Azimuthal asymmetries in the debris disk around HD61005

7.5 MB·

by  J. Olofsson

Astronomy & Astrophysics manuscript no. The_Moth (cid:13)cESO 2016
May 11, 2016
Azimuthal asymmetries in the debris disk around HD 61005(cid:63)
A massive collision of planetesimals ?
J. Olofsson1,2,3, M. Samland3, H. Avenhaus4,2, C. Caceres1,2, Th. Henning3, A. Moór5, J. Milli6, H.
Canovas1,2, S. P. Quanz7, M. R. Schreiber1,2, J.-C. Augereau8,9, A. Bayo1,2, A. Bazzon7, J.-L. Beuzit8,9, A.
Boccaletti10, E. Buenzli7, S. Casassus4,2, G. Chauvin8,9, C. Dominik11, S. Desidera12, M. Feldt3, R.
Gratton12, M. Janson3,13, A.-M. Lagrange8,9, M. Langlois14,15, J. Lannier8,9, A.-L. Maire12,3, D. Mesa12, C.
Pinte16,8, D. Rouan10, G. Salter15, C. Thalmann7, and A. Vigan15,6
6
(Affiliations can be found after the references)
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0
May 11, 2016
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y
ABSTRACT
a
M
Context.Debrisdisksoffervaluableinsightsintothelateststagesofcircumstellardiskevolution,andcanpossiblyhelp
ustotracetheoutcomesofplanetaryformationprocesses.Intheagerange10to100Myr,mostofthegasisexpected
0 to have been removed from the system, giant planets (if any) must have already been formed, and the formation of
1 terrestrial planets may be on-going. Pluto-sized planetesimals, and their debris released in a collisional cascade, are
under their mutual gravitational influence, which may result into non-axisymmetric structures in the debris disk.

] Aims.Highangularresolutionobservationsarerequiredtoinvestigatetheseeffectsandconstrainthedynamicalevolution
R
ofdebrisdisks.Furthermore,multi-wavelengthobservationscanprovideinformationaboutthedustdynamicsbyprobing
S different grain sizes.
. Methods. Here we present new VLT/SPHERE and ALMA observations of the debris disk around the 40Myr-old
h
solar-type star HD61005. We resolve the disk at unprecedented resolution both in the near-infrared (in scattered and
p
polarized light) and at millimeter wavelengths. We perform a detailed modeling of these observations, including the
-
o spectral energy distribution.
r Results. Thanks to the new observations, we propose a solution for both the radial and azimuthal distribution of the
t dust grains in the debris disk. We find that the disk has a moderate eccentricity (e∼0.1) and that the dust density is
s
a two times larger at the pericenter compared to the apocenter.
[ Conclusions.Withnogiantplanetsdetectedinourobservations,weinvestigatealternativeexplanationsbesidesplanet-

diskinteractionstointerprettheinferreddiskmorphology.Wepostulatethatthemorphologyofthediskcouldbethe
2
consequenceofamassivecollisionbetween∼1000km-sizedbodiesat∼61au.Ifthisinterpretationholds,itwouldput
v
stringent constraints on the formation of massive planetesimals at large distances from the star.
1
6 Key words. Stars: individual (HD61005) – circumstellar matter – Techniques: high angular resolution – Scattering
8
7
0
1. Introduction in a disk comparable to the Edgeworth-Kuiper belt in the
.
1 solarsystem.Thedustgrains,withsizesbetweenafewµm
Debris disks are the leftovers of star and planetary for-
0 to a few millimeters, located at tens of au from the central
6mation processes (see Wyatt 2008; Krivov 2010; Matthews star are heated by the stellar radiation and re-emit at mid-
1etal.2014forrecentreviews).Departurefromphotospheric
IR and mm wavelengths. Since the original discovery, and
:emission at infrared (IR) wavelengths was first discovered
v mostly thanks to space-based missions such as the Infrared
around Vega (Aumann et al. 1984) using the Infrared As-
i Space Observatory, Spitzer, and Herschel, several hundred
XtronomicalSatellite(IRAS).Thisexcessemissionwasorig-
of main sequence stars are known to harbor debris disks
inally thought to be the remnant of the cloud out of which
r (e.g., Eiroa et al. 2013; Chen et al. 2014).
aVega formed. Several decades later, we now know that the
dusty “debris” responsible for the IR emission are arranged Recentdecadeshaveseenincredibleprogressinthefield
ofdiskobservations(e.g.,Augereauetal.1999;Kalasetal.
(cid:63) Based on observations made with ESO Telescopes at the 2005; Buenzli et al. 2010; Lebreton et al. 2012; Millar-
ParanalObservatoryunderprogramsID095.C-0298and095.C- Blanchaer et al. 2015). Observations with ever improv-
0273. Data of Fig.1 is only available in electronic form at the
ing spatial resolution have revealed asymmetric disks (e.g.,
CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5)
Lagrange et al. 2015; Kalas et al. 2015) as well as com-
or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. Based
plex,moving,small-scalestructures(Boccalettietal.2015).
on Herschel observations, OBSIDs: 1342270977, 1342270978,
Nonetheless, spatially resolved observations of debris disks
1342270979, 1342270989, and 1342255147. Herschel is an
ESA space observatory with science instruments provided by remain relatively rare and even though there are theoret-
European-led Principal Investigator consortia and with impor- ical works focusing on the dynamical evolution of debris
tant participation from NASA. disks (e.g., Dominik & Decin 2003, Kenyon & Bromley
Article number, page 1 of 23
A&A proofs: manuscript no. The_Moth
2006), they still need to be confronted with the observa- brightness asymmetry between the two ansae is observed,
tions. The current paradigm is that the primordial gas- which cannot be fully explained by the off-centering. No
rich proto-planetary disks are thought to have a half-life planets were detected by Buenzli et al. (2010), for obser-
time of about 2−3Myr (Hernández et al. 2007). As a disk vations that should, in principle, have detected planets
evolvesPluto-sizedplanetesimalscanform(Johansenetal. with masses starting from a few Jupiter masses. The in-
2015)alongwithgiantplanetswhichmayaccretetheirmass tegrated luminosity of the disk is large at IR wavelengths
from the gas reservoir (core accretion or gravitational in- (L /L ∼ 3 × 10−3) and is best modeled by two spa-
disk (cid:63)
stabilityscenarios).AfterafewMyr,thegaseouscontentis tially separated dust belts. The main dust belt is the one
quicklyremovedfromthediskbyefficientprocessessuchas located at ∼60au presented in Buenzli et al. (2010), but a
photo-evaporation (e.g., Alexander et al. 2006; Owen et al. warmcomponentisusuallyrequiredtoreproducethespec-
2011).Onlyalreadyformedplanets,planetesimalsanddust tral energy distribution (SED). Ricarte et al. (2013) argue
grains will thus remain while the disk enters its debris disk thatthisadditionalbeltismandatorytomatchtheSEDat
phase. After a short phase of runaway growth, terrestrial about 20µm, however its location remains unconstrained.
planets may form in the inner regions of the disk, with In this paper, we focus on constraining the properties of
Pluto-sized bodies in the outer regions, via chaotic growth the debris disk which is resolved at unprecedented angular
of these oligarchs, on a timescale of 10−100Myr (Kenyon resolution at both near-IR and mm wavelengths. Studying
& Bromley 2006, 2008, 2010). The time evolution of the thepropertiesandoriginoftheswept-backwingsisbeyond
entire system then becomes more regular and less chaotic. the scope of this paper, since they are marginally detected
Thekm-sizedbodies,arrangedinoneormoreplanetesimal with these observations.
belt(s), evolve under their mutual gravitational influence.
