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) Articlenumber,page2of25 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 Articlenumber,page3of25 A&Aproofs:manuscriptno.HR4796_SPHERE_v7 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 Articlenumber,page4of25 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 Articlenumber,page5of25 A&Aproofs:manuscriptno.HR4796_SPHERE_v7 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