1908.09925.pdf

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RADIAL VELOCITY DISCOVERY OF AN ECCENTRIC JOVIAN WORLD ORBITING AT 18 AU

Sarah Blunt

1,2,3

, Michael Endl

, Lauren M. Weiss

5,6

, William D. Cochran

, Andrew W. Howard

, Phillip J.

MacQueen

,Benjamin J. Fulton

1, 18

, Gregory W. Henry

, Marshall C. Johnson

15,4

Molly R. Kosiarek

3,7

, Kellen

D. Lawson

, Bruce Macintosh

, Sean M. Mills

, Eric L. Nielsen

, Erik A. Petigura

, Glenn Schneider

Andrew Vanderburg

19, 20

, John P. Wisniewski

, Robert A. Wittenmyer

16,4

, Erik Brugamyer

, Caroline

Caldwell

, Anita L. Cochran

, Artie P. Hatzes

, Lea A. Hirsch

, Howard Isaacson

8,21

, Paul Robertson

14,4

Arpita Roy

, Zili Shen

Department of Astronomy, California Institute of Technology, Pasadena, CA, USA

Center for Astrophysics

Harvard & Smithsonian, Cambridge, MA, USA

NSF Graduate Research Fellow

McDonald Observatory and Department of Astronomy, The University of Texas at Austin, Austin, TX, USA

Institute for Astronomy, University of Hawai‘i, Honolulu, HI, USA

Beatrice Watson Parrent Fellow

Department of Astronomy & Astrophysics, University of California, Santa Cruz, CA, USA

Astronomy Department, University of California, Berkeley, CA, USA

Steward Observatory, The University of Arizona, Tucson, AZ, USA

Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA

Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA

Th ̈uringer Landessternwarte, Tautenburg, Germany, EU

University of California, Irvine, CA, USA

Department of Astronomy, The Ohio State University, Columbus, OH, USA

Centre for Astrophysics, University of Southern Queensland, Toowoomba, QLD, Australia

Center of Excellence in Information Systems, Tennessee State University, Nashville, TN, USA

IPAC-NASA Exoplanet Science Institute, Pasadena, CA, USA

NASA Sagan Fellow

Department of Astronomy, Unversity of Texas at Austin, Austin, TX, USA

University of Southern Queensland, Toowoomba, QLD 4350, Australia

ABSTRACT

Based on two decades of radial velocity (RV) observations using Keck/HIRES and McDonald/Tull,

and more recent observations using the Automated Planet Finder, we found that the nearby star HR

5183 (HD 120066) hosts a 3

minimum mass planet with an orbital period of 74

+43

−

years. The

orbit is highly eccentric (e

0.84), shuttling the planet from within the orbit of Jupiter to beyond

the orbit of Neptune. Our careful survey design enabled high cadence observations before, during,

and after the planet’s periastron passage, yielding precise orbital parameter constraints. We searched

for stellar or planetary companions that could have excited the planet’s eccentricity, but found no

candidates, potentially implying that the perturber was ejected from the system. We did identify a

bound stellar companion more than 15,000 au from the primary, but reasoned that it is currently

too widely separated to have an appreciable effect on HR 5183 b. Because HR 5183 b’s wide orbit

takes it more than 30 au (1”) from its star, we also explored the potential of complimentary studies

with direct imaging or stellar astrometry. We found that a Gaia detection is very likely, and that

imaging at 10

m is a promising avenue. This discovery highlights the value of long-baseline RV

surveys for discovering and characterizing long-period, eccentric Jovian planets. This population may

offer important insights into the dynamical evolution of planetary systems containing multiple massive

planets.

Keywords:

planets and satellites: detection - planets and satellites: fundamental parameters - stars:

individual (HR 5183)

INTRODUCTION

Radial velocity (RV) and transit surveys have char-

acterized very few planets beyond 5 au (Howard et al.

arXiv:1908.09925v1 [astro-ph.EP] 26 Aug 2019

Blunt et al.