Through collisions, they continuously release small parti-
cles in a collisional cascade. Small dust grains, in turn, are
2. Observations, data processing, and stellar
removed from the system either by radiation pressure or
parameters
Poynting-Robertsondrag.Therefore,onecanconsiderthat
after∼100Myr,planetaryformationhasstopped.Thesys-
Table1 summarizes the VLT/SPHERE and ALMA obser-
tem is left with one (or more) planetesimal belt(s) and,
vations presented in this study.
quite possibly, with planets of various masses. By observ-
ing systems in the range 10−100Myr, one can therefore
study the time evolution of debris disks. Spatially resolved 2.1. VLT/SPHERE IRDIS observations and data reduction
imagescanprovideconstraintsontheradialandazimuthal
distributionofthedust,givingusinsightaboutthedynam- The star HD61005 was observed with the VLT/SPHERE
ics at stake in these systems. (Beuzitetal.2008),withintheguaranteedtimeconsortium.
Here, we present Very Large Telescope (VLT) Spectro- The observations were obtained in different instrumental
PolarimetricHigh-contrastExoplanetREsearch (SPHERE) set-ups in February, March, and May 2015, using the dual-
and Atacama Large Millimeter/submillimeter Array bandimager(IRDIS,Dohlenetal.2008;Viganetal.2010),
(ALMA) observations of the debris disk around the so- theintegralfieldspectrograph(IFS,Claudietal.2008),and
lar type star HD61005 (G8V), located at a distance of the dual-polarization imager (IRDIS DPI, Langlois et al.
35.4±1.1pc (van Leeuwen 2007). The age of the system 2014).
is believed to be within 40+10Myr old, based on member-
−30
ship of the Argus association (Desidera et al. 2011; De
2.1.1. IRDIS dual-band observations
Silva et al. 2013; Elliott et al. 2014). The uncertainties
for the age are mostly related to the dispersion in ages The February observations were conducted in the H H
2 3
reported in the literature for both the Argus association dual band (centered on 1.59 and 1.67µm) for IRDIS and
and the IC321 super cluster. In the last ten years, it has theYJ band(0.95−1.35µm,atspectralresolutionR∼54)
been spatially resolved on multiple occasions with several forIFS.TheMarchobservationsusedtheK K filters(cen-
1 2
instruments; Hines et al. (2007, Hubble Space Telescope tered on 2.11 and 2.25µm) for IRDIS and the YH band
HST/NICMOS); Maness et al. (2009, HST/ACS); Buenzli (0.95 − 1.65µm, R∼ 33) for IFS. All of these observa-
et al. (2010, VLT/NaCo); Ricarte et al. (2013, Submillime- tions were performed using an apodized Lyot coronagraph,
ter Array SMA); and Schneider et al. (2014, HST/STIS). consisting of a focal mask with a diameter of 185milli-
The disk earned its nickname of The Moth because of the arcsec(N_ALC_YJH_S)andacorrespondingpupilmask.
swept-back wings first revealed in the HST observations of Coronagraphic observations were performed in pupil stabi-
Hines et al. (2007). The wings may originate from the in- lized mode to use angular differential imaging (ADI) post-
teraction between the interstellar medium (ISM) and the processing(Maroisetal.2006)toattenuateresidualspeckle
diskitself;asthestarmovesthroughthelocalISM,(small) noise. The observation strategy can be summarized as fol-
dust grains are set on eccentric orbits, drifting away from lows:1)Photometriccalibration:imagingofstaroffsetfrom
the central star. coronagraph mask to obtain PSF for relative photometric
While Hines et al. (2007) and Maness et al. (2009) calibration; 2) Centering: imaging with star behind mask
mostly studied the wings, the study presented in Buenzli with four artificially induced satellite spots for centering;
etal.(2010)resolvedthedebrisdiskasaring,thankstothe 3) Science: coronagraphic sequence; 4) Centering: same as
betterangularresolutionprovidedbytheNaCoinstrument. point two; 5) Photometric calibration: same as point one;
They found the disk to be almost edge-on (i = 84.3±1◦), 6) Sky background observation using same DIT as corona-
to have a semi-major axis of 61.25±0.85au with an eccen- graphic sequence. Finally, true north and plate scale are
tricity of e=0.045±0.015, which translates into an offset determined using astrometric calibrators as part of the
of 2.75 ± 0.85au of the star with respect to the disk. A SPHERE GTO survey for each run (Maire et al. 2015).
Article number, page 2 of 23
J. Olofsson et al.: The asymmetric disk around HD61005
Table 1. Log for the VLT/SPHERE and ALMA observations
VLT/SPHERE
Observing date Prog. ID Instrument Mode Filter Seeing Airmass Coherence time
[YYYY-MM-DD] [(cid:48)(cid:48)] [ms]
2015-02-03 95.C-0298 IRDIFS H H /YJ 0.67 1.01 22.0
2 3
2015-03-30 95.C-0298 IRDIFS_EXT K K /YH 1.24 1.04 1.7
1 2
2015-05-01 95.C-0273 IRDIS DPI B_H 1.16 1.29 1.7
ALMA
Observing date Prog. ID Mode Resolution Frequency range PWV Integration
[YYYY-MM-DD] [kHz] [GHz] [mm] [s]
Continuum 31250.00 211.91−228.97
2014-03-20 2012.1.00437.S 0.79 120.96
Gas 488.28 230.05−230.99
0.9 9
2 200
0.3
1
]
00 0
[
δ
-1
0.1
N
-2 0.1
1
E
2 2 2 2
1
]
00 0 0 0 0
[
δ
-1
-2 2 2 2
3 2 1 0 1 2 3 3 2 1 0 1 2 3 3 2 1 0 1 2 3
α [00] α [00] α [00]
Fig. 1. ReducedSPHEREobservationsofHD61005usedintheanalysis.Northisup,Eastisleft.Fromlefttoright;IRDISADI
in H and K bands (PCA with 6 components), and IRDIS DPI Q in H band. Top row shows the data in linear stretch, with a
φ
centralmaskof0.15(cid:48)(cid:48),andthebottomrowshowsestimatedsignal-to-noisemaps(seetextfordetail),withastretchbetween[−3σ,
3σ].
