Near-infrared scattered light properties of the HR4796A dust ring: a measured scattering phase function from 13.6deg to 166.6deg

1.7 MB·

by  Julien Milli

Astronomy&Astrophysicsmanuscriptno.HR4796_SPHERE_v7 (cid:13)cESO2017
January16,2017
Near-infrared scattered light properties of the HR4796A dust ring
A measured scattering phase function from 13.6◦ to 166.6◦
J.Milli1,2,A.Vigan3,D.Mouillet2,A.-M.Lagrange2,J.-C.Augereau2,C.Pinte2,4,D.Mawet5,6,H.M.Schmid7,A.
Boccaletti8,L.Matrà9,Q.Kral9,S.Ertel10,G.Chauvin2,A.Bazzon7,F.Ménard2,4,J.-L.Beuzit2,C.Thalmann7,C.
Dominik11,M.Feldt12,T.Henning12,M.Min11,13,J.H.Girard1,R.Galicher8,M.Bonnefoy2,T.Fusco14,J.deBoer15,
M.Janson16,A.-L.Maire12,D.Mesa17,J.E.Schlieder12,18,andtheSPHEREconsortium
7
(Affiliationscanbefoundafterthereferences)
1
0 Received:25November2015;accepted:16December2016
2

n
ABSTRACT
a
J
Context.HR4796Aissurrounded byadebrisdisc, observed inscatteredlight asaninclined ringwithahigh surface brightness.

3 Pastobservationshaveraisedseveralquestions.First,astrongbrightnessasymmetrydetectedinpolarisedreflectedlighthasrecently
1 challengedourunderstandingofscatteringbythedustparticlesinthissystem.Secondly,themorphologyoftheringstronglysuggests
thepresenceofplanets,althoughnoplanetshavebeendetectedtodate.

] Aims.Weaimhereatmeasuringwithhighaccuracythemorphologyandphotometryoftheringinscatteredlight,inordertoderive
P
thephasefunctionofthedustandconstrainitsnear-infraredspectralproperties.Wealsowanttoconstrainthepresenceofplanetsand
E
setimprovedconstraintsontheoriginoftheobservedringmorphology.
. Methods. We obtained high-angular resolution coronagraphic images of the circumstellar environment around HR4796A with
h
VLT/SPHEREduringthecommissioningoftheinstrumentinMay2014andduringguaranteed-timeobservationsinFebruary2015.
p
The observations reveal for the first time the entire ring of dust, including the semi-minor axis that was previously hidden either
-
o behindthecoronagraphicspotorinthespecklenoise.
r Results.WedetermineempiricallythescatteringphasefunctionofthedustintheHbandfrom13.6◦to166.6◦.Itshowsaprominent
t peakofforwardscattering,neverdetectedbefore,forscatteringanglesbelow30◦.Weanalysethereflectancespectraofthediscfrom
s
a the0.95µmto1.6µm,confirmingtheredcolourofthedust,andderivedetectionlimitsonthepresenceofplanetarymassobjects.
[ Conclusions.WeconfirmwhichsideofthediscisinclinedtowardstheEarth.Theanalysisofthephasefunction,especiallybelow45◦,

suggeststhatthedustpopulationisdominatedbyparticlesmuchlargerthantheobservationwavelength,ofabout20µm.Compact
3
Mie grains of this size are incompatible with the spectral energy distribution of the disc, however the observed rise in scattering
v efficiency beyond 50◦ points towards aggregates which could reconcile both observables. We do not detect companions orbiting
0
thestar,butourhigh-contrastobservationsprovidethemoststringentconstraintsyetonthepresenceofplanetsresponsibleforthe
5
morphologyofthedust.
7
0 Keywords. Instrumentation:highangularresolution-Stars:planetarysystems-Stars:individual(HR4796A)-ScatteringPlanet-
0 diskinteractions
.
1
0
71. Introduction 2015; Perrinetal. 2015; Millietal. 2015) and at visible wave-
1 lengthswithHST/STIS(Schneideretal.2009).
:The system HR4796A is a unique laboratory to characterise
v
dust in debris discs. Also known as TWA11A, this A0V star Modelling work by Augereauetal. (1999) indicated that
i
Xis partof the TW Hydra kinematicgroup,with an age recently planetesimals larger than one metre undergo a collisional cas-
re-estimated to 10± 3 Myr-old (Belletal. 2015) and at a dis- cade, producing dust particles down to a few microns. Sub-
r
atance of 72.8pc (vanLeeuwen 2007). It harbours one of the millimetre observations suggest that the system possesses be-
debris discs with the highest fractional luminosity, shaped as tween 0.25M and a few Earth masses of dust (Greavesetal.
⊕
a thin ring of semi-major axis ∼ 77 au inclined by ∼ 76◦. It 2000). Particles below the blowout size limit of ∼ 10µm
is bound to the M2 companion HR4796B orbiting at a pro- (Augereauetal. 1999) are expectedto be ejected fromthe sys-
jected separation of 560 au, and likely part of a tertiary sys- tem by the stellar radiation pressure. The planetesimals pro-
tem with an additionalM dwarf at a separation of ∼ 13500 au ducing the dust in debris discs are a natural outcome of the
(Kastneretal. 2008). The surrounding dust was first identified planet formation process. Although there is, to date, no direct
byJura(1991)fromtheinfraredexcessofthestar,andresolved detection of a planetary mass object in this system, striking
byKoerneretal.(1998)andJayawardhanaetal.(1998)atmid- evidence of one or multiple planets interacting with the disc
infrared wavelengths from the ground. It was then resolved at has been found in earlier observations (Lagrangeetal. 2012a;
near-infraredwavelengthswith NICMOS on the Hubble Space Wahhajetal. 2014). Theringhas steep edges,whichis notex-
Telescope (HST) (Schneideretal. 1999) and from the ground, pected because collisional evolution would cause a sharp ring
withadaptiveoptics(AO, Augereauetal.1999;Thalmannetal. to spread out with time. It could be explained by the interac-
2011; Lagrangeetal. 2012b; Wahhajetal. 2014; Rodigasetal. tion with gas (Lyra&Kuchner 2013) or with one or several
Articlenumber,page1of25
A&Aproofs:manuscriptno.HR4796_SPHERE_v7
planets shaping the inner and outer edges (e.g. Wisdom 1980; coronagraphicmaskwiththeneutraldensityfilterND_2,andby
Lagrangeetal.2012a).Theringisalsoeccentric,suggestingthat anacquisitionof sky frames.A sequenceof coronagraphicim-
itisbeingsecularlyperturbedbyaneccentricplanet.Inaddition ageswithfoursatellitespotsimprintedataseparationof20λ/D
to these intriguing morphological parameters, the observations byapplyingaperiodicmodulationtothedeformablemirrorwas
alsochallengeourunderstandingoflightscatteringbydustpar- alsorecordedtoregisterthelocationofthestarbehindthecoro-
ticles.Theansaewereseenbrighterintheeastthaninthewestin nagraphicmask.
