A Combined Subaru/VLT/MMT 1--5 Micron Study of Planets Orbiting HR 8799: Implications for Atmospheric Properties, Masses, and Formation

1 MB·English

by  Thayne Currie

Draftversion January19,2011
PreprinttypesetusingLATEXstyleemulateapjv.6/22/04
A COMBINED SUBARU/VLT/MMT 1–5 µM STUDY OF PLANETS ORBITING HR 8799: IMPLICATIONS
FOR ATMOSPHERIC PROPERTIES,MASSES, AND FORMATION
Thayne Currie1, Adam Burrows2, Yoichi Itoh3, Soko Matsumura4, Misato Fukagawa5, Daniel Apai 6, Nikku
Madhusudhan2, Philip M. Hinz7, T. J. Rodigas7, Markus Kasper8, T-S. Pyo9, Satoshi Ogino3
Draft version January 19, 2011
ABSTRACT
1 We present new 1–1.25 µm (z and J band) Subaru/IRCS and 2 µm (K band) VLT/NaCo data for
1 HR 8799 and a rereduction of the 3–5 µm MMT/Clio data first presented by Hinz et al. (2010). Our
0 VLT/NaCo data yields a detection of a fourth planet at a projected separation of 15 AU – “HR
2 8799e”. We also report new, albeit weak detections of HR 8799b at 1.03 µm and 3.3∼µm. Empirical

n comparisons to field brown dwarfs show that at least HR 8799b and HR8799c, and possibly HR
a 8799d,have near-to-mid IR colors/magnitudessignificantly discrepant from the L/T dwarf sequence.
J Standard cloud deck atmosphere models appropriate for brown dwarfs provide only (marginally)

8 statisticallymeaningfulfitstoHR8799bandcforunphysicallysmallradii. Modelswiththickercloud
1 layers not present in brown dwarfs reproduce the planets’ SEDs far more accurately and without the
need for rescaling the planets’ radii. Our preliminary modeling suggests that HR 8799b has log(g) =

] 4–4.5,T =900K,whileHR8799c,d,and(byinference)ehavelog(g)=4–4.5,T =1000–1200K.
P eff eff
Combining results from planet evolution models and new dynamical stability limits implies that the
E
masses of HR 8799b, c, d, and e are 6–7 M , 7–10 M , 7–10 M and 7–10 M . ”Patchy” cloud
J J J J
.
h prescriptions may provide even better fits to the data and may lower the estimated surface gravities
p and masses. Finally, contrary to some recent claims, forming the HR 8799 planets by core accretion
- is still plausible, although such systems are likely rare.
o
Subject headings:
r
t
s
a
[ 1. INTRODUCTION Marois et al. (2011) argue that the planets most likely
havemassesatthe low endofthe rangeallowedby cool-
The HR 8799planetarysystemis the firstdirectly im-
2 ing models. With masses of 5–13 M , the HR 8799
aged multiplanetary system (Marois et al. 2008). Along J
v planets then bridge the gap b≈etween the solar system’s
with Fomalhaut and β Pic, it is also the only imaged
3 gas giants/Jupiter-mass planets detected by radial ve-
systemwithcompanionmass ratiosandseparationsrea-
7 locity surveys (e.g. Howard et al. 2010) and low-mass
sonably close to the giant planets in the Solar System
9
1 (Kalas et al. 2008; Lagrange et al. 2009, 2010)10. After browndwarfcompanionstonearbystarssuchasGJ758B
and PZ Tel (Thalmann et al. 2009; Currie et al. 2010;
. the initial detectionof HR8799bcd,one ormoreplanets
1 Biller et al. 2010).
were recovered in prior datasets (Lafreniere et al. 2009;
0 Recentstudiescomplicateourunderstandingofthere-
Fukagawa et al. 2009; Metchev et al. 2009). Recently,
1 lationshipbetweenbrowndwarfs,thegasgiantsdetected
Marois et al. (2011) imaged a fourth planet – HR 8799e
1 in RV surveys, and the HR 8799 planets. The planets’
– which we independently detected (see 2).
v: Mass estimates based on cooling m§odels yield 5– massesaresignificantlylargerthanmostplanetsdetected
i 11 M for HR 8799b and 7–13 M for the other by radial velocity and transit methods. Marois et al.
X J J
(2008)notedthattheplanetsappearslightlyredderthan
planets (Marois et al. 2008, 2011). Dynamical con-
r the distribution of H/H-K colors for old field brown
straints placed by HR 8799bcd imply that the com- s
a
dwarfs. The K-band spectrum of HR 8799b is not well
panions likely have masses below the deuterium-burning
matched by typical L and T-type brown dwarf spectra
limit (Spiegel et al. 2010) and are kept stable by
(Bowler et al. 2010).
resonant interactions (Fabrycky and Murray-Clay 2010;
Comparisons between the HR 8799 planet photom-
Moro-Martinet al. 2010). Including the fourth planet,
etry/spectroscopy and atmosphere models reveal ad-
1 NASA-GoddardSpaceFlightCenter ditional difficulties in understanding their properties
2 DepartmentofAstrophysicalSciences, PrincetonUniversity withinthetheoreticalframeworkofstandard,clouddeck
3 GraduateSchoolofScience,KobeUniversity models that track the field L/T dwarf sequence. In the
4 Department of Astronomy, University of Maryland-College
discovery paper, Marois et al. (2008) briefly mention a
Park
5 Department of Earth and Space Science, Graduate School of discrepancy between temperatures derived from atmo-
Science,OsakaUniversity sphere models and those estimated from more simple,
6 SpaceTelescopeScienceInstitute andpresumablymostaccurate,coolingmodelestimates.
7StewardObservatory,DepartmentofAstronomy,Universityof
More recently, Bowler et al. (2010) provide a detailed
Arizona
8 EuropeanSouthernObservatory comparison between the HR 8799b spectra and 1.1–4.1
9 NationalAstronomicalObservatoriesofJapan µm photometry and predictions from standard atmo-
10 Here, we consider 1RXJ1609.1-210524b discovered by sphere models. They show that the ‘best-fit’ tempera-
Lafreniereetal.(2008)tobeamorecomplicated caseas itsmass
tures derived from modeling are inconsistent with cool-
ratioandseparationarecontinuouswithbrowndwarfcompanions
(seeDiscussionSection) ing model estimates. They also explicitly show that the
2
implied radii for best-fit models are well below the 1.1– datafirstpresentedbyHinz et al.(2010)usingourreduc-
1.3 R range allowed by standard cooling models (e.g. tion pipline, which utilizes advanced image registration,
J
0.3–0.5 R ). PSF removal, speckle suppression, and flux calibration
J
To interpret these modeling difficulties, Bowler et al. routines (e.g. LOCI Lafreniere et al. 2007a) also used in
(2010) argue that a different atmospheric structure, Marois et al. (2008).
namely atmospheres with stronger cloud coverage, may Allofourdataweretakeninangulardifferentialimag-
better explain the HR 8799b SED. Since atmospheric ing mode (Marois et al. 2006), where the instrument
dust entrained in clouds absorbs more efficiently at rotator is adjusted to stay at a fixed angle with re-
shorter wavelengths,photometry for HR 8799bat wave- spect to the (changing) parallactic angle, resulting in
lengths shortwardof J bandwouldprovidea crucialtest the field of view rotating with time. Combined with the
of the planet’s level of cloud coverage(cf. Burrows et al. Marois et al.data,wethushavedataspanningninepho-
2006). The Bowler et al. (2010) study also found dif- tometric filters that is largely reduced self consistently.
ficulty in reconciling their model fitting of detections Table 1 summarize basic properties of our observations.
fromMarois et al.(2008)with3–5µmupperlimitsfrom
Hinz et al. (2010). More sensitive photometry at these 2.1.1. VLT/NaCo Ks band Data
wavelengths would then provide better modeling con-
HR 8799 was imaged with VLT/NaCo on six separate
straints.
nightsinOctober2009asapartofaseparatestudyofthe
In this study, we investigate the atmospheres and dy-
HR 8799 planets (P.I. Daniel Apai; Apai et al. 2011, in
namics of the HR 8799 planets using new observations
prep.). Oncepublicallyavailable,thescienceandcalibra-
obtained at the Subaru Telescope and VLT and a rere-
tion data were downloaded from the ESO VLT archive
duction of MMT data presented by Hinz et al. (2010).
forOctober8–11,nightsoverwhichthefieldrotationfor
Combined with photometry presented by Marois et al.
the HR 8799 data was > 30–45 degrees, resulting in a
(2008), our data yield nine photometric points spanning
small (r 0.22”) inner working angle.
