Constraints on the structure of hot exozodiacal dust belts

1.4 MB·

by  Florian Kirchschlager

MNRAS000,1–14(2016) Preprint27January2017 CompiledusingMNRASLATEXstylefilev3.0
Constraints on the structure of hot exozodiacal dust belts
Florian Kirchschlager1(cid:63), Sebastian Wolf1, Alexander V. Krivov2, Harald Mutschke2,
and Robert Brunngr¨aber1
1Kiel University, Institute of Theoretical Physics and Astrophysics, Leibnizstraße 15, 24118 Kiel, Germany
2Friedrich Schiller University Jena, Astrophysical Institute and University Observatory, Schillerg¨aßchen 2-3, 07745 Jena, Germany
Accepted2017January20.Received2017January20;inoriginalform2016July18
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ABSTRACT
2
Recent interferometric surveys of nearby main-sequence stars show a faint but sig-

n nificant near-infrared excess in roughly two dozen systems, i.e. around 10% to 30%
a of stars surveyed. This excess is attributed to dust located in the immediate vicin-
J ity of the star, the origin of which is highly debated. We used previously published

6 interferometric observations to constrain the properties and distribution of this hot
2 dust. Considering both scattered radiation and thermal reemission, we modelled the
observed excess in nine of these systems. We find that grains have to be sufficiently
]
R absorbing to be consistent with the observed excess, while dielectric grains with pure
silicate compositions fail to reproduce the observations. The dust should be located
S
within 0.01 1au from the star depending on its luminosity. Furthermore, we find
h. a signifi∼cant tr−end for the disc radius to increase with the stellar luminosity. The dust
p grains are determined to be below 0.2 0.5µm, but above 0.02 0.15µm in radius.
- The dust masses amount to (0.2 3.5)− 10−9M . The near-infr−ared excess is prob-
o ⊕
− ×
ably dominated by thermal reemission, though a contribution of scattered light up to
r
t 35%cannotbecompletelyexcluded.Thepolarisationdegreepredictedbyourmodels
s
a is always below 5%, and for grains smaller than 0.2µm even below 1%. We also
[ modelled the observed near-infrared excess of ano∼ther ten systems with poorer data