Basic reduction of the IRDIS data (background sub- 2.1.2. IRDIS dual polarization observations
traction, flat fielding, centering) was performed using
On May 1, 2015, the target was observed using IRDIS in
the SPHERE Data Reduction Handling (DRH) pipeline
DPI mode in H band. The same coronagraph was used for
(Pavlov et al. 2008, version 15.0). The output consists of
theseobservations.IRDISDPIsplitsthelightintotwoper-
cubes for each filter, re-centered onto a common origin us-
pendicularpolarizationdirectionsimagedatthesametime
ingthesatellitespotreference.Thecubesarethencorrected
onthesamedetector.Fullcyclesofhalf-waveplate(HWP)
for the true north position determined from the astromet-
positions(0,22.5,45,and67.5◦)weretakentoconstructthe
ric calibrations and for distortion. We collapsed the two
Stokes Q and U vectors. The strategy of the observations
filters together to increase the signal-to-noise ratio (S/N),
was to take as long exposures as possible without saturat-
and from now on we will refer to the H H and K K
2 3 1 2
ingthedetectorjustoutsidethecoronagraphtoachievethe
datasets as H and K observations, respectively. The dat-
bestpossibleinnerworkingangleaswellasthebestS/Nfor
acubesinbothbandswerethenprocessedusingaprincipal
theouterpartofthedisk.Twointegrationtimes(DIT=64s
componentanalysis(PCA,usingtheimplementationofthe
with a total integration time of 768s and DIT=16s with a
scikit-learn Python package, Pedregosa et al. 2011) ap-
total integration time of 3008s) were used. IRDIS suffers
proach from all frames within the data-cube.
from a de-polarization effect at certain detector position
angles,whichdependontheparallacticangleatthetimeof
Article number, page 3 of 23
A&A proofs: manuscript no. The_Moth
observation. Because the parallactic angle changed rapidly S/Nmap,withalinearstretchbetween[−3σ,3σ].Thenoise
during the observations, we updated the detector angle at map is calculated from the reduced images and represents
regular intervals. the standard deviation in concentric annuli, centered on
The DPI data were reduced using a custom pipeline thestar,withaconstantwidth(2pixels).Wedidnotmask
that is different to the DRH pipeline, which closely follows out the disk when computing the noise maps, hence the
the processes described in Avenhaus et al. (2014), using uncertaintiesmightbeslightlyover-estimated.FortheDPI
thedouble-differencemethod(seealsoCanovasetal.2011) observations,thenoisemapiscomputedfromtheU image
φ
to construct Stokes Q and U vectors from the data. The which does not seem to contain any signal from the disk
pipeline has been adapted to suit the IRDIS instrument. (Fig.C.1 shows the U image with the same linear stretch
φ
The data were centered using the centering frames taken as the Q image in Fig.1).
φ
justbeforeandafterthescienceobservations.Ade-rotation We note that the disk is not homogeneously detected
was applied to bring all files to the same orientation (see at high S/N. The east side is detected at larger S/N in all
section above). Furthermore, the frames were corrected to datasets and it appears brighter than the west side. Such
take account of the fact that the IRDIS pixel scale differs asymmetry, already reported in Buenzli et al. (2010), are
slightly (∼ 0.6%) in the two principal detector directions. further investigated in this paper. For the sake of simplic-
The files were then corrected for true north as determined ity, in the rest of the paper, we refer to the ADI and DPI
for IRDIS. datasetsas“scattered” and“polarized” observations,respec-
Becausescatteredlightinanopticallythin(debris)disk tively.Strictlyspeaking,thisisnotcorrectaspolarizedpho-
is expected to be polarized perpendicular to the line be- tons must have been scattered by dust grains.
tween the star and the image point in question, we then
construct local Stokes Q and U vectors, denoted Q and
φ
U (see also Benisty et al. 2015). In case of single scatter- 2.2. ALMA observations
φ
ing of the stellar light, Q is expected to contain the disk
φ
HD61005 was observed with ALMA in Band6 (PI: David
signal, while U is expected to contain no signal (with pos-
φ
Rodriguez,program2012.1.00437.S),inthefrequencyrange
sible exceptions when the optical depth is large, Canovas
211.97−230.99GHz.Thetargetwasobservedseveraltimes,
et al. 2015) but noise on the same level as the Q image
φ
withprecipitablewatervaporrangingfrom5.19to0.79mm.
and can serve as a noise estimator. Q and U can be cal-
φ φ
Weonlykepttheobservationsperformedonthe20ofMarch
culated as:
2014 for which the water vapor was minimum. Out of the
Qφ =+Qcos(2Φ)+Usin(2Φ) four spectral windows, three were used to derive the con-
U =−Qsin(2Φ)+Ucos(2Φ), (1) tinuum emission (211.97−228.97GHz, with a 31250kHz
φ
resolution), while the last one was used to search for CO
where φ refers to the azimuth in polar coordinates, and Φ gas emission (230.05−230.99GHz, with a 488.28kHz reso-
is the position angle of the location of interest (x, y), with lution), which was not detected. Data processing was per-
respect to the stellar location (x , y ) as: formed within CASA using the standard scripts provided
0 0
bytheobservatory.Weonlykeptthespectralwindowsused
for the continuum observations and averaged the complex
x−x
Φ=arctan 0 +θ, (2) visibilities along the 128 different spectral channels (while
y−y
0 flaggingpointswithnegativeweights).FigureC.2showsthe
where θ corrects for instrumental effects such as a small (u, v) plane coverage for the continuum observations, with
misalignment of the half-wave plate. minimum and maximum baselines of 11.8 and 334.9m, re-
During the data reduction process, one HWP cycle spectively. The reconstructed image (with so-called briggs
equivalent to 256s of data (DIT = 16s) was taken out be- weighting and pixel size of 0.13(cid:48)(cid:48)) is shown in the left panel
cause the telescope had lost tracking for a short amount of Fig.2 (sensitivity of 0.09mJy/beam). The beam size is
of time, rendering this data unusable. The result are two 1.36(cid:48)(cid:48)×0.73(cid:48)(cid:48) (48au×26au)withapositionangleof−86.5◦.
pairs of Q and U images, one for the DIT=16s and Wedonotattempttomeasurethetotalfluxofthediskdi-
φ φ
DIT=64s observations each. These were then combined rectly from these observations, but we do estimate it when
with a weighted average to produce the final Q and U modeling the complex visibilities (Section3).
