Orbital Motion of the Wide Planetary-Mass Companion GSC 6214-210 b: No Evidence for Dynamical Scattering
Logan A. Pearce, Adam L. Kraus, Trent J. Dupuy, Michael J. Ireland, Aaron C. Rizzuto, Brendan P. Bowler, Eloise K. Birchall, Alexander L. Wallace
DD RAFT VERSION D ECEMBER
24, 2018Typeset using L A TEX twocolumn style in AASTeX62
Orbital Motion of the Wide Planetary-Mass Companion GSC 6214-210 b: No Evidence for Dynamical Scattering L OGAN
A. P
EARCE , A DAM
L. K
RAUS , T RENT
J. D
UPUY , M ICHAEL
J. I
RELAND , A ARON
C. R
IZZUTO , B RENDAN
P. B
OWLER , E LOISE
K. B
IRCHALL , AND A LEXANDER
L. W
ALLACE Department of Astronomy, University of Texas at Austin, Austin, TX, 78712, USA Gemini Observatory, Northern Operations Center, 670 N. A’ohoku Place, Hilo, HI 96720, USA Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia
ABSTRACTDirect-imaging exoplanet surveys have discovered a class of 5-20 M
Jup substellar companions at separations>100 AU from their host stars, which present a challenge to planet and star formation models. Detailed analysisof the orbital architecture of these systems can provide constraints on possible formation mechanisms, includingthe possibility they were dynamically ejected onto a wide orbit. We present astrometry for the wide planetary-mass companion GSC 6214-210 b (240 AU; ≈
14 M
Jup ) obtained using NIRC2 with adaptive optics at the Kecktelescope over ten years. Our measurements achieved astrometric uncertainties of ≈ . ± .
15 mas yr − (0.61 ± − ), the first detection of orbital motionfor this companion. We compute the minimum periastron for the companion due to our measured velocityvector, and derive constraints on orbital parameters through our modified implementation of the Orbits for theImpatient rejection sampling algorithm. We find that close periastron orbits, which could indicate the companionwas dynamically scattered, are present in our posterior but have low likelihoods. For all orbits in our posterior,we assess the detectability of close-in companions that could have scattered GSC 6214-210 b from a closerorbit, and find that most potential scatterers would have been detected in previous imaging. We conclude thatformation at small orbital separation and subsequent dynamical scattering through interaction with anotherpotential close-in object is an unlikely formation pathway for this companion. We also update stellar andsubstellar properties for the system due to the new parallax from Gaia
DR2.
Keywords: astrometry — brown dwarfs — stars: imaging — planetary systems — planets and satellites: indi-vidual (GSC 6214-210 b) — stars: individual (GSC 6214-210) INTRODUCTIONThe growing population of diverse exoplanetary systemsprovides opportunities to test theories of star and planetformation, particularly as planets are discovered at the ex-trema of parameter space. The population of directly im-aged sub-stellar companions near the deuterium burning limit( (cid:46)
13 M
Jup ) at very wide separations ( >
100 AU) from theirhost stars, referred to as wide planetary-mass companions(PMCs), is well positioned for studying star and planet for-mation, because their orbits make them relatively easy ob-serving targets and ideal for testing formation routes.Wide-orbit companions are not common, yet do seem tobe a standard outcome of star and planet formation. Oc-currence rates of these objects have been found to be 1–4%(Bowler 2016; Ireland et al. 2011). The dominant formationmechanism for these objects remains unclear. Fragmenta-tion from the same molecular cloud as the primary is capa-ble of producing appropriately-sized cores, but such coresmay struggle to prevent further accretion and instead growto stellar masses (Bate 2012). Gravitational instability in protostellar disks is capable of forming fragments of sev-eral Jupiter masses at wide separations, and so is a promis-ing pathway for PMC formation, but also requires a mecha-nism to limit growth to only ∼
10 M
Jup (Kratter et al. 2010;Dodson-Robinson et al. 2009). Fragmentation of a Class IIdisk, after much of the envelope has been exhausted, is alsoa viable path, however Andrews et al. (2013) showed this islikely to produce wide planetary-mass companions only inthe most massive disks. Classical planet assembly throughcore accretion is unrealistic in-situ at hundreds of AU ontimescales of the ages of the systems for which PMCs areobserved ( τ = 1-10 Myr) (Goldreich et al. 2004; Levison& Stewart 2001). Gas giant planet formation at wide sep-arations is hampered by exceedingly long timescales (longerthan the ages of observed systems) (Dodson-Robinson et al.2009), although pebble accretion can reduce the timescalesto below protoplanetary disk lifetimes out to 100 AU (Lam-brechts & Johansen 2012; Johansen & Lambrechts 2017),which is feasible for systems like HR 8799 (Marois et al. a r X i v : . [ a s t r o - ph . E P ] D ec P EARCE ET AL .2010). However many wide orbit companions in the plane-tary mass regime lie well beyond 100 AU.Finally, classical core accretion could form extremely mas-sive giant planets at close radii, near ice lines of 1-2 AU,which could then be ejected out to wide orbits through dy-namical interactions at any point in their lifetimes. If thismodel dominated, extremely eccentric orbits would be com-mon among these systems, and other, close in companions ofequal or greater mass would be needed in the systems to scat-ter the PMC to its current radius (e.g. Ford & Rasio 2008; Ve-ras et al. 2009). Thus the system would need to have formedseveral extremely massive planets.It remains unclear if there is one dominant formation chan-nel for the population as a whole. Observations are hamperedby population statistics: relatively few of these objects areknown, and fewer have been observed long enough to detectorbital motion and constrain their orbital parameters. Full or-bit studies are becoming feasible for close-in directly imagedgiant planets (e.g., HR8799 bcde: Konopacky et al. 2016; β Pic b: Nielsen et al. 2014; Fomalhaut b: Pearce et al. 2015,Beust et al. 2016; 51 Eri b: De Rosa et al. 2015). Most wideplanetary-mass companions, however, are still limited to lin-ear orbit arcs.Results from orbit studies of wide companions to date havereached mixed conclusions about formation mechanism be-cause of the wide range of orbital parameters among systems,and sometimes even different conclusions for the same sys-tem (e.g., GQ Lup; Ginski et al. 2014; Schwarz et al. 2016).The wide range in eccentricities found thus far does not sug-gest a clear common trend. There appear to be low eccen-tricities for ROXs 12 b and ROX 42B b (Bryan et al. 2016), ahigh eccentricity for PZ Tel (Ginski et al. 2014; Biller et al.2010), and a range for the systems analyzed by Blunt et al.2017. Additional studies of PMC system orbital architecturescan shed light on the range of possible formation pathwaysfor this population group.In this paper we test the ejection model for the formation ofthe wide-orbit substellar companion to GSC 6214-210. Weperform a detailed study of the relative astrometry and or-bital solutions from imaging data over a nine year observa-tional period. In Section 2 we describe previous studies ofthis system and update system parameters in light of the newparallax measurement from
Gaia data release 2. In Section3 we describe our observations, and in Section 4, we outlineour astrometric measurement and our detection of orbital mo-tion. In Section 5, we present our orbit fitting procedure andshow the constraints our orbital motion measurement placeson the orbit configuration. We also determine that the exis-tence of another, close-in companion cannot be completelyruled out, but is unlikely. Finally, in Section 6, we show thatthe ejection model cannot be ruled out, but in-situ formationis more likely to explain this PMC. SYSTEM PROPERTIES2.1.
