The Radial and Rotational Velocities of PSO J318.5338$-$22.8603, a Newly Confirmed Planetary-Mass Member of the $\beta$ Pictoris Moving Group

0.5 MB·

by  K. N. Allers

Draftversion January20,2016
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
THE RADIAL AND ROTATIONAL VELOCITIES OF PSO J318.5338−22.8603,A NEWLY CONFIRMED
PLANETARY-MASS MEMBER OF THE β PICTORIS MOVING GROUP
K. N. Allers
DepartmentofPhysicsandAstronomy,BucknellUniversity,Lewisburg,PA17837,USA;[email protected]
J. F. Gallimore
6 DepartmentofPhysicsandAstronomy,BucknellUniversity,Lewisburg,PA17837,USA
1
0
Michael C. Liu
2
InstituteforAstronomy,UniversityofHawaii,2680WoodlawnDrive,Honolulu,HI96822,USA
n
a
J Trent J. Dupuy

8 TheUniversityofTexasatAustin,DepartmentofAstronomy,2515Speedway C1400,Austin,TX78712,USA
1 Draft version January 20, 2016

] ABSTRACT
R
PSO J318.5338−22.8603 is an extremely-red planetary-mass object that has been identified as a
S candidatememberoftheβ Pictorismovinggroupbasedonitsspatialpositionandtangentialvelocity.
. WepresentahighresolutionK-bandspectrumofPSOJ318.5338−22.8603. Usingaforward-modeling
h
Markov Chain Monte Carlo approach, we report the first measurement of the radial velocity and
p
- v sin(i)ofPSOJ318.5−22,−6.0+−01..81km s−1and17.5+−22..38km s−1,respectively. Wecalculatethespace
o velocityandpositionofPSOJ318.5−22andconfirmthatitisamemberoftheβPictorismovinggroup.
r Adoptinganageof23±3MyrforPSOJ318.5−22,wedetermineamassof8.3±0.5M andeffective
t Jup
s temperature of 1127+24 K using evolutionary models. PSO J318.5338−22.8603 is intermediate in
a −26
mass and temperature to the directly-imaged planets β Pictoris b and 51 Eridani b, making it an
[
important benchmark object in the sequence of planetary-mass members of the β Pictoris moving

1 group. Combining our v sin(i) measurement with recent photometric variability data, we constrain
v the inclination of PSO J318.5−22to >29◦ and its rotational period to 5–10.2 hours. The equatorial
7 velocityofPSOJ318.5−22indicatesthatitsrotationisconsistentwithanextrapolationofthevelocity-
1 mass relationship for solar system planets.
7
Subjectheadings: browndwarfs-infrared:stars-planetsandsatellites: atmospheres-techniques: radial
4
velocities - techniques: spectroscopic - stars: rotation
0
.
1
0 1. INTRODUCTION tionofthe lithium depletionboundaries(e.g.King et al.
6 2000; Binks & Jeffries 2014). Though the estimated age
Objectswithmassesbelowthehydrogenburninglimit
1 of an individual group may vary by up to a factor of
(∼75M ;Burrows et al.2001)coolastheyage,result-
: Jup ∼2 depending on the method of age determination, the
v ing in a mass-age-luminosity degeneracy. Several-Gyr-
various methods agree on the relative ages of the groups
i oldbrowndwarfscanhavethesameluminositiesasmuch
X (e.g.Mentuch et al.2008;da Silva et al.2009;Bell et al.
younger,several-Myr-oldplanetary-mass(.13M )ob-
Jup 2015). In order to link an object to a local young mov-
r jects. Thus, to determine the mass of a single substellar
a ing group, its galactic kinematics (UVW) and position
object, one must have an independent constraint on its
(XYZ)mustagreewiththeotherknownmembersofthe
age.
group.
Asplanetary-massobjectsandbrowndwarfscool,they
PSOJ318.5338−22.8603(hereinafterPSOJ318.5−22),
also contract, increasing their surface gravity as they
discovered by Liu et al. (2013), is the first free-floating
evolve. Thus evidence of low gravity (e.g. weak FeH
object with colors and luminosity that overlap the
andalkalifeatures,strongVOabsorption)inaspectrum
young, dusty, planetary-mass companions to HR 8799
can corroborate the youth of an object. As noted in
and2MASSJ1207-39. Basedonitsparallax,propermo-
Allers & Liu (2013), however,spectroscopicages arenot
tion,andspectroscopicsignaturesofyouth(low-gravity),
particularly accurate, and objects of the same age and
Liu et al. identified PSO J318.5−22 as a candidate
spectral type can have different indicators of youth.