φ φ
images.
2.3. Spectral energy distribution
2.1.3. IFS observations
ThestarHD61005wasobservedbyHerschel(Pilbrattetal.
The IFS data proved difficult to be properly reduced at 2010) with the Photodetector Array Camera and Spec-
thetimeofthisanalysis,mainlybecauseofcenteringprob- trometer instrument (PACS, Poglitsch et al. 2010), within
lems. Presenting and analyzing these observations will be the program OT2_tcurrie_1. The observation numbers
postponed for a future study. (OBSID) are the two pairs 1342270977, 1342270978 and
1342270979, 1342270980 for the 70µm and 100µm obser-
vations, respectively. The 160µm map used the four OB-
2.1.4. Processed images
SID combined. The data were processed using the HIPE
Figure1 shows the final reduction for our dataset (with a software (build 12.0.2083, Ott 2010), the very same way
central mask of radius 0.15(cid:48)(cid:48) ). The top row displays the as described in Olofsson et al. (2013). HD61005 was also
IRDISADIdatainH andK bands(leftandmiddlepanels, observed with the Spectral and Photometric Imaging Re-
respectively),andtheIRDISDPIQ image(right),allwith ceiver instrument (SPIRE, Griffin et al. 2010) in small
φ
a linear stretch. For each image, the bottom row shows a scan map mode (OBSID: 1342255147 within the program
Article number, page 4 of 23
J. Olofsson et al.: The asymmetric disk around HD61005
Table 2. Broadband photometric measurements of HD61005, 2.5. Preamble on the modeling strategy
and the equivalent widths of the far-IR filters (see text for de-
tails). In this study, we aim to model observations from differ-
ent facilities, at different wavelengths, using different tech-
λ F σ EW Instrument niques (interferometry and direct imaging). Therefore, be-
ν
[µm] [mJy] [mJy] [µm] fore detailing the modeling strategy for each individual
0.428 895.17 14.02 TYCHO B dataset, we provide a quick preamble on the methodology.
0.534 1810.23 18.34 TYCHO V We first model the ALMA data (Section3) assuming
1.235 2753.74 65.94 2MASS J a circular disk, fitting the reference radius (r0, where the
1.662 2440.48 103.40 2MASS H dust density peaks), the outer slope for the dust density
2.159 1738.75 38.43 2MASS Ks distribution (αout), the position angle (φ), the inclination
3.353 819.28 31.69 WISE W1 (i), and the total flux at 1.3mm (f1300).
4.603 453.05 8.76 WISE W2 Prior to the modeling of the SPHERE observations, we
11.56 78.40 1.08 WISE W3 attempt to constrain some of the dust properties, to limit
22.09 44.28 1.55 WISE W4 the number of free parameters. We use the best fit results
68.92 717.00 5.33 21.41 PACS Blue for the inclination and position angle from the modeling of
97.90 703.58 6.84 31.29 PACS Green the ALMA data to derive the polarized intensity as a func-
153.94 472.65 14.58 69.76 PACS Red tion of the azimuthal angle from the Q image. We con-
φ
251.50 235.6 13.5 67.61 SPIRE PSW strain the minimum and maximum grain sizes (s and
min
352.83 118.9 7.6 95.75 SPIRE PMW s , respectively) as well as the porosity fraction of the
max
511.60 49.8 5.2 185.67 SPIRE PLW dustgrains(Section4.1).Thisenablesustoreducethepool
1300.0a 4.6 0.7 105.40 ALMA Band6 offreeparameterswhenmodelingtheSPHEREDPIobser-
(a) Results from the modeling of the ALMA data vations. For the SPHERE ADI observations, we use the
Henyey-Greenstein approximation for the phase function,
(Section3).
whichdisconnectsthemodelingprocessfromtheaforemen-
tioned dust properties. Thanks to thegreat complementar-
OT2_kstape01_1). We used the Timeline Fitter task in itybetweentheADIandDPIobservations,wemodelthem
HIPE to derive SPIRE photometry for our target. Calibra- simultaneously to best constrain the azimuthal and radial
tion errors (∼5.5%, Bendo et al. 2013) are included in the dust density distribution (Section4).
uncertainties. We also gathered photometric observations Finally,inSection5,wemodeltheSEDofHD61005,us-
using VOSA1 (Bayo et al. 2008) and the dataset used to ing the results inferred from the modeling of the SPHERE
buildtheSEDcanbefoundinTable2.Themeaningofthe data on the location of the disk to derive stringent con-
third column is explained in Section5. straints on the dust properties (minimum grain size, dust
composition, and total dust mass).
Finally, we downloaded the Spitzer/IRS spectrum
from the Cornell Atlas of Spitzer/IRS Sources database2
(Lebouteiller et al. 2011).
3. The parent planetesimal belt: constraints from
the ALMA observations
2.4. Stellar parameters
Roughly speaking, different wavelengths trace different
The stellar photospheric model is taken from the ATLAS9 grain sizes. Therefore, we chose to model the ALMA ob-
Kurucz library (Castelli et al. 1997) with an effective tem- servations independently of the SPHERE ones, the latter
perature of T = 5500K (Casagrande et al. 2011). With probing the small dust grains in the debris disk while the
(cid:63)
the dilution factor used to scale the photospheric model millimeter observations most likely trace a population of
to the optical and near-IR photometric measurements, at larger grains that more closely follow the parent planetesi-
a distance of 35.4pc, we find a radius R = 0.84R . We mals’ belt.
(cid:63) (cid:12)
derived a luminosity of L = 0.58L . To derive the stel-
(cid:63) (cid:12)
larmass,whichwillbecomeimportantwhendiscussingthe
3.1. Modeling strategy
dust properties and the effect of radiation pressure on dust
grains, we use isochrones from Siess et al. (2000), for an The modeling of the ALMA observations is performed in
age of 40Myr and effective temperature of 5500K. We find the Fourier space, attempting to reproduce both the real
that the stellar mass must be of about 1.1M(cid:12) (the corre- and imaginary parts of the complex visibilities (averaged
sponding luminosity matching our estimated L(cid:63)). We find along the spectral dimension). In AppendixA, we explain
a slightly smaller mass (1M(cid:12)) when using the isochrones how we generate synthetic images and the different nota-
from Baraffe et al. (2015), but the differences may arise tions are summarized in TableC.1. From a synthetic image
from different model prescriptions (e.g. overshooting). In at the wavelength of 1.3mm, we first scale the total flux
the following, we adopt a mass of 1.1M(cid:12). The SED with of the image to the free parameter f1300 (in mJy) before
thebroadbandphotometricmeasurements,theSpitzer/IRS computingtheFouriertransformoftheimage.Wethenin-
spectrum as well as the photospheric model are shown in terpolate the Fourier transform at the spatial frequencies
Fig.7 of Section5. of the observations. The goodness of fit is the sum of the
weights(estimatedinCASA3)timesthesquareddifference
1 http://svo2.cab.inta-csic.es/theory/vosa/ betweentheobservedandmodeledcomplexvisibilities(the
2 The Cornell Atlas of Spitzer/IRS Sources is a product of
theInfraredScienceCenteratCornellUniversity,supportedby 3 TheabsolutevaluesoftheweightsderivedwithinCASAmay
NASA and JPL. http://cassis.sirtf.com/atlas/query.shtml be inaccurate but their relative values are not.