2010; Mayor et al. 2011; Petigura et al. 2013; Fressin

et al. 2013), leaving the population characteristics of

long-period planets largely unknown. Direct imaging is

sensitive to such planets, but the current generation of

instruments is limited to planets several times the mass

of Jupiter orbiting young, massive stars (Bowler 2016;

Nielsen et al. 2019). Microlensing is also sensitive to

planets at large separations from their stars, and mi-

crolensing results already allow for occurrence calcula-

tions of planet mass as a function of separation (Suzuki

et al. 2016). However, mircolensing results will not en-

able detailed orbital or system architecture characteriza-

tion. On the other hand, RV surveys are limited by their

baselines. Several authors have used RV trends or other

incomplete orbital arcs to constrain the properties of

long-period planets and substellar objects (Wright et al.

2007, 2009; Knutson et al. 2014; Bouchy et al. 2016;

Rickman et al. 2019; Bryan et al. 2016), but it is chal-

lenging to pin down the physical parameters of planets

with orbital periods much longer than the survey base-

line. Some authors assume circular orbits in order to

cut down the wide parameter space of possible orbits

(e.g. Knutson et al. 2014), but even so posteriors over

semimajor axis and minimum mass span wide ranges.

Long-baseline RV surveys dating back to the mid-

1980s (Campbell 1983; Marcy 1983; Mayor & Maurice

1985; Campbell et al. 1988; Marcy & Benitz 1989; Zech-

meister et al. 2013; Fischer et al. 2014; Wittenmyer et al.

2014; Marmier et al. 2013; Moutou et al. 2015; Endl et al.

2016) are beginning to fill this characterization gap as

their time baselines increase. The long-period (

1 yr)

planets discovered by these surveys share characteris-

tics with the directly imaged planets and the shorter-

period RV-discovered planets. As these surveys mature,

they will allow us to characterize the transition from

older, less massive, shorter-period RV-detected planets

to younger, more massive, longer-period imaged planets.

These new discoveries will also enable us to calculate the

fundamental properties of planets in wider mass and age

ranges than those currently accessible to direct imaging

alone, examine the rarity of the Earth-Jupiter-Saturn

architecture, and test giant planet formation theories

(Cumming et al. 2008; Wittenmyer et al. 2006, 2011,

2016).

Here, we present the discovery of HR 5183 b, a highly

eccentric planet with a semimajor axis of 18

−

au or-

biting a

= 6

3 G0 star. HR 5183 has been moni-

tored for more than 20 years as part of the California

Planet Search at Keck/HIRES and the long-duration

RV planet survey at McDonald Observatory. After over

10 years of relatively constant RV measurements, HR

5183 began rapidly accelerating. In 2018, the RV mea-

surements flattened out and turned over, an event as-

sociated with the planet’s periastron passage. As we

discuss later in the paper, this periastron passage event

was information-rich, and allowed precise constraints on

the planet’s orbital parameters even without RV cov-

erage over the entire orbital period. With an orbital

period of 74

+43

−

years, HR 5183 b is the longest-period

planet with a well-constrained orbital period and mini-

mum mass detected with the RV technique.

This paper is organized as follows: in Section 2, we

present our RV measurements of HR 5183. In Section

3, we provide precise estimates of the stellar parame-

ters of HR 5183, and in Section 4, we characterize the

planet HR 5183 b. In Section 5, we describe an ex-

tremely widely-separated (

15,000 au) stellar compan-

ion to HD 5183, and present the results of searches for

additional stellar and planetary companions. In Sec-

tion 6, we discuss prospects for multi-method detection

of HR 5183 b. In Section 7, we relate HR 5183 b to

other exoplanet systems, comment on formation scenar-

ios, and conclude.

HIGH-RESOLUTION SPECTRA

We began Doppler monitoring of HR 5183 in 1997

at Keck/HIRES and in 1999 at McDonald/Tull. We

have also monitored HR 5183 on the Automated Planet

Finder (APF) with high cadence since its commissioning

in 2013. The RVs from all three spectrographs are shown

in Figure 1 and tabulated in Table 1.