History
GSC 6214-210 is a pre-main sequence star identified asa member of the Upper Scorpius subgroup of the Scorpius-Centaurus OB association in Preibisch et al. (1998). Theyobserved the star to have lithium absorption (EW = 0.38 Å)and H α emission (EW = –1.51 Å) in their survey of X-rayselected PMS candidates. Bowler et al. (2014) determineda spectral type to K5 ±
1, and mass of M (cid:63) = 0 . ± . (cid:12) based on their optical spectrum fit to models adjusted for ex-tinction. The median age for USco of 10 Myr (Pecaut et al.2012; Feiden 2016) has been adopted for recent studies ofthis system. There is no evidence of the primary being a bi-nary system (Kraus et al. 2008).GSC 6214-210 was discovered to host a wide planetary-mass companion by Ireland et al. (2011) in their adaptiveoptics imaging survey for wide companions in Upper Sco.They found the companion to be very red ( J − K = 1 . K − L = 1 .
05 mag). Bowler et al. (2014) measured a spectraltype of M9.5 ± c = 14 ± Jup for the companion.Bowler et al. (2011) reported evidence of Pa β emissionfrom the companion that is lacking from the star, implyingthe presence of a circumplanetary disk that is actively accret-ing mass, which may have contributed to the red color ob-served by Ireland et al. (2011). Bowler et al. (2011) studiedthe survivability of a circumplanetary disk in planet-planetscattering interactions, and infer from the continued presenceof the disk that GSC 6214-210 b likely did not form at closeradius and scatter to its current location through interactionwith another companion. ALMA observations of the systemin Bowler et al. (2015) found no observable emission abovebackground, which shows the disks around the primary andcompanion to be low mass ( (cid:46) Jup for the companion).They concluded that both GSC 6214-210 and its companionare likely at the end stages of formation.No radial velocity surveys have been conducted to searchfor other unresolved companions, and past studies did notreport any indication of an additional companion.2.2.
Updated properties
Previous studies of the GSC 6214-210 system adopted themean distance and age of Upper Sco ( d = 145 ±
14 pc; τ =5-10 Myr; Pecaut et al. 2012) for this system. However, Gaia
DR2 reported a parallax measurement of π = 9.19 ± d =108.8 ± There is some disagreement in the literature on the appropriate label forthe companion, “B” or “b”. The Simbad entry for the companion gives thelabel “b”, so we adopted the lowercase b for the companion in this work tomaintain consistency with Simbad.
RBITAL M OTION OF
GSC 6214-210 B Figure 1.
Example image of GSC 6214-210 and companion fromthe 2017 observation epoch. The companion, labeled “b”, can beseen at 2.2 (cid:48)(cid:48) to the south. ously assumed. The astrometric excess noise on the parallaxis 0.0, indicating a good parallax solution. We therefore up-date the system properties here.
Gaia
DR2 reported a proper motion of µ = (–19.38 ± ± -1 for GSC 6214-210 (Gaia Collabora-tion et al. 2018). This proper motion and distance places GSC6214-210 near the edge of proper motion space for the UScosubgroup (Rizzuto et al. 2011; Wright & Mamajek 2018).We used the matrices of Johnson & Soderblom (1987) andthe Gaia proper motion and radial velocity measurements tocompute new UVW velocities for the system, obtaining U =–4.53 ± -1 , V = –18.01 ± -1 , and W = –4.86 ± -1 . These velocities are still consistent withUSco membership, given the internal velocity dispersion ofthe association from Rizzuto et al. (2011) and Wright & Ma-majek (2018).The revised distance has implications for the primary starage and mass as well. To update the stellar parameters,we began with the effective temperature and luminosity ofT eff (cid:63) = 4200 ±
150 K and L (cid:63) = 0.38 ± (cid:12) reported inBowler et al. (2011), and calculated the new luminosity tobe L (cid:63) = 0.221 ± (cid:12) using the same spectral energydistribution calculation from that work. This new luminos-ity, and the temperature of Bowler et al. (2011), gives a massand age of M (cid:63) = 0.80 ± (cid:12) , τ = 24 + − Myr using theevolutionary models of Baraffe et al. (2015). We also com-pared the temperature and luminosity to the models of Fei-den (2016) for young star convection inhibited by magneticfields, which yielded M (cid:63) = 0.78 ± (cid:12) , τ = 41 ±
10 Myr. These ages are in conflict with each other, and highlydiscrepant with other age determinations of USco members(Pecaut et al. 2012; Rizzuto et al. 2016). However, giventhe existence of numerous other signatures of youth seen inthe primary star (such as lithium absorption, H α emission,and X-ray emission; Preibisch et al. 1998), its membershipin USco seems to remain secure.For this regime of luminosity and temperature, model-predicted masses depend strongly on age. Adopting a priorinformed by the age distribution of the broader populationtherefore can clarify the likely system parameters and the de-gree of tension between observations and expectations. Theages suggested for the subgroups of Sco-Cen members span5-20 Myr (Pecaut et al. 2012; Rizzuto et al. 2016; Pecaut &Mamajek 2016), so we also estimate the age and mass afterimposing linear-uniform priors over 5 < τ <
20 Myr and (tobroadly allow any possible mass) 0 . < M < . (cid:12) . Toimplement this prior, we first drew random (M, τ ) pairs fromthe linear-uniform distributions, and then computed a corre-sponding (L,T eff ) pair for each (M, τ ) pair by interpolatingthe Baraffe et al. (2015) and Feiden (2016) models. For eachpair, we then computed the likelihood that we would have ob-tained our inferred values of luminosity (L (cid:63) = 0.221 ± (cid:12) ) and temperature (T eff (cid:63) = 4200 ±
150 K), given our es-timated uncertainties, if that pair represented the true massand age of GSC 6214-210. The likelihood was adopted asa weight for that (M, τ ) pair. Finally, we computed weightedmeans of the age and mass across all pairs of potential massesand radii, yielding M = 0.78 ± (cid:12) , τ = 14 ± ± (cid:12) and τ = 16.9 + . − . Myr for the models of Feiden (2016).The magnetized models have been shown to more accuratelypredict mass and age for USco (Feiden 2016; Rizzuto et al.2016), so we adopted this mass and age for the primary.Bowler et al. (2011) used the substellar companion’s ob-served spectral energy distribution to estimate the bolometricluminosity of the companion, log(L/L (cid:12) ) –3.1 ± log ( L / L (cid:12) ) = –3.35 ± τ = 16.9 + . − . Myr for the GSC 6214-210 system, wehave compared the age and luminosity to the brown dwarfevolutionary models of Baraffe et al. (2003) that incorporateupdated BT-Settl atmospheres (Allard et al. 2012), as wellas to the models of Burrows et al. (1997). We find model-predicted masses of M c = 14.0 ± Jup and M c = 14.9 ± Jup respectively. To reflect both estimates while stillconveying the broad uncertainties in substellar evolutionarymodels, we adopt a mass of M c = 14.5 ± Jup for thecompanion for this study.Updated system properties are listed in Table 1. OBSERVATIONS P
EARCE ET AL . Table 1.