1–5 µm for a detailed comparison to the properties of ∼
The data were taken with the 13.27 mas pixel scale,
field brown dwarfs. This wavelength range also provides
without coronographic masks, and in pupil tracking
asensitiveprobeoftheeffectsofsurfacegravity,temper-
mode allowing for angular differential imaging. All data
ature,(non)equilibriumchemistry,metallicity,andcloud
consistofcoadded0.345sexposurestotaling 43sapiece
coverage. ∼
andarestoredinthestandardNaCodatacubeformat. In
We compare the planets’ SEDs to atmosphere mod-
this paper, we focus specifically on the October 8 data,
els exploring a phase space defined by these effects. By
which had the highest quality and greatest amount of
quantifyingthemodelfits,wedeterminetherangeofpa-
field rotation. Apai et al. (2011, in prep.) will later
rameterspacethatfailstocharacterizetheplanets’SEDs
present a larger study combining all October 2009 data
and identify the subset of models that more accurately
and Fall 2010 data.
reproducethedataandmaybetterrepresenttheiratmo-
spheres’ physical properties. These results will then be
2.1.2. Subaru/IRCS z(Y) and J band data
used to more thorougly and accurately probe the plan-
ets’atmosphericproperties ina companionpaper(Mad- HR 8799 was targeted for direct imaging on August
husudhan et al. 2011,in prep.). 15, 2009 with the Subaru Telescope using the Infrared
Our study is structured as follows. 2 describes our CameraandSpectrograph(IRCS;Tokunaga et al.1998)
observations, image processing, and det§ections for each and AO-188 adaptive optics system in natural guide
dataset. The first part of 3 compares the HR 8799 star mode. The data were taken in the Mauna Kea
planet photometry to the L/§T dwarf sequence and the J band filter ( 1.25 µm) and the z filter centered on
∼
IR properties of other very low-mass objects (M < 25 1.033 µm, analogous to the better-known Y band fil-
M ). The rest of 3 presents preliminary comparisons ter (e.g. Hillenbrand et al. 2002)11 During our observa-
J
between the HR 87§99 planet SEDs and planetary atmo- tions, conditions were photometric with fair natural see-
sphere models. 4 describes simple dynamical modeling ing ( 0.65–0.75”). AO-188 yielded a corrected image
ofthe systemto§identify the rangeof massesfor dynam- with∼FWHM(PSF) 0.06” in z and 0.064” in J. For all
∼
ically stable orbits. 5 summarizes our results, discusses observations,thenativepixelscaleis20.57mas/pixel;we
our work within the§context of previous studies of HR used the 0.8” diameter, non-transmissive coronographic
mask to block most of the primary starlight.
8799 and planet imaging in general, discusses how our
The z data were taken using 30 second exposures con-
results fit within the contextof planet evolutionmodels,
sistingof6coaddedframestoavoidsaturationatsepara-
and comments on the plausible formation mechanism(s)
tionscorrespondingtoHR8799bcdforatotalintegration
for the planets.
timeof4500s. TheJbanddataconsistof25secondcoad-
2. DATA ded exposures for a total integration time of 1080s. The
2.1. Observations zdatawereobservedthroughtransityieldingatotalfield
rotationof172degrees. The J dataweretakenaboutan
Our study combines data from three facilities –
VLT/NaCo, Subaru/IRCS, and MMT/Clio – at six
11 The zeropoint wavelength for the z filter listed on the IRCS
broadband filters centered on 1.03 µm to 4.8 µm. The
webpageis1.033µmwithawidthof0.073µm. TheY-bandfilters
VLT data are the most sensitive and were obtained to forcomparablecamerasareslightlywiderbutotherwisequitesim-
place limits on the presence of other candidate planets ilar: filters for Keck/NIRC (there called ”Z”), UKIRT/WFCAM
in the system. The Subaru data at 1.03–1.25 µm were andGemini/NIRI have zeropoint wavelengths of 1.032, 1.031 and
1.02 µm and widths of 0.156, 0.1 and 0.1 µm, respectively. The
takento probe the effect of clouds onthe planets’ atmo-
IRCSzfiltershouldnotbeconfusedwiththeSloanz’filter,which
spheres. Finally, we rereduced the 3–5 µm MMT/Clio coversshorterwavelengths.
3
houraftertransitresultinginverypoorfieldrotation( Further data reduction follows the ADI/LOCI reduc-
∼
6.4 degrees). tionproceduredescribedbyLafreniere et al.(2007a)and
Marois et al. (2008). We first subtract out the time-
2.1.3. MMT/Clio 3–5 µm Data independentcomponentofthestellarPSF,exploringtwo
methods. Inthefirstmethod,wemediancombineallim-
MMT/Clio observations were previously described by
agesforareferencePSFwhichwesubtractfromeachim-
Hinz et al.(2010). Briefly,HR8799wasimagedinthree
age, the simple ADI method used by Hinz et al. (2010).
separate observing runs – November 21, 2008, January
In the second method, we construct a two-dimensional
10, 2009, and September 12, 2009 – at the L’ (3.8 µm)
radial profile for each image and subtract it to remove
andBarrM(4.8µm)andashorterwavelengthfiltercen-
the smooth seeing halo.
teredon3.3µmmethaneabsorptionfeatureandextend-
Next, we perform the LOCI speckle suppression algo-
ingfrom3.12µmto3.53µm. WefocusontheNovember
rithmonthe residualimages,derotatethe processedim-
2008andSeptember2009runs,whichhadsufficientfield
agesandmediancombinethemfor afinalscience image.
rotationfor angulardifferential imaging. The pixel scale
We compared reductions for a range of LOCI input pa-
for all Clio data is 48.57 mas/pixel.
rameters – dr, N , Na, and geom (see Lafreniere et al.
The[3.3],L’,andMdatawereimagedfor6780s,5690s, δ
2007a, for definitions) – to identify the set that max-
and9600s: thetotalfieldrotationfordatainthesethree
imized the signal-to-noise of the planets, using the set
filters was 125.3 degrees, 72 degrees, and 31.8 degrees.
recommended by Lafreniere et al. (2007a) as a starting
While observing conditions for the L’ and M data were
point. Ourpipeline alsoproducesthe simple ADI reduc-
clear, the [3.3] micron data were taken through variable
tionasabyproduct,usefulforaseparate,sensitiveiden-
seeing in two sets between which the AO system failed
tification of HR 8799b, whose detection in some filters
to yield an acceptable correction.
(e.g. [3.3], M) may be more severely limited by photon
noise than by speckle noise.
