arX

iv:1

210.

6745

v3 [

astr

o-ph

.EP]

4 A

pr 2

013

Fomalhaut b: Independent Analysis of the Hubble

Space Telescope Public Archive Data

Raphael Galicher1,2,3, Christian Marois1, B. Zuckerman4, Bruce Macintosh51National Research Council Canada, Dominion Astrophysical Observatory, 5071 West

Saanich Road, Victoria, BC, V9E 2E7, Canada;2Dept. de Physique, Universite de Montreal, C.P. 6128 Succ. Centre-ville, Montreal, Qc,

H3C 3J7, Canada;3LESIA, Observatoire de Paris, CNRS, UPMC, Universite Paris Diderot, 5 place Jules

Janssen, 92210 Meudon, France;4Department of Physics and Astronomy, University of California, Los Angeles, CA 90095,

USA;5Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, California, 94550,

USA;

raphael.galicher@obspm.fr

Submitted to ApJ on Aug, 9th 2012

ABSTRACT

The nature and even the existence of a putative planet-mass companion (”Fo-malhaut b”) to Fomalhaut has been debated since 2008. In the present paperwe reanalyze the multi-epoch ACS/STIS/WFC3 Hubble Space Telescope (HST)optical/near infrared images on which the discovery and some other claims werebased. We confirm that the HST images do reveal an object in orbit aroundFomalhaut but the detailed results from our analysis differ in some ways fromprevious discussions. In particular, we do not confirm flux variability over atwo-year interval at 0.6µm wavelength and we detect Fomalhaut b for the firsttime at the short wavelength of 0.43µm. We find that the HST image of Fo-malhaut b at 0.8µm may be extended beyond the PSF. We cannot determinefrom our astrometry if Fomalhaut b will cross or not the dust ring. The opticalthrough mid-infrared spectral energy distribution (SED) of Fomalhaut b cannotbe explained as due to direct or scattered radiation from a massive planet. Weconsider two models to explain the SED: (1) a large circumplanetary disk aroundan unseen planet and (2) the aftermath of a collision during the past 50-150 yearsof two Kuiper Belt-like objects of radii ∼ 50 km.

Subject headings: Methods: data analysis, Methods: observational, Techniques: high

angular resolution, Techniques: image processing, : planetary systems.1

1. Introduction

Direct imaging is the appropriate tech-nique for the study of exoplanets withsemi-major axis larger than a few astro-nomical units (Marois et al. 2008, 2010;Kalas et al. 2008; Lagrange et al. 2009).As the planetary atmospheric thermalemission or scattered light is detected,detailed multi-band photometry or spec-trometry can be used to probe the at-mospheric composition and physical prop-erties. However, these studies are chal-lenging given the high contrast and smallangular separation between a star andplanet. In some systems the presenceof a planet before it is detected directlycan be suggested by the geometry of acircumstellar debris disk. For example,Wyatt et al. (1999), Kalas et al. (2005)and Quillen et al. (2006) had predicted thelikely existence of a planet around Fomal-haut and Mouillet et al. (1997) of a planetaround β-Pictoris.

In the case of Fomalhaut (440±40Myr,7.7 pc, Mamajek 2012; Van Leeuwen 2007),a candidate planet was announced byKalas et al. (2008, hereafter K08). Sur-prisingly, the candidate was not detectedin deep near infrared images in H and Lpbands, but rather in Hubble Space Tele-scope (HST) images in the visible whereplanets are not expected to emit muchthermal light. The K08 planet modelthat best fit the 2008 photometry isa < 3MJ Jovian planet surrounded by alarge circumplanetary disk; the observedoptical light is mostly scattered by thedisk, not by the planet itself. In thismodel, Hα emission (dust accretion or hotplanetary chromosphere) explains the un-usual 50% variability of the reported flux

at 0.6µm over a two year time interval.Based on their astrometric mesurements,Kalas et al. (2010) also announced thatFomalhaut b is likely to cross the dustring.

A few years later, as they did not de-tect the object at 4.5µm with Spitzer,Janson et al. (2012) concluded that ”thereis almost certainly no direct flux from aplanet contributing to the visible-light sig-nature” and they proposed an opticallythin dust cloud with or without a centralobject in the super-Earth regime to explainthe K08 photometry. Kennedy&Wyatt(2011) also rejected direct detection ofmassive planets and explain the photome-try at 0.6-0.8µm to be a consequence of aswarm of satellites around a 2-100MEarth

planet.

Motivated by the controversial statusof Fomalhaut b within the community, in-cluding even doubts of its actual existence,we decided to conduct an independentanalysis of the HST public data that wererecorded in 2004, 2006, 2009 and 2010.After describing the observational methodin § 2 and our data reduction in § 3, weanalyze the images to confirm that Foma-lhaut b is a convincingly real detectionand that it is gravitationally bound to thestar. In § 4.2 we study various possible or-bits to determine if the current astrometrycan confirm or reject a dust belt cross-ing trajectory (such as one announced byKalas et al. 2010). In § 4 we estimate theobject’s photometry and possible origin asa circumplanetary disk around a planet orthe aftermath of a collision of two KuiperBelt-like objects, while considering thatFomalhaut b is not (§ 4.3) or is (§ 4.4) spa-tially resolved in the HST images.

2

Date (UT) Instrument Spot diam. Filter Im. Exp. Roll FOV rot.(arcsec) (sec) (deg)

2004 Oct. 25-26 ACS/HRC 1.8 F606W 112 5615 3 8.02006 Jul. 14 ACS/HRC 1.8 F435W 9 6525 3 5.82006 Jul. 15-16 ACS/HRC 3.0 F435W 9 6435 3 5.82006 Jul. 19-20 ACS/HRC 3.0 F606W 28 7240 4 6.02006 Jul. 18 ACS/HRC 1.8 F814W 20 5280 3 6.02006 Jul. 19 ACS/HRC 3.0 F814W 27 4942 3 6.02009 Nov. 16 WFC3/IR - F110W 4 4772 4 15.02010 Jun. 14 STIS/50CORON 2.5 CLEAR 3 630

7 157.02010 Sep. 13 STIS/50CORON 2.5 CLEAR 16 3000

Table 1: Fomalhaut observing log. Column ”Im.” gives the number of useful images. Column”Exp.” is the total integrated time of the useful images. ”Roll” is the number of roll anglesin the sequence and ”FOV rot.” gives the total FOV rotation during the sequence.