System Properties for GSC 6214-210Property Previous Value Updated Value RefProperties of the PrimaryDistance (pc) 145 ±
14 108.8 ± µ α =-19.6 ± µ α =-19.38 ± -1 ) µ δ =-30.4 ± µ δ =-31.25 ± (cid:12) ) 0.38 ± ± (cid:12) ) 0.9 ± ± + . − . ±
150 – 4SpT K5 ± ± ± (cid:12) ))Age (Myr) 10 16.9 + . − . Jup ) 14 ± ± References —(1) de Zeeuw et al. (1999a); (2) Gaia Collaborationet al. (2018); (3) Zacharias et al. (2017); (4) Bowler et al. (2011);(5) Bowler et al. (2014); (6) de Zeeuw et al. (1999b); (7) Feiden(2016)
We used the near-infrared imaging camera NIRC2 coupledwith the adaptive optics system (Wizinowich et al. 2000) onthe Keck-II telescope to obtain high resolution imaging ofthe GSC 6214-210 system. We used a total of 77 images inthis study, summarized in Table 2. Observations from 2008,2009, and 2010 were previously reported in Ireland et al.2011, and were reanalyzed for this study. All images usedin this study were obtained with the K (cid:48) filter and the narrowcamera, with adaptive optics in natural guide star mode. Thedetails of each image are listed in Appendix C.Each science and calibration frame was linearized inPython using the methodology of the IDL task linearize_nirc2.pro (Metchev & Hillenbrand 2009). Science frames were dark-subtracted and flat-fielded using the corresponding dark andflat frames from each epoch. Bad pixel identifications wereadopted from Kraus et al. (2016) and replaced with the me-dian of surrounding pixels. An annotated and reduced imagecan be seen in Figure 1. ASTROMETRY4.1.
Relative Astrometry
PSF Fitting
We determined the relative position of the companion withrespect to the host star in each image through a custom Gibbs Figure 2.
Data, model, and residual map of the primary (top) andcompanion (bottom) for one image from the 2008 dataset. Themodel shown is built using the mean values of the parameter chainsfrom the MCMC fit for that image, and is plotted with a squareroot stretch to emphasize the faint residuals. The model capturesthe diffraction-limited core, but did not model the speckle structure.We used this approach to PSF fitting due to our need to robustlycharacterize the astrometric error for orbit fitting. We compare ourresults to results from an empirical model in Section 4.2
Sampler Markov Chain Monte Carlo (MCMC) PSF-fittingpipeline. We modeled the PSF of the primary and compan-ion as the sum of two 2-dimensional Gaussian functions —one to model the diffraction-limited core and another to cap-ture the wings. We found that 2 Gaussians were adequateto fully model the symmetric structure in the PSF; extendedspeckle structure around the primary was sufficiently faint asto not affect the fit, and would be poorly modeled by an az-imuthally symmetric function. Robust astrometric error barswere essential for orbit fitting, so we decided that in this case,modeling the PSF analytically was preferable to accuratelymodeling the speckle noise with empirical PSF templates.Figure 2 displays the data, model, and residual map for thehost star and the companion for one image from the 2008dataset, shown with a square root stretch to emphasize thefaint speckle structure.Our PSF fitter used a Metropolis-Hastings jump accep-tance criterion with Gibbs sampling of the 16 model param-eters: the x and y position of the primary, x and y positionof the companion, amplitude of the primary, amplitude of thecompanion, amplitude ratio between wide and narrow Gaus-sian, x and y pixel offset for the center of the wide Gaussianrelative to the narrow, background level, standard deviationin x and y direction for both wide and narrow Gaussians, androtation angles of wide and narrow Gaussians.We carried out our MCMC fit using the Texas AdvancedComputing Center (TACC) Lonestar 5 supercomputer in par-allel processing, with each of the 48 cores acting as an in-dependent walker. We ran each image on Lonestar 5 for12 hours, generating around 50,000 steps per parameter per RBITAL M OTION OF
GSC 6214-210 B x and y pixel position for star and companion. We com-puted a Gelman Rubin statistic for each parameter chain foreach image and all were below 1.1, which we interpret toindicate sufficient convergence.We inspected the covariances between each of the fit pa-rameters for each image. Most joint distributions appearedto be approximately Gaussian with symmetric tails, indicat-ing little covariance between the parameters of the fit. Somevariables were slightly correlated, however none of the vari-ables involved in determining the location of the centroid,our parameter of interest, were correlated in such a way asto bias the location. We therefore conclude that correlationsbetween model parameters did not influence our astrometricresult. Separation and position angle were uncorrelated inevery image. 4.1.2. Astrometric Calibration
The MCMC chains for the primary and companion pixelpositions were then fed into the second phase of our pipeline,which converted each pair of x and y pixel positions to on-skyseparation and position angle with appropriate corrections.To convert the ( x , y ) pixel measurements into on-sky rela-tive positions, we first corrected for optical distortion. Ob-servations before 2015 Apr 13 UT are interpreted to have aplate scale of 9.952 ± .
002 mas pixel − and PA offset of –0.252 ± ◦ between the on-chip orientation and on-skyorientation (Yelda et al. 2010), and observations after thisdate are interpreted to have a plate scale of 9.971 ± . − and PA offset of –0.262 ± ◦ (Service et al.2016), due to the realignment of the NIRC2 camera. FITSheader values are set at the start of the exposure, so for im-ages taken in vertical angle mode, we corrected the rotatorangles to correspond to the midpoint of the exposure. Wefinally applied corrections for differential aberration and at-mospheric refraction using the weather data provided in theNIRC2 headers, and computed a relative separation and po-sition angle for each of the 2 million ( x , y ) pixel-space mea-surements along each MCMC chain. We computed the finalmeasurement for an image as the mean and standard devia-tion of the separation and position angle chains.To capture the uncertainty in a single epoch, we adoptedthe weighted average for separation and position angle ineach image. To address systematic errors, we first accountedfor the residual error in (x,y) of 1 mas found in both the Yeldaet al. (2010) and the Service et al. (2016) distortion solutionsby adding a √ ρ and θ within each ditherposition. We then computed the weighted mean and uncer-tainty between the dither positions in a single epoch, to re-flect that the distortion uncertainty averages down with mul- tiple dither positions. To that epoch-wide uncertainty we thenadded in quadrature the pixel scale and orientation correc-tion uncertainties which are common to all dither positionsat a given epoch (0.002 mas pixel − and 0.009 ◦ for the Yeldaet al. (2010) distortion solution, 0.004 mas pixel − and 0.02 ◦ for the Service et al. (2016) distortion solution).Error bars in one image are consistent with image-to-imagescatter within one epoch, and the scatter around the subse-quent linear fit across all epochs (described in Section 4.2).The reduced chi-squared when combining images within oneepoch, and between epochs when doing the linear fit, areclose to 1. Because the companion is detected at low signal-to-noise, the MCMC is constrained by the Poisson error inthe companion, and dominates over any systematic error dueto PSF offset.4.2. Detection of Orbital Motion
A companion with such a wide separation, and thereforelow orbital velocity, requires precise astrometry to distin-guish orbital motion from measurement scatter. We mea-sured linear motion of the companion that is statistically sig-nificant above the noise, as reflected in the measurementslisted in Table 2 and displayed in Figure 3.We computed a linear fit to the separation and position an-gle as a function of time, also shown in Figure 3, which givesan angular velocity of µ ρ = − . ± .