member of the β Pictoris (hereinafter β Pic) moving
Another method to determine the age of a sub-
stellar object is via association with a young stellar group. Liu et al. estimate a mass of 6.5+−11..30 MJup
moving group. These groups have ages known from for PSO J318.5−22, based on evolutionary models for
the stellar members of the groups, either from model an isochronal age of 12+−84 Myr and the luminosity of
isochronefitting ofthe membersonanHRdiagram(e.g. PSO J318.5−22. Here, we report a determination of the
Zuckerman et al. 2001; Pecaut et al. 2012) or the loca- radialandrotationalvelocitiesofPSOJ318.5−22forthe
2 Allers et al.
firsttimeandassesstheprobabilitythatPSOJ318.5−22 Unfortunately, no radial velocity standard was ob-
is a member of the β Pic moving group. We re-estimate served as a part of our Gemini program. We use an ap-
the physical properties of PSO J318.5−22 based on re- proach similar to that described by Blake et al. (2010),
centdeterminationsoftheageoftheβ Picmovinggroup wherein we employ forward modeling to simultaneously
(23±3Myr;Mamajek & Bell2014). Withamassandef- fit the wavelength solution of our spectrum, the rota-
fective temperature intermediate to the directly-imaged tionalandradialvelocitiesofPSOJ318.5−22,thescaling
exoplanets β Pictoris b (Lagrange et al. 2009) and oftelluricline depths,andthe FWHMofthe instrumen-
51 Eridani b (Macintosh et al. 2015), PSO J318.5−22is tal LSF.
an important free-floating analog to these young plan-
ets. In addition, combining our measurement of v sin(i) 3.1. Creating a Forward Model
with the recent measurements of PSO J318.5−22’s or- Our observedspectrum ofPSO J318.5−22is the com-
bitalperiod(Biller et al.2015),weconstrainitsspinaxis bination of the spectrum of the brown dwarf, telluric
inclination and equatorial velocity. absorption,andeffectsfromtheinstrument(wavelength-
2. OBSERVATIONSANDDATAREDUCTION dependent response and line spread functions). We cre-
ate myriad model spectra and evaluate the best fit pa-
We obtained a high resolution (R ≈ 14000) spec- rameters by comparison to our observed spectrum of
trum of PSO J318.5−22 using the GNIRS spectrograph PSO J318.5−22. The components of our forward model
(Elias et al. 2006) on the Gemini-North Telescope. We
are:
usedthe111linesmm−1 gratingwitha0.15”slit,result-
ingina2.27–2.33µmspectrum. Ourqueueobservations • Wavelength Solution: When reducing ourdata,
wereobtainedonUT26November2013underclearskies thewavelengthsolutionofourobservedspectrumis
whiletheseeingwas0.49”. Sevenexposuresof600swere determinedfromsevenXenon-Argonarclineswith
obtained,nodding6′′alongtheslitbetweenexposuresfor wavelengthsof2.29-2.33µm. Therearenoarclines
a total integration time of 70 minutes. Immediately af- for the 2.27–2.29 µm portion of our spectrum. In
ter ourobservationsofPSO J318.5−22,we obtainedflat addition, the typical residuals to our wavelength
field and Xenon-Argon lamp images. We also observed solutionforeacharclinecorrespondto∼5kms−1.
an A0 star, HIP 110746,as a telluric standardusing the Our spectrum itself contains many telluric absorp-
same instrument setup. tion features which allow us to refine the wave-
Data were reduced using the REDSPEC reduction length solution as a part of our forward model-
package to spatially and spectrally rectify each expo- ing. We calculate the wavelength solution of our
sure, referencing the Keck/NIRSPEC Echelle Arc Lamp observedspectrum using a 2nd-degree polynomial.
Tool (http://www2.keck.hawaii.edu/inst/nirspec/ Rather than having the coefficients of the poly-
N7arclamps.html)toidentifythewavelengthsoflinesin nomial as our fitted parameters, we use barycen-
our arc lamp spectrum. After nod-subtracting pairs of tric Lagrangian interpolation (Berrut & Trefethen
exposures,wecreateaspatialprofilewhichisthemedian 2004; Waring 1779), solving for the wavelengths of
intensity across all wavelengths at each position along the first, middle, and last pixels of the spectrum
the slit. To remove any residual sky emission lines from anddeterminingthecoefficientsoftheunique2nd-
our nod-subtracted pairs and to determine the noise per degree polynomial that will fit these three points.
pixel at each wavelength, we identify pixels in the spa- We start by adopting the wavelengths of our re-
tialprofilethatdonotcontainsignificantsourceflux. At duced spectrum as the initial guess.