Table 1

. Radial Velocities and S-index values

Time

RV Unc.

Inst.

Unc.

(BJD - 2440000)

(m s

−

)

(m s

−

)

10463

1705

−

HIRES

0.14

0.01

10547

042

−

HIRES

0.14

0.01

10838

155

−

HIRES

0.14

0.01

10954

9271

−

HIRES

0.14

0.01

11200

1185

−

HIRES

0.14

0.01

11213

9789

−

TULL

0.15

0.02

Table 1 continued

HR 5183 b

Table 1

(continued)

Time

RV Unc.

Inst.

Unc.

(BJD - 2440000)

(m s

−

)

(m s

−

)

11241

8948

−

TULL

0.15

0.02

11274

8541

−

TULL

0.16

0.02

11310

9479

−

HIRES

0.14

0.01

11329

7947

−

TULL

0.15

0.02

Pre-upgrade HIRES measurement.

Note that the

values for each instrument do not have the same zero-point.

Pre- and post-upgrade HIRES S-values should be treated independently.

Note

—Table 1 is published in its entirety in the machine-readable format. A

portion is shown here for guidance regarding its form and content.

2.1.

HIRES Spectra

We obtained 78 high-resolution (

= 60

000) spectra

of HR 5183 with the HIRES spectrograph (Vogt et al.

1994; Cumming et al. 2008; Howard et al. 2010) between

1997 and 2019. HIRES underwent major upgrades in

2004, so for modeling purposes we treat pre- and post-

upgrade HIRES measurements independently (see Sec-

tion 4). Wavelength calibration for each RV measure-

ment was performed with a warm iodine-gas cell placed

in the light path in front of the slit, producing a con-

volved spectrum of the star, iodine gas, and point spread

function. Each spectrum was forward-modeled with a

deconvolved stellar spectrum template (DSST), an at-

las iodine spectrum, and a line spread function (Butler

et al. 1996). This technique is stable at the 2-3

−

level on timescales of more than a decade (Howard &

Fulton 2016).

To monitor chromospheric and stellar spot activity,

we extracted spectral information at and near the Ca II

H and K lines to calculate a Mt. Wilson style S-index

value (following Wright et al. 2004 and Isaacson & Fis-

cher 2010) for measurements taken after the 2004 instru-

ment upgrade. S-index values for HIRES measurements

taken before 2004 were pulled directly from Wright et al.

(2004). These values do not correlate significantly with

time, the RV measurements, or the RV residuals from

the maximum a posteriori (MAP) orbit (see Section 4).

In particular, the S-index values show no trends or cor-

relations with RV measurements on the timescale of the

proposed planet period.

2.2.

Tull Spectra

Between 1999 and 2019, we collected 175 high-

resolution (

= 60

000) spectra with the Tull Coud ́e

Spectrograph (Tull et al. 1995) on the 2.7 m Harlan J.

Smith telescope as part of the McDonald Observatory

planet search (Cochran et al. 1997; Hatzes et al. 2000).

For all observations, we inserted an iodine absorption

cell into the light path to obtain a precise wavelength

calibration. Combined with a template stellar spectrum,

this allowed us to reconstruct the shape of the instru-

mental PSF at the time of each observation. We used

the RV modeling code

Austral

(Endl et al. 2000) to

compute precise differential RVs.

We typically reach a long-term RV precision of 4 to

6 m s

−

for inactive FGK-type stars with the Tull spec-

trograph. A major advantage of the Tull RV survey is

that the instrumental setup has not been modified over

the duration of the program. For nearly 20 years, we

have been using the same CCD detector, the same io-

dine cell, and the same positions of the Echelle grating

and cross-disperser prism. This assures that there are

no RV zero-point offsets introduced into the RV time

series.

We determined the S-index values from the Ca II H&K

lines in the blue orders of the Tull spectra using the

method outlined in Paulson et al. (2002). These S-index

values also show no trend or correlation with RV mea-

surements over the duration of the observations.

2.3.