2. Observations

The data that we consider in this pa-per were obtained with HST with the Ad-vanced Camera for Surveys (ACS) in 2004and 2006 (programs 10390 and 10598),with the wide-field-camera 3 (WFC3) in2009 (program 11818), and the SpaceTelescope Imaging Spectrograph instru-ment (STIS) in 2010 (program 11818).The ACS data were acquired with the HighResolution Channel (HRC) in its coron-agraphic mode with 1.8′′ and 3.0′′ focalplane occulting masks and the F435W(430 ± 50 nm), F606W (595 ± 115 nm),and F814W (825 ± 115 nm) filters. TheF110W (1150± 250nm) filter was usedfor the acquisition of the WFC3 data.For the STIS data, the 50coron config-uration was used with its clear aperture(600 ± 220 nm). For all sequences, im-ages at several roll angles were taken sothat the stellar diffraction pattern can besubtracted while keeping the flux of anypoint sources. Tab. 1 gives the dates of

the observations, the instrument configu-rations (filter, coronagraph), the numberof useful images with the correspondingintegration time, and the number of rollangles as well as the total rotation of thefield of view.

3. Data reduction

3.1. ACS

We start from the drz drizzled imagesproduced by the ACS pipeline (geometricdistortion, photometry, and cosmic ray cal-ibrations). For each image, we create amap of pixels that deviate by more than3.5σ in a 20×20 pixel box and we replacethem with the median value in the box. Wemultiply each image by the photflam ofits header to convert the pixel counts toerg s−1 cm−2 A−1 arcsec−2. For the Fo-malhaut PSF registration, we first startwith the 2006 sequence at F606W that isrecorded with the 3.0′′ focal plane mask.We align every image maximizing its corre-

3

lation with the first image of the sequence(Table 1). The correlation is maximized inthe annulus with inner and outer radii of140 and 200 pixels where the central ver-tical band of width 240 pixel is removed(saturated detector) and where the coro-nagraphic focal plane bar is masked. Wecall this optimization area A. Once the im-ages are aligned to within 0.1 pixel, the ab-solute center of the star PSF is found bymedian-combining the aligned images andby registering the resulting image to theimage center by maximizing in A the cross-correlation of the diffraction spikes withthemselves in a 180◦ rotation of the im-age about its center. This procedure de-fines the absolute center within 0.5 pixeland we call R606 the registered median-image. We then register all images ofF606W sequences maximizing their cross-correlation with R606 in A. For the F435Wand F814W sequences, we scale R606 tothe corresponding wavelengths (814nm forF814W and 480nm1 for F435W) and callR435 and R814 the resulting images. Wethen register all F435W and F814W im-ages maximizing the cross-correlation in Awith R435 and R814 respectively. For ev-ery sequence listed in Tab. 1, we then sub-tract the stellar speckles.

As the field of view rotates only by a fewdegrees, there is almost no difference be-tween applying a locally optimized combi-nation of images algorithm (Lafreniere et al.2007; Marois et al. 2010b) or a basic an-gular differential imaging data reductionas described in Marois et al. (2006) for allfilters. We choose the second procedurewhich is less time consuming. Consider-

1Better match of the diffraction spikes than for

435nm.

ing one of the sequences, we subtract fromeach image a reference PSF that is the me-dian of all images that were recorded ata different roll angle. We then rotate theimages to put North up and median com-bine them. For the 2006 data, we workout the weighted mean of the reduced im-ages taken with the 1.8′′ and 3.0′′ masksin the same filter. As the fields-of-view donot exactly overlap, the contrast is not thesame in all parts of the images (Figs. 1 and2).

A point source (arrow) is detected in allimages South West from Fomalhaut A. Anextended object (red arrow, South East) isalso detected in 2004 and in 2006 (F814W).The motion of these two sources are consis-tent with them being background objects.Fomalhaut b (inside the circles) is detectedat F435W, F606W, and F814W with asignal-to-noise ratio of ∼ 3, 5-6, and 3 re-spectively and it does not have the samemotion as the background sources (Fig. 4).To confirm that Fomalhaut b is bound andthat we detect orbital motion, we have an-alyzed the astrometry of the South Westbackground source that is at ∼ 14 arcsecfrom the star (located at a separation com-parable to Fomalhaut b; see Fig. 5). As itfits well the expected positions of a back-ground source (proper motion and paral-lax), it means that mis-registration or un-corrected distortions do not bias the as-trometry in our images by more than theerror bars that we derive. We thus confirmthat Fomalhaut b is a real object orbitingFomalhaut.

3.2. STIS

The sx2 images that are provided bythe STIS pipeline (geometric distortions,

4

Fig. 1.— ACS images of the dust belt and the object b (circle) around Fomalhaut at F606Win 2004 (top) and 2006 (bottom). Two arrows point to background sources. The length ofthe segments giving the East and North orientations is 2.5′′. The intensity scale is linear andit is the same for the two images.

5

Fig. 2.— Same as Fig. 1 for F435W (top) and F814W (bottom) ACS images taken in 2006.

6

Fig. 3.— Same as Fig. 1 for the LOCI-processed WFC3 F110W image taken in 2009 (top)and 2010 STIS CLEAR image (bottom).

photometry, and cosmic ray calibrations)are used for our analysis. The flux density

is converted to erg s−1 cm−2 A−1 arcsec−2

by multiplying each image by the phot-

7

Fig. 4.— Fomalhaut b measured positionsin 2004, 2006 and 2010 images (blue andred crosses) and expected positions for abackground source (green crosses).

flam of its header and dividing it by theexposure time. The spider spikes are welldetected in these images and we registerthe first image of the sequence maximiz-ing the cross-correlation of the spikes withthemselves in a 180◦ rotation of the im-age about its center. The maximizationwas done around the spikes (±2 pixels) be-tween 100 and 230 pixels from the star.We then register the other images maxi-mizing the cross-correlation with the firstimage in the 200 pixel-radius disk wherethe 160 pixel central vertical band andthe 30 pixel central horizontal band aremasked. As the roll angles are well spreadin the 0-157◦ interval, we apply a locallyoptimized combination of images algo-rithm (Lafreniere et al. 2007; Marois et al.2010b) to suppress the stellar diffractionpattern. Using a LOCI algorithm, a PSF

Fig. 5.— Measured positions of the SouthWest background source in 2004, 2006and 2010 images (blue and red crosses)and expected positions for a backgroundsource (green crosses). Only epochs whereFomalhaut b is detected are shown.

reference image is built for each image ofthe sequence and it is subtracted. Aftersubtraction, the images are rotated to putNorth up and they are median-combined.The final image with the detection of Fo-malhaut b is shown in Fig. 3.