each wavelength, we fit a line to the intensity of these
• Brown Dwarf Atmosphere Model: Weusethe
background pixels vs. position along the slit. The fit-
BT-Settlmodelatmospheres(Allard et al.2012)as
ted line provides the background level as a function of
the intrinsic spectrum of PSO J318.5−22 in our
position and the scatter of the background pixels about
the line gives the noise per pixel.1 We then performed forward modeling. The BT-Settl models are pro-
vided for two different assumed solar abundances
a profile-weighted extraction (Horne 1986) on each ex-
(Asplundetal. 2009[AGSS]andCaffauetal. 2011
posure and combined the resulting spectra using a ro-
[CIFIST]). We use model grids with effective tem-
bustweightedmeanwiththexcombspecprocedurefrom
peratures (T ) of 1100–2500K and surface grav-
theSpeXtoolpackage(Cushing et al.2004). Themedian eff
ities (log(g)) of 3.5–5.5 dex (where g is in units of
signal-to-noise of our final spectrum is 21.
We determine the FWHM of the line spread function cm s−2.) We adjust the wavelengths of the model
(LSF) by fitting 1-dimensional gaussians to the Xenon atmospheretoaccountfortheradialvelocityofthe
and Argon lines in an extracted spectrum of the arc object, λ = λ0 + ((vr +vbary)λ0/c), where vr is
lamp image. For the seven arc lamp lines, we calculate the radial velocity of PSO J318.5−22, and vbary
a mean and standard deviation for the LSF FWHM of (28.1 km s−1) is the barycentric motion projected
of0.000163±0.000015µm,correspondingtoaresolution, away from PSO J318.5−22 at the time of our ob-
R=λ/∆λ=14100. servation. We then convolve the model spectrum
to account for rotation, v sin(i), using a convolu-
3. DETERMININGRADIALANDROTATIONAL tion kernel created by the LSF ROTATE task2. Our
VELOCITIES
velocity-shifted, rotationally broadened model at-
mosphereapproximatesthespectrumofthe brown
1 This assumes that the shot noise is dominated by the back-
dwarf itself.
ground. PSOJ318.5−22isfaint,sotheskybackgroundlevelis>3
timesbrighterthanthefluxofoursourceacrossallwavelengthsof
ourspectrum. 2 ApartoftheIDLAstronomyUser’sLibrary
llllloooooACgggggG(((((IgggggFS)))))IS=====S034455T9.....50505
PSO J318.5-22is a β Pic member 3
• Telluric Absorption: We use the telluric spec- 11..22••110044
trum of Livingston & Wallace (1991)3. We ad- 11..11••110044 CAGIFSISST09
just the depths of the telluric features and create log(g)=3.5
log(g)=4.0
a new telluric spectrum, T(λ) = T0(λ)τ, where 11..00••110044 log(g)=4.5
log(g)=5.0
T (λ) is the Livingston & Wallace (1991) spec-
0 log(g)=5.5
trum, and τ is one of the parameters of our fit. 99..00••110033
Thevelocity-shifted,rotationallybroadenedbrown χ2
88..00••110033
dwarf model atmosphere is then multiplied by the
telluric spectrum, approximating the spectrum of
77..00••110033
PSO J318.5−22as it enters the telescope.
66..00••110033
• Instrumental Effects: We approximate the in-
strumental LSF as a gaussian and fit for the 55..00••110033
FWHM of the gaussian convolution kernel. We 11220000 11440000 11660000 11880000 22000000 22220000 22440000
BTSettl Model T (K)
convolve the brown dwarf model atmosphere with eff
telluric absorption by this gaussian kernel. We ac- Figure 1. AMOEBA’s bestfitχ2 usingBT-Settl models. Themin-
count for any changes in spectral shape between imum χ2 occurs for the CIFIST model with Teff=1650 K and
ourmodelandtheobservedspectrumbytakingthe log(g)=5.0. Ingeneral,theCIFISTmodelsprovidemarginallybet-
ratio of our observed spectrum of PSO J318.5−22 terfitsthantheAGSS09models.
Overall, the CIFIST models provide better fits than
to our model spectrum, fitting the smoothed ra-
the AGSS models (Figure 1). Regardless of the as-
tio with a 3rd order polynomial, multiplying our
sumed solar abundance, T , or log(g) of the atmo-
modelbythefit,andthenscalingourmodeltothe eff
sphericmodel,wefindthatAMOEBAconvergesonaradial
median of our observed spectrum.
velocity of -7.4 to -2.3 km s−1 . In contrast, the v sin(i)
In total, our forward model has nine free parameters: that AMOEBA finds varies significantly (0 to 80 km s−1)
theT andlog(g)oftheatmosphericmodel,thev and depending on the model used. We find that the fitted
eff r
v sin(i) of PSO J318.5−22, τ for the telluric spectrum, v sin(i) and resulting χ2 of the model fit are correlated.
theLSFFWHM,andthewavelengthsofthefirst,middle For atmospheric models with fits having higher χ2 val-
and last pixels. The forward model is compared to our ues, AMOEBAconvergesonhighervaluesofv sin(i). From
observed spectrum, and the parameters used to create this analysis,it is unknown if the higher χ2 values mean
the forward model are adjusted to achieve the best fit. the v sin(i) of PSO J318.5−22is genuinely low, or if for
atmospheric models that do not approximate the spec-
3.2. Parameter Optimization with AMOEBA trumofPSO J318.5−22ahigher v sin(i)smearsout the
lines and results in a better fit.