unpolarisedopticalscattereredlight(Schneideretal.2009),but AsecondsetofobservationswasrecordedinFebruary2015
recentobservationsin polarisedlight showed a dramatic oppo- withadifferentinstrumentalsetup,knownastheIRDIFSmode2.
site asymmetrynearthesemi-minoraxis:thewestside ismore The SPHERE Integral Field Spectrograph (IFS, Claudietal.
than nine times brighter than the east side (Millietal. 2015; 2008) recorded spectral cubes of images from the Y band to
Perrinetal.2015).Manypossibilitieshavebeendiscussedtoex- the J band, while IRDIS recorded simultaneously images with
plaintheobservations:elongatedgrainslargerthan1µm,aggre- the dual-bandfilter H2H3 (λ = 1.593µm,λ = 1.667µm,
H2 H3
gates made of 1µm elementary particles, a non-axisymmetric ∆λ = 0.052µm,∆λ = 0.057µm) (Viganetal. 2010).The
H2 H3
dust distribution or a marginally optically thick disc. The lack conditionswere much better and much more stable, with a co-
ofdetailedknowledgeontheopticalscatteringpropertiesiscur- herence time above 10ms over the whole sequence. The IFS
rentlythemajorobstacletotheanalysisofthesedata(Starketal. dataset consists of 21000 spectra coveringa total field of view
2014;Millietal.2015) of1.73′′×1.73′′andwithanativespaxelsizeof12.25mas.The
Scatteredlightobservationsproducethehighestangularres- spectralresolutionis∼50.ThisIRDIFSsequencewasfollowed
olutionimages of circumstellardiscs, stronglyconstrainingthe by an unsaturated PSF measurement out of the coronagraphic
architecture of the underlying planetary system. We recorded maskusingtheneutraldensityfilterND_2.
deep coronagraphic images of HR4796A during the comis-
sioning and early guaranteed-time observations (GTO) of the
Spectro-Polarimetric High-contrast Exoplanet Research instru- 2.2.Datareduction
ment(SPHERE,Beuzitetal.2008).Wepresentfirstthedata,the
WedescribebelowthereductionperformedontheIRDISbroad-
reductionmethodsandthecontrastobtained(Section2),thenwe
bandHdata,theIRDISdual-bandH2H3dataandtheIFSdata.
measurethemorphologyinSection3andthedustpropertiesin
For the IRDIS broadband H data obtained in 2014, the atmo-
Section4includingthescatteringphasefunctionanddustspec-
spheric conditions degraded in the course of the observations,
tral reflectance. Finally, we discuss the new constraints on the
thisiswhyasevereframeselectionwasnecessarytoremovethe
dustpropertiesinSection5andspeculateontheoriginsofsuch
bad frames. Under good adaptive optics correction, the disc of
asharpoffsetringinSection6beforeconcludinginSection7.
HR4796AisvisibleinasingleDITintherawimage.Thedata
editingwasperformedbyinspectingvisuallytherawframesand
2. Observationsanddatareduction 74% of frames were removed (out of the complete 42 min se-
quence). The raw frames were sky-subtracted, flat-fielded and
2.1.Observations bad-pixelcorrectedusingtheSPHEREdatareductionandhan-
dling(DRH)pipeline(Pavlovetal.2008).Thissetofframesis
Two sets of near-infrared coronagraphic observations obtained
referred to as a cube, the third dimension being the time. The
ontwoepochsarepresentedhere,asshowninTable1.Bothob-
processedcubeswerethereafterre-centredusingthefoursatel-
servationsusedthepupil-trackingmodeofSPHERE,tokeepthe
lite spots imprinted in the image duringthe centring sequence.
aberrationsasstableaspossibleandbenefitfromthefieldrota-
With broadband filters, these satellite spots are elongated and
tiontoperformangulardifferentialimaging(ADI,Maroisetal.
weusedthetechniquedescribedinPueyoetal.(2015)basedon
2006). To reach a high contrast, both sets made use of the
a Radontransformto determinethe star location3. We checked
coronagraphic combination N_ALC_YJH_S corresponding to
that a visual adjustment of two lines passing through each op-
anapodizer,aLyotmaskofdiameter185masandanundersized
Lyotstop toblockthe starlightrejectedoffthemask aswellas positesatellite spotsagreeswith the retrievedstar location.We
estimate the absolute centring accuracy to 0.5px or ∼ 6 mas.
coverthetelescopespiders.
Theindividualimageswerenotrecentredbecauseanactivecen-
The first data set was recorded during the first commis-
sioning of the SPHERE instrument in April 20141. We used tring using the SPHERE differential tip/tilt sensor is dealing
with the relative frame-to-frame centring (Baudozetal. 2010).
the IRDIS subsystem (Dohlenetal. 2008) in classical imag-
Three reduction algorithms were used: classical ADI (cADI,
ing (Langloisetal. 2010) with the broadband H filter (λ =
1.625µm,∆λ = 0.29µm).TheIRDISimagersplitstheincom- Maroisetal. 2006), masked classical ADI (mcADI, Millietal.
2012)andPrincipalComponentAnalysis(PCA,Soummeretal.
inglightintwochannels,andinthecaseofbroadbandimaging,
2012;Amara&Quanz2012),showninFig.1.ThemcADIpro-
those two channels record the exact same information. IRDIS
provides a 11′′×11′′ field of view with a pixel scale of 12.25 ceedsin twosteps:abinarymaskisfirstappliedtothecubeof
pupil-stabilisedimagesto mask in each framethe pixelscorre-
mas. The star was observed after meridian passage, during 42
sponding to the ring. Because the disc rotates in the cube, the
minutesunderaveragetopooratmosphericconditions.Because
binary mask followsthis rotation. We computedthe median of
the conditions degraded during the observations, with a coher-
this masked cube to build a reference coronagraphicimage. In
encetimeofonly1msattheendofthesequence,onlythefirst
a secondstep, thisreferencecoronagraphicimageissubtracted
27minwereactuallyusedinthe datareduction,corresponding
to a parallactic angle variation of 21.5◦ out of a total available fromtheunmaskedcubeandthecubeisre-alignedandstacked.
of 31.2◦. The deep coronagraphicsequence was followed by a
point-spread function (hereafter PSF) measurement out of the 2 BasedonobservationsmadeattheParanalObservatoryunderESO
programme095.C-0298(H)
1 TheHR4796AimagefromtheApril2014datasetwaspartofthe 3 We used the Radon-based centring technique developed in
SPHERE first light images presented in the ESO press release 1417 the Vortex Image Processing pipeline (VIP, GómezGonzálezetal.
http://www.eso.org/public/news/eso1417/. 2017,submitted,availableathttps://github.com/vortex-exoplanet/VIP)
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J.Milli etal.:Near-infraredscatteredlightpropertiesoftheHR4796Adustring
Table1.LogofthetwosetsofSPHEREobservationsofHR4796A.