3.3. WFC3

The images that we use in our analysisare the multi-drizzle drz F110W imagesthat are provided by the WFC3 pipeline.This pipeline applies geometric distor-tions, photometry and cosmic ray cali-bration on all images. Given that theimages have been rotated to put Northup, the images are first rotated to alignthe pupil. The first image is registered atthe image center using a cross-correlation

8

analysis with a 180 degrees rotated im-age of itself. The other three imagesare then registered on the first imageusing again a correlation analysis. TheLOCI algorithm (Lafreniere et al. 2007;Marois et al. 2010b) is then applied in-side 20 pixels thick annulus without anypixel masking. The subtracted images arethen rotated to have North up and are me-dian combined. Due to a bright diffractionartifact, Fomalhaut b is not detected atF110W (see Fig. 3).

4. Data analysis

4.1. Belt geometry

The geometrical properties of the belthave been discussed previously (Kalas et al.2005; Acke et al. 2012; Boley et al. 2012)and it is beyond the scope of the presentpaper to refine them. However, we findan eccentric belt that reproduces the im-ages, with an eccentricity e=0.10-0.11, aradius between 136-148AU, a longitude ofascending node 156.5-157◦, an argumentof periapsis 35◦, and an inclination of 67◦.All the parameters are in good agreementwith the published values of K08 (31±6◦

for the argument of periapsis unlike the1±6◦ found by Acke et al. (2012)). We didnot use a mathematical fit to optimize val-ues of parameters and our best visual fit isonly used to estimate the belt geometry inour images.

4.2. Astrometry

We use the Tiny Tim (Krist et al. 2011)tool that generates HST template PSFs tobuild a model of a point source in our im-ages at the position of Fomalhaut b to ac-curately estimate its astrometry and pho-

tometry. We consider that Fomalhaut bis seen in scattered light. Thus, in theTiny Tim tool, we choose a source whichthe spectrum is a blackbody with temper-ature 8751K, (Di Folco et al. 2004). Wesimulate the images prior to the specklesuppression registering them at the po-sitions where they were recorded on thedetector to account for the ADI/LOCI ef-fects, the rotation we apply to put northup, and the weights of the weighted meansfor the 2006 data. We then adjust the po-sition and flux of the template to subtractfrom the image to minimize the residualnoise in a 0.25′′-radius aperture centered onFomalhaut b for the ACS and STIS data.Although the template is close to the realimage, the Tiny Tim tool cannot includeall variations of the PSF over the detector.That is why we choose the 0.25′′ aperture(10ACS pixels) as it is large enough tominimize the impact of these approxima-tions; and it is small enough to minimizethe impact of the surrounding noise. Thepositions we derive from the fit are given inTab. 2. Note that the uncorrected geomet-rical distortions induce a 0.01 and 0.1 pixelerror in ACS/HRC images (section 10.3in the handbook) and STIS images (sec-tion 16.1 in the data handbook) respec-tively. The uncorrected distortions arethus negligible with respect to the fit-ting errors. K08 measured in their imagesthat Fomalhaut b is at [ra, dec] = [-8.62′′, 9.20′′] and [-8.60′′, 9.38′′] from Fo-malhaut A in 2004 and 2006 respectively.We estimate the difference δi between K08positions and ours at epoch i as

δi =

√

δira2 + δidec2

σ2ra,i + σ2

dec,i

(1)

9

Date FilterOffset from A to b Separation PAra (′′) dec (′′) (′′) (deg)

2004 Oct. 25-26 F606W -8.59±0.02 9.19±0.02 12.58±0.03 316.9±0.12006 Jul. 14-15-16 F435W -8.61±0.03 9.36±0.03 12.72±0.04 317.4±0.22006 Jul. 19-20 F606W -8.64±0.02 9.36±0.02 12.73±0.03 317.3±0.12006 Jul. 18-19 F814W -8.64±0.03 9.36±0.03 12.73±0.04 317.3±0.22010 Jun. 14-Sep. 13 CLEAR -8.81±0.07 9.79±0.07 13.17±0.10 318.0±0.4

Table 2: Fomalhaut b astrometry with respect to Fomalhaut A.

where δira and δidec are the differencebetween K08 measurements and ours ofthe offset along the West-East directionand the South-North direction respec-tively. σra,i and σdec,i are our error bars (K08give no error bars). We find that our po-sitions are within 1.5σ of K08 positionsat the two epochs 2004 and 2006 (i.e.δi . 1.5). The difference with K08 couldresult from a different registering techniqueor from differences in the ACS pipelinethat have been upgraded since 2008.

As we have three epochs close in timeand large error bars for the 2010 data, wecannot strongly constrain the orbital pa-rameters. We then consider only two Ke-plerian orbits – one that crosses the dustring and a second that does not – and com-pare expected and measured positions.

The first orbit is a 0.19 eccentric or-bit with a 118AU semi-major axis, a 156◦

longitude of the ascending node, a 70◦ in-clination, and a 2◦ argument of periap-sis. The orbit does not cross the dustring and is represented in dashed lines inFig. 6 where the dust belt is bound bydashed-dotted lines. We use Eq. 1 replac-ing K08 positions with the expected posi-tions of Fomalhaut b on the keplerian orbitto estimate the differences δi between the

expected positions and our measurementsat each epoch i (2004, 2006, and 2010).Then, we estimate the total difference asδ =

∑

i δi. We find that the expected po-sitions are 1.1 σ from the measured posi-tions (δ = 1.1). The second keplerian or-bit (full lines) we consider has an eccen-tricity 0.28, a semi-major axis 145AU, alongitude of the ascending node 167◦, aninclination 67.5◦, and an argument of peri-apsis 8◦. The difference between expectedand measured positions is 1.5σ. If Fomal-haut b follows this orbit, it was inside thedust belt 140 years ago at ∼ 1AU fromthe center of the belt which the full ver-tical height is hr ∼ 3.5AU (Kalas et al.2005). Other trajectories at less than 2.4 σfrom the observations put Fomalhaut b in-side the belt ∼ 50 years ago. Some ofthese trajectories are highly eccentric andmay be consistent with results proposedby Kalas et al. (2013) and Graham et al.(2013) although we were not able to findall the parameters of their best fit. Thus,new data are required to conclude whetherFomalhaut b trajectory does or does notcross the belt.

10

Fig. 6.— Two trajectories with eccentricity 0.19 (dashed lines) or 0.28 (full line) that fit theFomalhaut b positions within 1.5 σ.

11

4.3. Fomalhaut b as a point source

We consider Fomalhaut b as a pointsource in this section. We estimate its pho-tometry and compare our results with K08fluxes (§ 4.3.1). We then examine mod-els discussed by K08 and J12 (§ 4.3.2and § 4.3.3).

