An Improved Near-Infrared Spectrum of the Archetype Y Dwarf WISEP J182831.08+265037.8

We present a Hubble Space Telescope/Wide-Field Camera 3 near infrared spectrum of the archetype Y dwarf WISEP 182831.08+265037.8. The spectrum covers the 0.9-1.7 um wavelength range at a resolving power of lambda/Delta lambda ~180 and is a significant improvement over the previously published spectrum because it covers a broader wavelength range and is uncontaminated by light from a background star. The spectrum is unique for a cool brown dwarf in that the flux peaks in the Y, J, and H band are of near equal intensity in units of f_lambda. We fail to detect any absorption bands of NH_3 in the spectrum, in contrast to the predictions of chemical equilibrium models, but tentatively identify CH_4 as the carrier of an unknown absorption feature centered at 1.015 um. Using previously published ground- and spaced-based photometry, and using a Rayleigh Jeans tail to account for flux emerging longward of 4.5 um, we compute a bolometric luminosity of log (L_bol/L_sun)=-6.50+-0.02 which is significantly lower than previously published results. Finally, we compare the spectrum and photometry to two sets of atmospheric models and find that best overall match to the observed properties of WISEP 182831.08+265037.8 is a ~1 Gyr old binary composed of two T_eff~325 K, ~5 M_Jup brown dwarfs with subsolar [C/O] ratios.


INTRODUCTION
The search for cool brown dwarfs with effective temperatures (T eff ) less than 700 K (approximately a spectral type of T8) was one of the driving science goals of wide-area, red-optical and infrared surveys such as the United Kingdom Infrared Deep Sky Survey (UKIDSS; Lawrence et al. 2007), the Canada France Brown Dwarf Survey (CFBDS; Delorme et al. 2008a) and its counterpart in the near-infared CFBDSIR (Delorme et al. 2010), and the Wide-field Infrared Survey Explorer (WISE ; Wright et al. 2010). With masses less than ∼20 M Jup at the typical age of the ultracool dwarf field population of 3 Gyr (Dahn et al. 2002), such cool brown dwarfs are most likely the least massive products of star formation.
While such cool brown dwarfs have been discovered using each of these surveys (e.g., Burningham et al. 2008;Delorme et al. 2008bDelorme et al. , 2010Liu et al. arXiv:2107.00506v1 [astro-ph.SR] 1 Jul 2021 2011; Kirkpatrick et al. 2011;Cushing et al. 2011) the vast majority of brown dwarfs with effective temperatures less than 500 K have been discovered using WISE data. The near-infrared spectrum of one such brown dwarf, WISEP J182831.08+265037.8 (hereafter WISE 1828+2650), was distinct enough from that of the late-type T dwarfs that Cushing et al. (2011) identified it has the archetype of the new Y spectral class. They originally assigned it a spectral type of >Y0 but its type was later revised to ≥Y2 after the discovery of the Y1 dwarf WISE 035000.32−565830.2 by Kirkpatrick et al. (2012). At the time of its discovery, WISE 1828+2650 had the reddest near-to mid-infrared color of any brown dwarf known at J−W 2= 9.29 ± 0.35 (mag). Atmospheric models indicated such a color corresponded to an effective temperature of less than ∼300 K.
Once its parallax was measured (Beichman et al. 2013;Dupuy & Kraus 2013), it became clear that WISE 1828+2650 was overluminous in nearly all color magnitude and color spectral type diagrams (Kirkpatrick et al. 2012;Beichman et al. 2013;Leggett et al. 2013;Dupuy & Kraus 2013). Several reasons for this overluminosity were suggested including misclassification (Kirkpatrick et al. 2012), a brightening in the spectral sequence due to an unknown physical mechanism (Kirkpatrick et al. 2012;Cushing 2014), and unresolved binarity (Beichman et al. 2013;Leggett et al. 2013). The subsequent measurement of the parallaxes for the even redder and cooler brown dwarfs WD 0806−661B (Luhman et al. 2011) and WISE J085510.83−071442.5 (hereafter WISE 0855−0714, Luhman 2014) strongly suggest binarity is the cause of WISE 1828+2650's over luminosity because these two objects appear to fall in line with the other Y dwarfs in color magnitude diagrams Tinney et al. 2014;Leggett et al. 2015;Schneider et al. 2016). Subsequent discoveries of brown dwarfs with similar effective temperatures like CWISEP J193518.59−154620.3 (Marocco et al. 2019), CWISEP J144606.62−231717.8 Marocco et al. 2020) and WISEA J083011.95+283716.0 (Bardalez Gagliuffi et al. 2020), have only strengthed the case for binarity but WISE 1828+2650 remains stubbornly unresolved in both Hubble Space Telescope (HST ) and ground-based adaptive optics imaging Beichman et al. 2013). However given the poor quality of model atmosphere fits to the near-to midinfrared spectral energy distribution of Y dwarfs (e.g., Schneider et al. 2015;Luhman & Esplin 2016;Leggett et al. 2017), missing or incomplete opacity sources and chemistry cannot be ruled out.