Date Set-up DITa(s)x Par. Seeing Coh. Wind True Platescaled
NDITxNEXP angleb(◦) (") timec(ms) (m/s) northd(◦) (mas/pixel)
2014/05/19 IRDISH 3x15x32 8.1;39.3 0.8;1.2 2.3;1.0 10.5 −134.87±0.6 12.238±0.020
IRDISH2H3 32x8x14 −134.155±0.006 12.257±0.03
2015/02/02 -9.3;39.4 0.6;0.7 11 3
IFSYJ 64x4x9 −33.65e ±0.13 7.46±0.02
Notes.(a)DITistheindividualdetectorintegrationtime(b)Parallacticangleatthestartandendoftheobservations.FortheApril2014observations,
notalltheavailablefieldrotationwasused(seeSection2fordetails).(c)Thecoherencetimeτ isdefinedasτ =0.31r /v,wherer istheFried
0 0 0 0
parametermeasuredbytheDIMMandvisthemaximumofthewindspeedmeasuredat30mheight,and0.4timesthepredictedwindspeedat
analtitudeof400mbar(Sarazin&Tokovinin2002).(d)ThecalibrationofthetruenorthandplatescalearedetailedinMaireetal.(2016).Thetrue
northindicatedhereincludestheoffsetbetweenthepupil-stabilisedandfield-stabilisedmode.(e) Arotationoffsetof−100.46±0.13◦ hasbeen
measuredbetweenIRDISandtheIFS.
Because theatmosphericconditionswerevariable,the starlight
leakingoutofthecoronagraphshowsstrongintensityvariations.
Inordertobetteraccountforthisvariabilityinthestarsubtrac-
tion procedure of the cADI and mcADI algorithms, we intro-
ducedascalingfactortoweightthecontributionofeachframein
thereferencecoronagraphicimagetobesubtracted.Thisturned
outtoimprovethelevelofresidualsofthefinalreducedimage
by scaling down the contribution of the images where a lot of
flux leakedoutofthe coronagraph.Eachframei ofthe cubeis
divided by a factor λ, subtracted by the median of the result-
i
ing cube of renormalised images and then re-multiplied by λ
i
inordertopreservethephotometryofthedisc.Thefactorλ is
i
thetotalfluxofframeiwithin1.75′′.Thecubeisthende-rotated
andmedian-combinedinordertoobtainthefinalreducedimage.
Forallthreereductions,bothIRDISchannelswerecombinedto
increasethesignal-to-noiseratio(S/N).
Fig.3.MaskedcADIandnon-ADIIRDISH2H3image,withacolour
Forthe2015IRDISdual-bandH2H3data,wealsousedthe scalelargerbyafactoroftenwithrespecttoFig.2toenhancethelarge
DRHpipelineforthestandardcosmeticcorrection,andthenper- dynamicalrangeoftheimagebetweentheverybrightsemi-minoraxis
formedfourGaussianfitsonthesatellitespotstodeterminethe inthewestandtherestofthering.
starcentrebehindthecoronagraphicmask.Weestimatedtheac-
curacy of the centring to 0.25px or 3mas. We applied similar
reduction algorithms as for the 2014 data set (without requir- The IFS data were reducedusing both custom routinesand
inganyrenormalizationhereduetostable conditions),namely, the DRH pipeline. The raw data were first sky-subtracted and
cADI, mcADI and PCA, as shown in Fig. 2. The H2 and H3 bad-pixelcorrected.Acorrectionofcross-talkbetweenspectral
filterswerecombinedinordertoincreasetheS/N,asnosignif- channelswasappliedtoremovethehighspatialfrequencycom-
icant variations were noticeable between the two images. The ponentofthecross-talk,asdescribedinViganetal.(2015).Af-
morestableconditions,inparticularthelongcoherencetime,re- ter building the master detector flat field, we called the DRH
sulted in smaller starlight residuals close to the coronagraphic pipeline on arc lamp calibration data taken in the morning fol-
mask,revealingunambiguouslyforthefirsttimetheentirering. lowing the observations to associate each detector pixel with
To enhance the dynamic range of the mcADI image, we have itscorrespondingwavelengthandobtainamapcalledthepixel
displayeditonFig.3withanunsaturatedcolourscaleshowing descriptiontable. Themaster flat field andpixeldescriptionta-
thefullrangeofdiscbrightness.Thestabilityofthisdatasetal- ble were used as inputfor the main science recipe of the DRH
lowed us to avoid resorting to ADI to detect the disc, enabling pipelinecalledsph_ifs_science_dr,thatbuildsthespectralcube
access to an unbiased view of the disc, free from ADI artifacts consisting of 39 spectral channels and resamples each channel
(Millietal.2012).ThisisshowninFig.3(right).Asimpleaz- on a square regular grid of size 7.4 mas per pixel. The wave-
imuthal median was subtracted from each individual frame of length calibration was then more accurately determined using
thecubebeforede-rotatingandstackingthecube.Thetwofea- the arc lamp calibration files and the chromatic radial depen-
turesextending45◦ counter-clockwisefromneartheringansae danceofthesatellitespots,asdescribedindetailinappendixA.2
are instrumental artefacts: these are two brighter regionsat the ofViganetal.(2015).Thespectralaccuracyofthisprocedureis
edge of the well-corrected area producedby a periodic pattern estimatedtobe1.2nm.Foreachspectralchannel,thesamethree
on the deformable mirror. This azimuthal asymmetry is totally algorithmsas those used to reduce the IRDIS images were ap-
subtractedinADIbutitisnotremovedbyanon-ADIreduction. plied, and the final images were normalised by the integrated
The de-rotation of the images smears this brighter region over flux within the central resolution element of the star observed
anarcwhoseazimuthalextentequalstheparallacticanglevaria- outofthecoronagraphicmask.Fig.4(lastpanel)showstheIFS
tion,asvisibleinthediagonalofFig.3(right-handpanel).This imageaveragedoverallspectralchannelsandweprovideinthe
doesnot,however,impedethe analysisonthe otherpartof the otherpanelsofFig.413normalisedimagesobtainedaftermean-
image, and confirms the view of the disc given by the mcADI combining every three adjacent spectral channels. Because the
image. disc diameter is slightly larger than the IFS field of view, the
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Fig.1.ImagesofthediscaroundHR4796AfromIRDISintheH-band,reducedwiththreedifferentreductionalgorithms:cADI,maskedcADI
andPCA(firstfiveeigenmodesremoved).Northisup,easttotheleft.Thecolourscaleisidenticalforallthreereductions.Theblackregionalong
thesemi-minoraxisofthemcADIimagecorrespondstoregionwerethediscisentirelyself-subractedthereforenoinformationcanberetrieved.