4.3.1. Photometry

For each filter and epoch, we derivethe photometry by integrating the fluxdensity of the PSF template that bestfits the data (§ 4.2). As the PSF tem-plate is generated in a 2.5×2.5 arcsec2 im-age, we use a 1.25′′ radius aperture forthe ACS data and a 1′′ radius for theSTIS data. The fractions of the PSFintegrated energy inside these aperturesare 0.960, 0.961, 0.918, and 0.996 for theF435W, F606W, F814W Sirianni et al.(2005), and CLEAR/STIS (STIS hand-book, chap. 14/CCDClearImaging) filtersrespectively. The F110W flux upper limitis derived by estimating the 5σ noise inthe area where Fomalhaut b is expected tobe located, after convolving the image bya 0.4 arcsec diameter aperture (aperturematching the WFC3 photplam parame-ter). To convert the estimated flux densi-ties Fλ in erg s−1 cm−2 A−1 to flux densitiesFν in erg s−1 cm−2 Hz−1 (i.e. 1023 Jy), weuse the photplam keyword recorded bythe ACS, WFC3, and STIS pipelines inthe fits headers:

Fν = Fλ photplam2 10−18.4768 (2)

The resulting flux densities (µJy) are givenin Tab. 3. The error bars σν in percentageare the inverse of the signal-to-noise ratios.In these ratios, the signal is the integrated

Date Filter Flux density (µJy)Kalas

2004 F606W 0.63±0.10 0.61±0.052006 F435W 0.36±0.09 <0.87 (5σ)2006 F606W 0.43±0.06 0.29±0.032006 F814W 0.36±0.07 0.37±0.042009 F110W <1.6 (5σ) -2010 CLEAR 0.61±0.21 -

Table 3: Photometry if Fomalhaut b is apoint source.

flux density inside a 0.25′′ radius aperturecentered on Fomalhaut b and the noise isthe square root of the total variance ofthe residual noise after subtraction of thebest PSF in the same area. K08 expresstheir Fomalhaut b photometry and upperlimits in Vega magnitudes. We converttheir measurements to µJy (last columnin Tab. 3) using the ACS handbook (sec-tion 5.1.1).

Most of the flux densities (Tab. 3)are consistent with K08 values exceptour F606W/2006 point which is ∼ 2 σbrighter (σ is the quadratic sum of K08error bars and ours). Moreover, our er-ror bars are larger than K08’s ones. Thus,even if we still detect a variability in theF606W filter between 2004 and 2006, it isnot as significant (1.7 σG) as it is in K08 (5-6 σK) – where σG and σK are our errorbars and K08 ones respectively. We alsofind that the flux density measured in theCLEAR filter (its bandpass roughly cor-responds to F435W+F606W+F814W) isconsistent with the three ACS flux den-sities given the large error bar. Finally,we (marginally) detect Fomalhaut b atF435W unlike K08 who have an upper

12

limit.

We plot the photometry of our detec-tions (crosses) in Fig. 7 along with 5 σupper limits from the literature (K08,Marengo et al. 2009, and J12) at vari-ous wavelengths. J12 find that to comply

Fig. 7.— Fomalhaut b flux density (µJy)for various wavelengths (µm) in the casethe object is unresolved. Crosses corre-spond to our detections (four black forACS and one light blue for STIS). Theblack arrow is our 5 σ upper limit forthe flux in the F110W filter. Arrowsare 5 σ upper limits from the literature:green, red, and blue for K08, J12, andMarengo et al. (2009) respectively. Thesolid line represent a cloud-free atmospheremodel for a 1MJ planet at 400Myr. Themagenta line give the expected fluxes froma model of a cloud of refractory carbona-ceous material (see text).

with their 4.5µm upper limit, the plane-tary mass upper limit is 1MJ at 400Myr.

Thus, we compare the measurements witha model of a cloud-free atmosphere fora 1MJ planet at 400Myr with the so-lar metallicity (Siegel&Burrows 2012) (fullline in Fig. 7). Our new F110W upper limitis consistent with the expected planet fluxat that wavelength given the J12 Spitzer4.5µm upper limit. It is clear that aplanet-only model for Fomalhaut b is notconsistent with the visible observations.K08 proposed two other models: a cloudof dust (§ 4.3.2) or a disk of dust arounda Jovian-planet (§ 4.3.3). We revisit thesetwo models in light of our updated pho-tometry.

4.3.2. Cloud of dust

We consider the model introduced in K08with a 0.53AU diameter cloud composedof dust grains with a differential size dis-tribution dn/da ∝ (a/a0)

−3.5 where theradius a goes from amin to 1000µm. UsingMie theory, K08 calculate the apparentmagnitudes of such a cloud composed ofwater ice (density=1, mice) or refractorycarbonaceous material (density=2.2, mLG)with amin = 0.01µm (hereafter m0.01)or 8µm (hereafter m8). The total massin grains is adjusted such that the inte-grated light in F814W from the modelmatches K08’s observations (K08’s andour photometry in F814W are in agree-ment). We convert the Vega magnitudesprovided in K08’s Tab. S3 to flux densitiesin µJy (Tab. 4). The last line gives theerror ǫ between the expected flux densi-ties Fe,ν and the observed densities Fν :

ǫ =

√

∑

ν

(Fν − Fe,ν)2

σ2ν

(3)

13

Filter m0.01ice m0.01

LG m8ice m8

LG

F435W 0.71 0.58 0.63 0.46F606W 0.55 0.50 0.46 0.45F814W 0.37 0.37 0.37 0.37ǫ 2.0 1.3 1.7 1.0

Table 4: Expected flux densities Fe,ν (µJy)derived from the cloud models (m0.01

ice ,m0.01

LG , m8ice, and m8

LG) proposed in K08.The last line gives the difference be-tween Fe,ν and our measured photome-try Fν (see text for details).

K08 reject the possibility that Fomal-haut b can be explained by one of thesecloud models because 1/ they do not de-tect the object at F435W (they do not re-ject m8

LG for this reason), 2/ the red colorthey observe does not match the model,and 3/ they cannot explain the F606Wvariability. All these reasons do not ap-ply to our new photometry because 1/ wedetect Fomalhaut b at F435W, 2/ the ex-pected flux densities match the observedflux densities within 1.7 σ for three of thefour models (ǫ < 1.7), and 3/ the F606Wvariability is not significant in our images.K08 also explain that such a cloud couldresult from a collision of two planetesimalsand that the probability of such an eventis lower at the Fomalhaut b position thancloser to the star or closer to the belt.However, as suggested by J12, the prob-ability of a collision is not the probabilityof its detection because the speckle noiseand the high brightness of the ring mayprevent detections of such clouds close tothe star and the belt respectively. More-over, the collision could have occurred in-side the ring of dust and the resulting ma-

terials could have moved from the ring tothe current position of Fomalhaut b. Fi-nally, K08 argue that such dust cloudswould be sheared due to differential grav-itational forces and rapidly spatially re-solved by HST. However, assuming a cloudwith diameter 0.5AU (maximum size foran unresolved source) only subject to grav-itational forces from the star and no initialvelocity, we find that its image would belarger than 2 pixels (∼fwhm) and 4 pixelsafter ∼100 years and ∼200 years respec-tively. It would take ∼500 years to shearthe cloud of dust so that it could be spa-tially resolved in the HST images with nodoubt. Thus, we find no strong argumentsto reject K08 models of a dust cloud withradius ∼ 0.5AU, composed of water ice orrefractory carbonaceous small grains, andyounger than ∼ 500 years. We over plot aline that gives the expected fluxes for them8

LG model in Fig. 7.