The spectrum of WISE 1828+2650 presented by Cushing et al. (2011) was obtained with the G141 grism in the Wide Field Camera 3 (WFC3; Kimble et al. 2008) on-board the HST and covered 1.1 to 1.7 µm at a resolving power of R ≡ λ/∆λ ≈ 130. However because WFC3 is slitless, extreme care must be taken in order to avoid contamination by light from stars nearby on the sky. At the time of the observations, we had yet to perfect our methodology for roll angle selection and so the resulting spectrum was contaminated by light from such a star. In this paper, we present an improved, contaminationfree HST /WFC3 spectrum that covers an even larger wavelength range of 0.9-1.7 µm.
In §2, we describe the acquisition and reduction of the spectrum. In §3, we discuss the characteristics of this unique spectrum in detail, revisit the spectral classification of WISE 1828+2650 based on our new spectrum, and construct a spectral energy distribution covering 0.9-4.5 µm using previously published photometry. §4 presents our estimates for the bolometric luminosity and effective temperature of WISE 1828+2650. The latter quantity was determined using both evolutionary models and two different sets of atmospheric models. Finally in §5, we discuss the model spectra fits to the data and the implications for the properties of WISE 1828+2650.

OBSERVATIONS AND DATA REDUCTION
WISE 1828+2650 was observed with the WFC3 onboard HST as a part of a Cycle 20 program to obtain grism spectroscopy of late-type T and Y dwarf candidates (GO-12970, PI=Cushing). The WFC3 uses a 1024 × 1024 HgCdTe detector with a plate scale of 0. 13 pixel −1 which results in a field of view of 123 × 126 . WISE 1828+2650 was observed with the G102 grism, which covers the 0.8−1.15 µm wavelength range at a resolving power of R ≡ ∆λ/λ∼210, and the G141 grism, which covers the 1.075−1.70 µm wavelength range at a resolving power of R∼130. Direct images through the F105W (λ pivot =1.0552 µm, ∆λ = 0.265 µm) or F125W (λ pivot =1.2486 µm, ∆λ = 0.2845 µm) filter were also obtained before the G102 and G141 grism images, respectively. A log of the observations is given in Table  1. Both the spectroscopic and photometric observations were reduced as described in Schneider et al. (2015); the resulting G102+G141 spectrum is shown in Figure  1 while the F105W and F125W magnitudes are given in Table 2. There is a 2% uncertainty in the absolute flux calibration of the spectrum (Kuntschner et al. 2011) and the signal-to-noise ratio (S/N) of the spectrum at the peaks of the Y , J, and H bands (1.05, 1.27, and 1.6 µm), ranges from 15 to 20. We also computed the F140W (λ pivot =1.3923µm, ∆λ = 0.384 µm) magnitude of WISE 1828+2650 using the direct images obtained with the original G141 grism spectrum and that is also given in Table 2.

THE SPECTRUM
The spectrum exhibits deep absorption bands of CH 4 and H 2 O typical of late-type T dwarf spectra (e.g., Burgasser et al. 2006) but the heights of the Y -, J-, and Hband peaks are approximately equal in units of f λ . This atypical characteristic prompted Cushing et al. (2011) to identify WISE 1828+2650 as the first Y dwarf.
We tentatively identify the 3(ν 1 , ν 3 ) band head of H 2 O at 0.925 µm in the spectrum of WISE 1828+2650. This band head is prominent in the spectra of the T dwarfs (Burgasser et al. 2003;Kirkpatrick et al. 2011) and has even been detected in the spectrum of the Y0 dwarf WISEPC J205628.90+145953.3 (Leggett et al. 2013). However given the low S/N at these wavelengths and the fact that the feature falls at the end of the spectrum, a higher S/N spectrum will be required in order to confirm the band head is real and carried by H 2 O.