Fig.2. Imagesof thediscaround HR4796AfromIRDISintheH2H3filter,reduced withthreedifferent reductionalgorithms:cADI,masked
cADIandPCA(firstfiveeigenmodesremoved).Thecolourscaleisidentical.
ansaearenotvisibleduringthewholesequenceofobservations, processed using a PCA algorithm that subtracts from 1 to 500
andthebackgroundnoiseishigherbeyond1.7′′,forexamplein modesin steps of ten. The same processis appliedto the orig-
the ansae of the disc. Moreover, the disc being offset from the inalcubeofimageswherefakecompanionshaveinitially been
star towardsthe south-west(SW), the SW ansa spendsa larger injected, in order to retrieve the S/N level of each companion
amountoftimeoutsidetheIFSfieldofviewthanthenorth-east in the reduced image. Fake planets are injected at separations
(NE)ansa,resultinginanapparentlowerS/N. from100masto750masonaspiralpatterntoavoidanyspatial
orspectraloverlapduringthespecklesubtractionalgorithm.To
properlysamplethewholefield,theanalysisisrepeatedwiththe
2.3.Contrastandplanetdetectionlimits fakeplanetsmap injectedatten distinctorientations.Theposi-
tion of all injected fake planets is illustrated in Fig. 5 left. The
ThederivationofthedetectionlimitsfortheIFSdatawasdone
S/N is definedas the maximumpixelvalueof the image at the
followingthemethodologydescribedinViganetal.(2015).We
knownlocationof the planetafter convolutionwith a kernelof
summarizeherethemainsteps.Todetectpointsources,bothan-
one resolution element size, divided by the rms of statistically
gularandspectraldifferentialimagingareusedhere.Theimages
independentpixelsinanannuluslocatedatthesameseparation
arefirstrescaledspatiallysothatthespecklepatternmatchesat
as the planet. The penalty term from the small sample statis-
all wavelengths. This leads to a rescaled cube of both spectral
ticsdescribedbyMawetetal.(2014)istakenintoaccount.This
and temporal images, where the signal of a potential compan-
processis repeateduntila S/N of5 is reached,the correspond-
ion would move both with time and wavelength. This cube is
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J.Milli etal.:Near-infraredscatteredlightpropertiesoftheHR4796Adustring
Fig.4.MaskedcADIimagesobtainedafterbinningthreeadjacentspectralchannelsoftheIFS.TheimageswerescaledbythefluxofthePSFand
thecolourscaleisidenticalforallimages.ThelastimageisthecombinationobtainedbystackingallspectralchannelsoftheIFS
ingcontrastinmagnitudeisshowninFigure5.Thefakeplanets
8
are injected with the spectra of the central star HR4796A, for
examplewithaconstantcontrastwithrespecttothestarateach 14.4 9
wavelength, which is a conservative assumption because spec- 1.0 13.6
tral self-subtraction degrades the detection limits. An average 10
c
contrast of 15 magnitudes is reached at 0.7′′ close to the edge se 0.5 12.8 ag
ofofrtheFeaocfirheIlRsdpDeocIfStvr,aielthwceh,aadnnendteeacltvbioaynlureelidmoufict1isn3gairstehoecbotdamaitnpaeudutesaditn0gin.2ad′i′Pv.iCdAuaallly- Distance in arc−00..05 1112..20 Contrast in m111312
gorithmremovingonesingle modeoverthe wholeimage from
10.4
0.02′′ to 2.4′′. The flux losses due to the ADI process are also −1.−01.0 −0.5 0.0 0.5 1.0 14
computedusingfakeplanetsinjectedatincreasingradiiinthree Distance in arcsec 9.6
branchesatalevelofabout5σ.ThecontrastmapshowninFig.6 15
8.8
forH2isdefinedasthermsinaboxof3×3resolutionelements, 0.0 0.1 0.20.30.4 0.50.6 0.7
correctedforthefluxlossesandthesmallsamplestatistics.The Separation in arcsec
contrastmapfortheH3channelisalmostidentical.Aconstrast
Fig.5.Left:Mapofthe5σdetectionlimitsexpressedinmagnitudefor
of16magnitudesisreachedoutsidethecorrectionradiusofthe
adaptiveopticssystem at2′′, anda valueof13.2is obtainedat theIFS.Thedetectionlimitswerecomputedatthepositionoftheblack
dots,byinjectingfakeplanetsasdetailedinViganetal.(2015).Right:
0.5′′.
Radialcurveof thedetectionlimits.Eachpoint corresponds toafake
Thedetectionlimitsincontrastwereconvertedinmassusing planetintheleftimage.Thecontrastisindependentofthewavelength
the AMES-Cond-2000evolutionarymodel(Allardetal. 2011), becauseweassumedastellarspectrum.
assuminganageof10Myrsforthesystem(Belletal.2015).For
the IFS, we used the mass to luminosity relation in broadband
J, asvalidatedbyViganetal.(2015).Theyindeedperformeda IFS wavelength range, if one uses the longest IFS wavelength,
detailedderivationofthedetectionlimitsforanotherAstar,Sir- theJbandinourcase,toconverttheplanetluminsoityinmass.
ius,basedontheinjectionoffakeplanetsusingplanetaryatmo- TheIFSobservationsaredeeperthanIRDISandprobelessmas-
spheric models. They showedthat the results are well approxi- sive planets below 0.4′′, they are equivalent between 0.4′′ and
matedbyusingastellarspectraforthefakeplanets,forexample, 0.5′′, and IRDIS is slightly deeper above 0.5′′. A comparison
aconstantcontrastbetweenthestarandtheplanetthroughoutthe with the best existing detection limits on the system, obtained
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inFig.7.Thefullwidthathalf-maximum(FWHM)ofthedisc
16.0 7
measuredalongtheansaeis0.12′′atH2,comparedtoaFWHM
15.2 8 of0.046′′ for the PSF. The PSF profile hasbeen overplottedin
14.4 9 Fig.7toillustratethisresult.
e
Distance in arcsec−−02112 1111101223.....42086 contrast in magnitud5σ 1111140312 PstacnemaiSvrsuFamacsM.lloelueI(reetnMrrhaeovestcuafhuytslier0utncei.aeglnm1lnse8f&eoao4bnrfr′e-tW′0situn±h.y1osfeer0a1fadwt.′ttr0′he±ti12oded′00t′,ch.t10iorg2nub1nr)eor′sa.′outSwriavnnacdeidihdtern-hyntnbheteihawniKseodgiefdedbdeerutaffh-mesnbeettdaeccarnat(olisPd.onnue(fgfiir2rntenra0hmitern0eheme9eHen)cetotSrnmasipTttltie.smicha2/caseoa0Slucwl1Trbha5eeIeaf)Sdd---,
−2 −1 0 1 2 9.6
0.102′′ intheH band(Wahhajetal.2014),0.14′′±0.03′′ from
Distance in arcsec 8.8 15 1 to 4µm (Rodigasetal. 2012) and < 0.14′′ in the L band
8.0 16 (Lagrangeetal. 2012a), all after correction for the PSF convo-
0.0 0.5 1.0 1.5 2.0
Distance in arcsec lution.