APF Spectra

Finally, we obtained 104 spectra of HR 5183 with the

Automated Planet Finder (APF; Radovan et al. 2014;

Vogt et al. 2014) between 2013 and 2019. The APF is

an automated 2.4 meter telescope at Lick Observatory

on Mt. Hamilton, CA. It is equipped with the Levy

Spectrograph, a dedicated high-resolution echelle spec-

trometer that sits at a Nasmyth focus. The Levy Spec-

trograph achieves

R >

120

000 and covers a wavelength

range of 374.3-980.0 nm. Spectra of HR 5183 were ob-

served through a warm iodine-gas cell for wavelength

calibration. The RVs were calculated with the pipeline

described in Fulton et al. (2015), which descends from

Blunt et al.

the Butler et al. (1996) pipeline, and is essentially identi-

cal to the HIRES reduction pipeline discussed in Section

2.1. As with the HIRES data, we calculate S-index val-

ues following Isaacson & Fischer (2010). These S-index

values similarly appear independent of the RV measure-

ments over the duration of the observations.

STELLAR PROPERTIES

HR 5183 is a nearby slightly evolved G0 star. We

derived precise stellar parameters for HR 5183 using

the method described in Fulton et al. (2018). Briefly,

this method uses Gaia DR2 parallaxes (Gaia Collabo-

ration et al. 2018), spectroscopic effective temperatures

computed from our Keck template spectrum with the

SpecMatch

code (Petigura 2015), and 2MASS photom-

etry (Skrutskie et al. 2006) to compute precise stellar

radii. log

, [Fe

H], and

sin

are also calculated from

the Keck spectrum using

SpecMatch

. Stellar mass, age,

and distance are derived using the

isoclassify

pack-

age (Huber et al. 2017). The stellar properties derived

from this analysis are presented in Table 2, along with

other useful stellar parameters.

Allen & Monroy-Rodr ́ıguez (2014) found evidence

that HR 5183 is in the halo of the Milky Way using re-

duced proper motion diagrams following Salim & Gould

(2003). However, HR 5183 is younger and more metal-

rich than typical galactic halo objects (Carollo et al.

2016), which led us to scrutinize this claim. To investi-

gate HD 5183’s galactic population membership, we per-

formed a kinematic analysis of its galactic orbit, follow-

ing Johnson et al. (2018). We used the

galpy

package

(Bovy 2015) to compute 50 random realizations of galac-

tic positions and U,V,W space velocities for HR 5183

consistent with its Gaia DR2 parameters (Gaia Collab-

oration et al. 2018). For each realization, we then cal-

culated the galactic orbit of HR 5138 in

galpy

’s “MW-

Potential2014” galactic potential. The resulting orbits

never achieve a height above the galactic midplane of

more than 200 pc. This result supports the claim that

HR 5183 is a thin-disk member, and not a halo object.

Table 2

. Stellar Properties

Parameter

Value

Unit

R.A.

13 46 57

hh:mm:ss

Decl.

+06 20 59

dd:mm:ss

HD Name

HD 120066

—

2MASS ID

J13465711+0621013

—

Gaia Source ID

3721126409323324416

—

Parallax

757

039

mas

mag

eff

5794

100

log

dex

[Fe

dex

sin

kms

−

∗

−

∗

Age

−

Gyr

Distance

Note

—

eff

, log

, [Fe

H], and

sin

were calculated from

the stellar spectrum using the

SpecMatch

code.

∗

was

calculated as described in Section 3.

∗

, age, and distance

were calculated using the

isoclassify

code.

GitHub.com/danxhuber/isoclassify

GitHub.com/jobovy/galpy

PLANET PROPERTIES

The curvature we saw in the RVs (see Figure 1) alerted

us to the existence of HR 5138 b, and motivated us to

characterize its orbital properties. We modeled the RV

HR 5183 b

100

RV [m s

]

P = 72.85 yr

e = 0.84

Msini = 3.24 M

APF

HIRES

HIRES pre 2004

McDONALD

2000

2010

2020

Year

10000

12000

14000

16000

18000

20000

22000

JD - 2440000

Residuals

17600

17800

18000

18200

18400

18600

JD - 2440000

100

RV [m s

]

2017

2018

2019

Year

Figure 1

. Top: RVs of HR 5183 from the Keck-HIRES, McDonald-Tull, and APF-Levy spectrographs as a function of time.