2.2. Image Processing/Data Reduction
2.2.1. Basic Image Processing and Image Registration 2.3. Planet Detections and Astrometry
To identify detected planets in our images, we com-
For our Subaru/IRCS and VLT/NaCo data, we first
pute the standard deviation and signal-to-noise ratio
performed standard dark subtraction, flat fielding, and
of pixel values in concentric annuli (Currie et al. 2010;
badpixelmasking. WhiletheNaCodatafollowedafour-
Thalmann et al. 2009). As a check on our results, we
point dither pattern which should wash out image dis-
compare our astrometry for candidate detections in a
tortion errors, the IRCS data were not dithered. Thus,
given filter with that obtained by us in other filters and
each IRCS frame was corrected for image distortion us-
fromMarois et al.(2008,2011) during the Fall 2008and
ing polynomial fits, resulting in a revised pixel scale of
2009 epochs. We claim a detection of a planet indepen-
20.53 mas/pixel.
dent of other datasets if SNR > 5. For SNR = 3–5, the
For the MMT/Clio data we then performed sky sub-
centroid of the candidate planet detection must be the
traction. We constructed Clio sky frames from median-
same as that reported for the planet data where SNR
combinedimagesobtainedforeachnodpositionandsub-
> 5 within astrometric errors (typically 0.5 pixels). We
tractedtoremovetheskybackground. Finalpixelvalues
centroid the planet using the IDL functions gcntrd.pro
for each VLT/NaCo image were nominally constructed
and cntrd.pro and adopt a minimum astrometric uncer-
from the average pixel value drawn from each frame in
taintyof 0.5pixels to accountfor image registrationand
the datacube. For regions within 1” of estimated stellar
centroiding/orientationerrors. The rightmostcolumn of
centroid, we determined the average pixel value after it-
Table 1 summarizes our planet detections and Table 2
erativelyclipping5σoutliers. Foralldatasets,badpixels
lists their astrometry.
were identified as outliers within a moving-box median
filter, flagged, and interpolated over.
2.3.1. VLT/NaCo Detections
Our image registration procedure closely follows that
Figure 1 shows our reduced VLT/NaCo K band im-
ofLafreniere et al.(2007b)andMarois et al.(2008). We s
age. HR 8799 b and c are detected at better than 25
first copied each image into a larger blank one, coarsely
σ, while HR 8799d is detected at 10 σ. The planets are
registeringthemusingaprioriknowledgeaboutthecen-
also free of deep, negative flux troughs at the same sep-
terofthecoronographicmask(forIRCS)oragaussianfit
arationbut slightly different position angles that results
to a convolved version of the image using the IDL func-
fromLOCIbeingappliedtodatasetswithpoorfieldrota-
tiongcntrd.pro. Forpreciseimageregistration,wecenter
tionorthosewheremostexposuresaretakenwellbefore
one image using a 2D cross correlation function relating
or well after transit (e.g. Marois et al. 2010).
it to a 180degree rotationofitself. We then identify the
Additionally, our data show a detection of an another
fractional pixel offsets between the reference image and
point source located interior to and in the same quad-
subsequent images yielding the highest correlation. The
rantas HR 8799dconsistentwith a fourth planet – ”HR
regionofinterestusedtoregisterIRCSimagesisfocused
8799e”. Recently,Marois et al.(2011)announcedamul-
on diffracted light from the secondary spider. For the
tiepoch detection of HR 8799e in K-band and L’-band
Clio and NaCo images we used the non-saturated por-
using Keck/NIRC2. Their detection significance in K-
tions of the stellar PSF, since the diffracted light from
band using Keck/NIRC2 is slightly better than ours (
the spider is highly suppressed.
∼
5 σ vs. our 4 σ). Our photometry using methods de-
∼
scribedin 2.4yieldsanabsolutemagnitudeofm(K )=
2.2.2. Localized Combination of Images (LOCI) Speckle § s
12.89 0.26, consistent with Marois et al.’s estimate of
Supression Processing ±
12.93 0.22.
±
4
Figure 2 comparesour astrometry. We measurea cen- 2.4. Photometry for Detections and Upper Limits for
troid position of [E,N] = [-0.306” 0.007”, -0.217” Non-Detections
± ±
0.007”],implyingaprojectedseparationof14.8AU 0.4
± Photometry for each dataset was performed with
AU.TheaverageoftheAugustandNovember2009posi-
IDLPHOT with the aperture radius set to the
tions from Marois et al. (2011) is [-0.304,-0.203]with an
0.5 FWHM . In all exposures, the stellar PSF
image
intrinsic uncertainty 0.01”. Our position is then con- ×
core is either saturated or obscured. For initial pho-
∼
sistentwiththeirstowithin1.4σ. Ourimpliedprojected
tometric calibration, we obtained observations of the
physical separation is consistent with Marois et al.’s es-
stellar primary viewed through a neutral density filter
timates from multiepoch data: 14.5 AU 0.5 AU.
(MMT/Clio,VLT/NaCo)orobservedstandardstarsim-
±
mediately prior to and after our science exposures (Sub-
2.3.2. Subaru/IRCS Detections aru/IRCS).
Faint companions to stars observed in ADI and pro-
Figure3showreducedimagesatJandzobtainedwith cessedwithLOCI loseflux due to fieldrotationandself-
IRCS.Inspiteofpoorfieldrotationseverelylimitingthe subtraction. To further calibrate our photometry, we
performanceoftheADI/LOCIprocessingandprecluding introduceandmeasurethe flux forfaintpointsourcesat
detectability of objects within 1”, we clearly detect randompositionanglesoverseparationsencompassingto
∼
the b planet in our J band data at a 10 σ significance theHR8799planets(0.25”–2”)ineachregisteredframe,
∼
(top panels). In spite of good seeing conditions, good rerun our ADI/LOCI pipeline, compute the attenuated
field rotation, and a 70-minute integration time, we fail flux in the final, processed images, and correct for this
to detect any of the planets at a > 5 σ significance in z attenuation. Figure 7 illustrates this flux loss, compar-
band(bottompanels). Ourreducedimagerevealsaweak ing the input and output flux for fake points sources for
detection of HR 8799b with SNR 3.7 (bottom-right our MMT/Clio L’ data. While images processed using
∼
panel)andacentroidwithin0.25pixelsofitscentroidin a simple ADI reduction lose 20% of their flux, self
the J-band data obtained one hour later with the same subtraction is stronger with LO∼CI, especially at separa-
instrument. However, we do not detect HR 8799c or tions less than 0.75”. The attenuation curves obtained
d in our z data. To verify that our low signal-to-noise fordata inother filters donotdiffer qualitatively: LOCI
detection of HR 8799b and nondetections for the other always attenuates more flux than a simple ADI reduc-
planetsdonotresultfromerrorsinderotationorajump tionandattenuationissignificantlymoresevereatsmall
in parallactic angle near transit12, we introduced fake separations.
planets into each image with a flux equal to 10 times To place limits on our nondetections, we compute
∼
the local noise of the final image, reran our reduction 3σ upper limits where we correct our nominal sensitiv-
pipeline separately for frames before and after transit, ity limits for point source self-subtraction inherent in
and recoveredtheir detections. ADI/LOCI. The noise is defined in concentric annuli as
before,sinceinmostcases(forHR8799candd)radially-
dependentspecklenoisedominatesoverradiallyindepen-
2.3.3. MMT/Clio Detections
dent photon noise. Despite using LOCI, our detection
Figures4,5,and6showreducedimagesobtainedwith upper limit at 3.3 µm for HR 8799d is brighter than
MMT/Clio in the L’, [3.3], and M filters. In the L’ fil- the magnitude listed by Hinz et al. (2010). Moreover,
ter, we detect HR 8799bcd with signal-to-noise higher our upper limits for HR 8799bcd at M are consistently
thanthatreportedbyHinz et al.(2010)andcomparable brighter than those reported by Hinz et al..
to that obtained in shorter Keck/NIRC2 exposures by In both cases, the disagreement is likely explainable
Marois et al. (2008). In the [3.3] filter, we detect the c by our correctionfor point source self subtraction in de-
planet at SNR > 5. We marginally detect the b planet riving upper limits from the standard deviation of pixel
at SNR 3.8. Hinz et al. (2010) formally report a non- values. Hinz et al.constructareferencePSFbymedian-
detection∼for b at [3.3] as they adopt a 3σ threshold for combining all frames and then subtract this reference
detections, though they identify a cluster of pixels 2.8 PSF from each image. For the 3.3 µm data, our reduc-
σ above the background consistent with b and rou∼ghly tion pipeline predicts that this processing should atten-
coincident with our MMT/Clio and VLT/NaCo detec- uate about half of the point source flux at HR 8799d’s
tions. position13. For the M band data,field rotationis poorer
Conversely, we do not detect HR 8799d in [3.3], while and thus self subtraction with this reduction procedure
Hinz et al. (2010) report a low-significance detection. is severe,reachingover75%at the position ofHR 8799d
This disagreement is surprising since LOCI greatly im- as nearly half the frames are obtained 3 hours after
∼
provesthe planetsensitivityatsmallseparationssuchas transit and thus at essentially one position angle. Thus,
that for the d planet (Lafreniere et al. 2007a). Further- the gain in sensitivity due to LOCI is reduced by self
more, there is a 40mas offset between the reported HR subtraction, resulting in brighter 3 σ upper limits.