in the mid-infrared. The basic results for these systems appear qualitatively similar,
2
yet the constraints on the dust location and the grain sizes are weaker.
v
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Key words: (stars:) circumstellar matter – interplanetary medium – planets and
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satellites: fundamental parameters – zodiacal dust – infrared: planetary systems –
2
techniques: interferometric
7
0
.
1
0
7 1 INTRODUCTION exozodiacaldust,wasfirstdetectedaroundVegabyadeficit
1 of the interferometric visibility compared to that expected
The zodiacal dust cloud in the solar system has been stud-
: from the star alone. Excluding close companions, stellar
v ied intensively by in situ spacecraft measurements, remote
i oblateness or gas emission, such a visibility deficit in the
X observations at visible and infrared wavelengths, and theo- near-infrared (NIR) K waveband (Absil et al. 2006) is at-
reticalmodelling(e.g.Mannetal.2004).Dustispresentat
r tributed to thermal reemission of hot dust or scattering of
a all heliocentric distances, down to a few solar radii, where
stellarradiationonthesegrains(e.g.Akesonetal.2009;De-
itisseenastheF-corona(e.g.Kimura&Mann1998;Hahn
fr`ereetal.2011;Robergeetal.2012).Sofar,anexozodiacal
etal.2002).Thetotalzodiacaldustmasshasbeenestimated
dust environment has been detected through a signature in
to10−9−10−7M (Leinert1996;Fixsen&Dwek2002).For
⊕ the NIR around about two dozens of main-sequence stars
comparison, the dust mass of the Kuiper belt amounts to
(Absil et al. 2009, 2013; Ertel et al. 2014).
(3−5)×10−7M (while the total mass in the Kuiper-belt
⊕
objects is ∼ 0.12M⊕; Vitense et al. 2012). Most of the zo- The exozodis have been inferred to be by about three
diacal dust is believed to originate from desintegration of order of magnitude brighter than the zodiacal cloud in the
short-period comets, with some contribution from asteroids solarsystem.Incontrasttothesolarsystem’szodiacalcloud,
(Nesvorny´ et al. 2010). their origin remains unclear. Also unclear are the mecha-
Zodiacal dust around stars other than the Sun, called nismsthatsustaintheexozodiacaldustattheobservedlevel.
Poynting-Robertson effect, stellar radiation blow-out, and
graincollisionsareonlyasmallselectionofprocesseswhich
(cid:63) E-mail:[email protected] should remove the dust and disperse the disc within a few
©2016TheAuthors
2 F. Kirchschlager et al.
interferometricsurveysusingCHARA/FLUOR(Absiletal.
2013) and VLTI/PIONIER (Ertel et al. 2014) resulted in
Distance: < 1 AU 1-10 AU > 10 AU
detections of exozodiacal dust around main-sequence stars
with an incidence rate of 10% to 30%.
Hot dust Warm dust Cold dust
Basedontheobservationaldataavailable,weintendto
putstrongerconstraintsontheexozodiacaldustdistribution
than those that were derived previously. For this purpose,
u.] inthispaperwemodelselectedNIRtoFIRobservationsof
a. systems for which NIR long-baseline interferometric obser-
[
Fn vations indicate the presence of hot dust close to the star.
Our sample of systems and the methods we use to analyse
their observations are described in Sect. 2. The results are
NIR MIR FIR presentedinSection3.Adiscussionofpossiblemechanisms
thatmaycreateandsustaintheexozodiacaldustisgivenin
0.1 1 10 100 1000
l [m m] Section 4. Section 5 summarises our findings.
Figure1.Illustrationofso-calledhot,warm,andcolddusttraced
through their contributions to different parts of the SED. The
stellarphotosphere(blacksolidline)correspondstoasolartype
2 ANALYSIS
star(T(cid:63)=5777K).Theheightoftheexcesscurvesisarbitrary.
Inthissectionwepresentbothourselectionofsystemsand
themethodsweusetoconstraintheparametersofthespa-
millionyears(e.g.Wyatt2008;Krivov2010;Matthewsetal.
tialdistributionofthedustandthesizesofthedustgrains.
2014). At small distances to the star, dispersal mechanisms
The survey of stars with hot exozodiacal dust is introduced
have particularly short time scales, making the presence of
in Section 2.1 and the disc and dust model are described
exozodiacaldustatoldagesaconundrum(e.g.Riekeetal.
in Section 2.2. The procedure and the observational data
2005).
applied to constrain the model parameters are presented in
ComparedtocolddustlocatedinKuiperbeltanalogues
Section 2.3 and 2.4, and the calculation of the sublimation
at radii larger than 10au, causing an excess in the mid-
radiusisdescribedinSection2.5.Adiscussionoftheimpact
(MIR) and far-infrared (FIR) wavelength range, NIR ob-
of the limitedspatialresolutionof the NIR andMIR obser-
servations trace the disc region within or around 1–10au
vations is given in Section 2.6.
from the central star (see Fig. 1). Thus studies of exozodis
offer a way to better understand the inner regions of ex-
trasolarplanetarysystems.Besides,thepossiblepresenceof
2.1 Survey of stars with NIR excess
smallgrainsinexozodiacalcloudsisapotentialproblemfor