Two effects mainly affect the measured width of the ring:
Fig.6.Left:Mapofthe5σdetectionlimitsexpressedinmagnitudefor theconvolutionwiththePSFandthepotentialbiasfromthere-
IRDISintheH2band.Right:Azimuthalmedianofthe2dcontrastmap ductiontechnique.Weintroducedafakediscintherawimages
displayed on the left. The bump at 0.8′′ is the limit of the correction at 90◦ from the real one, reduced the images with mcADI and
radiusoftheadaptiveopticssystem.
non-ADIagain,andperformedthewidthmeasurementsonboth
ansaeofthefakedisc.Wefound,asalsoshowninLagrangeetal.
Table2.DetectionlimitsinJupitermassesfromtheseobservationcom-
(2012a),thatthemostimportanteffectisduetothePSFconvo-
paredtothepreviousbestlimitssetonthesystembyVLT/NaCointhe
L′ band (Lagrangeetal. 2012a), comparable to that of Rodigasetal. lution,whichincreasesthewidthby26%andthatmcADIdoes
(2014)obtainedatL′withMagAO/Clio-2. notbiasthemeasuredwidthwithrespecttothewidthofthecon-
volveddisctomorethan1%.InnonADI,theimagessufferfrom
Separationin′′ VLT/NaCoa VLT/SPHEREb ahighresidualnoise,hencealargerdispersion.
0.1 32 15 TheFWHM aftercorrectionforthePSFconvolutionisdis-
0.2 32 5 playedinTable3.Tocomputetheerrorbar,weassignedanerror
0.5 3.5 2 to each pixel of the ansa radial profile, defined as the standard
1.0 3.0 1.5 deviationofthepixelswithinanannulusatthesameradius(af-
1.5 2.0 1.5 termaskingthering).WethenmeasuredagaintheFWHMafter
addinggaussiannoiseto theansa profileandrepeatedthispro-
Notes.(a)ThedetectionlimitsarefromtheSparseApertureMaskmode cess 104 times to estimate the dispersion. Because of the low-
of NaCo (Lacouretal. 2011) below 0.3′′ and from classical imaging frequencynoiseinthenon-ADIimages,thisuncertaintyappears
above 0.3′′. (b) The detection limits are from the IFS below 0.4′′ and large but it is fully consistent with the mcADI values, and one
fromIRDISabove0.4′′. hastobearinmindthatthisisthefirsttimesuchameasurement
ispossibleonanimagewithoutperforminganystar-subtraction
withNaCointheL′ bandisshowninTable2forafewsepara- algorithm.TheringwidthisnarrowerthanthatoftheSTISdata
andwesuspectthatthisarisesfrombothasystematicbiasanda
tions. We discussthe presenceof planetsbasedonthese detec-
physicaleffect.Indeed,apurephysicaleffectwitharingwiderin
tionlimitsinSection6andalsoshowtheremorespecificradial
theopticalmightbeexpectedifsmallgrains,whicharelesseffi-
curves of the detection limits along the semi-major and semi-
cientnear-infraredscatterers,arebeingblownoutofthesystem.
minoraxisofthedisc.
Inthiscase,theouterhalf-widthathalf-maximum(HWHM)is
expectedto be wider in the optical.We howevermeasuredthat
3. Observeddiscmorphology boththeinnerandouterHWHM aresmallerwithIRDISinthe
near-infraredthanwith STISin the optical.Therefore,a physi-
Allreductions(Fig.1to4)revealthediscwithahighsignalto caleffectisnotenoughtoexplainthisdiscrepancy.Itishowever
noise.The2015datashowtheentirering,eventhesemi-minor likely to play a minor contribution, because the discrepancy is
axis which has, so far, always been hidden by strong starlight smallerfortheouterHWHM.Wethinkthatthemainexplanation
residuals at such a short separation (∼ 0.24′′). The 2014 data comesfromasystematicbiasbetweenthetwomeasurements.In
showastrongerS/Nintheansae,duetothewiderspectralband- particularwesuspectthatthesimplequadraticsubtractionused
pass, but suffers from increased noise at short separations due tocorrectforthePSFconvolutionwithSTISunderestimatesthe
tothepooreratmosphericconditions.Strongresidualsfromthe intrinsicFWHMoftheringduetotheverysteepinnerandouter
diffractionbythefourspidersofthetelescopeareindeedvisible profiles,asdetailedbelow.
within0.25′′inFig.1. The disc profile is asymmetric, with a slope steeper inside
thanoutside.Toquantifythisasymmetry,wefittedapowerlaw
ofequationΛ×r−αtotheinnerandouterradialprofile.Wemea-
3.1.Surfacebrigthnessradialprofiles
suredtheinnerslopeα over0.06′′ or4.5au,priortothepeak
in
The disc appears as a thin elliptical ring. It is clearly resolved brighntessofthering,andtheouterslopeα over0.21′′ or15
out
radially both with IRDIS in the H or H2H3 filter and with the au,after thepeak.Figure8 illustrates thismeasurementforthe
IFSintheYband.Wemeasuredtheradialprofileofthediscat H2 image reduced with mcADI. The measurement is sensitive
regularintervalsalong the ellipse. The profilesalong the semi- totheboundariesusedforthefit. Forhomogeneityofthe mea-
major axisfor the mcADI andnon-ADIreductionsprovidethe surementspresentedhere,wehaveusedthesameboundariesfor
leastbiasedmeasurementsoftheringtruewidth.Weshowthem alltheimageswherethefitwasperformed(differentfiltersand
Articlenumber,page6of25
J.Milli etal.:Near-infraredscatteredlightpropertiesoftheHR4796Adustring
102 102
PSF H2 Fit outer slope αout=−17.7
nonADI H2 NE Fit inner slope α =23.2
in
mcADI H2 NE PSF H2
101 nonADI H3 NE 101 mcADI H2 NE
U U
D mcADI H3 NE D
A A
n mcADI H NE n
x i x i
u u
Fl Fl
100 100
10-1 10-1
102 102
Separation in au Separation in au
102 102
PSF H2 Fit outer slope αout=−13.3
nonADI H2 SW Fit inner slope α =23.3
in
mcADI H2 SW PSF H2
101 nonADI H3 SW 101 mcADI H2 SW
U U
D mcADI H3 SW D
A A
n mcADI H SW n
x i x i
u u
Fl Fl
100 100
10-1 10-1
102 102
Separation in au Separation in au
Fig.7.Radialprofilesofthediscalongthesemi-majoraxis(NEansa Fig.8.Radialprofilesalongthesemi-majoraxisofthediscasmeasured
atthetop,SWansaatthebottom),shownherefordifferentreductions, in the H2, mcADI-reduced image. The vertical red dotted lines show
andfilters.Forcomparisonweoverplottedthemeanradialprofileofthe theboundaryusedforthefitoftheinnerandouterprofilewithapower
measuredPSFintheH2filter.Theprofileshavenotbeennormalisedbut law.TheprofileofthePSFisindicatedasareference.Thetopimage
havebychanceasimilarfluxinADUforthefiltersshownhere. correspondstotheNEansaandthebottomonetotheSWansa.