4.3.3. Material surrounding a Jupiter-

like planet

A second scenario proposed by K08 isan unseen Jovian planet surrounded by adisk of dust with a radius of 16-35 planetradius. As the K08 photometry is close toours and K08 only work out rough numbers(they could not constrain all the param-eters with only two photometric points),the 16-35 planet radius disk surroundingan undetected Jupiter-like planet is con-sistent with our photometry. J12 rejectthis model because 1/ it does not explainthe F606W variability and 2/ the belt ge-ometry would be strongly affected con-sidering a ring-crossing orbit for Fomal-haut b (Kalas et al. 2010). As we do notfind a significant F606W variability and

14

our new astrometry cannot reject an orbitthat does not cross the ring, we cannot ruleout this model using the K08 arguments.J12 also consider that if the spin of thestar is aligned with the plane of the disk,the north-west side of the disk is closer toEarth than the south-east side. In thatcase, Fomalhaut b is between its star andEarth in the radial direction and J12 claimthat it would be difficult to explain howan optically thick disk can reflect so muchlight towards Earth. It is true if we ob-serve the non-illuminated side of the diskbut we can imagine an inclined disk suchthat we observe the illuminated part of thedisk even if Fomalhaut b stands betweenFomalhaut and Earth.

4.4. Is Fomalhaut b resolved?

4.4.1. Extended source vs PSF

Given that a possible model for Fomal-haut b involves a cloud of dust, it would bepossible that object has slowly expanded intime. We test here the possibility that theFomalhaut b images are slightly spatiallyresolved.

First, we combine all the Fomalhaut bACS images weighting the images bythe SNRs of the detections (linear andquadratic weighting give very similar re-sults), and we fit a 2D-Gaussian functionto the combined image. The best Gaussianfunction FWHM is 6± 1 pixels.

Then, we test how our processing canwiden the image of a point-like source. Foreach filter/epoch of ACS observations, weextract a small subimage close to Fomal-haut b (at 50 pixels maximum from Fomal-haut b). We add this noise to the PSF tem-plates generated in § 4.2 adjusting the noise

level to reach the same SNRs as we havefor the Fomalhaut b detections. We com-bine the four epoch/filter images weight-ing by the SNRs and we fit a 2D-Gaussianfunction to the combined image. Apply-ing this analysis for noises picked at eightdifferent locations in each filter/epoch im-age, we find the PSF FWHM estimationis 2.8 ± 0.5 pixels. We repeat the samefull analysis replacing the PSF templatesby the detected South-West backgroundsource images, and we find the backgroundsource image FWHM is 3.8 ± 0.5 pixels.Assuming this source is not spatially re-solved, we conclude that our data process-ing can widen the image of a point-likesource by ∼ 1± 0.7 pixel.

We now model an extended object as-suming a uniform intensity distributionover a disk with radius R. We convolve theobject model by the PSF templates (§ 4.2)and obtain the object image templates forall epochs/filters. We adjust the SNRsof the detections adding noise subimagespicked around the Fomalhaut b images.We combine the images accounting forthe SNRs and fit a 2D-Gaussian function.FWHMs found for sources with R between0.39 and 0.78AU are at less than 1 σ (esti-mated from noises picked at eight differentlocations) from the 6 pixel FWHM mea-sured for the Fomalhaut b image.

Finally, we find that the Fomalhaut bimage FWHM is ∼ 2 σ from the widen-ing induced by our data processing, sug-gesting that Fomalhaut could be resolved,but it is not yet conclusive. We alsofind that a basic model of an extendedsource could explain the measured Fomal-haut b extension. It is clear this low SNRanalysis is not sufficient to fully conclude

15

whether Fomalhaut b is or is not spatiallyextended; new observations are required.However, in the rest of section § 4.4, weconsider an extended source which the in-tensity distribution is a uniform disk withradius 0.58AU (3ACS pixels).

4.4.2. Unlikely an instrumental effect

Assuming the image is resolved, we in-vestigate what instrumental effect or dataprocessing could explain such an extendedsource.

The ACS/HRC PSF is contaminated bya halo for red sources, especially at F814W(section 5.1.4 in the ACS handbook). Thehalo which adds to the ”normal” PSF hasa diameter (42-2.36λ) pixels and containsa total fractional intensity 2 (λ−0.45)3 forthe wavelength λ in microns. A 10 pixeldiameter halo requires a dominant flux atλ ∼ 11µm from this expression, whichdoes not make sense because it is well out-side the sensitive bandpass of the detector.Moreover, even if the signal-to-noise ratiois low, we do not observe in the F814W im-age a PSF plus a halo but only an extendedimage.

A second explanation for such an imagecould be a misregistering of the raw im-ages. In that case, after the rotations thatput north up in the ADI process, all theFomalhaut b images would not fall at theexact same position, resulting in a blurredimage. If this happens, any source in thefield of view would be affected the sameway. This effect is included in the esti-mated widening induced by our process-ing (§ 4.4.1).

The last instrumental effect that weforesee is a differential geometric distortionof & 1 pixel at the Fomalhaut b position

between the images of a same sequence.The ACS pipeline corrects for the distor-tions with an accuracy 0.01 pixels (sec-tion 10.3 in the ACS handbook). Thus,it would require differential distortions 100times larger than the pipeline accuracy atthe Fomalhaut b position but almost nodistortions at the background source po-sition which is roughly at the same angu-lar separation from the star. This scenarioseems very unlikely.

Finally, we find no instrumental effectsthat could explain the possible spatial res-olution of Fomalhaut b in our images.Since the current paper was submitted,Kalas et al. (2013) mentioned that Fomal-haut b image appears slightly extended inthe 2012 images, which is qualitatively con-sistent with our analysis of the three earlierepochs. However, we insist that more ob-servations with higher SNR are needed toestablish whether or not Fomalhaut b isextended in the HST images.