AMOEBA uses a downhill simplex method
Our AMOEBA fitting provides a useful first estimate of
(Nelder & Mead 1965) to find the minimum of a
the best fit parameters but lacks a straightforward way
multivariate function. We used IDL’s implementation
to determine their uncertainties. In addition, the corre-
of AMOEBA, which is based on Numerical Recipes in C
lation between χ2 and v sin(i) motivates a more sophis-
(Press et al. 2007). We run our AMOEBA optimization for
ticatedanalysistodetermineourbestfitparametersand
eachmodel atmosphere havingT = 900- 2500K and
eff
their associated uncertainties.
log(g)= 3.5-5.5in the CIFIST andAGSS grids. AMOEBA
does not conduct a thorough search of parameter space,
3.3. Parameter Optimization with MCMC and
so it is important to seed it with reasonable parameter
estimates. We initialize AMOEBA with v = 0 km s−1 DREAM(ZS)
r
and v sin(i) = 15 km s−1, typical of observed values of Tobetter determine the bestfit parametersofour for-
ultracooldwarfs(Blake et al.2010). We use the FWHM wardmodelaswellastheirmarginalizedposteriordistri-
of the LSF as determined from our arc lamp spectrum butions, we use a Markov Chain Monte Carlo (MCMC)
(§2) as a starting point. To get a starting point for approach. We create forward models in the manner de-
τ, we divide our observed telluric standard spectrum scribedabove but in addition allow for a continuous dis-
by an LSF-convolved telluric absorption spectrum and tributionofTeff andlog(g)by linearlyinterpolatingbe-
find the value of τ (0.7) that, by eye, results in a tween atmosphere models in the CIFIST grid. We em-
featureless spectrum (as expected for an A0 star from ploy the DREAM(ZS) algorithm of ter Braak & Vrugt
2.27–2.33µm). (2008), which involves an adaptive stepper, updating
We find that the atmospheric model giving the best model parameters based on chain histories. A brief de-
overall fit (minimum χ2), is the CIFIST model hav- scription of the algorithm follows.
ing T = 1650 K and log(g) = 5.0, in reasonable Three chains are run in parallel, and each chain is a
eff
agreement with the temperature (1400–1600 K) and history of accepted parameter vectors p. Current values
log(g) (4.0–4.5) of the atmospheric models which fit the of the 3 chain vectors are stored in the array X, and
low-resolution 0.8–2.5 µm spectrum of PSO J318.5−22 chainhistoriesarestoredinthe arrayZ. Tosimplify the
(Liu et al. 2013). The best fit parameters returned for notation,X[i]referstothen-dimensional,i-thparameter
this model are: FWHM of LSF=0.000169 µm, τ=0.868, vector currently stored in X (i.e., the i-th chain in X),
v sin(i)=11.6 km s−1, and v =-7.4 km s−1. and we adopt the same notation for the history array,
r
Z[i]. We initially seedeachchainwiththe parametersof
3 available for download at ftp://ftp.noao.edu/catalogs/ the best-fit model as determined by our AMOEBAanalysis
atmospheric_transmission/transdata_1_5_mic.gz (§3.2).
4 Allers et al.
Werun105iterations,which,takingintoaccountthree
1.6
chains and ten steps per interval, corresponds to 3×106
1.4 functionalevaluationsofthe model. Parameterdistribu-
tions and summary statistics are derived from the final
1.2
Fλ state of the history array Z. Since we initialize Z using
ed 1.0 random draws from the parameter support regions, the
aliz early values of Z are drawnfar from the equilibrium pa-
m 0.8
or rameter distribution and represent expectedly poor fits
N
0.6 to the data. These initial “burn-in” values are identi-
fied based on an evaluation of χ2 values, and they are
0.4
discarded before analysis of the chains. Formally, we di-
0.2 videtheχ2 vectorinto20equalintervals. Theboundary
0.4 betweennon-equilibriumandequilibriumintervalsis de-
als 0.2 terminedusingtheGeweke(1992)diagnostictoevaluate
du 0.0 the difference of means between a giveninterval and the
Resi−0.2 final interval.