11 mas yr − in separa-tion, and µ θ = − . ± .
10 mas yr − in position angle, with µ = 1 . ± .
15 mas yr − in total. The reduced chi-squaredstatistic of this fit is χ / v = 0.89 for 10 degrees of freedom(14 observations fit with 4 parameters), so we conclude thatthe linear fit is sufficient to describe the data and our errorsare of appropriate magnitude.We compared our results to astrometry conducted usingthe empirical PSF-fitting method StarFinder (Diolaiti et al.2000), e.g., as described in Dupuy et al. (2016), whichfound µ ρ = − . ± .
13 mas yr − in separation, and µ θ = − . ± .
08 mas yr − in PA. Both are consistent with our re-sult at ∼ σ , thus uncertainties due to choice of pipeline donot dominate over stochastic uncertainties.The companion has been well-established to be co-movingwith the primary (Ireland et al. 2011), and if we treat it asa non-moving background object, we would expect to ob-serve a relative motion of 36.77 ± − due to theproper motion of the primary. This disagrees by ≈ σ with our measured total velocity. If the companion wereinstead another member of USco located at the mean dis-tance of 145 ±
15 pc (Rizzuto et al. 2011; Wright & Mamajek2018), it would exhibit a smaller proper motion for the samespace velocity, and its relative velocity would also disagreesignificantly from our measurements. If we instead treat thecompanion as completely co-moving, the chi-squared statis- P
EARCE ET AL . P.A. (mas) ( m a s ) Total Relative Motion: 1.12 ± 0.15 mas/yr
Median ErrorPer Epoch: (a) ( m a s ) Years P . A . ( m a s ) (b) Figure 3. (a): Astrometry results showing a linear trend and orbital motion, plotted as change in angular and radial distance over time. Dotsindicate results from each image, and error bars are the mean epoch value. Thick error bars represent the weighted average uncertainty due toscatter in each epoch, thin error bars show additional systematic uncertainty. Error bars to the left represent median error for a single image.(b): Astrometry and linear fit for each parameter as a function of time. Error bars represent the total error in each epoch, and match the thinerror bars in (a). Deltas reflect change referenced from the average 2008 position, at (0,0). tic is χ = 127.03 ( χ / v = 12.7), confirming the linear trendis statistically significant above noise.If the object were in a circular, face-on orbit, the expectedvelocity at its observed position would be 1 . ± .
05 kms − in the plane of the sky. At the distance of GSC 6214-210( d = 108 . ± . . ± .
09 km s − , indicating that the object is eithernear apastron, in an inclined orbit, or in a wider orbit whichappears close when projected. At a projected separation of240 au, the only measurements we can make with a 10 yeartime baseline is projected instantaneous separation and pro-jected orbital velocity. If the separation vector is in the planeof the sky (causing maximum acceleration), then the acceler-ation would be predicted to be only 6 × − au yr − , resultingin only a 0.05 mas yr − velocity change. This is well beneathour detection limits, meaning that our data do not constrainacceleration.Additionally, the observed motion is much smaller than themean velocity dispersion observed in USco of σ = 1 . ± .
21 km s − (Wright & Mamajek 2018). This is further ev-idence that this is a bound companion and fitting Keplerianorbital parameters to this motion is justified. With the maxi-mum acceleration of 0.05 mas yr − , deviation from linear mo- tion by more than 3- σ (3 mas) would be observable in ap-proximately 11 years.This linear velocity allows a wide range of possibilities foreccentricity and inclination in our orbit fit but still providesa joint constraint on the posterior distribution of orbital ele-ments. 4.3. Minimum Periastron
If the companion were constrained to a face-on orbit, andthus the most tightly bound, our velocity vector provides theminimum allowed periastron distance, which we computedanalytically.Using conservation of angular momentum and energy, wecan compute that: L obs = L peri (1) E obs = E peri (2)where obs denotes values at our observation time, and peri denotes values at periastron. Thus, m (cid:126) r obs × (cid:126) v obs = m (cid:126) r peri × (cid:126) v peri (3) RBITAL M OTION OF
GSC 6214-210 B Table 2.
Keck/NIRC2 NGS AO Astrometry for GSC 6214-210 bEpoch MJD Filter N images N Dithers t int Tracking Separation Position Angle(sec) (mas) (deg)2008.46 54634.34 K p
20 2 20 PA 2201.96 ± .
09 175.623 ± . p ± .
20 175.585 ± . p ± .
40 175.578 ± . p ± .
12 175.506 ± . p ± .
64 175.452 ± . p
10 1 20 VA 2198.24 ± .
10 175.433 ± . p
13 1 20 PA 2197.11 ± .
13 175.368 ± . p ± .
12 175.375 ± . OTE — 0.026 deg = 1 mas tangential angular distanceN
OTE — N images is the number of images in each epoch. N
Dithers is the number of different dither positions ineach epoch. Integration time per image (t int ) is determined as integration time per coadd times the numberof coadds. Tracking mode is either Position Angle Mode (PA) or Vertical Angle Mode (VA). − GM ∗ m c r obs + m c v obs = − GM ∗ m c r peri + m c v peri (4)Given that (cid:126) r peri × (cid:126) v peri = | (cid:126) r peri || (cid:126) v peri | sin θ , rearranging andsubstituting for v peri , we obtain the quadratic equation (cid:0) − GM ∗ r obs + v obs (cid:1) r peri + GM ∗ r peri −
12 ( r obs v obs sin θ ) = 0 (5)Solving this equation for r peri , given the measured meanvelocity of v obs = 0 .
61 km s − and assuming a face-on orbitwith r obs = 239.4 AU, we compute a minimum periastron of r peri = 10.0 AU. Repeating this calculation for a 3- σ slowervelocity of v obs = 0 .
34 km s − , we compute a periastron of r peri = 3.0 AU. This gives the minimum allowed periastron to3- σ , constrained by our measurement of an orbital velocityvector.This places an analytical constraint on the minimum, mosttightly bound orbit for the companion. To fully sample theposterior distributions of orbital elements consistent with ourastrometric velocity vector, we performed an orbit fittinganalysis described below. ORBIT FITTING5.1.