4.4.3. Photometry

For each filter/epoch, we consider thetemplate To for a 1.16AU diameter object.We adjust its flux to minimize the residualnoise in a 0.25′′ radius aperture when wesubtract it from the observations. We fol-low the steps described in § 4.3.1 to convertthe flux densities to Jy and estimate the er-ror bars. The results are given in Tab. 5.

As expected, the fluxes are larger thanin the case of a point source. Moreover,the flux variation at F606W is larger thanin the point source case but it is still lessthan 2.5σG, thus not yet significant. Anunfortunately situated speckle at less than3 pixels from Fomalhaut b could explain

16

Date Filter Flux density (µJy)

2004 F606W 0.91±0.102006 F435W 0.63±0.092006 F606W 0.60±0.082006 F814W 0.48±0.092009 F110W < 1.6 (5σ)2010 CLEAR 1.04±0.20]

Table 5: Photometry if Fomalhaut bis 1.16AU large.

this variation. Finally, the flux densitymeasured in the large band of STIS is con-sistent with the average flux density mea-sured in the ACS filters within 1.8σG. Inthe case we resolve Fomalhaut b, we plotthe photometry of our detections (crosses)in Fig. 8. In Fig. 8, we add the fluxes de-rived from them8

LG K08 model of a cloud ofrefractory carbonaceous material (§ 4.3.2).We multiply the three fluxes by 0.47/0.38,i.e. we adjust the F814W flux and assumethe ratios between filters are the same. Themodel seems to be in good agreement withthe data.

In the case of a spatially resolved Fo-malhaut b, we propose one basic modelthat assume that Fomalhaut b is the re-sult of the collision of two Kuiper belt ob-jects (§ 4.4.4) and we adapt a model of cir-cumplanetary swarm of satellites (§ 4.4.5)proposed by Kennedy&Wyatt (2011).

4.4.4. Collision of Kuiper belt objects

In this section, we propose a basicmodel to roughly estimate the size andthe amount of light that is scattered by acloud of dust produced by the collision of

Fig. 8.— Same as Fig. 7 in the case the ob-ject is resolved. The magenta line give theexpected fluxes from a cloud of refractorycarbonaceous material (see text).

two Kuiper belt objects (KBO). The objec-tive is not to derive the exact radius, massand velocity of the KBOs that could createFomalhaut b but to show that the collisionof two KBOs is not completely inconsistentwith the observations. First, we estimatethe total grain mass that can explain thefluxes received from Fomalhaut b. Then,we show that the amount of dust can bethe result of a collision of two 50 km radiuscolliders. We evaluate the rate of collisionsof two such KBOs around Fomalhaut. Fi-nally, we estimate when the collision mayhave occurred to reproduce the size of theFomalhaut b images.

If the particles of dust are spheres withradius a and if the cross section of the par-ticles equals their geometric albedo, themass Md of a cloud of dust that lies at

17

a distance D from its star is (Jura et al.1995)

Md &16 π

3ρD2 a

Lsc

L∗

(4)

where ρ is the mass density of the dustgrains, and Lsc and L∗ are the luminos-ity of the light scattered by the cloud andthe luminosity of the star respectively. In-stead of estimating the ratio of the lu-minosities, we work with the fluxes Fsc

and F∗ received at the telescope. We es-timate Fsc from the measured fluxes (Fi)in the ACS filters (i=F435W, F606W, andF814W, Tab. 5)

Fsc =∑

i

Fi∆νi (5)

with ∆νi the bandwidths of the filters. Ourestimation of Fsc only includes the scat-tered energy in the F435W, F606W, andF814W bandpasses. F∗ has to be calcu-lated for the same bandpass. Assuming aPlanck law, F∗ in the bandpass [λmin =435− 50 nm, λmax = 825 + 115 nm] is

F∗ = F∗,tot

∫ umax

umin

u3/(exp u− 1) du∫

∞

0u3/(exp u− 1) du

(6)

where umin,max = h c/(k T λmax,min) withthe Planck constant h, the speed of lightin vacuum c, the Boltzmann constant k,the stellar effective temperature T (8751K,Di Folco et al. 2004), and the stellar fluxF∗,tot received at the telescope (8.914e-6 erg.cm−2, Kalas et al. 2008). For D ∼

120AU and dust grains with radius a =10µmand ρ = 2g.cm−3, we find from Eqs. 4, 5,and 6 that the total grain mass needed toreproduce the photometry of Fomalhaut bis Md ∼ 4.1019 g.

Jewitt (2012) estimates the mass me ofparticles that are ejected after a collision of

two KBOs with a mass Mkbo, a radius r, adensity ρ, and a relative velocity U

me

Mkbo

= A

[

r

√

8 πGρ

3

]−1.5

U1.5 (7)

where A equals 0.01 and G = 6.67 10−11m3

kg−1 s−2 is the gravitational constant.Jewitt (2012) assumes the particles haveradii in the range 0.1µm . a . 0.1m witha power law distribution in radii with in-dex ∼ 3.5 (see also Kadono et al. 2010).For typical KBOs in the ring, U is the or-bital velocity times hr/(2D) with hr thefull vertical height of the ring at radius D.With hr ∼ 3.5AU (Kalas et al. 2005) atD ∼ 120AU, U is close to 60m s−1. As-suming KBOs with radius r = 50 km, thetotal debris mass me after the collision isroughly 1% of the mass Mkbo of one of thetwo colliders with a density ρ = 2g cm−3.Given the approximations in the models,the expected mass of dust (1%Mkbo) thatis ejected after a collision of two 50 kmradius KBOs is consistent with the massestimated from the photometry of Fomal-haut b (4%Mkbo for a 50 km radius KBO).

We assume a maximum post-collisonoutflow velocity at infinity equal to theescape velocity, r

√

8 πGρ/3. Consider-ing this upper limit, the diameter s of thecloud is 2 r t

√

8 πGρ/3 at the date t af-ter the collision and reaches the observedsize s = 1.16AU (§ 4.4.1) after ∼ 50 years,which is then a lower limit to the time sincethe collision of the putative Kuiper Beltobjects. We can also estimate from the ex-pansion expression that, after ∼ 150 years,the source would have a diameter ∼ 3.5AUand would be ∼ 10 times fainter thanthe current detections assuming the sameamount of reflecting dust. It would not be

18

detected in our images. Thus, if Fomal-haut b is the product of a collision, theevent should have occurred between ∼ 50and 150 years ago to be consistent withour detections. This range is consistentwith the possible trajectories that put Fo-malhaut b inside the ring of dust 50− 150years ago (§ 4.2). As the size of the possi-ble extended source is very approximative,we keep in mind that these numbers arecoarse estimations.

