, the data set with the smallest quoted uncertainty in the total proper motion. All parallaxes are given on the absolute reference grid; data from Tinney et al. (2003) and Tinney et al. (2014), along with USNO data from , were converted from relative to absolute as described in section 8 of . The values listed for proper motion are a mixture of relative and absolute measurements. Readers are encouraged to cite the source of those values if this distinction is important for their research.
The source of the astrometry is given in column AS. An explanation of the single-letter code for this column can be found in the table comments.

A.4. JHK Photometry
Column J MKO lists J-band photometry on the MKO system, J 2MASS lists J-band photometry one the 2MASS system, H lists H-band photometry on either the MKO or 2MASS system, K MKO lists K-band photometry on the MKO system, and K S(2MASS) lists K S -band photometry on the 2MASS system. See section 5.1.1 for details. Photometric values listed without corresponding errors are magnitude limits.
The source of the photometry is given in column PhotS. An explanation of the five-letter code for this column can be found in the table comments.
A.5. CatWISE2020 Data Columns RA_C2, Dec_C2, pmra_C2, pmdec_C2, W 1mag_C2, W 2mag_C2, and par_C2 contain astrometric information from the CatWISE2020 Catalog and Reject Table (Marocco et al. 2020b). The first two columns are the J2000 equinox RA and Dec positions from the moving-object solution at epoch MJD 57170.0, the next two columns are the measured proper motion and Table A1. Amassed Spectroscopic, Astrometric, and Photometric Data for Objects Listed in Tables 5, 6 , 7, 8, 9, 10, and 11 T Name SpO SpIR SpAd