Orbits for the Impatient
We created a custom orbit fitting algorithm based on theOrbits for the Impatient (OFTI) method of Blunt et al. (2017).Briefly, OFTI uses rejection sampling adapted from the meth-ods of Ghez et al. (2008) to generate probable orbits morequickly than MCMC, but with the same posterior PDF. Ourimplementation of OFTI randomly generates four orbital pa-rameters from uniform distributions for eccentricity ( e ), ar-gument of periastron ( ω ), mean anomaly, and cos( i ). The semi-major axis ( a ) for all orbits was initially fixed at 100AU, and position angle of ascending node ( Ω ) was initiallyfixed at 0 ◦ . Host star mass and distance were drawn froma Gaussian distribution centered at the updated values fromSection 2.2 value. Period ( P ) was computed from Kepler’s3rd law for each orbit. Epoch of periastron passage ( T ) wasderived from the mean anomaly. OFTI then scaled a and ro-tated Ω to match a single observational reference epoch. Wefound the reference observation which resulted in the high-est acceptance rate, and thus the most efficient, to be onewith the minimum error in the astrometry. Astrometric er-rors were incorporated into the fit by randomly drawing theseparation and position angle at the reference epoch from aGaussian distribution described by our astrometric uncertain-ties. We placed no additional restrictions on orbital configu-rations tested by our algorithm.Like Blunt et al. (2017), our implementation generatedrandom orbits in batches of 10,000, performed a rejectionsampling accept/reject decision on each orbit. As orbitswere generated, the minimum χ found was continuouslytracked, and periodically the previously accepted orbits werere-examined with the latest minimum χ to determine if theyshould have instead been rejected. This was repeated until aminimum of 100,000 orbits were accepted.5.2. Orbital Elements
Constrained fits
We begin by studying the most extreme limitations our ob-served velocity vector can place on allowed orbits for thecompanion. We performed two OFTI fits with restricted pa-rameters, a face-on fit ( i = 180 o ) and a circular orbit ( e = 0 . EARCE ET AL . Table 3.
Summary of Orbital ParametersElement Circular Face-on Full Orbit FitInner (blue) Outer (purple) Median Mode 68.3% Min CI 95.4% Min CIa (AU) 246 + − + − + −
230 130 (125, 300) (124, 1360)e 0.0 0.0 0.92 + . − . + − + −
180 111 105 (100, 122) (94, 150) ω (deg) ... ... + −
83 71 (32, 135) (3, 183) Ω (deg) 133 + − + − ... 53 179 (0, 132) (2, 180)T0 (yr) ... ... + −
320 1300 (-1000, 1200) (-20000, 2000)Periastron (AU) ... ... 10.3 + . − . OTE —Orbital parameter posteriors for a circular orbit fit (e = 0), a face-on orbit fit (i = 180 o ), and a fit with no constrained parameters. Theface-on constraint gave well constrained posterior distributions for all parameters, with a 3-sigma minimum periastron distance of 2.8 AU.The circular constraint gave two unique orbit solutions, displayed in Figure 4, an inner, tighter orbit plotted in blue, and an outer, wider orbitplotted in purple. Errors on values for the circular and face on constraints represent 68% confidence intervals. For the full OFTI parameterfit posterior distributions we report the median, mode, and 68.3% and 95.4% minimum credible intervals, with marginal posteriors shown inFigure 5 and joint distributions displayed in Appendix B D e c ( " ) (a) D e c ( " ) (b) Figure 4.
100 orbits randomly selected from the posterior of the twoconstrained orbit fits shown in Table 3. Figure a: Posterior orbitsfrom an OFTI fit with the inclination fixed at a face-on orientationof i = 180 o . This is the configuration that places the companiondeepest in the potential well. Figure b: Posteriors from a fit witheccentricity constrained to be circular ( e = 0 . The results from the two constrained fits are shown in Table3. The face-on fit gave a mean periastron that agrees with ouranalytic calculation in Section 4.3. When confined to a cir-cular orbit, we find two unique families of solutions, shownin Figure 4(b) – a tighter orbit plotted in blue, and a wider or-bit plotted in purple. Both solutions place constraints on theinclination. The wide orbit (purple) would place the com-panion outside the NIRC2 field of view for the majority ofthe orbit, while the tight orbit (blue) would only hold if wewere coincidentally seeing the companion exactly at maxi- mum projected separation. Neither scenario is ruled out byour observations, but they would only hold if we had coin-cidentally discovered the companion at a very specific epochin its orbit. 5.2.2.
Full orbit fit
We performed an OFTI fit with all free parameters. Ourposterior sample is comprised of 100,000 accepted orbitalconfigurations outputted from OFTI. Figure 6 shows a selec-tion of 100 orbits from the sample. A wide range of orbitalparameters were found to fit the data reasonably well, withwide marginal distributions for most parameters. However,the orbit arc provides a joint constraint on the posteriors ofeach element. Figure 5 displays the joint credible intervals ofsemi-major axis, eccentricity, and periastron with inclination,and the marginal distributions for all fit parameters and peri-astron. Appendix B displays the full joint and marginal pos-terior distributions for the parameters for all orbits acceptedby our fitting algorithm. A large range of values for mostparameters were accepted by our OFTI analysis, indicating awide distribution of possible orbits that satisfy our data. Wereport in Table 3 the median, mode, and 68.3% and 95.4%minimum credible intervals for the orbital parameters for ourfull orbit fit.Finally, because we were interested in the possibility ofscattering from close radii, we examined the periastron pos-terior resulting from each orbit solution in our unconstrainedfit posterior. We find 2% of orbits having a periastron lessthan 10 AU. All orbits with a periastron less than 5 AU havelikelihoods less than 5%, and thus a companion on these or-bits would have led to the observed data with a probability
RBITAL M OTION OF
GSC 6214-210 B . . a ( AU ) i ( d e g ) . . . . . e a (1 e ) ( AU ) a ( AU ) . . . e i ( deg ) ( deg ) ( deg ) T yr ) a (1 e ) ( AU ) Figure 5.