Ammonia is also a important opacity source in the atmospheres of cool brown dwarfs because it becomes the dominant equilibrium chemistry nitrogen-bearing species (A(N 2 )/A(NH 3 ) < 1) at T 700 K (Lodders & Fegley 2002). The ν 2 fundamental band is found in the spectra of T dwarfs at 10.5 µm (Roellig et al. 2004;Cushing et al. 2006) but the overtone and combination bands in the near infrared (1.03, 1.21, 1.31, 1.51, 1.66, 1.98, and 2.26 µm) have defied clear detection because they are intrinsically weaker than the fundamental bands and often overlap in wavelength with strong H 2 O and CH 4 overtone and combination bands.
It has long been suggested that the emergence of these bands could trigger the creation of a new spectral class Leggett et al. 2007;Kirkpatrick 2008) and indeed Cushing et al. (2011) set the transition between the T and Y dwarfs where the Delorme et al. (2008b) NH 3 -H spectral index, which measures the strength of the NH 3 absorption band on the blue side of the H-band peak, indicated a significant increase in absorption. Bochanski et al. (2011) identified weak NH 3 features in a moderate resolution (R = 6000) spectrum of the T9 dwarf UGPS 0722−05 across the entire near-infrared wavelength range but many of the identifications were later called into question by Saumon et al. (2012). More recently, Zalesky et al. (2019) measured the abundances of NH 3 in the atmospheres of 8 Y dwarfs through a retrieval analysis of the Schneider et al. (2015) HST /WFC3 spectra but no clear detection of NH 3 absorption features were reported.
The peak absorption coefficients of the near-infrared NH 3 bands decrease steadily as one moves to shorter wavelengths (Saumon et al. 2012) which suggests that all else being equal, longer wavelength bands would be easier to detect. While our spectrum does not extend to the K band, a search for the 1.98 and 2.26 µm NH 3 bands would be difficult since the K-band flux of late-type T and Y dwarfs is heavily supressed due to strong CH 4 and collision-induced H 2 absorption. The 1.66 µm band is centered beyond the wavelength limit of our spectrum but is also overwhelmed by CH 4 absorption and so would nevertheless be difficult to identify. Visual inspection of the red side of the H-band peak shows no distinctive absorption feature due to the 1.51 µm NH 3 band, although this could be a result of the low S/N and/or low resolving power of the spectrum. We have computed the NH 3 -H spectral index of Delorme et al. (2008b) for WISE 1828+2650 and a sample of T and Y dwarfs and the results are shown in Figure 2. WISE 1828+2650 deviates significantly from the trend set by the T and other Y dwarfs. If the index is actually measuring NH 3 absorption, then the WISE 1828+2650 value suggests that either NH 3 is absent from the spectrum, or the index is no longer sensitive to NH 3 at this spectral type. The 1.21 and 1.31 µm NH 3 bands are difficult to identify because they overlap in wavelength with the CH 4 bands that give rise to the J-band emission peak and thus simply help to confine the emergent flux to an ever narrowing wavelength range.
In contrast, the 1.03 µm 2ν 1 + 2ν 4 band is centered near the peak of the Y -band which suggests it will be more easily identified. However Schneider et al. (2015) found no evidence of this feature in HST /WFC3 spectra of other late-type T dwarfs and Y dwarfs. The first panel in the left column of Figure 3 shows the spectrum of WISE 1828+2650 centered on the Y -band peak. There is a weak double-peaked absorption feature centered at 1.015 µm that at first appears to be consistent with this NH 3 band. However also plotted in the second panel of the left column is the opacity cross-section spectrum of NH 3 at T =100 K and P =0.1 bar generated using the Yurchenko et al. (2011) NH 3 line list. The position of the absorption feature in the spectrum of WISE 1828+2650 clearly does not match the position of the NH 3 band. Several possibilities present themselves: 1. The feature is real and is carried by NH 3 but the Yurchenko et al. (2011) line list is in error. Laboratory observations of NH 3 at similar temperatures and pressures by Cruikshank & Binder (1969), Irwin et al. (1999), and Bowles et al. (2008) confirm the position of the band and its substructure therefore we eliminate this possibility.