8799d centroid from Hinz et al. and that from our 10 σ
3. PHOTOMETRICANALYSIS:CONSTRAININGTHE
VLT/NaCo detection obtained three weeks later. While ATMOSPHERICPROPERTIESOFTHEHR8799
theirdetectionislikelyinsteadresidualspecklenoise,our PLANETS
qualitative conclusionthat HR 8799dis veryfaint at 3.3 Combining our data with that from Marois et al.
µm is consistent with theirs. As with Hinz et al. (2010), (2008) yields planet flux measurements at nine separate
we do not detect any of the planets at M band.
13 Whilethetotalfieldrotationislarge,∼127degrees,thevast
12 For an example of this phenomenon, see majority of the frames were taken over a time interval with only
http://www2.keck.hawaii.edu/inst/nirc2/vertAngJump.html 30degreesoffieldrotation.
5
wavelengths from 1 to 5 µm. In this section, we use this L dwarf sequence between J/[J-H,K ] = 11/[0.6,1.2]and
s
richmultiwavelengthsamplingofHR8799’splanetSEDs 15/[1.2,2]towards fainter magnitudes and redder colors.
to provide an empirical comparison with other cool, HR 8799d’sposition coincides with that of HD 203030b,
substellar-mass objects and simple atmospheric model- while HR 8799b is located closest to 2M 1207b. The
ing constraints on the planets’ properties. H/Y-H color-magnitude diagram shows that HR 8799c
alsoislikelyred/underluminous;HR8799bis2.5magni-
3.1. Near-to-Mid IR Colors of the HR 8799 Planets tudes too red in Y-H for its H-band magnitude, indicat-
ing that it is underluminous comparedto the L/T dwarf
3.1.1. Methodology
sequence at both Y and J.
To compare the near-to-mid IR properties of the HR
Figure8overplotslociofstandardBurrows et al.mod-
8799planetswiththoseforothercool,substellarobjects,
els for parameters covering a range expected for low-
we primarily use the sample of L/T dwarfs compiled by
mass, cool brown dwarfs – T = 800-1800K, log(g) =
eff
Leggett et al. (2010). The L/T dwarf sequence defined 4–5– and two metallicities (solarand 3 solar)14. With
by the Leggett et al. sample allows us to determine how ×
the exception of some L/T dwarf transition objects, the
the HR 8799 planet SEDs deviate from those for brown
dispersion in color-magnitude positions for L/T dwarfs
dwarfs of similar temperatures. To explore how the HR
is well reproduced by model atmosphere loci. This in-
8799planetSEDscomparetothoseforotherplanet-mass
dicates that L/T dwarf atmospheres can be explained
objects and very low-mass brown dwarfs with T =
eff within the phase space encompassed by the models’ as-
800-1800K, we include 2M 1207b (5 M ), 1RXJ1609.1-
J sumedcloudstructureandrangeintemperature,gravity,
210524 (9 M ), AB Pic (13.5 M ), and HD 203030b
J J and metallicity (Burrows et al. 2006).
( 25 M ) (Chauvin et al. 2004; Lafreniere et al. 2010;
∼ J The HR 8799 planets, especially HR 8799b,are differ-
Chauvin et al. 2005; Metchev and Hillenbrand 2006).
ent. They consistently lie below the region enclosed by
Table 4 lists photometry for these objects.
thestandardmodelatmosphereloci,indicatingthattheir
Weusecolor-magnitudediagramsconstructedfromthe
near-IRluminositiesareweakercomparedtoluminosities
Y, J, H, K , and L’ filters to determine whether the HR
s expectediftheircloudstructurewerewellrepresentedby
8799 planets are similar to or under/overluminous com-
the models. HR 8799bin particularprobes a completely
paredtothe LeggettL/Tdwarfsequence. Forsimplicity
differentrangeofparameterspace,lying0.75magnitudes
and because there is no published response function for
or more redder than any standard atmosphere predic-
the IRCS z band filter, we treat the IRCS z-band mag-
tion regardless of temperature. Thus, Figure 8 suggests
nitudes/upper limits forthe HR8799planets as synony-
a strong contrast between the atmospheric properties of
mous with its Y-band magnitude.
L/T dwarfs and the HR 8799 planets.
To provide a physical point of reference for the L/T
To summarize, all three HR 8799 planets – especially
dwarf sequence and the HR 8799 color-magnitude po-
HR 8799 b – have near-IR colors that cannot be easily
sitions, we overplot loci for standard, chemical equi-
understood within the field L/T dwarf sequence. They
librium atmosphere models from Burrows et al. (2006).
areconsistentlyredandunderluminousatYandJ,indi-
We specifically choose the Model E case, which assumes
catingthatthe1–1.25µmportionoftheirSEDsaresup-
that the clouds are confined to a thin layer, where the
pressedinflux. TheHR8799planetsalsoliewelloutside
thickness of the flat part of the cloud encompasses the
thelociofstandardatmospheremodelsusedtointerpret
condensation points of different species with different
the physical properties of L/T dwarfs. Thus, the HR
temperature-pressureinterceptpoints. Aboveandbelow
8799planetatmospheresarenotsimply’scaleddown’(in
theflatportion,thecloudshapefunctiondecaystothe-6
mass) versions of the atmospheres of field brown dwarfs
and -10 power. Thus, above and below the flat portion,
defining the L/T dwarf sequence.
thecloudshavescaleheights 1/7thand1/11ththatof
∼ On the other hand, the planets’ atmospheres show
the gas. See Burrows et al. (2006) for more details.
strong similarity to those for planetary-mass/low-mass
brown dwarf companions to nearby stars. Specifically,
3.1.2. Results
HR 8799 c and d have similar near-IR colors to HD
Figure8showsourcolorcomparisons. Atleastthreeof 203030b,whileHR8799bconsistentlyshowsnear-IRcol-
theHR8799planetshaveK /K -L’positions(upper-left ors similar to 2M 1207b. The planetary-mass compan-
s s
panel)roughlyconsistentwiththosefortheLeggettL/T ions 1RXJ1609.1-210524b and AB Pic b are also red-
dwarf sequence and with 2M 1207b. HR 8799cde have der in near-IR colors compared to the L/T dwarf se-
positions overlapping with objects near the L/T dwarf quence but not underluminous. Within the narrow con-
boundary; HR 8799b has a similar K -L’ color but is text of our analysis, planetary-mass companions in gen-
s
underluminous comparedto the three other companions eral might not follow the L/T dwarf sequence.
and 2M 1207b by a factor of two. It is unclear how its
position compares to those for field L/T dwarfs because 3.2. Fiducial Model Atmosphere Fits to the HR 8799
the sequence is poorly sampled at HR 8799b’s Ks band Planet SEDs
magnitude.
Our color comparisons motivate a further investiga-
The other three panels of Figure 8 clearly show that
tion of the HR 8799 planet SEDs to better understand
HR 8799c, d, and especially b have near-IR colors that
the source of the differences between their near-IR col-
departfromthe L/Tdwarfsequence. InJ/J-Hand J/J-
ors and those for field L/T dwarfs. To further explore
K ,theL/Tdwarfsequenceturnstowardsbluecolorsby
s
up to 1.5 mag starting at the L/T transition. While HR
14 Weincludethe3×solarmodelsbecausetheyproduceredder
8799c’s position is roughly coincident with T0 dwarfs,
near-IR colors and the HR 8799 planets are red in the near-IR
HR 8799b and d follow an extension of the slope of the comparedtotheL/Tdwarfsequence.