Table3.RingradialFWHMalongthesemi-majoraxis.Theuncertainty
isgivenat3σ.
patible and show that the disc displays an overall inner slope
Dataset Side Unit mcADI non-ADI
α = 18±3.5andanouterslopeofα = −13±2.3(meanof
′′ 0.092±0.011 0.111±0.043 in out
IRDISH2 NE thenonADI measurements,least biasedby the reductiontech-
au 6.7±0.8 8.1±3.1
nique).Theinnerslopeisverysteepbutnotassteepastheslope
′′ 0.096±0.014 0.137±0.050
IRDISH2 SW ofthe measuredPSF(see Fig. 7).As anexercise,we modelled
au 7.0±1.0 9.9±3.6
a disc with a sharp step-like transition for the inner and outer
′′ 0.099±0.014 0.099±0.050
IRDISH3 NE edges,andmeasuredafterconvolutionandmcADIreductionan
au 7.2±1.0 7.2±3.6
innerslopeof35±1.4andanouterslopeof−32±1.8.Themea-
′′ 0.099±0.013 0.123±0.113
IRDISH3 SW surements of Fig. 9 are therefore not compatible with a sharp
au 7.2±1.0 9.0±8.2
transitionfortheouteredgeofthediscandonlymarginallycom-
′′ 0.096±0.011 NA
IRDISH NE patiblewithasharpinneredge.
au 7.0±0.8 NA
′′ 0.088±0.014 NA
IRDISH SW
au 6.4±1.0 NA
3.2.Centreoffsetofthering
reduction techniques). For the inner profile, we cannot use re- The ring is known to be offset from the star. Several authors
gionsatmorethan73masfromthepeaktowardsthestar,either previsouly measured the geometry of the ring using the max-
because of self-subtraction in case of the mcADI reduction or imum merit procedure described in Buenzlietal. (2010) and
because of strong starlight residuals in non-ADI. For the outer Thalmannetal.(2011).Because thedisc isnowdetectedalong
profile,welimitedthefittingareatoregionswithin0.25′′ofthe allazimuths,wedevelopedanalternativemethodbasedonadis-
peak,asshowninFig.8. cretesamplingofthering,whichturnsouttobemoresensitive
The measured slopes are displayed in Fig. 9. The different totheellipseparameters.Foragivenazimuth,wefittedasmooth
measurements display a large uncertainty but are overall com- combinationoftwopowerlawsdescribedbythefollowingequa-
Articlenumber,page7of25
A&Aproofs:manuscriptno.HR4796_SPHERE_v7
Table5.Weighted-averageddiscdeprojectedparameterscombiningall
bands.Theuncertaintyisgivenat3σandincludesmeasurementuncer-
−5
NE nonADI H2 tainties, systematics from the instrument and from the data reduction
−10
pe NE mcADI H2 algorithm.
slo−15 NE nonADI H3
er −20 NE mcADI H3 a(mas) 1065±7
Out−25 NE mcADI H e 0.06±0.014
−30 i(◦) 76.45±0.7
0 10 20 30 40 50 60 ω(◦) −74.3±6.2
−5 Inner slope
SW nonADI H2 Ω(◦) 27.1±0.7
−10
pe SW mcADI H2
slo−15 SW nonADI H3
er −20 SW mcADI H3
Out−25 SW mcADI H Asasanitycheckofthisnewmethodintroducedtomeasure
themorphologyofa ring,we fita modeldiscdirectlyfromthe
−30
0 10 20 30 40 50 60 reduced image, using the GraTeR code (Augereauetal. 1999),
Inner slope aproceduremoresimilartothemaximummerittechnique.This
givesa verygoodagreementwith the new techniquedescribed
Fig.9.Innerandouterslopeofradialbrightnessprofilealongthesemi-
above.Thedescriptionandresultsofthissanitycheckaregiven
major axis (NE ansa on the top, SW ansa on the bottom), with a 3σ
errorbar. inAppendixB.
Moreover,ADIisknowntointroducebiasesinthemorpho-
logicalparametersextractedfromthereducedimage(Millietal.
tion initally introduced by Augereauetal. (1999) to the radial 2012).Here,theuseofmaskedcADIdoesindeedminimisedisc
profileoftheimage: self subtractionand biases but it doesnottotally removethem.
Therefore,we analysed these biases by repeating the measure-
mentproceduredescribedpreviouslyonamodeldiscimagegen-
1/2
eratedwithknownparameters.Weusedthebestellipseparame-
2
I(r)=I0×(cid:16)rr0(cid:17)−2κin +(cid:16)rr0(cid:17)−2κout . (1) ttaeegrceshin(naiq,aeu,fei,aωfko,eΩrpt)huaepsiHld-2setrabivbaeinldidsi.enWdTceaubtbhleeen4w,iinfthrsoetmrhteetdhsaethmdeeedppirsoocsjeimttieoodndiemalniagmglee-
asintherealH2observations.Weconvolvedeachimagebythe
We derived the radius of the maximum brightness of the ring
PSF measured at H2, reduced the cube with the mcADI algo-
forthatazimuth.Werepeatedthismeasurementfordifferentaz-
rithm,andrepeatedthemeasurementproceduredevelopedabove
imuths in order to sample regularly the disc every resolution
toretrievethediscparameters.Wefoundthatthebiasfromthe
element (one FWHM). We then found the best ellipse pass-
PSFconvolutionandADIdatareductiononthesemi-majoraxis
ing throughthese points. An illustration of those measurement
a of the disc is negligible (0.1%), as well as on the inclination
pointsalong with the bestellipse is givenin the top righthand
of the disc (deviationof less than 0.2◦, smaller than the uncer-
imageofFig.A.1,A.2,A.3andA.4inAppendixA.Tofindthe
tainty).Howeverthedeviationisoftheorderoftheuncertainty
bestellipsepassingthroughthemeasurementpoints,weimple-
fortheeccentricity(0.009)andfortheargumentofpericentreω
mented the non-linear geometric fitting approach described in
(8◦),andthereisasignificantbiasof0.9◦ onthePA oftheline
Ray&Srivastava(2008).WeusedaMarkovchainMonteCarlo
ofnodesΩ.Wethereforeincludethissystematicsourceoferror
technique(hereafterMCMC)tofindthebestellipseminimising
inthefinalerrorbargiveninTable5.