OFTI posterior distributions for the orbital elements for GSC 6214-210 b. Top: Parameter correlations shown as a 2d probabilitydensity, with contours indicating 1-, 2-, 3-, and 4- σ regions. These parameters are the most strongly covariant. Bottom: 1d histograms of theposterior distributions for the fit parameters, plus periastron (defined as r peri = a × (1 − e )). In the absence of radial velocity information, there isa degeneracy between solutions with Ω , and consequently ω , which differ by 180 o . Here, we follow the convention of selecting the ascendingnode 0 o ≤ Ω ≤ o . Should future radial velocity measurements indicate Ω + 180 o is the ascending node, then 180 o should be added to ourmeasurements of Ω and ω . We show corner plot with all of the marginalized two-dimensional credible intervals in Appendix B. less than 5%. We therefore conclude that these orbits are notlikely to have generated the observations we measured.5.3. The Detectability of Potential Scatterers
If dynamical scattering were a feasible explanation for theformation of wide PMCs, the observed companion wouldhave been scattered outward by another companion that waslikely of equal or larger mass (Veras & Armitage 2004; Veraset al. 2009; Ford & Rasio 2008; Matsumura et al. 2017). Noradial velocity surveys to search for unresolved companionshave been conducted on this system, and there is no indica-tion of stellar binary companions in spectroscopy on the hoststar. The radial velocity scatter and an astrometric jitter termof zero reported by
Gaia
DR2 also argues against the exis-tence of a close-in stellar companion, but is not sufficient toplace limits on a substellar companion. We tested the de-tectability of another, close-in substellar companion in high-contrast imaging, which could have scattered GSC 6214-210b to its current wide orbit.We modeled the scattering interaction with the simplify-ing assumption that both objects began on circular orbits at the current periastron distance of each orbit in the posteriorsample. While this is unrealistic physically, it represents themost conservative case because it gives the largest changein orbital energy for the companion, and drives the scattererdown the potential well by the maximum possible amount.We determined the change in the companion’s orbital energydue to the scattering interaction as ∆ E = − GM (cid:63) m c (cid:16) a c − r (cid:17) (6)where r is the initial radius of the companion’s initial circularorbit (equivalent to its current day periastron for any givenorbital configuration), and a c is the companion’s final semi-major axis for that orbital configuration. Assuming all energylost by the scatterer was transferred to the companion, thefinal energy for the scatterer is E sc = − GM (cid:63) m sc r − ∆ E (7)0 P EARCE ET AL . RA (") D e c ( " ) (a) ( m a s ) Years P . A . ( d e g ) (b) Figure 6.
100 orbits randomly selected from the distribution of over 100,000 accepted orbits for GSC 6214-210 b. Left: randomly selectedorbits around the host star (the yellow star located at 0,0) plotted in right ascension and declination. Right: the same 100 randomly selectedorbits plotted in position angle and separation over time, with the observations from Table 2 over-plotted. A variety of orbital configurationscomprise the posterior of our orbit sample.
The semi-major axis and eccentricity for the potential scat-terer’s final orbit are therefore given by: a sc = − GM (cid:63) m sc E sc ; e sc = ra sc − r ) isthe scatterer’s new apastron distance, again to conservativelypredict the least detectable possible orbital configuration. Werandomly drew a new orbital inclination for the scatterer andorbital phase for the simulated observation, then applied de-tection limits to determine if the simulated scatterer wouldhave been detected in imaging data. We performed this sim-ulation for a scatterer mass equal to the companion (14.5M Jup ), 1.5 times companion mass (22 M
Jup ), twice the com-panion’s mass (29 M
Jup ), and five times the companion’smass (72.5 M
Jup ).As we describe in Appendix A, we have determined up-dated detection limits for additional companions to GSC6214-210 from each imaging epoch, including those thatwere previously reported by Ireland et al. (2011), as wellas several epochs of non-redundant masking (NRM) interfer- ometry. Given the moderate contrast of GSC 6214-210 b withrespect to its primary star, companions of equal or greatermass (i.e., equal or lesser contrast) would be observable quiteclose to the primary star, enabling detection in a large frac-tion of cases. The innermost limit for an equal-brightnesscompanion was found on 2016 Jun 16, where such a com-panion would have been detected at ρ >
22 AU. Similarly,the limit for a scatterer at 1.5 time the companion’s mass was8.2 AU (on 2011 Jun 04), twice the companion’s mass was1.8 AU (on 2014 Jul 30), while the limit for a scatterer at fivetimes the companion’s mass was 1.7 AU AU (on 2014 Jul30).To ensure the most conservative estimate, we repeated thisanalysis for the most energetically limiting case. The min-imum possible initial energy for the scattering object is theone in which results in the final orbit of the scatterer hav-ing eccentricity = 1 and semi-major axis = half companion’scurrent periastron distance (and thus apastron at the compan-ion’s current periastron), because any angular momentum thescatterer had has been fully transferred to the companion.Any lower initial scatterer energy could not have produced
RBITAL M OTION OF
GSC 6214-210 B DISCUSSIONWe have used the orbit of the companion to look for cluesregarding its formation mechanism, specifically determiningthe likelihood of formation at a close radius followed by ejec-tion via scattering. Here we present evidence that dynamicalscattering is a possible but not likely explanation for the for-mation of this object.Unlike some other studies of wide PMC orbits (e.g., Bryanet al. 2016), this study was unable to entirely rule out higheccentricity orbits with close periastron. Orbits with eccen-tricity near 0.9 are common in our posterior, and orbits withperiastron less than 10 AU have high likelihoods. We can-not rule out dynamical scattering based on orbital parameterposteriors alone.While orbits with periastron less than 10 AU compriseabout 2% of the posterior, orbits with periastron less than 5AU (0.03% of all orbits), all have low statistical likelihoods.So, we conclude that orbits which would have allowed thecompanion to form inside of Jupiter’s orbit, and near ice linesat ∼ Gaia
DR2 reported an astrometric excessnoise of 0.0, implying absence of an invisible companionlarge enough to scatter GSC 6214-210 b and supporting theconclusion that an inner companion is unlikely.While we cannot conclusively rule out dynamical scatter-ing, these lines of evidence form a picture for which scatter-ing is not a likely explanation for this PMC. This conclusionis in agreement with the dominant body of work for wide-orbit planet formation, discussed in Section 1, and continuesto point to in-situ formation at the more likely scenario. Mea-suring the orbital architecture of additional wide PMC sys-tems would provide more evidence to support or challengethis conclusion. SUMMARYWe conducted an astrometric study and orbital motion de-termination for the wide-orbit planetary mass companionGSC 6214-210 b, yielding the first statistically significantmeasurement of orbital motion for this object. We used aGaussian PSF model with an MCMC to measure relative as-trometry in ten years of AO imaging data from NIRC2 atKeck, and then developed a custom implementation of theOrbits for the Impatient rejection sampling algorithm (Bluntet al. 2017) to fit orbital parameters.Our results demonstrate that a wide range of orbital pa-rameters fit the data, including some with low periastron dis-tances. However, we also demonstrate that the tightest orbitsstill produce a relatively poor fit, with low likelihood to havebeen observed. We also demonstrate that for most of the al-lowed orbits, the scattering object would likely have been de-2 P
EARCE ET AL . N u m b e r Companion mass totaldetected0.5 1.0 1.5 2.0 2.5 3.0 3.5log(Periastron) (AU)010002000300040005000 N u m b e r Companion mass totaldetected
Figure 7.