6
the physical properties of the HR 8799 planets we com- We weight each datapoint equally. To account for vari-
pare their photometry to atmospheric models. Because ability in emission and absolute calibration uncertain-
the color-magnitude comparisonsindicate that standard ties, we set a 0.1 mag floor to σ for each datapoint (see
model atmospheres provide poor fits to the planet data, Robitaille et al. 2007). Because of incomplete line lists
we introduce a new set of models to explore additional nearthe1.6µmCH band,wedonotcomparethemod-
4
phase space not covered by the standard models, specif- els to data at the CH l filter (see Bowler et al. 2010;
4
ically a different cloud structure: Saumon et al. 2007; Leggett et al. 2007). However, we
confirmed that this choice has no consequential bearing
The Burrows et al. (2006) Model A Thick
• on our results.
Cloud Layer prescription – Like the Model
The z, [3.3], and M photometry include many non-
E case, this model defines a cloud base at the
detections. We quantitatively incorporate nondetections
hightemperatureinterceptionpointwiththeshape
in the following way. For model predictions consistent
function at higher temperatures/pressures decay-
with the 3σ upper limits estimated for each nondetec-
ing to the -10 power. However, the cloud den-
tion, we treat the model as perfectly consistent with the
sity tracks the gas density at lower tempera-
data and do not penalize the χ2 value. For model pre-
tures/pressures (s = 0 in their terminology).
1 dictionsinconsistentwiththe 3σ upper limits,wedonot
Thus,cloudsinthiscasearefarmoreextendedhigh
automatically discard the model. Rather, we penalize
in the atmosphere than in the standard Model E
the χ2 value by determining the flux ratio between the
case.
model prediction and the 3 σ upper limit. Specificially,
AsnotedinBurrows et al.(2006),thesemodelsare a model prediction 2 and 4 times brighter than the 3 σ
qualitatively similar to the AMES-DUSTY mod- upper limit will be contribute 12 (3 4) and 48 (3 16)
els (Allard et al. 2001). However, they are bluer to the final χ2 value, respectively. × ×
and brighter than AMES-DUSTY in the near IR We fit atmosphere models in two cases. First, to pro-
because Allard et al. (2001) adopts the interstellar videastraightforwardcomparisonbetweenourdataand
medium particle size distribution. The Model A the luminosity and colors predicted from atmosphere
case fails to reproduce the L/T dwarf sequence as models we keep the radii fixed to the Burrows et al.
it is consistently too red and underluminous in IR (1997)dwarfradii. Second,wevarythe radiusandiden-
color-magnitudediagrams(Burrows et al.2006). If tify the scaling factor, C = (R /R ), that
k scaled nominal
the HR 8799planets have thicker clouds than L/T minimizes χ2 for a particular model:
type brown dwarfs, these models – or some hybrid
n
between them and the ”E” models – should repro- f F /σ2
duce the planets’ SEDs far better than the Model P data,i model,i data,i
C2 = i=0 . (2)
”E” case alone. k n
F2 /σ2
P model,i data,i
Changingthecloudprescriptionradicallyalterstheen- i=0
tire shape of the SED (Figure 9). The K and L’ band
We nominally only allow the radius to vary by 10%
fluxes are similar. However, the Model A/thick cloud ±
fromtheassumedBurrows et al.(1997)valuestoencom-
prescription is underluminous over the Y and J pass-
passtherangeofradiifor5–20M objectsat30–300Myr
bands by an order of magnitude, underluminous at 1.65 J
( 1.1–1.3 R ).
µm by a factor of two but overluminous in the 3.3 µm ∼ J
We determine which models are formally consistent
regioncoveringthetroughproducedbymethaneabsorp-
with the data by comparing the resulting χ2 value to
tion in the Model E cloud prescription. Overall, the
that identifying the 3 and 5 σ confidence limits. For the
ModelA SED is muchflatter from1 to 4 µm. Addition-
first case, where the planet radius is fixed, the appropri-
ally, the Model A prescription washes out the methane
ate χ2 limits are 21.85 and 41.80 for 8 datapoints and
absorption feature at 1.65 µm used to identify the L/T
seven degrees of freedom. For the second case – a vari-
dwarf transition (see also discussion in Burrows et al.
able planet radius – the limits are 20.1 and 39.4 for 8
2006).
datapoints and 6 degrees of freedom.
Boththestandardmodelsandthickcloudlayermodels
To select the best-fit models, we follow Bowler et al.
use the formalism described in Burrows et al. (2006) for
(2010) by identifying the model with the smallest χ2
temperatures T = 700–1800 K, gravities with log(g)
eff and computing the ∆χ2 limit for a 3 σ confidence limit.
= 3.75–5, and solar/super-solar abundances of metals.
’Best-fit’ models satisfy χ2 -χ2 < χ2 . We do
For both models, we assume modal particle sizes of 60 model best 99.73%
this separately for the Model A and E cloud prescrip-
µm–100 µm and a particle size distribution appropriate
tions.
forclouds(Deirmendjian1964). Forbothmodelswealso
assume radii from Burrows et al. (1997).
3.2.2. Results for Standard Cloud-Deck Models
3.2.1. Fitting Method Table5summarizesourentirefittingresultsformodels
Our atmosphere model fitting follows a simplified ver- with the standard cloud deck prescription. Figure 10
sion of the fitting procedure employed by Bowler et al. displayssomeofthesefittingresultswiththeplanetradii
(2010) to model the near-IR spectrum and photometry fixed to the Burrows et al. (1997) values. The top-left
for HR 8799b. Nominally, we quantify the model fits panel shows the distribution of χ2 values for HR 8799b;
with the χ2 statistic, the top-right panel compares the HR 8799b SED to the
n ’best-fit’ model.
χ2 =X(fdata,i−Fmodel,i)2/σd2ata,i. (1) haFvoerteeamchpeprlaatnuerte,sthweitmhionde1l0s0wKitohftthheolsoewdesetriχve2dvafrluoems
i=0
7
coolingmodels: Teff =900K,1200K,and1100KforHR 3.2.3. Results for Thick Cloud Layer Models
8799b, c, and d (see Marois et al. 2008). Models with a
Figure 11 shows and Table 6 summarizes our fitting
3 solar abundance of metals have marginally smaller
χ×2 values. Adopting the ∆χ2 criterion, χ2 +χ2 , results for the thick cloud layer models. Best-fit models
min 99.73% for the HR 8799 planets cover a similar range in T
the minimum χ2 values for modeling b, c, and d are eff
as the standard model fits and cooling model predic-
300.9, 133.2, and 38.9. The range of temperatures and
tions. For HR 8799b, the best-fit model assumes T
eff
gravities fulfilling this criterion are T = 900–1000K,
eff = 900K and log(g)=4.25; the range of best-fit models
1100–1300K,1000–1300Kandlog(g)=4.5–5,4.5–5,and
cover log(g)=4–4.5 and T = 900–1000K. The range
eff
4–5 for the b, c, and d planets.
in log(g) for HR 8799c and d are similar to that for b
However, the fits are quantitatively very poor for HR
(log(g)=4.25–4.5and4–4.5),whereastheirtemperatures
8799cand(especially)b. AsshownbyFigure10(top-left
are slightly higher (1100–1200Kand 1000–1200K).
panel), the minimum χ2 value for HR 8799b is a factor
As illustrated by Figure 11, models with thick cloud
of 5.5 times higher than the formal 5 σ confidence
layers provide far better fits to the SEDs of all three
lim∼it. The minimum χ2 value for HR 8799c is twice as planets. Quantitatively,theχ2 minimashrinkbyfactors
large. The large χ2 difference between that for ’best-fit’
of 6, 2, and 5 for HR 8799b,c, and d compared to those
modelsandtheformal5-σ confidencelimitsuggeststhat
for Model E fits. For HR 8799b and c, the minima ap-
the models do not provide meaningful fits to the data.
proach the formal 5-σ confidence limit. For HR 8799d,
Fits to the HR 8799d SED are not quite as poor but multiplemodelshaveχ2 minimalessthantheformal3-σ
include only one model with χ2 < χ2 . Allowing the
99.73% confidence limit.
planetary radii to vary over the range plausible for 5–20
The righthand panels of Figure 11 illustrate why the
M objectsdoesnotqualitativelyimprovethemodelfits
J thick cloud layer models are more accurate. For HR
for the b and c planets (Table 5).