2. The feature is real and is carried by NH 3 but a wavelength calibration error in the The Delorme et al. (2008b) NH3-H spectral index as a function of spectral type. The black points are for the T5-Y1 spectral standards. The grey points were computed using SpeX/IRTF spectra from the SpeX Prism Library and the T dwarf spectra from Schneider et al. (2015) while the red points were computed using the Y dwarf spectra from Schneider et al. (2015) and from this work.
WISE 1828+2650 spectrum has shifted the feature blueward. We eliminate this as a possibility because other Y dwarf G102 spectra reduced by Schneider et al. (2015) in the same manner do not appear discrepant with the spectra of other T/Y dwarfs.
3. The feature is not real and is an artifact of the data reduction. Such an "absorption feature" could arise in a low S/N spectrum if a cluster of bad or noisy pixels conspire to produce an emission-like feature at ∼1.0 µm thereby creating an apparent absorption feature at ∼1.03 µm. In this case, the identification of the absorption feature would be a result of our a priori expectations of finding NH 3 absorption. Five individual spectra are combined to produce the final spectrum and we can visually identify the absorption feature in four of the five spectra and so we eliminate this possibility.
4. The feature is real but its carrier is a molecule other than NH 3 . Since the wavelengths of the NH 3 absorption coefficients are correct, and we cannot identify an error in our data reduction, we conclude that the feature is probably real but is car-riered by a molecule other than NH 3 . We explore this possibility in more detail presently.
In a search for the carrier of this feature, we identified an absorption feature in the reflected-light spectra of Jupiter, Saturn, Uranus, and Neptune (Rayner et al. 2009) whose rough central wavelength and width matches that of the unidentified feature (see right panel of Figure 3). The presence of this band in all of the solar system giant planets strongly suggests the carrier is methane as ammonia is sequestered well below the clouds in Uranus and Neptune. Indeed a comparison of the giant planet spectra to models generated with and without CH 4 opacity also indicate the feature is carried by CH 4 (P. Irwin, private communication). The third and fourth panels of the left column of Figure 3 therefore show the cross-section spectrum of CH 4 at T =100 and 300 K (P =0.1 bar) from Yurchenko & Tennyson (2014) and Irwin et al. (2010); they have been smoothed to R=210 and resampled onto the wavelength grid of the WISE 1828+2650 spectrum. The T =100 K Yurchenko & Tennyson (2014) spectrum provides the best match to structure of the absorption feature. In particular, the double-peaked cross-section spectrum matches the structure of the absorption band and the "emission-like" feature at ∼1.0 µm is naturally explained by the lack of opacity at that wavelength. However the Yurchenko & Tennyson band is shifted slightly redward of our feature which taken at face value weakens the case for the feature being carried by CH 4 . Interestingly, the position of the Irwin et al. band does not match that of the Yurchenko & Tennyson band which suggests some uncertainty in the theoretical position of this band. The apparent match between the low-temperature methane opacity structure and the observed feature is puzzling. For a cloudless atmosphere models indicate that the flux in this spectral region emerges from quite deep in the atmosphere, where the local temperature is around 800 K. If the carrier of the feature is methane, this may be an indication that water clouds, which form around 300 K, are limiting the depth of the visible atmosphere here. A complete analysis of this will be the subject of future work.

Spectral Classification