Finally, we evaluate the rate of a col-lision of two r = 50 km KBOs inside thering of dust. We first find the collision timewhich reads

tcol =1

4 π n r21

U(8)

with n the number of KBOs with ra-dius r per unit volume. To estimate nwe need the mass Mdisk of the debrisdisk around Fomalhaut. We assumeMdisk=40MEarth because 1/ estimates ofthe mass of the Sun’s early Kuiper beltis 40MEarth (Schlichting&Sari 2006), and2/ estimates of the mass of the Vega de-bris belt is 10MEarth in objects with radii< 100 km (Muller et al. 2010) whereas theVega IR luminosity is 4 times fainter thanthat of Fomalhaut. Simplifying by settingthe radii of all the KBOs to 50 km does notqualitatively alter the collision frequencyestimated below. Under these conditionsand considering the belt surrounding Fo-malhaut A has a volume 2 πD∆Dhr with∆D ∼ 0.13D (Kalas et al. 2005), thenumber of KBOs is

n 2 πD∆Dhr =Mdisk

Mkbo

∼ 2× 108 (9)

Using U = π h√

M∗/M⊙ (1AU/D)3, and

Eqs. 8 and 9, we can write

tcol =0.13

2 π

(

D

r

)2Mkbo

Mdisk

√

(

D

1AU

)3M⊙

M∗

(10)Finally, the rate κ of collisions of twoKBOs with radii r is the ratio of the num-ber of KBOs (Eq. 9) to tcol

κ =2 π

0.13

( r

D

)2(

Mdisk

Mkbo

)2√

(

1AU

D

)3M∗

M⊙

(11)Eq. 11 with Mdisk = 40MEarth, and M∗ =2M⊙ indicates that ∼ 1 collision of twor = 50 km KBOs occurs every century inthe ring around Fomalhaut A. The rate islow enough to explain that we detect onlyone event around Fomalhaut as each eventwould be detectable during ∼ 200 years inour images. At the same time, it is highenough to make such a ∼ 50 to 150 year-old event plausible.

In summary, we conclude that it is plau-sible that Fomalhaut b is a cloud of dustthat was produced ∼ 50 − 150 years agoinside the dust belt by the collision of twoKBOs with radii ∼ 50 km.

4.4.5. Circumplanetary satellite swarm

Kennedy&Wyatt (2011, KW11) pro-pose a model of circumplanetary satelliteswarms that they apply to Fomalhaut b.They find that the planet mass can be ∼2-100MEarth surrounded by a swarm thatlies at 0.1-0.4 Hill radii. The swarm masswould be of the order of a few lunar masses.But these numbers are derived from K08photometry of an unresolved source.

Here, we use the same model underthe same assumptions (body size dis-tribution and maximum/minimum body

19

sizes, dust density, etc) but we con-sider a swarm of satellites with diam-eter 1.16AU, our photometry (Tab. 5),and a star with age 440Myr instead of200Myr (Mamajek 2012). We do not de-scribe the model as it is done in KW11.We only use the meaningful equationsto constrain the planet mass and theswarm mass and size following the stepsin § 3.3.1 and § 3.3.2 of KW11. First,we derive the total cross-sectional area ofdust σtot from our photometry: σtot =6.12 × 10−4AU2, assuming a geometricalbedo 0.08, a phase function 0.32 (Lam-bert sphere at maximum extension fromits host star), the star effective tempera-ture 8,751K (Di Folco et al. 2004), and astellar luminosity 6.34.1027W (K08).

As we assume that we resolve Fomal-haut b, we can write 2 η RHill = s, where ηis the semimajor axis of the satellites ofthe swarm relative to the Hill radius RHill

at the Fomalhaut b separation (118AU)and s is the swarm diameter. As explainedin § 4.4.1, the size of the extended sources=1.16AU is approximate and at F814W,the image of Fomalhaut b could be re-produced by a source with radius up tos=2.32AU. Thus, we consider 1.16AU<s <2.32AU. Using the Hill radius expres-sion Eq. 1 in KW11) and 2 solar massesfor Fomalhaut (KW11), we derive two con-

straints: 0.61/M1/3pl < η < 1.22/M

1/3pl ,

where Mpl is the planet mass expressed inEarth masses.

Considering a collision-limited satelliteswarm around Fomalhaut b (i.e. swarmhas just started to suffer collisions) thatreproduces the observed σtot, it imposesa minimum limit for the satellite semi-major axis η > 0.29/M0.12

pl for a 440Myr

system (i.e. a 440Myr collision time,see KW11 for details).

KW11 also study the collision velocitiesthat are required to destroy a large ob-ject at the Fomalhaut b position. Assum-ing a steady-state collisional cascade anda two-phase size distribution for the par-ticles, KW11 link the collision velocity tothe swarm size η and the planet mass Mpl.Using their equations in the case of a re-solved object we set a constraint that readsη > 0.69/M0.46

pl (KW11).

Moreover, KW11 assume that satel-lite orbits with η > 0.5 are not sta-ble and do not consider them. Finally,we account for the 1MJ upper limitthat Janson et al. (2012) put from thenon detection at 4.5µm for a 400Myr sys-tem (close enough to 440±40Myr proposedby Mamajek 2012). We plot all the con-straints in Fig. 9 that gives the semimajoraxis η of the satellites against the plane-tary mass Mpl. The parameters for whichKW11’s model can reproduce the photom-etry of a 1.16AU source are within thedashed area. The minimum and maximumplanetary masses are ∼2MEarth and 1MJ

and the swarm has a total mass 2-11MMoon

and lies at 0.15-0.5 Hill radii around theplanet.

In the case of an unresolved object (Fig. 7in KW11), KW11 find that the mass of theplanet (< 100MEarth) is not sufficient for itto have a significant gaseous envelope andenable mechanisms that could explain themigration of Fomalhaut b that presum-ably originates somewhere closer to thestar. KW11 also argue that a single planetwith mass < 100MEarth – which is simi-lar or less than the mass of the main de-bris ring (1-300MEarth, Wyatt&Dent 2002;

20

Fig. 9.— Semimajor axis η of satellites of the swarm versus planetary mass Mpl diagramthat shows the different constraints derived in the text. The parameters that could explainthe Fomalhaut b images are inside the dashed region.

Chiang et al. 2009) – is unlikely responsi-ble for shaping the dust belt. In our case ofa source with diameter 1.16AU, the rangeof the planetary mass goes up to 1MJ anda Jupiter-like planet can have a significantgaseous envelope and shape the dust belt.