8799b,thebest-fitmodelspredictaflat,risingSEDfrom
The top righthand panel and lower panels of Figure
1 to 1.5 µm, consistent with the planet’s weak Y and J
10 illustrate how the models fail to reproduce the SEDs
bandemission. The best-fitmodels also predictstronger
of HR 8799bcd. For example, for HR 8799b the ’best
3.3 µm emission than in the standardmodel case and in
fit’ model provides a good estimate of its K band and
s better agreement with HR 8799b’s measured [3.3] flux.
L’ band fluxes and is consistent with its upper limit at
While the best-fit model for HR 8799c underpredicts its
M band. At [3.3], however, the model predicts too deep
J-band flux while overpredicting its [3.3] and L’ band
of a trough due to methane absorption, underpredicting
flux, the discrepancies are weaker than in the standard
the flux by a factor of 3–4. Moststrikingly,the model
cloud model case. With the exception of the CH l filter
∼ 4
overpredicts the flux at Y and J band by over an order
data, which was not incorporated into our fitting, the
of magnitude. The model overestimates the H band and
best-fitthickcloudmodel(log(g)=4.25,T =1100K)
eff
CH s flux by a factor of 2. Compared to the best-
4 for HR 8799d accurately reproduces the planet’s flux at
∼
fitting models,HR8799calsohastoostrongofa3.3µm
every datapoint.
flux and too low of a Y band upper limit.
Allowing the planet radii to vary by 10% slightly
For modeling results discussed in Figure 10, the scal- ±
improves the model fits. More importantly, results in
ing factors for the radii are almost always Ck =0.9 for moremodelswithχ2 valuesbelowtheformal3σ and5-σ
temperatures greater than those predicted from cooling
confidence limits (Figure 12). For these models, the HR
models and 1.1 for lower temperatures. To see which
8799b’s range of best-fit models have log(g) = 4.25–4.5,
radii formally yield the smallest χ2 values, we allow the
and T = 900–1000K,and C = 0.9–1.02;HR 8799c’s
eff k
radiustovarybetween0.2and2timestheBurrows et al.
have log(g)=4.25–4.5, T = 1100–1200K, and C =
(1997) values. The resulting trend of χ2 vs. T for all eff k
eff 0.9–0.975;and HR 8799d’s have log(g) = 3.75–4.5;T
eff
planetschanges,astheminimaaresystematicallypushed
= 1000–1200K;and C = 0.9–1.09. As before, the scal-
k
towardshigherT (T =1300–1400K).However,ra-
eff eff ing factor for each model is correlated with the model’s
dius scale factors for the best-fit models imply that the
temperature compared to the cooling model estimates.
planetsareunphysicallysmall–R 0.4,0.6,and0.7
b,c,d
∼
R .
J 3.3. Estimates for “Patchy”/Partly Cloudy Models
In summary, atmosphere models with standard, cloud
deckprescriptionsappropriateforbrowndwarfsonlypro- The two models used to fit our data define limiting
vide statistically meaningful fits to HR 8799b and c for cases for the cloud structrure in planet atmospheres.
unrealistically small radii (see also Bowler et al. 2010, The Model A thick cloud layer prescription fits the
for HR 8799b). Assuming radii characteristic of planet- data for each planet far better. However, intermediate
mass objects, we fail to find a single model that pro- cases – with far thicker clouds than the Model E case
videsastatisticallymeaningfulfittotheHR8799bandc but slightly thinner than Model A or a “patchy” cloud
dataindicatingthatsuchmodelsprovideapoordescrip- coverage – may be more physically realistic. The two
tion of the planets’ atmospheres (see also Marois et al. processes may be tied together: Ackerman and Marley
2008;Janson et al.2010;Hinz et al.2010). Theseresults (2001)showthatcloudsmaybecomepatchyastheysed-
are independent of surface gravity for log(g) = 4–5 and iment below photospheric pressures. Near-IRphotomet-
whether the planets have solar or 3 solar metallicity. ricvariabilitydetectedfromtheT2.5browndwarfSIMP
These results then motivate us to see×if models with dif- J013656.5+093347isconsistentwithgrainfree,cloudless
ferent cloud prescriptions fare better in reproducing the regionsandgrain-bearingcloudy regionsrotatingin and
SEDs of HR 8799bcd. out of view (Artigau et al. 2009). Cloud patchiness may
also be important for defining the L/T dwarf transition
(e.g. Marley et al. 2010, and references therein).
8
We leave a detailed construction of such models to a CasesAandB.ToexpandupontheMarois et al.(2011)
future paper (Madhusudhan et al., in prep.) but here investigation, we considered a wider range of masses for
we qualitatively explore how intermediate cases may af- HR 8799bcde – 10, 13, 13, and 13 M – with the same
J
fectthepredictedplanetspectrum(seealsoMarley et al. double resonance configuration as Case B. We refer to
2010). Similar to Burgasser et al. (2002), we follow a this set of initial conditions as Case C. In all cases, we
highlysimplified,crudeapproachbycombiningweighted simply require the system to be stable for 30 Myr – the
sums of Model A and E cloud prescriptions to approx- minimum age of HR 8799 – to be consistent with the
imate an atmosphere whose cloud thickness varies over data.
the seeing disk of the planet15. For simplicity, we com- Wedotwosetsof8000simulationsforeachcase. Inthe
pare two parameterizations: a “partly cloudy” approxi- first set, we allow HR 8799e to vary in separation from
mation where we weight the thick cloud model by 60% 13.1 AU to 15.7 AU. This allows us to identify general
and a “mostly cloudy” approximation where we weight trends in the time to instability vs. separation for HR
90% of the surface by the Model A case. 8799e. In the second set, we more finely sample initial
Figure 13 shows modeling results for these two cases orbitalpropertiesfortheplanetsassumingarangeof14–
compared against the thick cloud layer results for log(g) 15 AU for HR 8799e to better identify stable solutions.
= 4 and 4.5. Our approximations yield smaller χ2 min-
ima for HR 8799b and c; models with partly/mostly 4.2. Results
cloudyapproximationshavethesmallestχ2. Thebest-fit Figure 14 illustrates our simulation results. The top
model for HR 8799b has Teff = 900K, consistent with panel displays the time to instability for Case A. The
the thick cloud layer model, while temperatures for HR bottom-left and bottom-rightpanels show the same plot
8799c and d are lower by 100K. for Cases B and C, respectively. The first set of simula-
While our approach is entirely ad hoc, it indicates tions allowing HR 8799e to range from 13.1 AU to 15.7
that slightly weakening clouds compared to the limiting AU are shown as orange lines; the second set are shown
Model A case may provide better fits, at least for low as black lines.
surfacegravitymodels(log(g)=4). Madhusudhanetal. Our results show that the HR 8799 companions must
(2011) present a set of new atmosphere models with a havemassesbelowthe deuterium-burning limit based on
rangeofcloudcoveragesintermediatebetweentheModel dynamics alone. CaseCconfigurationsaretypicallyonly
AandEcasesto explorehowvaryingthe cloudstrength stablefor0.01Myrandnever stableformorethan10–20
between these two extremes affects fits to the data. Myr. BecauseHR8799isamainsequencestar,itcannot
beasyoungas10–20Myr. Therefore,companionmasses
4. DYNAMICALSTABILITYANALYSIS forHR8799cde 13M anda massforHR8799b 10
J
≥ ≥
As shown by Fabrycky and Murray-Clay (2010) and M can be ruled out.