Error bars show observational errors and instrument-specific jitter values added in quadrature. The best-fit Keplerian orbit is

shown (blue solid line). Residuals are inset below. Bottom: close-up of the grey region in top plot. The RV curve peaks in

January 2018 during periastron passage, and declines monotonically afterward in all three data sets.

Blunt et al.

timeseries using the open-source toolkit

radvel

(Ful-

ton et al. 2018). The code and data used to perform

the analysis in this paper are available on GitHub

. We

chose to perform this fit using the following parametriza-

tion of the Keplerian RV function: log

, T

√

cos

√

sin

, and log

. We imposed uninformative uni-

form priors on each of these parameters except log

for which we defined an “informative baseline prior.”

Because we detected a long-period planet by observing

a single, short-duration event (the planet’s periastron

passage), we made an analogy to detection by transit

and defined the following prior on period, often used

in the exoplanet transit community (e.g., Kipping 2018;

Vanderburg et al. 2016):

(

P,t

) =







−

< B

(

)

else

(1)

where

is the duration of the event (in this case, the

periastron passage),

is the orbital period, and

the observing baseline. See Section 4.1 for a justifica-

tion of this choice of prior and detailed comparison to

other possible models and prior parameterizations. Un-

like in the case of a transit detection, the “duration”

of HR 5183’s periastron passage event is not easily de-

fined. We performed fits with

= 0 and

= 3

5 yr,

ultimately finding that the results were indistinguish-

able and sidestepping this issue. We adopted

= 0 for

convenience.

We also included jitter (

) and RV offset (

) terms

for each of our four RV datasets (we treated HIRES pre-

2004 and post-2004 measurements as separate data sets

in our fit; see Section 2.1). We assumed uninformative

uniform priors on each of these instrumental terms as

well. The logarithm of the complete likelihood for this

model is:

−

∑

[

(

−

)

(

jit

)

+ 2ln

√

(

jit

)

]

(2)

where n is the total number of RV measurements,

is the

th RV measurement,

is its uncertainty,

is the Keplerian model prediction for observation

, and

jit

is the jitter parameter for the instrument that took

observation

(Fulton et al. 2016).

We computed the MAP fit with

radvel

, obtaining

an orbital period of 72.85 years, a minimum mass of

3.24

, and an eccentricity of 0.84. This orbital solu-

https://radvel.readthedocs.io/en/latest

https://github.com/California-Planet-Search/planet-pi

tion is shown in Figure 1, and a bird’s-eye view compar-

ing this orbit to the orbits of the solar system planets

is shown in Figure 2. We next performed an Affine-

invariant Markov Chain Monte Carlo (MCMC) explo-

ration of the parameter space with the ensemble sam-

pler

emcee

(Foreman-Mackey et al. 2013). Our MCMC

analysis used 8 ensembles of 50 walkers and ran for 1552

steps per walker, achieving a maximum Gelman-Rubin

(GR; Gelman et al. 2003) statistic of 1.001. A corner

plot showing posterior distributions and covariances be-

tween

sin

−

, and

is shown in

Figure 3. These values are also recorded in Table 3.

[au]

Figure 2

. The MAP orbit of HR 5183 b compared to the

orbits of the planets in our solar system (blue: Neptune,

teal: Uranus, purple: Saturn, red: Jupiter, grey: Mars, black

dashed: HR 5183 b). The sizes of the colored circles show the

relative sizes of the solar system planets (not to scale with

respect to their orbits). We assume a radius of 1 R

for HR

5183 b. The orbital locations of the planets are computed

on 7-31-2019, approximately 1.5 years after the periastron

passage of HR 5183 b. HR 5183 b’s Ω and

are set to

arbitrary values. At periastron, HR 5183 b is closer to its

star than our asteroid belt is to the Sun, and at apastron, it

is more distant than Neptune.