5. Conclusions

Our independent analysis of the ACS,WFC3 and STIS data taken in 2004, 2006,

2009, and 2010 confirms that Fomalhaut bis real and is not a speckle artifact aswe clearly detect the object at the threeepochs at several filters (Figs. 1, 2, and 3).In this way, we confirm the Kalas et al.(2008, K08) detection. However, we finddifferences in our analysis concerning as-trometry and photometry of Fomalhaut b.

Unlike Kalas et al. (2010), we cannot af-firm that the object follows a trajectory

21

that crosses the belt of dust because ourastrometry is consistent within 1.16 σ withcrossing and non-crossing orbits (§ 4.2).

We detect Fomalhaut b in the shortwavelength filter F435W whereas K08 findan upper limit. We also derive an up-per limit at F110W using WFC3. In thecase of an unresolved source, our photome-try is consistent with K08 at F606W/2004and F814W/2006 but differs at F606W inthe 2006 data (§ 4.3.1). As a consequence,unlike K08, we detect no significant vari-ability of the F606W flux between 2004and 2006. Considering the reduced andpossible lack of variability at F606W andthe detection at F435W, several dust cloudmodels discussed by K08 cannot be ruledout anymore (§ 4.3.2). K08 propose alsoa model of a Jovian planet surrounded bya large disk of dust. Janson et al. (2012)exclude this explanation mainly because ofthe variability at F606W and the assumeddust belt crossing trajectory. Given ournew photometry and astrometry, we can-not reject this model (§ 4.3.3).

In the second part of our analysis, westudy the possibility that Fomalhaut bis spatially resolved in our images. Thesignal-to-noise ratios of the detections arelow and more data are required to con-firm the result but we find that our im-ages are more consistent with an extendedsource with diameter 1.16AU than with apoint source (§ 4.4.1 and 4.4.2). The pho-tometric variability of an extended sourcemodel at F606W is larger than for a pointsource but it is not yet significant (< 2.5 σ,§ 4.4.3). Two models are considered to ex-plain the size and the photometry of anextended source. First, the measurementsare consistent with a cloud of dust pro-

duced by a collision of two Kuiper beltobjects with radius 50 km that would haveoccurred ∼ 50 − 150 years ago (§ 4.4.4).The second model is an adaptation ofthe circumplanetary satellite swarm modelproposed by Kennedy&Wyatt (2011). Itis consistent with the data when consid-ering a 2MEarth-1MJ planet surroundedby a swarm that lies at 0.15-0.5 Hillradii (§ 4.4.5).

The nature of the Fomalhaut b objectis still uncertain. However, from the twoindependent current and K08 analysis ofthe HST data, we can claim that Fomal-haut b is a real object that orbits Fomal-haut A.

6. Acknowledgment

The authors are grateful to the ACSteam, John Blakeslee, and Travis Bar-man for helpful discussions. The authorsalso thank Paul Kalas and James Grahamfor useful communications on their analy-sis, and the anonymous referee for usefulsuggestions. Partial financial support forthis research came from a NASA grantto UCLA.

REFERENCES

Acke, B., et. al., 2012, The AstrophysicalJournal, 540, A125.

Boley, B., et. al., 2012, The AstrophysicalJournal Letters, 750, L21.

Chiang, E., and Kite, E., and Kalas, P.,and Graham, J. R., and Clampin, M.,2009, The Astrophysical Journal, 693,734–749.

Di Folco, E., et al., 2004, Astronomy andAstrophysics, 426, 601-617.

22

Graham, J., Fitzgerald, M., Kalas, P., andClampin, M., 2013, American Astro-nomical Society, 221, 324.03.

Janson, M., et al., 2012, The AstrophysicalJournal, 747, id. 116 (J12).

Jewitt, D., 2012, The Astronomical Jour-nal, 143, id. 66.

Jura, M., et al., 1995, The AstrophysicalJournal, Part 1, 445, 451–456.

Kadono, T., et al., 2010, Earth, Planets,and Space, 62, 13–16.

Kalas, P., Graham, J. R., Clampin, M.,2005, Nature, 435, 1067–1070.

Kalas, P., et al., 2008, Science, 322, 1345–(K08).

Kalas, P., Graham, J., Fitzgerald, M., andClampin, M., 2010, In the Spirit of Lyot2010, Update on Fomalhaut b.

Kalas, P., Graham, J., Fitzgerald, M., andClampin, M., 2013, American Astro-nomical Society, 221, 324.02.

Kennedy, G. M., and Wyatt, M. C.,2011, Monthly Notices of the RoyalAstronomical Society, 412, 2137–2153(KW11).

Krist, J., Hook, R., Stoehr, F., 2011, SPIE,8127.

Lafreniere, D., Marois, C., Doyon, R.,Nadeau, D., Artigau, E, 2007, The As-trophysical Journal, 660, 770–780.

Lagrange, A. M., et al., 2009, Astronomyand Astrophysics, 493, L21-L25.

Mamajek, E. E., 2012, The AstrophysicalJournal Letter, 754, L20.

Marengo, M., et al., 2009, The Astrophys-ical Journal, 700, 1647–1657.

Marois, C., Lafreniere, D., Doyon, R.,Macintosh, B., Nadeau, D., 2006, TheAstrophysical Journal, 641, 556–564.

Marois, C., et al., 2008, Science, 322,1348–.

Marois, C., Zuckerman, B., Konopacky,Q. M., Macintosh, B., Barman, T.,2010, Nature, 468, 1080–1083.

Marois, C., Macintosh, B., Veran, J.-P.,2010b, SPIE, 7736.

Mouillet, D., Larwood, J. D., Papaloizou,J. C. B, Lagrange, A. M., 2010b,Monthly Notices of the Royal Astro-nomical Society, 292, 896–.

Muller, S., Lohne, T. and Krivov, A. V.,2010, The Astrophysical Journal, 728,1728–1747.

Quillen, A. C., 2006, Monthly Notices ofthe Royal Astronomical Society, 372,L14–L18.

Schlichting, H. E., and Sari, R., 2011, TheAstrophysical Journal, 728, id.68.

Sirianni, M., et al., 2005, The Publicationsof the Astronomical Society of the Pa-cific, 117, 1049-1112.

Spiegel, D. S., and Burrows, A., R., 2012,The Astrophysical Journal, 745, 174.

Van Leeuwen, F., 2012, Astronomy andAstrophysics, 474, 653–664.

23

Wyatt, M. C., et al., 1999, The Astrophys-ical Journal, 527, 918–944.

Wyatt, M. C., and Dent, W. R. F., 2002,Monthly Notices of the Royal Astro-nomical Society, 334, 589–607.

This 2-column preprint was prepared with the

AAS LATEX macros v5.2.

24