J
Moro-Martinet al. (2010), stability analysis of the HR Lowerplanet massesare stronglypreferredondynam-
8799 system constrains the planet masses independently ical grounds, consistent with the results of Marois et al.
of planet cooling and atmospheric modeling. Here, we (2011). Only seven Case B configurations are stable for
investigate the plausible mass range of companions im- 30Myr,nearlyallofwhichrequireseparationsforHR
∼
posedbydynamicalstability. Later,wewillcombinethe 8799e more than 1-σ different from the position implied
results of these simulations with the implied mass range byourastrometry. Onlytwoarestablefor100Myr,and
from atmospheric modeling to identify planet masses theselikewiserequireanomalouslysmallseparations. On
consistent with both atmospheric modeling and dynam- the other hand, sixty Case A configurations are stable
ical stability analysis. for 30 Myr. Three are stable for 100 Myr, one of which
places HR 8799e at a separation consistent with our as-
4.1. Procedure trometry. Our dynamical stability results are in rough
Using the Swifter N-body code, an updated version agreementwith Marois et al. (2011)’s results. They find
of the Swift package (Duncan et al. 1998), we integrate 12solutions out of105 possible solutions stable for more
the equations of motion for the HR 8799 planets. We than100Myr,whereHR8799evariesbetween14.35AU
adopt the Burlirsh-Stoer method to treat close encoun- and 14.56 AU. We find 3 out of 1.6 104 solutions are
×
ters. For all simulations we use an accuracy parameter stable for 100 Myr over this semimajor axis range.
of 10−12 and dynamically evolve the system until one or Insummary,wecanruleoutcompanionmassesgreater
more planets are ejected or until 100 Myr is reached. than 10 MJ for HR 8799b and 13 MJ for the others.
We expand the analysis of Marois et al. (2011) who The companions cannot be brown dwarfs. Systems with
searched for stable orbital configurations for two sets of masses of 5 MJ for HR 8799b and 7 MJ for the others
planet masses incorporating HR 8799e – 5, 7, 7, and 7 are characteristically far more stable than systems with
M ; 7, 10, 10, 10 M for b, c, d, and e. We assume a larger masses. We fail to find any stable configuration
J J
single-2:1resonancebetweencanddfortheformeranda with 7, 10, 10, and 10 MJ for HR 8799bcde’s masses
double-2:1 resonance for d-c and c-b pairs for the latter. that place HR 8799e at a position consistent with our
We hereafter refer to these sets of initial conditions as astometry. While our investigation is not exhaustive, it
implies that masses of less than 7 M for HR 8799band
J
15Technically,thisisnotphysicallyrealisticasthetemperature- less than 10 MJ for the others are most plausible.
pressure profiles for cloud layer and cloud deck regions would
be discontinuous. On the other hand, for a given Teff self- 5. DISCUSSION
consistent models with intermediate cloudiness (Marleyetal. Our primary result in this paper is that the atmo-
2010)havecolor-magnitudepositionsintermediatebetweenthetwo
spheresofatleasttwoandpotentiallyalloftheHR8799
extremes, broadly consistent with simple parameterizations (e.g.
Burgasseretal.2002). planets do not easily fit within the empirical IR color
9
sequence for L/T type brown dwarfs of similar temper- istry incorporated into thick or “patchy” cloud models
atures, nor can they be well fit by standard atmosphere may yield better fits to 1–5 µm photometry and mid-
models used to infer the properties of brown dwarfs. IRspectroscopyofthe planets. Highersignal-to-noiseL’
Adoptingrealisticassumptionsaboutplanetradii,allat- band spectra and detections/more stringent upper lim-
mosphere model fits to data for HR 8799b and c are far its at M will better identify evidence of non-equilibrium
poorerthananymeaningfulthresholdidentifyingmodels chemistry in the planets’ atmospheres.
consistent with the data. The models primarily fail by
underpredicting the 3.3 µm flux and badly overpredict- 5.2. Comparisons with Planet Evolution Models and
ing flux at 1–1.3 µm. Implied Masses
Our analysis suggests that having “thicker” clouds –
Withinthecontextofthe Burrows et al.(1997)planet
ones with larger vertical extents – is key to reproducing
cooling models, a particular combination of log(g) and
the planets’ SEDs. Compared to cloud structures as-
T defines an object with a mass M and age t. Tak-
eff
sumed in standardL/T dwarfatmosphere models, these
ing the gravity and temperature range implied by our
clouds are more optically thick at a given T , so they
eff modeling at face value, we can then identify the mass
are visible (in the photosphere) at a lower T even
eff and age range implied. Our modeling efforts succeed in
thoughthecloudbaseislocatedfarbelowatmuchhigher
yielding planets with physically realistic radii. However,
pressures. Adopting a thick cloud layer prescription, we
if our range of log(g)and T were to imply wildly dis-
eff
succeed in identifying models for each planet that quan-
crepantmassescomparedtocoolingmodelestimatesand
titatively are good-fitting models. Moreover, the tem-
dynamical stability requirements or widely varying ages
peratures of these models are consistent with simpler,
our analysis would have solved one problem only to cre-
presumably more accurate cooling model estimates.
ate comparably serious ones.
Here, we combine all modeling results to identify the
5.1. Comparisons with Previous Studies of HR 8799
range of best-fit parameters and implied parameters –
The most direct comparisonto this work is the recent mass and age – from atmosphere models that we con-
analysis of the HR 8799b K-band spectrum and 1.1–4.1 sider. We then determine whether the atmospheric and
µm photometry from Bowler et al. (2010) whose mod- dynamicalmodelingconstraintsareconsistentand,ifso,
eling formalism we largely follow. Bowler et al. (2010) what mass and age range they imply.
alsofinds difficulties inusing standardatmospheremod-
els to fit HR 8799b’s SED and interpret its properties HR 8799b – The minimum χ2 value for HR 8799b
(see also Marois et al. 2008). Likewise, they find that • for thick cloud models is 27.6 if we allow the ra-
temperatures inferred from standard atmosphere mod- dius to vary by up to 10% from the Burrows et al.
els disagree with cooling model predictions and that the (1997) values and 48.9 if we don’t. For the
former require unphysically small radii. “patchy” cloud approximation, the corresponding
OurresultsindicatethatincludingY/zbanddataonly χ2 minima are 20.6 and 51.4. Considering the
exacerbates the already serious disagreement between best-fit models passing the ∆χ2 threshold in each
standard cloud deck model predictions and the planet’s case, this range covers log(g) = 4–4.5 and T =
eff
SED. Our analysis confirms Bowler et al. (2010)’s infer- 800–1000K.Thus, our modeling yields log(g) = 4–
ence that HR 8799b’s atmosphere is exceptionally dusty 4.5, T = 800–1000K. Using the Burrows et al.
eff
comparedto field browndwarfs. Our results extend this (1997)evolutionarymodels,thisimpliesamassand
inference, indicating that HR 8799c and, plausibly, HR age range of M, t = 5 M , 30 Myr to 15 M , 300
J J
8799d are also dusty compared to field brown dwarfs. Myr.
Janson et al. (2010) noted that while standard atmo-
sphere models – the COND models in their case – can HR8799c,d, ande –The minimum χ2 valueshere
•
reproduce the mean brightness of HR 8799c’s L’-band for thick cloud models are 43.5 and 60.7 for c and
spectrumtheyincorrectlypredictthespectralslopefrom 5.7 and 5.3 with and without radius rescaling. For
3.9 µm to 4.5 µm. They cite greater atmospheric dust the“patchy”cloudapproximation,thecorrespond-
absorptionand,especially,non-equilibriumcarbonchem- ing χ2 minima are 14–14.1 for c and 2.8–7.4 for
istry as features that may bring the models into better d. For HR 8799c, the range of models passing the
agreement. Hinz et al. (2010) argue that incorporating ∆χ2 threshold for the thick and patchy cloud pre-
non-equilibrium chemistry is necessary to reproduce the scriptionscoverlog(g)=4–4.5andT =1000K–
eff
mid-IR photometry of HR 8799bcd since the chemical 1200K. This yields a mass/age range of 7 M , 30
J
equilibrium models they use (Saumon et al. 2006) pre- Myrto15–17.5M at150–300Myr. ForHR8799d,
J
dict M-band fluxes larger than the upper limits they re- therangeislog(g)=3.75–4.5,T =1000-1200K,
eff
port. yielding5M at10Myrto15–17.5M at150–300
J J
Non-equilibrium carbon chemistry has little ef- Myr. Since HR8799elikelyhasa bolometriclumi-
fect on the near-IR portion of the SED (e.g. nosityandK-LcolorscomparabletoHR8799cand
Hubeny and Burrows2007). Thus,ouranalysisindicates d, its range of masses is plausibly consistent with
thatthickerclouds–and,byimplication,strongeratmo- those derived for HR 8799c and d.