WISE 1828+2650 was originally classified as >Y0 by Cushing et al. (2011) because its 1.1−1.7 µm spectrum exhibited unique characteristics unseen in the spectra of late-type T dwarfs and Y0 dwarfs. Its type was later revised to ≥Y2 after the discovery of the Y1 dwarf WISE 035000.32−565830.2 (Kirkpatrick et al. 2012). With an improved spectrum in hand, we can return to the question of its spectral type.   Figure 4 shows a sequence of late-type T and Y dwarf spectra all observed with the G102+G141 WFC3 grism combination (Schneider et al. 2015, this work). The new WISE 1828+2650 spectrum is still clearly distinct from that of the T dwarfs and therefore the spectral type should remain a Y dwarf. Trends in spectral morphology at the T/Y boundary noted by Kirkpatrick et al. (2012) and Schneider et al. (2015) continue with the addition of the WISE 1828+2650 spectrum: 1) the Y -band peak becomes more symmetrical, 2) the Y -band peak wavelength becomes bluer, 3) the H-band peak becomes more symmetrical, and 4) with the exception of WISEA J053516.87−750024.6 (whose G102 spectrum may still be contaminated (Schneider et al. 2015)), the Y -, J-, H-band peaks evolve towards having equal intensities. Interestingly, the tentative new CH 4 band appears weakly in the spectrum WISEA J053516.87−750024.6, although the S/N is quite low. Since the spectrum of WISE 1828+2650 smoothly extends the Y dwarf spectral sequence beyond Y1, its spectral type should remain ≥Y2 until the near-infrared spectra of cooler objects like WISE 0855−0714 are obtained.   Schneider et al. (2015) while the spectrum of WISE 1828+2650 is from this work. The H-band spectrum of WISEA J053516.87−750024.6 is missing because it was contaminated by first-order light from a nearby star (Schneider et al. 2015). Uncertainties for each spectrum are shown as gray bars. Figure 5 shows the spectral energy distribution of WISE 1828+2650 constructed by combining the new HST spectrum and the MKO K-band (Leggett et al. 2013 =4.487 µm, and λ W 1 iso = 3.3526 µm, λ W 2 iso =4.602 µm using the zero points and wavelengths in Tokunaga & Vacca (2005), Reach et al. (2005), and Jarrett et al. (2011), for the MKO, Spitzer, and WISE photometry, respectively. For clarity, we do not include photometric measurements at wavelengths that are sampled by the HST spectrum. The large amount of flux emerging at [4.5]/W 2 is a result of the fact that this wavelength range is relatively free of stronger absorbers like CH 4 , NH 3 , and H 2 O which allows the observer to see to deeper and thus hotter layers of the atmosphere were T > T eff .

Bolometric Luminosity
A brown dwarf's bolometric luminosity is arguably the easiest fundamental parameter to measure since knowledge of only distance d and bolometric flux f bol is required. The spectral energy distributions of hotter L and early-to mid-type T dwarfs peak at red-optical and near-infrared wavelengths where spectra are easily obtained from the ground. Integration of a spectral energy distribution consisting of a red optical and near-infrared spectrum, an L-band photometric point and/or WISE W1 and W2 points, and a Rayleigh Jeans tail to account for (unobserved) emergent flux at longer wavelengths therefore provides a reasonably accurate estimate of F bol Filippazzo et al. 2015). However the shift in the peak of the Planck function to longer wavelengths for the cooler late-type T dwarfs and Y dwarfs complicates the calculation of their bolometric fluxes because more and more energy emerges at wavelengths that are either difficult or impossible to access with current instrumentation (Marley & Leggett 2009).
We constructed a continuous spectral energy distribution of WISE 1828+2650 as follows. We first assumed that no flux emerges at wavelengths shortward of 0.90 µm and then extended the HST spectrum by piecewise linear interpolation through the K-band, W 1, [3.6], [4.5], and W 2 photometric points. WISE 1828+2650 has W3=12.444±0.338 (S/N=3.2, Cutri et al. 2013) but visual inspection of the atlas tile shows no clear source. We therefore do not use it or the W4 upper limit in the construction of the spectral energy distribution. To account for the flux at wavelengths longer than W 2, we extend a Rayleigh Jeans tail from the flux density point at 4.602 µm (the isophotal wavelength of the W 2 filter) to λ = ∞. Integrating over the spectral energy distribution, we measure a bolometric flux of f bol = (1.015 ± 0.01) × 10 −16 W m −2 , which is the mean and standard deviation of 10,000 Monte Spectral energy distribution of WISE 1828+2650. The spectrum (black) is from this work, while the K-band photometric point is from Leggett et al. (2013), the CatWISE2020 W1 and W2 photometry is from Marocco et al. (2021), and the Spitzer [3.6] and [4.5] photometry is from Kirkpatrick et al. (2019). The photometry is plotted at the nominal or isophotal filter wavelengths and the widths of the filters are denoted with horizontal lines.