4.1.

Model Choice

We performed three additional orbit fits to evaluate

our choice of model. First, we performed two fits with-

out informative baseline priors on log

: one fitting in

and

(as opposed to log

and log

), and another

in log

(fitting in log

versus

imposes an implicit

GitHub.com/dfm/emcee

HR 5183 b

Jeffrey’s prior on

). Period posteriors obtained from

these two models and the informative prior are com-

piled in Table 4. All three orbital period posteriors are

consistent within 1-

, but the informative baseline prior

pushes the median orbital period to shorter values. Nei-

ther of these priors significantly change the posteriors

on the other orbital parameters; for example, fitting in

log

gives

sin

= 3

−

and e = 0

05.

The slight dependence of the solution on our prior choice

ultimately points to the need for more data, but in the

meantime we adopt the informative prior.

Next, we performed a fit including a ̇

parameter to

account for potential additional wider-separation com-

panions influencing the RV signal of the star. Adding

this free parameter has the effect of pushing the eccen-

tricity posterior to higher values (e = 0

03) and

the period posterior to lower values (P = 71

+52

−

yr),

but the posterior distribution of ̇

is consistent with 0

( ̇

= 0

−

m s

−

). The adopted model has

lower BIC (∆BIC = 5.4) and AIC values (∆AIC = 1.7),

indicating that the added free parameter does not sub-

stantially improve the fit. We can’t unequivocally rule

out a trend, but since including one is not statistically

warranted and does not affect the conclusions of the pa-

per, we adopt the fit with no trend.

The lack of an unambiguous trend in the RVs is con-

sistent with our failure to detect companion objects in

the HST and NaCo images (see Section 3 and Appendix

B). The possible bound companion at 15,000 au (Section

5.2.1) would not produce a measurable ̇

Table 3

. Fit Parameters & Derived Planet Properties

Parameter

Median Value & 68% CI

MAP Value

Unit

−

10.2

ln(days)

18965

+44

−

18964

JD - 2440000

√

cos

0.86

√

sin

−

-0.32

3.64

ln(m s

−

)

(HIRES pre-upgrade)

−

3.09

m s

−

(HIRES post-upgrade)

3.16

m s

−

(Tull)

−

5.67

m s

−

(APF)

−

3.58

m s

−

(HIRES pre-upgrade)

−

-52.5

m s

−

(HIRES post-upgrade)

−

-52.4

m s

−

(Tull)

−

-19

m s

−

(APF)

−

-47.2

m s

−

+43

−

72.85

−

38.21

−

0.84

−

-0.35

rad

58121

58120.0

JD - 2440000

sin

−

3.24

−

18.0

−

)

−

2.89

(peri)

171

−

170.94

(apo)

−

50.58

Note

—

values were calculated assuming a visible albedo of 0.5.

Note

—

refers to the orbit of the star HR 5183 induced by the planet HR 5183 b.

Blunt et al.

Table 4

. Period Prior Comparison

Prior

Median Period & 68% CI

uniform in

125

+113

−

uniform in log

& log

103

+103

−

inf. baseline prior (adopted)

+43

−

4.2.

Orbit Information Density

Our measurements of this planet’s properties may

seem surprisingly precise (see Table 3) given observa-

tions spanning only about one third of the orbit. These

constraints are possible because we tracked the system

through periastron passage, when the information den-

sity of the Keplerian signal is highest.

High-eccentricity orbits have unique shapes that sen-

sitively depend on

and

(see Fig. 2 of Howard &

Fulton 2016 for a helpful visualization). The shape of

the HR 5183 RV curve is fit only by a narrow range of

these parameters, as Figure 3 shows.

The relatively flat RV curve from

∼

1998–2015 followed

by a sharp uptick and subsequent turnover are consis-

tent only with

8 and

' −

4. All other Keple-

rian curves have

shapes

that are inconsistent with our

measurements. More complicated models involving ad-

ditional planets or a ̇

term are also excluded by the

peculiar RV pattern.