Eq.15ofRay&Srivastava(2008). We chosetoimplementthe
MCMC with the affine-invariant ensemble sampler called em- Theaverageofthesemeasurementsissummarisedinthelast
cee (Foreman-Mackeyetal. 2013). By doing this, we retrieved column of Table 5, including all sources of errors. These mea-
the parameters of the projected ellipse in the plane of the sky: surements show that the disc is elliptic with a mean ellipticity
theprojectedsemi-majoraxisa′,theprojectedsemi-minoraxis of 0.059 ± 0.020 (average for the "deprojected ellipse" tech-
b′, the offsets ∆α and ∆δ in right ascension and declination of nique),in goodagreementwith Rodigasetal. (2014) who esti-
the ellipse centre with respect to the star location, and the po- mated0.060±0.020.Theargumentofpericentreωis−74◦±12◦,
sition angle PA. These parameters are given in Table 4, in the which means that it is close to the semi-minor axis of the pro-
rowscorrespondingto"projectedellipse",togetherwiththeun- jected image of the disc, in the north-east quadrant. We note
certaintymeasureddirectlyon the posteriorprobabilitydensity that the value of ω reported here is compatible with the Fig.
functionofthefittedparameters.UsingtheKowalskydeprojec- 3 of Rodigasetal. (2014) but not with their numerical value
tiontechniquedescribedinSmart(1930)forbinarysystemsand of 110.6◦ ± 12.6◦ and we suspect that the definition of ω for
also appliedbyStarketal.(2014);Rodigasetal. (2015)onde- botharticlesdiffersbyafactor180◦ becauseoftheoppositeas-
brisdiscs,wederivedtheparametersofthetrueellipsedescribed sumptionfortheforward-scatteringside.Theinclinationiscom-
bythedustparticlesintheorbitalplane:thetruesemi-majoraxis patiblewithpreviousmeasurementsbyThalmannetal.(2011);
a,theeccentricitye,theinclinationi,theargumentofpericentre Schneideretal.(2009)andRodigasetal.(2014)
ω and the longitude of ascending node Ω. This technique uses Figure10showsthedeprojectedimageofthediscatH2,as-
theexactsameinputasthedirectellipticalfitandthesamemet- suming the ring has no vertical thickness. Because the on-sky
ric to compute the distance between a modeland the measure- projectedimageistheoriginaldiscconvolvedbythePSFofthe
ments;theonlydifferencebeingthattheparameterspaceisthe instrument, the image appears after deprojection convolved by
ellipsetrueorbitalelementswhicharethenconvertedinthesky an elliptical PSF, which biases our view of the disc. We there-
planebeforecomputingthelikelihoodofeachmodel.Theresult fore deconvolved the image prior to deproject it. We used the
is given in Table 4, in the rows corresponding to "deprojected deconvolutionalgorithmMISTRAL(Conanetal.1999)adapted
ellipse". foradaptiveopticsimageswithimpreciseknowledgeofthePSF.
Articlenumber,page8of25
J.Milli etal.:Near-infraredscatteredlightpropertiesoftheHR4796Adustring
Table4. Projectedand deprojected ring parameters. Theerror isgiven at a3σ level and contains only thestatisticalerror fromthefit and no
systematicerrorfromthetruenorthorstarregistration.
Typeoffit Parameter IRDISH IRDISH2 IRDISH3 IFS
a′(mas) 1064±6 1064±8 1066±8 1059±4
ed e b′(mas) 252±4 249±3 248±3 249±2
roject ellips ∆∆αδ((mmaass)) −−248±±45 −−243±±46 −−233±±46 −−174±±24
P PA(◦) 27.69±0.26 27.00±0.25 26.99±0.27 26.81±0.16
a(mas) 1066±6 1064±8 1067±8 1061±5
d
cte e e 0.070±0.011 0.059±0.010 0.057±0.011 0.052±0.007
proje ellips ωi((◦◦)) −7762.3.434±±05.2.140 −7763.4.083±±06.2.941 −7761.5.650±±07.2.742 −7860.4.125±±04.1.454
De Ω(◦) 27.71±0.25 27.02±0.25 27.02±0.27 26.82±0.16
Thedeprojectedviewenhancesthebrightasymmetryduetothe
anisotropicphasefunctionofthedisc,asalreadyseenonthepro-
jectedimage.Thebrightestpartoftheringappearsalsothicker. Pericenter
Apossibleexplanationisthesmallbutnon-zeroverticalheight
of the disc combined with a very anisotropic scattering phase
function. It is also seen on model discs combining those two
properties. Indeed, along the semi-minor axis towards the star,
the scattering angle can be smaller than 13.6◦ above the mid-
plane,ifthediscisnotverticallyflat.Averysteepphasefunction
couldthereforecompensatethesmallerdustdensityawayfrom
the midplane to make the ring appear thicker towards the star.
Ontheotherhand,tworegionsappearfainter,inthenorth-west Lin
(NW) and south-west (SW), apart from the pericentre. This is e of n
probablyphysicalandcanoriginatefromadipinthescattering od
e
phasefunctionofthedust,asdiscussedinthenextsection,ora s
decreaseinthedustdensityclosetothetruesemi-minoraxisof
Apocenter
thedisc.WealsonotethatatthisSWposition,previousobserva-
tionstentativelyshowedadistortioninthering(Lagrangeetal.
2012a;Thalmannetal.2011),butthesenewobservationsdonot
confirmthisfeature.Thedeprojectedimagealsoshowsblobsin
the regions initially the closer to the star before the deprojec-0.00e+00 2.52e+03 1.67e+04 9.68e+04 5.44e+05
tion. They are probably artifacts resulting from the deconvolu- Fig. 10. Deprojected view of the ring, after deconvolution of the H2
tion,laterelongatedperpendiculartothelineofnodesbythede- image.Thecolourscaleislogarithmic,northisup,easttotheleft.The
projection.ThegapsseenintheSEansaareprobablynotphys- yellowcrossindicatesthelocationofthestar.
ical, and are relatedto the largeflux losses fromADI occuring
along the semi-minoraxis of the disc (detailed later in Section
tionsaretwofold.Firstwemustassumethatthedischasaneg-
4).