spheric dust absorption – are far more important than
non-equilibrium chemistry in reproducing the HR 8799 Dynamical constraints require that HR 8799b is less
planet 1–5 µm SEDs. Nevertheless, the HR 8799 planet than 7 M and HR 8799cde are less than 10 M (Sec-
J J
atmospheres are plausibly not in local chemical equilib- tion 4 of this work; Marois et al. 2011). The 5 M mass
J
rium. Since departures from chemical equilibrium alter estimate for HR 8799dcan be ruledout because the pri-
the spectralstructure at4–5µm,non-equilibriumchem- mary star is on the main sequence and thus cannot be
10
10 Myr old. Coupled with the range in surface gravities stable,wide-orbitsystemslikeHR8799’s. Theyconclude
and temperatures, the implied range in masses are then thatmassive,wide-separationgasgiantslikeHR8799bcd
6–7 M for HR 8799b, 7–10M for HR 8799c,and 7–10 form by disk instability and ”can certainly rule out core
J J
M for HR 8799 d. If HR 8799e’s atmospheric proper- accretion”.
J
tiesmirrorthoseofcandd,itsplausiblerangeofmasses CriticaltoDodson-Robinson et al.’sconclusionistheir
is also 7–10 M . Conversely, for these ranges of masses, treatment of the core growth rate. The growth rate
J
thesurfacegravitiesofHR8799bcdeshouldbenogreater strongly depends upon the planetsimal approach veloc-
than log(g) 4.25. ity, which they fix at v = ΩR . They claim this ve-
a hill
≈
These estimates are consistent with cooling model es- locity yields an “optimistically high” growthrate. Their
timates from Marois et al. (2008, 2011). For the lower formalismimplicitly assumesthat planetesimals havean
end ofthe mass ranges,the systemage correspondingto isotropic velocity dispersion (v v ), which is valid
a z
∼
thesemodelsis 30MyrandputsHR8799’sageonthe as long as the scale height of planetesimals accreted by
≈
lowendofthe30–160MyrrangequotedbyMarois et al. cores (v /Ω) is larger than the core’s impact parameter,
z
(2008). The(disfavored)highendofthe massrangecor- Rcorep(1+θ) (Rafikov 2004), where θ is the Safranov
responds to 100 Myr-old objects. number. However, if the planetesimals are dynamically
∼
Despite our success in arriving at self-consistent an- coldsuch that vz √pΩRHill (where p = Rcore/RHill),
swers for the planets’ masses and ages, we strongly cau- ≤
this condition is violated (Dones and Tremaine 1993;
tion against overinterpreting these results. Our results
Rafikov 2004). The core can then accrete the entire ver-
do not prove that, above the cloud base, the vertical
ticalcolumnofplanetesimalsatavastlyhigherratesince
density/pressure profile of clouds follows that of the gas
accretion is now essentially two-dimensional (Rafikov
as a whole (e.g. s = 0), as opposed to being truncated
1 2004).
at higher pressures. Neither do our results prove that
Asaresult,Dodson-Robinson et al.(2009)catastroph-
other models with slightly different assumptions about
ically underestimate the maximum growth rate by a
the clouds, grain particles, atmospheric chemistry, etc. factor of p−1/2, or up to 114, 85, and 68 at the po-
providebetterfitstothedata. Inparticular,slightmod-
sitions of HR 8799b, c, and d (cf. Equations 78,
ifications to our models may improve the fit at L’ band, 80, and 82 in Rafikov 2004; see also Rafikov 2010)16.
thedatapointresponsibleformuchoftheχ2contribution
Detailed numerical simulations confirm that this rapid
for HR 8799b. Even within the context of our adopted
growthphase can be reachedif collisionalfragmentation
physical models, our sampling in temperature and grav-
andgasdragareproperlytreated(Kenyon and Bromley
ity is also too coarse to precisely estimate best-fit atmo-
2009). The Dodson-Robinson et al. planet-planet scat-
sphere parameters.
teringsimulationsalsowereconductedassuminggasfree,
On the other hand, our analysis provides compelling
planetesimal-free conditions and assumed that planets
evidence for thick clouds, motivates future modeling
could not further grow after scattering. However, gas
work to test how different assumptions about thick
draganddynamicalfrictionfromplanetesimalsarecriti-
cloudsaffectmodelfitstoplanetaryatmospheres,anden-
callyimportantastheypromoteorbitcircularizationand
couragesfurtherobservationsofsubstellarobjectstotest
stability (e.g. Goldreich et al. 2004; Ford and Chiang
these models. Madhusudhan et al. (2011) will develop 2007)17. Cores with masses sufficient for rapid gas ac-
and better assess model fits for varying cloud strengths
cretion can circularize after being scattered to the outer
and more precisely and accurately determine tempera-
disk (Bromley and Kenyon 2011, S. Kenyon 2010, pvt.
tures and gravities for the HR 8799 planets and other
comm.). SimulationsbyThommesetal. (inprep.) show
planetary-mass objects.
thattheHR8799planetcorescouldacquiremostoftheir
gas after scattering.
5.3. Constraints On The Formation of the HR 8799
The mass ratio and semimajor axis distribution of
Planetary System
wide planets and low-mass brown dwarfs may help con-
The planets’ large masses and wide orbits make them
strain the formation mechanism for HR 8799’s plan-
a particularly interesting probe of planet formation.
ets (Kratter et al. 2010). Core accretion preferentially
The favored theory invoked to explain the formation
forms planets with smaller masses and orbital sepa-
of gas giant planets is core accretion (e.g. Mizuno
rations, while disk instability has difficulty producing
1980; Pollack et al. 1996; Kenyon and Bromley 2009;
lower-mass gas giants and forming them close to the
Chambers et al. 2010), where cores that have grown to
star (e.g. Rafikov 2005; Kratter et al. 2010). There-
5–10 M⊕ rapidly accrete much more massive gaseous fore, if HR 8799bcde formed by core accretion (disk
≈
envelopes. Alternatively, planets could form by disk in-
stability (Boss 1997, and later papers), where the pro- 16 At first glance, Equation (17) in Rafikov (2010) appears
toplanetarydisk is massiveandgravitationallyunstable, to imply that the limiting distance for core accretion in shear-
forming multiple self-gravitatingclumps of gas thatcoa- dominated growth is comparable to Dodson-Robinsonetal.’s es-
timate (44 AU vs. their 20–35 AU). However, Rafikov’s result of
lesce into bound, planet-mass objects.
44 AU is valid for a Minimum Mass Solar Nebula case (Hayashi
HR 8799’s planets are often described as confounding 1981). Adoptinginitialassumptionsmorecomparabletothosethat
eitherplanetformationmodel(e.g.Marois et al.2011)or Dodson-Robinsonetal. assumes – e.g. a disk more massive than
being clear examples of disk instability-formed planets, theMinimumMassSolarNebulaoralonger-livedonewithτdisk=
5Myrinsteadof3Myr–impliesthatgasgiantscaninsomecases
as claimed by Dodson-Robinson et al. (2009). They find
formbycoreaccretionatseparationscomparabletoHR8799cand
that coresat distances characterizingthe HR 8799plan- b.
ets cannot reach 10 M⊕ in mass to undergo runaway 17 In fairness, they clearly acknowledge that their study does
gas accretion even∼under the most favorable conditions. notconsiderplanet-planetscatteringinagaseousdisk,whichmay
resultinamorefavorableoutcomeforcoreaccretion.
They claim that planet-planet scattering cannot create