In our earlier AMOEBA analysis, we found that the un-
−0.4
certainties in our measured spectrum were systemati-
2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34
Wavelength (µm) cally smaller than the residuals of the fit. Adding in
anadditional∼10%uncertaintybringstheresidualsand
Figure 2. OurobservedspectrumofPSOJ318.5−22(black)com- uncertainties into reasonable agreement. This discrep-
paredtoourtheforwardmodelwithourbestfitparameters(red).
ancy could be due to underestimated uncertainties in
The median residual of the fit is 0.079 (in normalized Fλ units),
whichislargerthanthemedianuncertainty(0.048)ofourobserved our observed spectrum and/or systematic uncertainties
spectrum. Thermsoftheresiduals(0.12)indicatessystematicun- in our telluric spectrum and the brown dwarf model at-
certaintiesof≈10%. mospheres. To account for the effect of these system-
atic uncertainties in the posterior distributions of our
At each iteration and for each chain X[i], two param-
MCMC analysis, we include a uniform 10% systematic
eter vectors Z[j] and Z[k] are selected at random and
uncertainty4 which is added in quadrature to the mea-
without replacement from Z. A trial parameter vector,
surement errors of our observed spectrum.
x, is then calculated by the difference,
Our spectrum of PSO J318.5−22 as well as the best
x[i]=X[i]+(1+e)γ(Z[j]−Z[k])+ǫ, (1) fit model is displayed in Figure 2. The best fit model
has T =1325+330 K and log(g)=3.7+1.1 dex. We de-
whereγisaconstantoforderunity,eisann-dimensional terminefefa best−fi1t2LSF FWHM of 0.00−001.61±0.00001µm,
vector of uniformly-distributed random numbers span-
in agreement with the LSF FWHM from our arc lamp
ning [−0.05,0.05], and ǫ is a vector of normally- spectrum (0.00016±0.00002 µm). The reduced χ2 for
distributed random numbers with zero mean and σ =
our best fit model is 1.24. Figure 3 shows the marginal-
10−6.
ized posterior distributions for v and v sin(i). We find
r
The trial vector is accepted or rejected using the v =−6.0+0.8 km s−1 and v sin(i)= 17.5+2.3 km s−1 for
standard Metropolis-Hastings likelihood ratio criterion r −1.1 −2.8
PSO J318.5−22.
(Metropolis et al. 1953; Hastings 1970). We assume
normally distributed uncertainties. Therefore, the log- 4. MEMBERSHIPINβ PICTORIS
likelihood of a parameter vector is given by ln(p) =
Based on its parallactic distance and proper motion,
C−χ2/2,where C is anormalizationconstantthatcan-
Liu et al. (2013) identified PSO J318.5−22 as a likely
cels out in the likelihood ratio, and χ2 is the usual chi-
β Pic member. The Bayesian analysis of Gagn´e et al.
squared statistic.
(2014) found a 99.7% probability that PSO J318.5−22
Every ten iterations (the thinning interval), the cur-
is a β Pic member and predicted a radial velocity
rent chain values X are appended to the history array of −6.4±1.7 km s−1. To determine the full, three-
Z. Note that once the chains are appended to Z, they
dimensional velocity and position of PSO J318.5−22,
lose identity, so that the difference vectors that deter-
we combine our v measurement with the updated
r
mine the step for any one chain depends on the history
parallax and proper motion from Liu et al. (2015,
of all three chains. This property allows any chain in X in preparation): π = 0′.′0450 ± 0′.′0017; µ cosδ =
α
to hop between modes in the posterior distributions of 0′.′1362 ± 0′.′0011 yr−1; µ = −0′.′1441 ± 0′.′0012 yr−1.
the parameters. To search for modes and allow their in- δ
Using the three-dimensional velocity and position of
clusion in the parameterdistribution, the algorithmsets
PSO J318.5−22, we recalculated membership probabili-
γ =1 every ten iterations.
tiesusingtheBANYAN-II webtool5 (Gagn´e et al.2014;
TheDREAM(ZS)algorithmalsoemploysamorecom-
Malo et al. 2013) and find that the probability of mem-
plicated ”snooker” updater that relies instead on three
bershipinβPicincreasesto99.98%. Thus,ourmeasured
draws from Z. ter Braak & Vrugt (2008) demonstrated
radial velocity is consistent with membership in β Pic.
thatthesnookerupdatercomplementsthedifferenceup-
We determine galactic XYZ position and UVW ve-
daterdescribedabove,arguablyallowingamoreefficient
search of parameter space than would be provided by
4 Because AMOEBA does not propagate uncertainties, includinga
difference steps alone. In our implementation, there is systematic 10% uncertainty reduces the χ2 of our AMOEBA fits,
a 10% chance of a given iteration using snooker rather butdoesnotaffectthebestfitparameters.
than difference updates. 5 http://www.astro.umontreal.ca/~gagne/banyanII.php
PSO J318.5-22is a β Pic member 5
20 25
%) 20
es ( 15
pl
m
a
S 15
o
arl
C 10
e
nt
o
M 10
of
n
o
cti 5
a
Fr 5
0 0
−11 −10 −9 −8 −7 −6 −5 −4 −3 −2 0 5 10 15 20 25 30
vr (km / s) vsin(i) (km / s)
Figure 3. Histogramsofthemarginalizedposteriordistributionsforvr andv sin(i)fromourMCMCanalysis. Thedashedlinesindicate
themedianofeachdistribution. Thedottedlinesindicatethe68%confidence limits(1-σ)centeredonthemedian.