We offer two arguments to build intuition. First,

imagine decomposing the RV fitting into a process that

matches three orbital properties of the Keplerian curve:

1) the shape (from

and

); 2) the vertical scale (

);

and 3) the horizontal scale (

). Once the shape has

been determined by matching the appropriate Keplerian

curve, the horizontal and vertical scales can be measured

using RVs spanning less than a full orbit, provided the

information-rich close approach is covered. Second, con-

sider the how the planet’s speed varies over its orbit. We

can define the “fastest half orbit” as the portion of an

orbit near closest approach, when the true anomaly (

)

is between

−

π/

2 and

π/

2. The time for the planet to

pass through the fastest half orbit,

fho

, can be computed

using the relationship between

and time (

√

−

(

)

dt,

(3)

where

is the distance between the orbiting planet and

the star (Seager 2010, Eq. 2.44). Substituting an ex-

pression for

(

) (Seager 2010, Eq. 2.20),

fho

−

)

∫

π/

−

π/

1 +

cos

(4)

For a circular orbit,

fho

integrates to

2, as ex-

pected. Eccentric orbits have much shorter timescales

of close approach though. Numerically integrating Eq. 4

with

= 0

84, we find

fho

≈

6. That is, the planet

completes the fastest half of its orbit nearly an order of

magnitude more quickly than in the circular case. While

our fitting procedure did not actually measure

fho

and

scale it by a factor of 18.6 to determine

, this exercise

illustrates how highly eccentric orbits contain informa-

tion related to orbital period on short timescales, and

thus allow us to measure

with higher precision than

one might expect.

This is not to say that we have ruled out hundred-year

or more periods and higher (

0.91) eccentricities. Such

orbits appear in our posterior, but because there is less

posterior volume in this region of parameter space, they

are less probable overall.

ADDITIONAL BOUND COMPANIONS

5.1.

Search for Additional Planets in the System

We searched for other significant periodic signals in

the RV data using the

difference technique described

in Howard & Fulton (2016). In brief, we started by

calculating the

of a flat line fit to the RVs, and in-

jecting additional Keplerian orbits into the model. We

calculated the change in

(∆

) when including each

additional Keplerian orbit over a grid of periods and ec-

centricities. We constructed a periodogram of the ∆

values as a function of trial period and fit the distribu-

tion of periodogram peak heights to infer an empirical

false alarm probability (eFAP) for each detected peak.

We detected no signals with an empirical false-alarm

probability (eFAP) greater than 1%, indicating no ad-

ditional planetary companions down to our sensitivity

limits.

We characterized our sensitivity limits over a grid

of semimajor axes and

sin

values by applying the

search algorithm described above to each injected plan-

etary signal. The results of this analysis are shown in

Figure 4. As expected, we are most sensitive to Jupiter-

mass and heavier planets with

a <

30 au. Our data are

not sensitive to Earth-mass planets. HR 5183 b itself

is at our detection limits because of its large semimajor

HR 5183 b

100

150

200

250

P [yr]

2.7

3.0

3.3

3.6

3.9

Msin

]

a [au]

2.6

2.8

3.0

3.2

a(1-e) [au]

0.75

0.80

0.85

0.90

18075

18100

18125

18150

18175

[JD - 2440000]

[deg]

100

150

200

250

P [yr]

2.7

3.0

3.3

3.6

3.9

Msin

]

a [au]

2.6

2.8

3.0

3.2

a(1-e) [au]

0.75

0.80

0.85

0.90

[deg]

Figure 3

. Corner plot displaying posterior distributions and covariances of HR 5183 b orbital parameters of interest: time

of periastron passage (T

), orbital period (

), minimum mass (

sin

), semimajor axis (

), minimum orbital separation

(

−

)), eccentricity (

), and argument of periastron (

). Importantly, these probability distributions were derived from the

fitted posteriors; among the parameters shown here, only T

is actually a parameter in the fit. Time of periastron passage,

minimum mass and minimum orbital separation are very well constrained, while orbital period remains uncertain and correlated

with eccentricity.