ligible scale heightwith respect to the radialextension, so that
each point along the ring correspondsto a unique value of the
4. Observeddustscatteringproperties scatteringangle.Second,wemustalsoassumethatthedustden-
sity distribution is uniform azimuthally and the dust properties
With the new IRDIS observations, we can now probe the scat- areidenticalazimuthally.Inotherwords,aftercorrectingforthe
teringphasefunction(hereafterSPF)atanglesneveraccessible distance between the scatterers and the star, the ADI flux loss
uptonow.Byincreasingthisrangeofscatteringangles,wein- andtheconvolutionbythePSF,anyazimuthalbrightnessvaria-
tendtoconfirmthatwhatwasinterpretedin thepastasa slight tionalongtheringisentirelyattributabletotheshapeoftheSPF.
preferentialforwardscattering(e.g.Schneideretal.2009)turns Thedataareconsistentwiththesetwoassumptions,asweshall
outtobeaslightpreferentialbackwardscattering,withapeakof see.ToretrievetheSPF,weproceededasfollows:
forward-scatteringontheothersideofthedisc, asalreadypro- First,weregularlysampledthebestellipse(asdefinedinthe
posed to explainrecentscattered lightobservations(Millietal. firstrowofTable4).Thespacingbetweeneachpointwassetto
2015; Perrinetal. 2015). These new conclusions enable us to oneresolutionelement.We associatedto eachpointatposition
reconcile the polarised and non-polarised images without the angleθintheplaneoftheskyauniquescatteringphaseangleϕ
needforanopticaldepthaboutunity,asproposedbyPerrinetal. givenbythefollowingexpression
(2015).
1
ϕ=arcsin . (2)
4K.n1o.wPihnagstehefutnrucetioonrboitfatlheeledmisecntsofthering(Table4),wecan qsin2(θ−Ω)/cos2i+cos2(θ−Ω)
derive the SPF of the dust, as it was done for the debris disc Weusedinthisexpressiontheaverageinclinationiandaverage
around HD181327(Starketal. 2014). The underlyingassump- positionangleofthe lineofnodesΩ fromTable5. We consid-
Articlenumber,page9of25
A&Aproofs:manuscriptno.HR4796_SPHERE_v7
N Unconvolved model Convolved model Reduced model
.6°
E
=
3 0 23 45 68 90
Fig.12.Discimageswiththesamecolourscaleshowingtheeffectof
theconvolutionandthemcADIreduction.
0.0
−0.1
1.0
−0.2
Fig.11.Schematicsofthering,definingtheanglesθandφusedinEq. c 0.5 −0.3
2.Weplottedasanillustration3pointsalongthering,definedbythe se
PAθiandcorrespondingtoascatteringangleφi e in arc 0.0 −−00..54
c
an −0.6
eredvaluesofϕbetween0and180◦,assumingthattheforward- Dist−0.5 −0.7
scatteringsideofthedisc(0≤ ϕ ≤ 90◦ )isontheNW(seedis-
cussionbelow).Aschematicsillustratingthoseanglesisshown −0.8
−1.0
inFig.11. −0.9
Second, for each location, we performed aperture photom- −1.0
−0.5 0.0 0.5
etry on the as-observed (projected) view of the ring, requiring
Distance in arcsec
thereforeellipticalaperturestoaccountfortheprojectioneffect.
Each ellipticalaperturewere orientedalongthe PA of the disc,
Fig. 13. Map of the flux loss resulting from the mcADI reduction. A
had a semi-majoraxis 0.1′′ (aboutthe FWHM of the ring)and valueof0indicatestheabsenceoffluxlosswhileavalueof-1means
withthesamemajortominoraxisratioasthedisc(i.e.4.25).Us- allthediscfluxisremovedbyADI.
ingellipticalapertureswithsuchanaspectratioontheprojected
image is identical as using circular apertures on a deprojected
imageofthedisc.Withtheformertechnique,thenoiseestima- age on a large region. A map of the flux loss is shown in Fig.
tioniseasierbecauseitisonlyradiallydependentontheon-sky 13.
projected image, whereas it also depends on the azimuth for a The final result was normalisedto one at the NE ansa. The
deprojectedimage. resulting curve for the H2 (top) and H3 filters (bottom) are
Last, we corrected the flux measured in each aperture by shown in Fig. 14. No spectral dependance in the phase func-
threeterms:theinversephysicaldistancesquaredduethestellar tion is observedbetween the two filters, within error bars. The
illumination, a correction term to account for ADI flux losses, curvesshowasteepdecreasefromthesmallestscatteringangle
andacorrectiontermtoaccoundfortheconvolutionbythein- ϕ = 90◦ −i = 13.6◦ to 40◦ followed by an increasing and lin-
strumentalPSF.Thosethreetermsdependonthepositionalong eartrenduntilthelargestscatteringangleϕ = 90◦+i = 166.6◦
theringandthereforehaveanimpactonthederivedphasefunc- seengiventhediscviewingangle.Theincreasedetectedbeyond
tion. To computethe last two terms, we used an isotropicscat- 160◦ on the north side is likely to be an artifact resulting from
tered light model of the disc created with the GrAteR code aquasi-staticspecklepinnedonanAiryringatthisexactloca-
(Augereauetal. 1999), with the parameters described in Table tionandsmearedasan arcdueto the derotationofthe images.
5,illustratedinFig.12left.Wecomparedtheellipticalaperture There are several reasons for which we do not believe in this
photometryoftheinitalunconvolvedmodeldiscwiththatofthe feature. First it is not seen on the southern side of the disc, al-
finalimageafterinsertionofthemodelinafakepupil-stabilised thoughthe SPF as derivedfromthe northernandsouthernside
cube, convolutionby the PSF and mcADI reduction.To do so, mustbeidentical.Thisbrightfeatureclearlyappearsinthefinal
weinsertedthemodelinafakepupil-stabilisedcubeofimages, imageasaportionofacircularringwhereasthedisccurvature
with the same orientation as seen during the observations and isverysmallalongthesemi-minoraxis.Last,wesuspectthatit
each image was convolved by the PSF. Fig. 12 middle shows may correspond to the location of a PSF Airy ring for the H2
thisconvolvedmodel.Theeffectoftheconvolutionismainlyto andH3wavelengths,asshowninFig.15.Thesharpincreaseof
enhance the ansae. Then the cube is reduced using the mcADI thephasefunctionforscatteringanglesbelow30◦ isinterpreted
algorithm (Fig. 12 right). With the masking strategy, the ADI asforwardscattering,meaningthatthe westernside isinclined
fluxlossesareminimisedtolessthan10%inmostareasofthe towards the Earth. Although this has been a matter of debate
disc, and affect mostly the semi-minor axis because the mask (seeforinstanceMillietal.2015;Perrinetal. 2015),thephase
was slightly undersized with respect to the disc true width to functionanalysis now clearly supports this assumption. Indeed
avoidbeingunabletoevaluatethe referencecoronagraphicim- Hapke(2012)analysed495varietiesofparticlesincludingsolar
Articlenumber,page10of25