Table 1
GalacticPositionsandVelocities
Name X Y Z U V W
··· pc pc pc kms−1 kms−1 kms−1
β PicGroupa 8.4±31.9 -5.0±15.4 -15.0±8.0 -10.9±1.5 -16.0±1.4 -9.2±1.8
PSOJ318.5−22 15.2±0.6 7.2±0.3 -14.6±0.6 -10.4±0.7 -16.4±0.6 -9.8±0.8
Offset 6.7±31.8 12.2±15.4 0.4±8.0 0.5±1.6 -0.4±1.7 -0.6±2.0
a FromMamajek&Bell(2014). TheuncertaintiesinUVW includebothuncertaintiesinthe
meanUVW forthegroupaswellasthe1σdispersionofthegroupmembers.
locitiesforPSOJ318.5−22usingitsparallaxandproper the β Pic group.
motions and our radial velocity measurement. We use a
5. THEPHYSICALPROPERTIESOFPSOJ318.5−22
MonteCarloapproachwith10000iterationstodetermine
uncertaintiesinourcalculatedparameters(UVWXYZ) Liu et al.(2013)estimatedthemassofPSOJ318.5−22
based on the uncertainties in our measured quantities. based on an age of 12+8 Myr for β Pic. Recently, re-
−4
Table 1 includes the XYZ positions and UVW ve- vised age estimates indicate that the group is older.
locities for both PSO J318.5−22 and the β Pic group Mamajek & Bell (2014) determined an age of 23 ±
(Mamajek & Bell 2014). As shown in Table 1, the dif- 3 Myr by combining isochronal ages (Mamajek & Bell
ference in the galactic position and velocity between 2014; Malo et al. 2014) and lithium depletion boundary
PSO J318.5−22 and the β Pic group are well within ages (Binks & Jeffries 2014; Malo et al. 2014). For a
the uncertainties. The total velocity of PSO J318.5−22 uniformly-distributedage of23±3 Myr anda normally-
is 0.8 ± 1.8 km s−1 from the mean velocity of the distributed luminosity of log(Lbol/L⊙) = −4.52 ±
β Pic group. The reduced χ2 for membership based on 0.04dex,wedeterminethemass,T ,radiusandlog(g)
eff
UVWXYZ and associated uncertainties (Table 1) for of PSO J318.5−22using model isochrones (Table 2). In
PSO J318.5−22 and the β Pic group is a mere 0.15. general, the parameters determined from all four sets
For comparison, we calculated the velocity offset from of models agree quite well. The cloud-free evolutionary
the mean velocity of the β Pic group for each of the models (Ames-COND and Saumon & Marley cloudless)
stars listed as “bona fide” β Pic moving group members yield slightly lower masses and smaller radii than mod-
in Gagn´e et al. (2014)6. We find that PSO J318.5−22 els with clouds (Ames-DUSTY and Saumon & Marley
is a closer match to the mean kinematics of the β Pic f = 2). PSO J318.5−22 has incredibly red J − K
sed
group than 46 out of 50 of the Gagn´e et al. ”bona colors, indicating a very cloudy atmosphere (Liu et al.
fide” members. Figure 4 shows the galactic position 2013). The Ames-DUSTY models are not recommended
and velocities of PSO J318.5−22 compared to young for use with objects having T cooler than 1700 K
eff
moving groups from Torres et al. (2008). Regardless of (Allard et al. 2001). Thus, we adopt the physical prop-
which list of known members is used for comparison erties as determined by the Saumon & Marley f =
sed
(Mamajek & Bell 2014; Gagn´e et al. 2014; Torres et al. 2 models: mass=8.3 ± 0.5 M , T =1127+24 K,
Jup eff −26
2008), PSO J318.5−22is determined to be a member of radius=1.464+0.009 R , and log(g)=4.01±0.03 dex.