Article number, page 5 of 23
A&A proofs: manuscript no. The_Moth
Table 3. Best fit results for the modeling of the ALMA obser-
vations.
Parameter Uniform prior σ Best-fit value
kde
r [au] [40,80] 0.2 66.4+6.1
0 −8.7 3
αout [−15,−1.5] 0.1 −6.6−+16..41 6
φ [◦] [55,85] 0.1 70.7−+12..93 αout 9
i [◦] [79,89] 0.1 84.5+2.9 12
−2.5 5
f [mJy] [1,20] 0.1 4.6+0.7 1
1300 −0.6 8
7
2
7
φ
weightsareproportionalto1/σ2).Weconsiderthefollowing 66
free parameters: the inclination i, the position angle φ, the 60
5
total flux of the disk at 1.3mm f , the reference radius4 7.
1300 8 0
r , and the outer power-law slope for the dust distribution 5.
0 8
i 5
α , which is parametrized as 2.
out 8
0
0.
8
(cid:34)(cid:18) r (cid:19)−2αin (cid:18) r (cid:19)−2αout(cid:35)−1/2 7.5
n∝ + , (3) 0
r0 r0 f130046..5
0
whereristhedistancefromthestarandnthenumberden- 3.
0 8 6 4 2 05 2 9 6 3 0 6 2 8 0 5 0 5 0 5 0 5
tseitsyt.sTinhdeiicnantienrgptohwiesrp-laarwamsleotpeeriissspeototrolyαicno=nst5r,apinreeldimbiynathrye 4 4 5r06 7 81 1 αout 6 6 φ7 7 80. 82.i85. 87. 3. 4.f1360.0 7.
observations. To find the most probable solution, we use Fig. 3. One-andtwo-dimensional(diagonalandlowertriangle,
an affine invariant ensemble sampler Monte-Carlo Markov respectively) projections of the posterior probability distribu-
Chain, implemented in the emcee package, using 200 walk- tionsfortheresultsofthemodelingoftheALMAobservations.
ers, a burn-in phase of 500 iterations and a total length of
thechainsof2000iterationsaftertheburn-inphase.Atthe
end of the run, we find that the mean acceptance fraction sameparametersasfortheobservations.Wenotethatthere
(themeanfractionofstepsacceptedforeachwalkerwithin are some residuals on the east side that may suggest that
thechain)isof0.48(agoodsignofconvergenceandstabil- the disk is brighter on one side, even at mm wavelength.
ity,Gelman&Rubin1992).Themaximumauto-correlation However, these residuals are below 3σ, therefore we can-
timeforalltheparametersisof60steps,indicatingthatthe not conclude they are significant. The apparent brightness
chainsshouldhavestabilizedbytheendofthesimulations. asymmetrycouldbeduetotheasymmetric(u,v)coverage
of the observations.
3.2. Results Overall, we find that most of the parameters are well
constrained, except for the outer power-law slope of the
The projected posterior probability distributions are dis-
dust density distribution, for which we can safely exclude
playedinFig.3,forthedifferentfreeparameters(usingthe
slopes shallower than α = −4. This is explained by the
triangle Python package, Foreman-Mackey et al. 2014). out
beam size of the observations which is larger than the de-
To derive the best-fit values as well as the uncertainties,
bris disk for steep values of α . Otherwise, we find the
we smooth the distributions with a kernel density estima- out
reference radius of the disk to be r ∼ 66au, the position
tor (the width of the Gaussian kernel σ are reported in 0
kde angle φ ∼ 70.7◦, the inclination i ∼ 84.5◦, and the flux at
Table3), and the best-fit value is the peak position of the
1.3mm f ∼ 4.6mJy. These results agree well with the
distribution. The confidence intervals (a , a ) for the pa- 1300
1 2 parameters reported in Buenzli et al. (2010, i =84.3±1◦,
rameter a are estimated as follows:
φ = 70.3 ± 1◦, r = 61.25 ± 0.85au) and Ricarte et al.
0
(cid:90) a1 (cid:90) amax 1−γ (2013, r0 = 67±2au, φ = 71.5±5◦). The relatively large
p(a)da= p(a)da= , (4) beamsizeoftheALMAobservationscanexplaintheslight
2
amin a2 discrepancy for r between the modeling of the ALMA
0
data and the value inferred by Buenzli et al. (2010). This
where γ = 0.68 and p(a) is the smoothed posterior proba-
value will be revisited when modeling the SPHERE obser-
bility distribution (integral normalized to 1) for parameter
vations (Section4). Ricarte et al. (2013) obtained a total
a(e.g.,Pinteetal.2008).Wenotethatnotallthedistribu-
flux of 7.2±0.3mJy at 1.3mm with their SMA observa-
tions reach zero on each side of their maximum (especially
tions (Steele et al. 2016 obtained 8.0±0.8mJy analyzing
for α and i) and, therefore, these uncertainties should
out
the same observations), while we find the total flux to be
be treated carefully. Table3 summarizes our results for the
well constrained at 4.6 ± 0.7mJy (within the SMA and
modeling of the Band 6 observations, and Fig.2 shows the
ALMA respective 3σ uncertainties). The shortest baselines
observations, the best-fit model, and the residuals (from
being of B ∼ 11 and 16m (for the ALMA and SMA
left to right). The synthetic image of the best fit model is min
observations, respectively), the largest scales the observa-
processed through CASA (using the ft method with the
tions are sensitive to are of the order of 14.2(cid:48)(cid:48) and 10.1(cid:48)(cid:48),
same antenna configuration as the observations) and the
respectively (0.6λ/B ), much bigger than the disk. It is
image is reconstructed with the clean algorithm with the min
therefore unlikely that flux from the disk is filtered out by
4 Here we assume the disk is circular. the interferometers. The differences between the SMA and
Article number, page 6 of 23
J. Olofsson et al.: The asymmetric disk around HD61005
3 3 3
2 2 2
1 1 1
]
[δ00 0 0 0
1 1 1
2 2 2
3 3 3
3 2 1 0 1 2 3 3 2 1 0 1 2 3 3 2 1 0 1 2 3
α [00] α [00] α [00]
Fig. 2. From left to right: observations, best-fit model and residuals of the ALMA data. For all panels the color map is a
linear stretch between −0.27 and 1.23mJy/beam. The standard deviation estimated in an empty region of the observations is of
0.09mJy/beam.Forboththeobservationsandthemodelthecontoursaresetat[3,5,7.5,10]σ,and[−σ,σ]fortheresiduals(no
residuals beyond the 2σ level). The beam size is shown in the lower left corner of each panels.