Carlo realizations of f bol that account for the 2% uncertainty in the absolute flux calibration of the HST spectrum and the uncertainties in the individual spectral and photometric points. Using a relative parallax of π = 100.7 ± 2.3 mas (Kirkpatrick et al. 2019), we find log(L bol /L N ) = −6.50 ± 0.02, where L N is the International Astronomical Union (IAU) nominal solar luminosity of 3.828 × 10 26 W (Mamajek et al. 2015). We urge caution when using the f bol and L bol /L N measurements because they are likely dominated by systematic uncertainties due to the fact that the emergent spectra of cool brown dwarfs at wavelengths longward of W 2 are not Planck functions (e.g., Burrows et al. 2003;Cushing et al. 2006) and the Rayleigh-Jeans tail extension contributes ∼62% of the total bolometric flux in units of f λ . Dupuy & Kraus (2013) computed the bolometric luminosity of WISE 1828+2650 using near-infrared and Spitzer Space Telescope/Infrared Array Camera (IRAC) photometry and model atmospheres to account for the emergent flux at other wavelengths. Interestingly, they measured a value of log(L bol /L ) = −6.13 +0.20 −0.16 which is significantly brighter than our value, even when taking into account the uncertainties in our respective measurements. Our bolometric flux measurements agree within the uncertainties and so the difference in bolometric luminosities can be almost completely explained by the difference in parallaxes used to compute the distance to WISE 1828+2650, 70±14 mas in the case of Dupuy & Kraus and 100.7±2.3 mas in the case of Kirkpatrick et al.. The relative uncertainty in Kirkpatrick et al. parallax is a factor of 9 lower than the Dupuy & Kraus parallax so hereafter we will use our value of log(L bol /L N ).

Effective Temperature
Estimating the effective temperature of WISE 1828+2650 has proven difficult given its intrinsic faintness and contaminated spectrum. Cushing et al. (2011) estimated the effective temperature to be less than 300 K based on the near equal height of the spectral peaks in the J and H bands and its extreme J − W 2 color while Leggett et al. (2013) suggest that WISE 1828+2650 is actually a ∼2 Gyr old binary with M =10, 7 M Jup , T eff =325, 300 K and log g=4.5, 4.0 [ cm s −2 ]. Beichman et al. (2013) fit multi-band absolute photometry in various combinations and found T eff ∼ 250-450 K but noted that the "estimated physical parameters should be taken with a grain of salt" given how poor the models fit the data. Dupuy & Kraus (2013) used their bolometric luminosity measurement (see §4.1) and evolutionary models to estimate an effective temperature of 470 to 640 K for ages between 1 and 5 Gyr, but this rather high value is a result of their relatively low-precision parallax measurement.
We can make a zeroth-order estimate of the effective temperature of WISE 1828+2650 by making the reasonable assumption that its radius is R ≈ 1R N J -the nominal value for Jupiter's equitorial radius of 7.1492×10 7 m (Mamajek et al. 2015) -since the radii of all evolved brown dwarfs are with ∼30% of this value due to the competing effects of Coulomb and electron degeneracy effects (Burrows et al. 2001). With T eff = (d 2 f bol /σR 2 ) −1/4 , where σ is the Stefan-Boltzmann constant, we find T eff =426 K. If WISE 1828+2650 is an equal-luminosity binary, the effective temperature of each component would be T eff =351 K. Both values are consistent with previous estimates (with the exception of the Dupuy & Kraus estimate which is result of their large bolometric luminosity measurement) confirming that WISE 1828+2650 is still one of the coolest brown dwarfs known, especially if it is a binary. In the following two sections, we make additional estimates of the effective temperature of WISE 1828+2650 using both evolutionary and atmospheric models.

Bolometric Luminosity & Evolutionary Models
With an estimate of WISE 1828+2650's bolometric luminosity, we can use evolutionary models to estimate its effective temperature following the method described by Saumon et al. (2000). Figure 6 shows the evolution of solar metallicity cloudless brown dwarfs in the effective temperature/surface gravity plane (Marley et al., 2020). The locus of points with bolometric luminosities equal to that of WISE 1828+2650 for ages between 0.1 and 10 Gyr is shown as a near-vertical blue line which constrains its effective temperature to lie between 386 ≤ T eff ≤ 461 K. This is significantly lower than the value found by Dupuy & Kraus (2013) using a similar technique, but as noted previously this is simply a result of using a different parallax value to compute the bolometric luminosity.
The near-vertical red line corresponds to the locus of points with bolometric luminosities equal to half that of WISE 1828+2650 which is appropriate if it is an equalbrightness binary. In this case, the effective temperature of the two components must lie between 325 ≤ T eff ≤ 376 K which is more consistent with previous estimates based on analyses of the colors and spectral energy distribution of WISE 1828+2650.