−0.008 Jup
The T determined by forward-modeling our spec-
eff
6 https://jgagneastro.wordpress.com/banyanii/ trum, 1325+330 K, is significantly higher than the T
−12 eff
6 Allers et al.
0 0
−10
PSO 318.5−22 −5 −5
V (km/s) −15 TWA β Pic W (km/s)−10 W (km/s)−10
−20
Tuc−Hor −15 −15
−25 Columba Carina
AB Dor −20 −20
−20 −15 −10 −5 0 −20 −15 −10 −5 0 −25 −20 −15 −10
U (km/s) U (km/s) V (km/s)
100 100 100
50 50 50
c) c) c)
p 0 p 0 p 0
Y ( Z ( Z (
−50 −50 −50
−100 −100 −100
−100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100
X (pc) X (pc) Y (pc)
Figure 4. ComparisonofthegalacticpositionandvelocityofPSOJ318.5−22tomembersofknownyoungmovinggroupsfromTorresetal.
(2008). Ellipses represent the rms formembers of the group. The uncertainties in UVW and XYZ forPSO J318.5−22 are smallerthan
theplottedredcircle.
Table 2
PhysicalPropertiesfromEvolutionaryModels
EvolutionaryModel Mass Teff Radius log(g)
Name Ref MJup K RJup dex
PSOJ318.5−22(log(Lbol/L⊙)=−4.52±0.04dex5;age=23±3Myr7):
AMES-COND 1 7.9±0.4 1176+26 1.358±0.010 4.03±0.03
−25
AMES-Dusty 4 8.7±0.4 1154+25 1.417±0.007 4.00±0.02
−27
Saumon&Marleycloudless 8 7.9±0.4 1164+26 1.373±0.010 4.04±0.03
−27
Saumon&Marleyfsed=2 8 8.3±0.5 1127+−2246 1.464±0.010 4.01±0.03
β Picb(log(Lbol/L⊙)=−3.86±0.04dex6;age=23±3Myr7):
Saumon&Marleyfsed=2 8 12.8±0.2 1583+−3303 1.576±0.010 4.135±0.003
2M1207b(log(Lbol/L⊙)=−4.68±0.05dex2;age=10±3Myr3):
Saumon&Marleyfsed=2 8 4.5±0.5 1006+−2246 1.515+−00..001163 3.71±0.06
References. — (1) Baraffeetal. (2003); (2) Barmanetal. (2011); (3) Belletal. (2015);
(4) Chabrieretal. (2000); (5) Liuetal. (2013); (6) Malesetal. (2014); (7) Mamajek&Bell
(2014);(8)Saumon&Marley(2008)
inferredbyevolutionarymodels. Thisdiscrepancyissim- (2013). This can be attributed to the revised (older)
ilartothe resultfoundbyLiu et al.(2013)usingamuch age of the β Pic moving group. For comparison to
lower resolution spectrum spanning a larger wavelength PSO J318.5−22, we calculate the properties of β Pic b
range. This hints that atmospheric models over-predict and 2M1207b (Table 2) using the Saumon & Marley
T when fitting either the broad-band spectral mor- f = 2 evolutionary models and accounting for re-
eff sed
phology seen in low-resolution spectra or the depths of cent revisions to the ages of the β Pic and TW Hydra
spectral lines seen in high resolution spectra. moving groups. The mass of PSO J318.5−22 (8.3 ±
The mass we determine for PSO J318.5−22 is some- 0.5 M ) is intermediate to the two known directly-
Jup
whathigherthanthe6.5+1.3 M reportedbyLiu et al. imaged exoplanets around β Pic members, β Pic b and
−1.0 Jup
PSO J318.5-22is a β Pic member 7
Our constraints on its equatorial velocity (17.5–
36 km s−1) allow us to compare the rotation of
110000..00 PSO J318.5−22 to recent measurements of the rota-
tionofother planetary-massandsubstellarobjects. The
PSO 318.5−22 equatorial velocity of β Pic b, 25 km s−1(Snellen et al.
2014), is consistent with our constraint on the equa-
−1m s)1100..00 S J 2M1207βb Pic b ptoerriiaoldvoeflo2cMity12o0f7bPS(OZhoJu31e8t.5a−l.2220.15T)hies s1l0ig.7h+−ty10..28lohnoguerr
k than our upper limit on the period for PSO J318.5−22.