ALMAdatamayarisefrommissingfrequencies,differences and modeled, then we present the modeling strategy and
in beam sizes, or calibration uncertainties (the uncertain- summarize the results we obtain.
titesreportedbySteeleetal.2016beingmoreconservative
than the ones reported by Ricarte et al. 2013).
4.1. Phase function of the polarized light
Finally, we note that the famous wings responsible for
the disk’s nickname are not detected in the ALMA data. To compute the polarized phase function from the DPI
Despite a good angular resolution, a disk model (without dataset, we define an elliptical mask with the following pa-
wings) can successfully reproduce the observations, and we rameters: inner and outer radii (r and r ), the inclina-
in out
see no trace of the wings in the residuals (with an rms of tion i, and the position angle φ. For each pixel within the
∼ 0.09mJy/beam). Our results therefore agree with the elliptical mask, we compute the scattering angle as the dot
ones of Ricarte et al. (2013); only small dust grains are productofthelineofsightandthelocationofthepixelwith
likely present in the wings. respecttothestar.Wedividetheellipticalmaskintwo,for
the east and west sides and, for each side, we compute the
minimum and maximum scattering angles. We then divide
4. Constraining the dust radial distribution from eachsideofthemaskinto30smallerregionscorresponding
todifferentbinsofthephasefunction(seeFig.C.3foranil-
the SPHERE observations
lustration).Eachpixelismultipliedbyitssquareddistance
WemodeltheSPHEREimagesbyproducingsyntheticim- to the star, to account for illumination effect. The mea-
ages at the central wavelength of the H-band observations, sured phase function is found by averaging the flux in the
λ =1.63µm.GiventhelowS/NoftheK-bandADIobser- observations, in each individual region. Since the observed
c
vations, preliminary attempts to model these data showed uncertainties σi are not the same for each pixel within a
that the dust distribution cannot be better constrained given intersection, the “average” uncertainty in the inter-
thanwiththeH-bandobservations.Wethereforefocusthe section is computed as follows:
modeling effort on the H-band ADI and DPI data.
(cid:32) N (cid:33)−1/2
Figure1 highlights the complementarity of both the (cid:88) 1
σ = , (5)
scatteredandpolarizedlightimages;theADIandDPIdata σ2
have very different S/N at the ansae and along the semi- i=1 i
minor axis of the disk. Combining both datasets, there- where N is the number of pixels in the considered region.
fore, offers the opportunity to study the dust distribution The phase function is then normalized to its maximum
in great detail. value (east and west sides are divided by the same value).
The modeling process has a high dimensionality with Fortheellipticalmask,weusethebest-fitresultsofthe
many possible free parameters, and regions of intermediate modeling of the ALMA observations (see Table3) for i and
to low S/N. Therefore, to obtain novel yet reliable con- φ and choose r and r small and large enough (50 and
in out
straints on the dust distribution we choose to perform a 72au,respectively)sothattheyencompassthetraceofthe
prior analysis on the observations to reduce the number of debris disk. Figure4 shows the phase function for the DPI
free parameters. Having a proper description of the polar- H-band observations, the east side being in black, and the
ized phase function prior to the modeling of the DPI ob- west side in red. The uncertainties are shown in a shaded
servations greatly helps reducing the dimensionality of the color,andthegrayareaindicatesregionsoflowS/N,which
modeling (e.g., the minimum and maximum grain sizes as wereestimatedfromtheS/NmapderivedfromtheU data.
φ
well as the porosity of the dust grains). In this section, we As can be seen in Fig1 (bottom right panel), the disk is
first describe how the polarized phase function is derived onlydetectedforanarrowrangeofazimuthalanglesonthe
Article number, page 7 of 23
A&A proofs: manuscript no. The_Moth
We then compute the best scaling factor f (to be mul-
Best fit tiplied to S1a2vg) that will minimize the diffSer12ence between
1.0 East the profiles Savg and Sobs (with uncertainties σ)
12 12
West
0.25 s 0.3 µm (cid:18)Sobs×Savg(cid:19)
s]0.8 0.35 s 0.4 µm (cid:80) 12 12
nit σ2
u f = . (7)
bitrary 0.6 S12 (cid:80)(cid:18)S1σa2vg(cid:19)2
ar
s [
nt0.4 We perform a simple grid search over the following param-
u
Co eters: smin, smax, and the optical properties of the dust
grains.Wefixp=−3.5,asexpectedforacollisionalcascade
0.2
in a debris disk (Dohnanyi 1969). For the dust composi-
tion,weconsiderabasemediumofamorphoussilicatewith
olivine stoichiometry (MgFeSiO , Dorschner et al. 1995) to
0.0 4
0 20 40 60 80 100 120 140 160 180 whichwecanaddsomeporosityusingtheBruggemanmix-
Scattering angle [◦]
ingrule.Theminimumgrainsizecanvarybetween0.01and
Fig. 4. Azimuthal dependency of the polarized intensity in the 10µm. To constrain the maximum grain size, we vary the
DPI H-band observations, in black and red for the East and quantity ∆s (= s −s ) between 0.01 and 100µm (in
max min
Westsides,respectively.Theshadedcurvesarerepresentativeof log space), and finally the porosity can change by steps of
the uncertainties estimated from the noise map and the shaded 10%.Wefindthatthepolarizedphasefunctionat1.63µmis
grayareadenoteslowS/NregionsestimatedfromtheS/Nmap
bestreproducedbysmallsphericaldustgrains,withtypical
inFig.1.Thethinsolidlinesdisplayexamplesfordifferentgrain
sizesintherange0.3≤s≤0.35µmandaporosityfraction
sizes for the same dust composition as the best fit.
of ∼80%. The best-fit solution is shown with a thick cyan
line in Fig.4, and reproduces well both the overall shape
and the peak position of the observed phase function. Also
west side. This strongly suggests that we underestimated
shown in Fig.4 are two examples for different grain size
the uncertainties calculated using Eq.5.