Atmospheric Models
We also estimate the effective temperature of WISE 1828+2650 by fitting the HST spectrum and  (Ackerman & Marley 2001) and h is a parameter that ranges from 0 to 1 that describes the fraction of the atmosphere that can be described by a cloud-free column Marley et al. (2010). Larger values of f sed imply thinner clouds and a value of h = 0.5 implies a 50% cloud coverage. F λ (θ atm ) = [F λ (θ atm , λ 1 ), F λ (θ atm , λ 2 ), F λ (θ atm , λ 3 ), ..., F λ (θ atm , λ n )]. In order to compare each of the j models in a given grid to the observations of WISE 1828+2650, we must simulate observing the model spectra with the techniques used to collect our data. The spectroscopic portion of the data is given by, (1) where K(λ) is a Gaussian kernel that smooths the jth model F λ (θ atm,j ) to the resolving power of the data, h(λ) is a resampling kernel that resamples the smoothed model spectrum onto the wavelength grid of the data, and * denotes a convolution. The resolving powers of the HST spectrum are given in §2 and we used a linear interpolation kernel for h(λ).
The photometric portions of the data can be simulated by integrating the model spectra over the appropriate bandpasses. The MKO K-band point is given by, where S(λ) is the system response function of the Kband which we assume to be given by the product of the filter transmission and the typical atmospheric transmission at an air mass of 1. The λ inside the integral converts the energy flux densities to photon flux densities which ensures that the integrated fluxes are proportional to the observed photon count rate. The [3.6] and [4.5] IRAC points are given by, where ν 0 is the nominal frequency, and where S(ν) is the system response function of the telescope plus instrument plus detector system in units of e − per photon where S(λ) is the system response functions. Note that we do not include the factor of λ found in the integral like in Equation 2 because the filter transmission curves have already been multiplied by λ. The jth model at the surface of the brown dwarfs is then given by, In order to compare a model spectral energy distribution M(θ atm,j ) to the data, we first need to multiple it by (R/d) 2 , where R is the radius of the brown dwarf and d is its distance, in order to convert the flux densities at the surface of the brown dwarf to flux densities observed on or near Earth. While the distance to WISE 1828+2650 is known to be 9.93 pc (Kirkpatrick et al. 2019), its radius is unknown and so we can only compare the relative shapes of the model spectra and data. We identify the best fitting model spectrum in each grid following Cushing et al. (2008) where for each model j, we compute a χ 2 statistic, where n is the number of data points, f i and M j,i are the flux densities of the data and jth model respectively, s i is the uncertainty in the ith data point 3 , and C j is an unknown multiplicative constant. For each model j, we determine the value of C j by minimizing χ 2 with respect to C j to give, The best fitting model in each grid is that with the lowest χ 2 value. We fit both grids of model spectra to the HST spectrum and then to the entire spectral energy distribution (the HST spectrum and photometry) and the results are given in columns 1-8 in Table 3 and shown in Figure 7. (3) (8) (10) The atmospheric parameters of the best-fit model spectrum can be used to infer additional properties of WISE 1828+2650 when they are combined with evolutionary models because the models provide a unique mapping between the structural parameters of radius (R), mass (M ), age (τ ), and luminosity (L bol ) and the atmospheric parameters of effective temperature and surface gravity and so columns 9-11 in Table 3 gives the mass, radius, age, and luminosity of WISE 1828+2650 according to the Bobcat Sonora evolutionary models (Marley & Saumon 2020, Marley et al., submitted). The scale factor C is equal to (R/d) 2 and so with the evolutionary model radius R(θ atm ) we can empirically estimate the distance to WISE 1828+2650 and compare it to the known distance of d=9.93±0.23 pc (Kirkpatrick et al. 2019). Alternatively, we can use the known distance to estimate its radius which can then be compared to the predictions of evolutionary models. These estimates are given in columns 13 and 14 of Table 3. The location of the best-fit values in the effective temperature/surface gravity plane with respect to the evolution of cloudless brown dwarfs is also shown in Figure 8.
Given that WISE 1828+2650 is overluminous in nearly all color magnitude diagrams, we also fit the data to model binary stars. For each grid, we simulated a collection of binary systems by scaling each of the model spectra by R(θ atm ) 2 (the radius given by the evolutionary models that corresponds to θ atm ) and then summed pairs of models (k, l) as: However, we placed the following constraints, on the components of the binary to ensure that they have similar compositions and ages. While it is reasonable to assume that the components of a binary have identical ages and compositions, the course sampling of the atmospheric parameters requires weakening this constraint in order to avoid creating only equal-parameter binaries. The results of these fits are given in columns 1-8 in Table 3 and shown in Figures 8 and 9. The corresponding structural parameters are given in columns 9-12. Since the model spectra are first scaled by R(θ atm ) 2 , the scale factor is simply given by C = (1/d) 2 and so we can provide an empirical estimate of the distance as d C = 1/ √ C, and the results are given in column 13 of Table 3.