Top: Number of scatterers that would have been detectable for a scatterer of equal mass, 1.5 times companion’s mass, twice thecompanion’s mass, and five times the companion’s mass, plotted as a function of companion’s periastron distance, assuming both objects wereon an initially circular orbit at the companion’s current periastron. Each plot shows the number of detected scatterers (gold) over-plotted atopthe number of total orbits (purple). The detection limit for each mass is plotted as a red vertical line. In the vast majority of cases, a secondcompanion of equal or greater mass would have been detected in existing observations, so it is unlikely for GSC 6214-210 b to have beenscattered from close radii, unless it both originated from deep in the potential well and was scattered by a similar-mass companion. Bottom:Fraction of detected scatterers in the most limiting energy case, a scatterer orbit with eccentricity = 1 and apastron at the companion’s currentperiastron distance. We see that in this most conservative case, the fraction of detected scatterers is smaller, but the overall conclusion of thesimulation remains the same — in the majority of cases the scatterer would have been detected in imaging. tected in past high-resolution imaging data, unless the com-panion was scattered from the tightest orbits and specificallyby a scatterer of similar mass. We cannot rule out core accre-tion with subsequent dynamical scattering as a viable forma-tion pathway for this companion, however we conclude thatit is much less likely than in-situ mechanisms such as gravita-tional instability of the protostellar disk. This is in agreementwith prior work on other wide PMC systems, and suggeststhat scattering is not likely to play a key role in producingPMCs.The data presented herein were obtained at the W. M. KeckObservatory, which is operated as a scientific partnershipamong the California Institute of Technology, the Universityof California and the National Aeronautics and Space Ad-ministration. The Observatory was made possible by the gen-erous financial support of the W. M. Keck Foundation. Thisresearch has also made use of the Keck Observatory Archive (KOA), which is operated by the W. M. Keck Observatoryand the NASA Exoplanet Science Institute (NExScI), undercontract with the National Aeronautics and Space Adminis-tration. The authors wish to recognize and acknowledge thevery significant cultural role and reverence that the summitof Maunakea has always had within the indigenous Hawaiiancommunity. We are most fortunate to have the opportunity toconduct observations from this mountain.L.A.P. was supported by a NASA/Keck Data AnalysisGrant and by the McDonald Observatory Board of Visi-tors, the Cox Endowment Fund of the UT-Austin Departmentof Astronomy, the Barry Goldwater Scholarship and Excel-lence in Education Foundation, and the Astronaut Scholar-ship Foundation.T.J.D. acknowledges research support from Gemini Obser-vatory.M.J.I. was supported by the Australian Research CouncilFuture Fellowship (FT130100235)
RBITAL M OTION OF
GSC 6214-210 B Gaia
Gaia
Gaia
Multilateral Agreement.This research has made use of the SIMBAD database, op-erated at CDS, Strasbourg, France
Facility:
Keck:II (NIRC2), Texas Advanced ComputingCenter (TACC)
Software:
StarFinder (Diolaiti et al. 2000), Numpy(Oliphant 2006), Astropy (Price-Whelan et al. 2018), Mat-plotlib (Hunter 2007)APPENDIX A. DETECTION LIMITSOver the 8 years since we reported the results of Ireland et al. (2011) we have observed the GSC 6214-210 system numerousadditional times with both imaging and nonredundant mask (NRM) interferometry, while also improving our understanding of thenoise properties of the NIRC2 camera. We therefore are now able to provide updated detection limits for additional companionsinterior to GSC 6214-210 b.For the 2016 epoch that we describe in Section 3, we conducted PSF subtraction and candidate identification using the methodsdescribed by Kraus et al. (2016). To briefly summarize, each image was first calibrated and cleaned of hot pixels and cosmicrays. To determine optimal detection limits at wide separations, we then subtracted the azimuthally-averaged flux profile of theprimary star, computed the flux at every integer pixel location through a photometric aperture of diameter λ/ D , and searched forany such flux values that were + σ outliers compared to the distribution of all such values at that projected separation. To searchfor companions at smaller separations, we then repeated the same procedure while subtracting the best-fitting PSF as selectedfrom all observations of apparently single stars within the NIRC2 archive, based on the χ fit at radii of 0.15–0.45 (cid:48)(cid:48) . We did notfind any candidate detections at > + σ , establishing an upper limit for additional companions at the corresponding flux.For the 3 NRM epochs that we have taken of GSC 6214-210 (one in the L (cid:48) filter, two in the CH4S filter), we analyzed the datausing the pipeline described by Kraus et al. (2008, 2011). To briefly summarize, the data analysis takes three broad steps: basicimage analysis (flatfielding, bad pixel removal, dark subtraction), extraction and calibration of squared visibilities and closurephases, and binary model fitting. Unless testing fits for close, near-equal binaries, we fit only to closure phase, as this is thequantity most robust to changes in the AO point-spread function. The detection limits are found using a Monte-Carlo methodthat simulates 10,000 random closure-phase datasets of a point source, with closure-phase errors and covariances that match thecalibrated target data set. This routine then searches for the best fit for a companion in each randomized dataset. Over eachannulus of projected separation from the priamry star, the 99.9% confidence limit is set to the contrast ratio where 99.9% of theMonte-Carlo trials have no best binary fit with a companion brighter than this limit anywhere within the annulus. We did not findany cases where a companion was detected above that limit in a dataset, so we adopt those contrast values as our limits on theexistence of additional companions in the system.In Table 4, we list the detection limits for additional companions in the 2016 dataset, and in Table 5, we similarly list thedetection limits for additional companions in each NRM dataset. The deepest example of each dataset was used as an input forthe limits on potential scatterers, as we describe in Section 5.3.4 P EARCE ET AL . Table 4.
Contrast limits for NIRC2 imaging of GSC 6214-210Epoch MJD Number of Integration Contrast Limit ( ∆ K (cid:48) in mag) at Projected Separation ( ρ in mas)Frames Time (s) 150 200 250 300 400 500 700 1000 1500 20002016.46 57555.47 10 20 5.0 5.9 6.3 6.6 7.1 7.3 8.1 8.3 8.3 8.2 Table 5.
NRM Contrast limits for GSC 6214-210Epoch MJD Filter Number of Limits (mag) atFrames 10 mas 20 mas 40 mas2011.42 55716.34 L (cid:48)
RBITAL M OTION OF
GSC 6214-210 B B. ORBITAL PARAMETERS JOINT CREDIBLEINTERVALSFigure 8 reports the full joint credible intervals for the fitparameters, plus periastron, for the unconstrained orbit fit.6 P
EARCE ET AL . T ( y r s ) e i ( d e g ) ( d e g ) ( d e g ) a ( AU ) l o g ( a ( e )) ( A U ) T yrs ) . . . . . . e i ( deg ) ( deg ) ( deg ) . . . . . . . . log ( a (1 e ))( AU ) Figure 8.
Two-dimensional marginalized credible intervals for the orbital elements for the companion to GSC 6214-210. The one-dimensionalmarginalized distributions of each element is shown on the diagonal. Parameters plotted are semi-major axis (a) in AU, epoch of periastronpassage (To), eccentricity (e), inclination (i) in degrees, argument of periastron ( ω ) in degrees, and longitude of periastron ( Ω ) in degrees, andperiastron distance ((1-e) a) in AU. The contours in the histograms correspond to the 1-, 2-, 3-, and 4- σ levels. RBITAL M OTION OF
GSC 6214-210 B C. IMAGE ASTROMETRYIn Table 6, we report the observational details and our in-dividual fit results for each of the images we consider in this work. The individual measurements were combined into asingle measurement at each epoch (Table 2) using the meth-ods described in Section 4.1.