distributions around 0.25−0.3µm and 0.35−0.4µm, to il-
Thedifferenceinbrightnessbetweenthetwosidesofthe lustrate how sensitive the phase function is with respect to
disk is striking in Fig.4 and the east side appears almost thegrainsizes.Wenotethat,withinsuchanarrowrangeof
twice as bright as the west side for most of the scattering sizes, the value of the slope p of the grain size distribution
angles. Even though the S/N for the west side is relatively remainsunconstrained.Inthissection,weassumedthatthe
low it seems that the polarized phase function peaks at an polarizedfluxisdirectlyproportionaltoS ,whileitisalso
12
angle compatible with the east side. related to the dust density in the disk. In the rest of this
To alleviate the number of free parameters, we aim to paper, we try to determine the azimuthal distribution of
constrainthegrainsizedistributionforthemodelingofthe the dust in the disk. Therefore, this prior analysis must be
DPIobservationsdirectlyfromthephasefunctiondisplayed regarded as a first order approximation. The motivation of
in Fig.4. We emphasise that we do not have access to the this prior analysis was to reduce the dimensionality of the
(cid:112)
polarization degree ( (Q2+U2)/I) as we do not have an modeling, but it also comes at a slight cost in the interpre-
unbiased measure of the total intensity I prior to the mod- tation of the grain size distribution. The main conclusion
eling. Indeed, the ADI process introduces self-subtraction of this section is that it does not seem that we observed
effects (e.g., Milli et al. 2012), which can eventually be large dust grains (which would have a stronger S signal
12
quantifiedwithamodelthatdescribestheobservationswell at small scattering angles). In Section6.1 we discuss this
(whichwedonotyethave).Sincethewestsidesuffersfrom result further, but it could also be the consequence of low
low S/N, we perform the modeling on the east side’s phase S/N along the semi-minor axis of the disk.
function. To reproduce the phase function, we assume that
the signal in the Q image is proportional to the size de-
φ 4.2. Modeling strategy
pendent S (s) element of the Müller matrix. The matrix
12
enables us to compute the Stokes vectors I and Q for the Since both the ADI and DPI datasets were taken at the
scatteredandpolarizedlight,respectively.Assumingsingle samewavelength,foragivensetofparameterswecompute
scattering event (reasonable assumption in low density en- two images: an unpolarized light image using the Henyey-
vironment such as debris disks), the scattered light will be Greenstein (HG) analytical prescription of phase function
the product of the first diagonal element of the matrix S11 S11 (Henyey & Greenstein 1941) and a polarized light im-
times the stellar intensity I0. The polarized intensity will age using the Mie theory. Using the HG approximation,
beproportionaltothesecondelementofthefirstcolumnof which is parametrized by the anisotropic scattering factor
thematrixS12 timesI0.WecomputeS12 fordifferentgrain g (−1≤g ≤1),givesusmorecontrolwhentryingtorepro-
sizes between smin and smax, using the Mie theory, and we duce the observed phase function (hence less free parame-
averageS12 overagrainsizedistributionwithaslopep<0 ters to be considered during the modeling). To reproduce
(dn(s)∝spds) as follows, the DPI observations, we use the grain properties derived
previously(Section4.1).Theabsorptionandscatteringeffi-
(cid:82)smaxS (s)×spds ciencies,aswellastheMüllermatrixelementS12,arecom-
Savg = smin 12 . (6) putedwiththeMietheory,whichisvalidforcompactspher-
12 (cid:82)smaxspds ical grains. This approach may not appear self-consistent,
smin
Article number, page 8 of 23
J. Olofsson et al.: The asymmetric disk around HD61005
but it is a way to disentangle the modeling of unpolarized Table 4. BestfitresultsfortheADIandDPIH-bandobserva-
tions.
and polarized light that may not be well accounted for by
spherical grains (e.g., Milli et al. 2015).
Parameter Uniform prior σ Best-fit value
Thepooloffreeparametersincludesthereferenceradius kde
r [au] [40,80] 0.1 60.4+0.8
rψ0,,atnhdeitnhcelinouattieornpio,wthere-lpaowsitsiloonpeanαgoluetφfo,rthteheopdeunsitndgeannsgitlye i0[◦] [75,88] 0.1 84.1−+−000...252
distribution.Preliminarytestsindicatedthatwecanhardly αout [−10,−1.75] 0.01 −2.70+−00..11
constrain the inner power-law slope, so we fixed α = 5. e [0,0.6] 0.0025 0.093+0.018
in −0.014
This enables us to focus on other parameters that describe Φ [◦] [0,360] 1. 127.3+12.7
e −4.3
thegeometryofthedebrisdisk.Forinstance,Buenzlietal. φ [◦] [65,75] 0.1 70.6+0.2
−0.3
(2010) conclude that the eccentricity of the disk was not η [0,1] 0.0025 0.47+0.02
enough to explain the brightness asymmetry between the −0.04
Φ [◦] [0,360] 1.0 138.1+7.2
eastandthewestsides,andweaimtoaddressthisinterpre- η −5.6
w [◦] [5,180] 1.0 51.7+8.8
tation of previous observations. Therefore, we include the −3.2
ψ [0.02,0.12] 0.005 0.058+0.001
eccentricity e, the rotation angle Φe, the density damping −0.002
η, and its azimuthal shape (via the width w of the Gaus- g [0,0.95] 0.001 0.54+0.01
−0.02
sian profile) and its reference angle Φ (see App.A). The f [3,8.5] 0.01 6.20+0.09
η ADI −0.07
azimuthal profile has the shape of a Gaussian profile with
a σ = w, a peak of 1 for the azimuthal angle Φ and a
η
minimum value of η ≥0 (hence an amplitude of 1−η). use the emcee Python package, with 100 so-called walkers
Because we now consider azimuthal variations for the in the chain, and first burn in 500 runs for each of these
dust density distribution, it is parametrized slightly dif- walkers. We then run the chain for 2000 iterations in to-
ferently. The semi-major axis of the disk is defined as tal (see Millar-Blanchaer et al. 2015 for a similar modeling
r /(1−e2). Although the formal denomination of r is the approach). To speed up the process, we cropped and re-
0 0
so-called semi latus rectum, we will simply refer to it as sampled the SPHERE images. The size of one pixel in the
the reference radius in the rest of the analysis. The radius new image (or cube) is resampled to be 2.25 times bigger
at which the dust density peaks now depends on the az- than in the original images, the size of the new image be-
imuthalangleθ.Thisradiusr isdefinedasr /(1+e×cosθ), ing 200×200 pixels, and we use a central mask of radius
θ 0
and the azimuth-dependent dust density distribution n(θ) 0.15(cid:48)(cid:48). We chose not to convolve the synthetic images by a
is parametrized similarly to Eq.3, replacing r with r for PSFbecausethecroppedanddown-sampledimageshavea
0 θ
each azimuthal angle. pixel size of 0.028(cid:48)(cid:48), while the approximation of the instru-
The dust mass M is not varied, but the synthetic mental PSF with a Gaussian profile would have a width of
dust
images are scaled during the fitting process. For the polar- 0.024(cid:48)(cid:48) (approximating the PSF as an Airy disk for an 8m
izedimages,themodeledimageistheabsolutevalueofthe telescope).Attheendoftherun,wefindthatthemeanac-
Stokes Q parameter (we are assuming that there are no ceptance fraction (the mean fraction of steps accepted for
φ
multiple scattering events in the debris disk). We scale the each walker within the chain) is of 0.35, with a maximum
modeled image by a factor f , which is found analyti- auto-correlation time of 79 steps.