(
y Given 2M1207b’s lower mass and younger age (see §5),
ocit N it is expected to rotate more slowly than β Pic b
el and PSO J318.5−22. Indeed, the equatorial veloc-
V U
al ity of 2M1207b is 17.3±1.5 km s−1as calculated from
ri its rotational period and evolutionary-model inferred
o 11..00
at radius. The agreement in equatorial velocities for
u
Eq E 2M1207b, PSO J318.5−22 and β Pic b hints that
the angular momentum evolution of free-floating and
M gravitationally-bound planetary mass objects is simi-
lar. For comparison, we calculate the equatorial veloc-
00..11 ities for field brown dwarfs with measured periods in
11xx1100−−44 11xx1100−−33 11xx1100−−22 11xx1100−−11 11xx110000 11xx1100++11 11xx1100++22 Metchev et al. (2015) and with estimated masses and
Mass (M ) radii from Filippazzo et al. (2015). We find that field
Jup
brown dwarfs have a relatively broad range of equato-
rial velocities ∼6–80 km s−1. Additional rotation mea-
Figure 5. A variation on Figure 2 of Snellenetal. (2014) com- surements for planetary-mass objects are needed to de-
paringthe equatorial velocities ofplanets andbrowndwarfs. The
termine if the field brown dwarf spread in equatorial
red bar indicates our constraints on the equatorial velocity of
PSO J318.5−22. The blue data point shows the equatorial ve- velocity extends to lower masses. Figure 5 compares
locity(Snellenetal.2014)andestimatedmass(see§5)ofβPicb. the equatorial velocity of PSO J318.5−22 to that of
Thegreendatapointshowstheequatorialvelocityof2M1207bcal- β Pic b (Snellen et al. 2014), planets in our solar sys-
culated from its rotation period (Zhouetal. 2015) and estimated
radius (Table 2). The gray open circles indicate the equatorial tem7, and field brown brown dwarfs. Solar system plan-
velocities of field brown dwarfs calculated from period measure- ets have a log-log velocity-mass relationship. 2M1207b,
mentsinMetchevetal.(2015)andmassandradiusestimatesfrom β Pic b and PSO J318.5−22 are slower rotating than
Filippazzoetal. (2015). Solar system objects are plotted as the
would be expected from the extrapolation of the solar
firstletter oftheirname. MercuryandVenus areexcludeddueto
their extremelylow equatorial velocities. Thedotted lineshows a system velocity-mass relationship. This is likely due to
linearfittolog(mass)vs. log(velocity)forthesolarsystemplanets theiryoungages. Bythetime theyaretheageofourso-
plotted. larsystem,theequatorialvelocitiesof2M1207b,β Picb,
and PSO J318.5−22 should increase by a factor of ∼1.5
51 Eri b (∼2 M ; Macintosh et al. 2015). In addition,
Jup asthey contractto aradiusof∼1R , putting them in
PSO J318.5−22 is an excellent free-floating analog to Jup
good agreement with the velocity-mass relation seen for
β Pic b and 2M1207b, the only other planetary-mass
the solar system planets.
objects having constraints on their rotation.
6. CONSTRAININGTHEROTATIONANDINCLINATION 7. CONCLUSIONS
OFPSOJ318.5−22 Using forward modeling techniques, we have mea-
Ourmeasurementofv sin(i)=17.5+−22..38 km s−1 allows sured the radial velocity (−6.0+−01..81 km s−1) and v sin(i)
us to constrainthe equatorialvelocity and inclination of (17.5+2.3 km s−1) of PSO J318.5−22. Combining
−2.8
PSO J318.5−22. Biller et al. (2015) report the detec- our v with an updated parallax and proper motion
r
tionof JS-bandvariability,likely due to rotationalmod- of PSO J318.5−22, we determine its UVW veloci-
ulation of inhomogeneous cloud cover. Unfortunately, ties. We find that the galactic position and motion of
the measurements of Biller et al. (2015) do not cover a PSO J318.5−22 are consistent with membership in the
long enough time span to measure a full rotational pe- β Pic moving group. The luminosity ofPSO J318.5−22,
riod of PSO J318.5−22, but they constrain the period combined with recent age determinations of the β Pic
to ≥5 hours. Assuming a radius of PSO J318.5−22 moving group allow us to use evolutionary models to
of 1.464 RJup, a period of >5 hours corresponds to an estimate its mass, Teff, radius, and log(g). Using
equatorial velocity of <36 km s−1. Thus, our v sin(i) our v sin(i) measurement and recently published vari-
measurementincombinationwiththeBiller et al. result ability results, we determine that the inclination of
constrains the equatorial velocity to 17.5–36 km s−1and PSO J318.5−22 must be greater than 29◦ and the ro-
the inclination of PSO J318.5−22 to i ≥ 29◦. In addi- tational period is constrained to 5–10.2 hours. Our con-
tion, our v sin(i) measurement places an upper limit on straints on the equatorialvelocity of PSO J318.5−22in-
the rotational period of 10.2 hours. A period of 5–10.2 dicate that its rotation is consistent with an extrapo-
hours is slightly longer than the typical ∼3 hour peri- lation of the velocity-mass relationship of solar system
ods of L/T transitionfield browndwarfs (Radigan et al. planets.
2014), which is expected given that PSO J318.5−22 is
young and still in the process of contracting. 7 http://nssdc.gsfc.nasa.gov/planetary/factsheet/
8 Allers et al.
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National Science Foundation (United States), the Na-
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