DISCUSSION
Statistically speaking, all of the model spectra are poor fits to the data since the χ 2 values of the fits are factors of 20-40 times larger than the number of degrees freedom. Given the complexity of the models atmospheres, statistically poor fits to brown dwarf spectra are not uncommon, especially when the observations span a broad wavelength range (e.g., Cushing et al. 2008;Stephens et al. 2009;Schneider et al. 2015;Luhman & Esplin 2016;Morley et al. 2018). As a result, we do not attempt to provide statistical uncertainties on the derived parameters. Nevertheless, it is still instructive to take the fits at face value because they not only provide some insight into the physical properties of the brown dwarfs but they also allow us to identify wavelengths where the models need improvement.
The HST spectrum is best fit by the Sonora model spectrum (upper right panel of Figure 7) because it more accurately reproduces the heights of the J-and H-band peaks. Both models fit the Y -band peak poorly because the NH 3 band in both models is too strong. This is most likely a result of the fact that the atmospheric models assume equilibrium chemistry and it has been shown that vertical mixing within an atmosphere keeps the nitrogen chemistry from coming into equilibrium such that the abundance of N 2 is increased relative to equilibrium and the abundance of NH 3 is decreased relative to equilibrium (e.g., Saumon et al. 2003Saumon et al. , 2006. The presence of this NH 3 band also makes it difficult to assess whether they exhibit the 1.015 µm CH 4 band that we tentatively identified in the data in §3. The  . The Sonora Bobcat model gives a more realistic age of 3.14 Gyr, but either has a large disparity between the d C values of 17.9 pc and the known distance of 9.93±0.23 pc or an unphysical R C of 0.56 R N J . Turning to the fits of the full spectral energy distribution shown in the bottom row of Figure 7, we see that while both models generally reproduce the very red nearto mid-infrared color of WISE 1828+2650, the Morley et al. (2014)  The mismatch at [3.6] between the data and the models that assume solar abundances is a well known problem (e.g., Leggett et al. 2017) and so the much better agreement between the [3.6] point and the Sonora Bobcat models is most likely a result of the fact that the  4.5] bands sample this side of the peak, so little emission emerges from the model brown dwarf in the short-wavelength half of the [3.6] band that small changes in the emission peak results in a large change in the [3.6] magnitude. Previous work by Morley et al. (2018) and Zalesky et al. (2019) have also shown that subsolar [C/O] values are required in order to match the observations of Y dwarfs. The aforementioned vertical mixing also impacts the carbon chemistry and thus the abundances of CO and CH 4 . Since the opacity of these molecules sculpt the 5 µm flux peak, non-equilibrium carbon chemistry can also have an impact on how well the Spitzer and WISE points are reproduced by the models (e.g., Hubeny & Burrows 2007;Miles et al. 2020). Including both non-solar C/O ratios and non-equilibrium carbon chemistry in forward-model fits to Y dwarf observations may therefore be required in order to accurately reproduce the spectral morphology of the 5 µm flux peak. Finally, we also plot the best fitting models to the HST spectrum over the best fitting models to the spectral energy distribution and vice versa. The differences between the fits at near-infrared wavelengths is minimal, but the HST spectrum fit fails to reproduce the dramatic rise in flux at ∼ 5µm. This underscores the difficulty of estimating the atmospheric properties of Y dwarfs with datasets that have limited wavelength coverage (see also Schneider et al. 2015).
The fits to the binary models are shown in Figure  9. With the exception of the Sonora Bobcat fit to the entire spectral energy distribution (lower right panel), the binary models provide identical fits to those of the single models (the d C values of these models are a factor of √ 2 larger than the single fits and remain a poor match to the observed distance of 9.93 pc). However, the Sonora Bobcat binary model fits the 5 µm peak much better than a single model and as a result, the χ 2 falls from a value of 7838 to 7286. Perhaps most importantly, d C = 9.03 pc which is reasonably close to the measured value of 9.93. As a result, a rough but consistent picture between the data and the atmospheric and evolutionary models emerges whereby WISE 1828+2650 is a ∼1 Gyr old binary composed of two T eff ∼325 K, ∼5 M Jup brown dwarfs with subsolar [C/O] ratios.