DPI
cally to minimize the residuals (similarly to Eq.7). For the
ADIdataset,thisapproachisnotpossiblebecausethepost-
4.3. Results
processing of the data cube can introduce self-subtraction
effects.Wethereforeoptedforaforwardmodelingstrategy, The projected posterior probability distributions are dis-
similar to the one described in Thalmann et al. (2014). For played in Fig.B.1, for the different free parameters. To de-
a given set of parameters, we compute one synthetic image rive the best-fit values as well as the uncertainties, we pro-
at the wavelength 1.63µm. We then produce a cube of 64 ceed similarly as in Section3.2. The results are presented
images, each one rotated to match the parallactic angles in Table4 and Fig.5 shows the observations, the residuals
of each frame of the observations (total rotation of 93.3◦). andthebest-fitmodels(fromlefttoright)fortheADIand
Each frame of the cube of synthetic images is multiplied the DPI data (top and bottom rows, respectively).
by fADI and is then subtracted from the corresponding ob- All parameters seem to be well constrained. The most
served frame. The PCA process is performed, keeping only probable solution has a semi-major axis of 60.9au (r /[1−
0
the six main components. Another approach would be to e2]) for an eccentricity of 0.093. With a rotation angle of
performthePCAontheobservations,savethecoefficients, Φ ∼ 127◦ the pericenter is located slightly toward the
e
and apply them to the modeled cube. But the observations observer, on the east side5. An azimuthal density varia-
contain signal from the disk that may be accounted for in tion seems to be necessary to reproduce the observations
someoftheprincipalcomponents(eventhoughtheyshould with a damping factor η of ∼ 0.47 with a reference an-
besimilarlysubtractedinthemodeledcube).Therefore,to gle of ∼138◦ (hence almost co-located with the pericenter
ensureaslittlesubtractionaspossible,wechosetoperform of the eccentric disk). The azimuthal variation of the dust
thePCAonthemodel-subtractedcube.Theendgoalbeing density distribution is a Gaussian profile with a width of
to minimize the flux in the final image. ∼ 50◦. The position angle and inclination are consistent
The goodness of the fit is the sum of the squared ra- withtheresultsfromBuenzlietal.(2010).Theaspectratio
tio between the final images (residuals for the scattered
and polarized data) and the noise map (bottom row of 5 ForΦ =180◦,thepericenterwouldbealongthesemi-major
e
Fig.1). For the modeling of both the ADI and DPI ob- axis on the east side. Smaller angles would move the pericen-
servations, we therefore have a total of 12 free parameters: ter towards the observer, while larger angles would move the
r , i, α , e, Φ , φ, η, Φ , w, ψ, g, and f . Here, we also pericenter towards the back side of the disk.
0 out e η ADI
Article number, page 9 of 23
A&A proofs: manuscript no. The_Moth
2
1
]
[00 0
δ
1
2
2
1
]
[00 0
δ
1
2
2 1 0 1 2 2 1 0 1 2 2 1 0 1 2
α [ ] α [ ] α [ ]
00 00 00
Fig. 5. Left to right: observed, residuals, and best-fit models for the ADI and DPI datasets (top and bottom, respectively).
ofψ ∼h/r ∼0.06agreeswellwithnumericalsimulationsof tionisthatweseenoindicationofthistypeofabeltinthe
theverticalstructuresofdebrisdisks(e.g.,Thebault2009). DPI observations, but the noise is larger in the innermost
Finally, the phase function is anisotropic for low scattering regions of this dataset. One possible way to address this
angles with g ∼0.54. The dust density distribution for the point would be to detect gas, which could trace velocities
best-fit model, viewed from above the disk, is displayed in compatible with a radius smaller than 61au. Yet no CO
Fig.B.2. was detected in the ALMA observations (Section6.2).
Nonetheless, as shown in the residuals of the ADI ob-
servations, our best-fit model does not manage to remove 5. Constraining the dust mineralogy from the SED
all the signal along the semi-minor axis of the disk. It suc-
TheSEDofthedebrisdiskaroundHD61005isconstructed
cessfully suppresses most of the signal at larger scattering
from the fluxes reported in Table2 and the Spitzer/IRS
angles, but the best-fit model seems to fail at properly de-
spectrum. Modeling an SED from unresolved observations
scribing the scattering at smaller angles. We tried to im-
isadegenerateproblem.Wearebasicallytryingtofindthe
plement a phase function with two weighted HG functions,
adequate temperature of the grains, which can be changed
but could not significantly improve the residuals. We in-
either by their radial distances, their sizes, or their nature.
cluded all the “basic” parameters related to the geometry
The modeling of the SPHERE images provide strong con-
of the disk (i, φ, r , ψ) and yet failed to perfectly match
0 straintsonthegeometricparametersofthedisk,andwecan
the observations. Possible explanations can be related to
therefore focus on better constraining the dust properties.
the phase function (the HG phase function remains an ap-
proximation),theradialsegregationofthegrainsizedistri-
bution,ortheazimuthaldustdensitydistribution(thiswill 5.1. Modeling the thermal emission from the disk
be further discussed in Section6.1). We crudely assumed
To model the SED of HD61005, for a given set of parame-
a Gaussian profile for the azimuthal distribution, but the
ters, the goodness of fit is computed as
actual distribution could be skewed in one or another di-
rection which could explain the brighter region along the
semi-minor axis. Another (highly speculative but interest- χ2 =(cid:88)ω ×(cid:20)Fobs(λi)−F(cid:63)(λi)−Fmodel(λi)(cid:21)2, (8)
ing) explanation could be that we may be seeing an inner i σi
i
disk. Because of the high inclination of the disk, an inner
dust belt may appear to the observer as if it was merging where F is the observed flux with its associated un-
obs
with the main belt. The main challenge with this explana- certainty σ , F the stellar contribution, and F the
i (cid:63) model
Article number, page 10 of 23