Table 6 . Astrometric Measurements by ImageImage t int
Tracking ρ PA S/N S/N FWHMFilename (sec) Mode (mas) (deg) Primary Companion (mas)2008 Jun 17 (JD 2454634.5) PI: IrelandN2.20080617.29357.fits 20.0 PA 2202.23 ± .
57 175.624 ± .
015 1836 105 44.51 ± . ± .
58 175.607 ± .
016 2103 120 44.81 ± . ± .
64 175.624 ± .
017 2075 100 44.44 ± . ± .
57 175.619 ± .
015 2155 109 44.74 ± . ± .
62 175.616 ± .
017 2068 100 46.13 ± . ± .
67 175.615 ± .
018 2041 109 46.01 ± . ± .
57 175.607 ± .
015 1945 109 44.56 ± . ± .
60 175.616 ± .
016 2089 113 44.81 ± . ± .
62 175.618 ± .
017 2198 102 45.09 ± . ± .
55 175.624 ± .
014 1591 120 41.03 ± . ± .
54 175.639 ± .
014 1555 117 42.40 ± . ± .
50 175.630 ± .
013 1516 137 40.86 ± . ± .
52 175.632 ± .
013 1646 124 41.10 ± . ± .
53 175.629 ± .
014 1496 136 40.65 ± . ± .
55 175.631 ± .
014 1561 136 43.81 ± . ± .
56 175.615 ± .
014 1359 118 42.01 ± . ± .
56 175.633 ± .
014 1368 115 41.50 ± . ± .
55 175.620 ± .
014 1310 126 41.07 ± . ± .
51 175.626 ± .
013 1162 138 41.22 ± . ± .
59 175.629 ± .
015 1277 126 41.72 ± . ± .
09 175.623 ± . ± .
51 175.566 ± .
038 1890 46 40.77 ± . ± .
43 175.575 ± .
033 2459 10 39.25 ± . ± .
39 175.556 ± .
033 2455 10 39.20 ± . ± .
73 175.597 ± .
040 2276 46 40.23 ± . ± .
69 175.610 ± .
040 2240 49 40.41 ± . ± .
44 175.605 ± .
034 2109 48 38.72 ± . ± .
39 175.595 ± .
032 2240 46 38.61 ± . ± .
50 175.584 ± .
039 2043 54 40.77 ± . ± .
55 175.583 ± .
040 1885 44 40.77 ± . ± .
20 175.585 ± . Table 6 continued
EARCE ET AL . Table 6 (continued)
Image t int
Tracking ρ PA S/N S/N FWHMFilename (sec) Mode (mas) (deg) Primary Companion (mas)N2.20100426.52760.fits 10.0 PA 2201.54 ± .
58 175.545 ± .
013 3238 51 37.99 ± . ± .
54 175.590 ± .
012 2781 136 38.53 ± . ± .
60 175.550 ± .
013 2867 129 38.69 ± . ± .
55 175.570 ± .
012 2710 145 37.86 ± . ± .
62 175.636 ± .
013 2782 115 38.11 ± . ± .
03 175.584 ± .
025 1503 101 65.30 ± . ± .
90 175.602 ± .
021 1698 115 58.86 ± . ± .
71 175.562 ± .
015 1681 110 61.09 ± . ± .
40 175.578 ± . ± .
60 175.488 ± .
032 1887 61 41.16 ± . ± .
37 175.489 ± .
028 1835 63 40.63 ± . ± .
70 175.534 ± .
031 1283 67 40.60 ± . ± .
76 175.521 ± .
033 1310 54 41.45 ± . ± .
60 175.521 ± .
031 1442 61 39.68 ± . ± .
22 175.493 ± .
024 1754 89 39.55 ± . ± .
12 175.506 ± . ± .
22 175.449 ± .
091 1743 22 38.69 ± . ± .
47 175.479 ± .
084 1351 30 51.15 ± . ± .
34 175.455 ± .
036 2136 55 41.23 ± . ± .
87 175.461 ± .
025 3220 92 40.04 ± . ± .
83 175.457 ± .
022 3719 87 44.72 ± . ± .
90 175.436 ± .
023 3307 77 38.58 ± . ± .
64 175.452 ± . ± .
52 175.493 ± .
105 1559 18 40.20 ± . ± .
81 175.405 ± .
134 1380 16 47.76 ± . ± .
56 175.411 ± .
073 1495 21 51.45 ± . ± .
78 175.459 ± .
087 1294 23 50.22 ± . ± .
72 175.438 ± .
048 1647 37 47.42 ± . ± .
39 175.421 ± .
041 1635 35 47.97 ± . ± .
66 175.451 ± .
047 1616 35 52.75 ± . ± .
49 175.454 ± .
044 1652 44 50.60 ± . ± .
64 175.368 ± .
052 1509 35 55.11 ± . ± .
35 175.443 ± .
043 1517 38 51.91 ± . ± .
10 175.433 ± . ± .
94 175.364 ± .
023 708 74 41.54 ± . ± .
08 175.386 ± .
026 835 67 41.38 ± . Table 6 continued
RBITAL M OTION OF
GSC 6214-210 B Table 6 (continued)
Image t int
Tracking ρ PA S/N S/N FWHMFilename (sec) Mode (mas) (deg) Primary Companion (mas)N2.20170628.26728.fits 20.0 PA 2197.70 ± .
10 175.391 ± .
028 764 65 45.83 ± . ± .
78 175.394 ± .
020 701 75 44.50 ± . ± .
57 175.357 ± .
014 609 92 42.12 ± . ± .
60 175.354 ± .
015 643 106 42.29 ± . ± .
02 175.375 ± .
027 708 50 45.87 ± . ± .
15 175.413 ± .
033 565 37 49.66 ± . ± .
82 175.333 ± .
021 556 65 43.60 ± . ± .
83 175.344 ± .
021 514 76 44.26 ± . ± .
66 175.387 ± .
017 545 99 43.86 ± . ± .
60 175.351 ± .
016 499 83 43.15 ± . ± .
68 175.399 ± .
017 503 89 42.77 ± . ± .
13 175.368 ± . ± .
62 175.363 ± .
014 2534 104 38.62 ± . ± .
67 175.375 ± .
015 1897 91 37.64 ± . ± .
61 175.384 ± .
014 1694 88 38.18 ± . ± .
63 175.389 ± .
015 1822 91 39.05 ± . ± .
60 175.365 ± .
014 2199 105 38.63 ± . ± .
12 175.375 ± . OTE —All images were obtained with the NIRC2 imager on Keck II in the K (cid:48) filter with no coronagraph. Integration time (t int ) is determinedas integration time per coadd times the number of coadds. Tracking mode is either Position Angle Mode (PA) or Vertical Angle Mode (VA).SNR is computed as a ratio of the sky-subtracted sum of pixel values within an aperture centered over the object to the standard deviation ofpixel values in an annulus outside the object’s PSF. FWHM is determined as 2.355 x the larger of the two sigmas of the 2D Gaussian fit.
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