the detection of terrestrial planets in the habitable zone of InTable1thosesystemsofthesurveysofAbsiletal.(2013)
these systems (e.g. Agol 2007; Beckwith 2008). This pro- in K band and Ertel et al. (2014) in H band are compiled
videsanothermotivationtostudytheexozodiacaldustand whichshowasignificantNIRexcessthatisindicativeofhot
its properties. exozodiacal dust. In addition, HD 216956 (Fomalhaut) is
Previouslypublishedconstraintsfavourdiscsconsisting included,whichwasobservedwithVLTI/VINCIinKband
ofsmallparticlesinanarrowringaroundthestar(e.g.Rieke (Absil et al. 2009). Stars for which a detected NIR excess
et al. 2016). The dust has to be located beyond the subli- can be attributed to a different mechanism or a companion
mation radius of the grains, which typically amounts to a (Mawet et al. 2011; Absil et al. 2013; Bonsor et al. 2013a;
few solar radii (Mann et al. 2004). For Vega, Fomalhaut, Marionetal.2014)havebeenexcludedfromthisstudy.Be-
and β Leo, small refractory particles (∼ 10−500nm) at sides HD 7788 (κ Tuc), for which a temporal variability of
distances of ∼ 0.1−0.3au in narrow rings are required to theexcesswasdetected(Erteletal.2016),thelistofknown
account for the hot excess (Absil et al. 2006; Akeson et al. systems with hot exozodiacal dust is complete. Ertel et al.
2009; Defr`ere et al.2011;Lebretonetal. 2013). Rieke et al. (2016)alsofoundatentativeindicationforatemporalvari-
(2016) obtained similar results, constraining the maximum ability of the excess of HD 210302 (τ PsA). However, since
grain size to ∼200nm. thisvariabilityisnotsignificant,thesystemisconsideredin
Due to the proximity to the star, spatially resolved di- our study. All of the listed stars are at or close to the main
rectimagingobservationsoftheexozodiacaldusthostingen- sequence, with spectral classes ranging from A0 to G8 and
vironmentsaremissing.AlthoughRiekeetal.(2016)founda luminosities from L ∼0.4L to ∼40L .
(cid:63) (cid:12) (cid:12)
weakly but significantly bluer photometric colour for these To derive the flux of the NIR excess from the observed
systems compared to stars without exozodiacal dust, the visibilities, uniformly bright emission was adopted in the
detection of these systems was only possible so far through whole field of view (Di Folco et al. 2004). We divide the
interferometric observations. The observing strategy is to selected systems in two groups: Group I comprises all sys-
measure the visibility using a suitable set of baseline con- tems with interferometric flux measurements at λ=8.5µm
figurations. A significant deficit of the interferometric vis- whichwillhelptofindstrongconstraintsforthediscmodel.
ibility at low spatial frequencies indicates the presence of Group II contains all systems without such observations at
dust material spatially resolved and beyond their sublima- λ=8.5µm. As we will see in Section 3.4, the dust parame-
tiondistance,enablingdirectdeterminationofthefluxratio tersinthesesystemscannotbeconstrainedastightlyasfor
between disc and central star (Di Folco et al. 2004). Two the Group I-targets.
MNRAS000,1–14(2016)
Constraints on the structure of hot exozodiacal dust belts 3
Table1.ParametersoftargetswithNIRexcess(Absiletal.2009;Absiletal.2013;Erteletal.2014)whichisattributedtocircumstellar
dust.GroupI/GroupIIcomprisesallsystemswith/withoutinterferometricobservationsatλ=8.5µm(Mennessonetal.2014).
NotestotheIR-excesses:“H”excessintheHband;“K”excessintheKband;“(K)”observedinKband,butwithoutinformationon
the excess (Defr`ere et al. 2012);“/”no interferometric observation;“-”no significant excess detected;“(+)”excess uncertain, discussed
differentlyinliterature,SEDmakesnoclearstatement;“+”weaksignificantexcess;“++”strongsignificantexcess
HD HIP Alter. d T(cid:63) L(cid:63) Spectral Age NIR 8.5µm 24µm 70µm Ref.
number number name [pc] [K] [L(cid:12)] class [Gyr] excess excess excess excess excess
GroupI
10700 8102 τ Cet 3.7 5290 0.46 G8V 10 K - - + (a),(b),(c),(d)
22484 16852 10Tau 13.7 5998 3.06 F9IV-V 6.7 K - - + (d),(e),(f)
56537 35350 λGem 28.9 7932 27.4 A3V 0.5 K - - - (d),(g),(h)
102647 57632 β Leo 11.1 8604 13.25 A3V 0.1 K + + ++ (d),(i)
172167 91262 αLyr 7.8 9620 37 A0V 0.7 H,K - - ++ (d),(i),(j),(k)
177724 93747 ζ Aql 25.5 9078 36.56 A0IV-V 0.8 K - - - (d),(l),(m)
187642 97649 αAql 5.1 7680 10.2 A7IV-V 1.3 K - - - (c),(d),(g),(n)
203280 105199 αCep 15.0 7700 19.97 A7IV-V 0.8 K - - - (d),(l)
216956 113368 αPsA 7.7 8590 16.6 A3V 0.4 K - + ++ (d),(o),(p),(q)
GroupII
2262 2072 κPhe 23.5 9506 16 A5IV 0.7 H / + + (i)
14412 10798 12.7 5371 0.38 G8V 3.7 H / - - (f)
20794 15510 eEri 6.1 5401 0.66 G8V 8.1 H / (+) (+) (r),(s)
28355 20901 bTau 49.2 7852 16 A7V 0.7 H / + ++ (i)
39060 27321 β Pic 19.3 8203 13 A6V 0.02 H,(K) / ++ ++ (i)
104731 58803 24.2 6651 4 F5V 1.6 H / - - (f)
108767 60965 δ Crv 26.9 10209 40 A0IV 0.3 H / - - (i)
131156 72659 ξ Boo 6.5 5483 0.6 G7V 0.3 K / - - (g)
173667 92043 110Her 19.1 6296 6.01 F5.5IV-V 3.4 K / - (+) (e),(s)
210302 109422 τ PsA 18.7 6339 2.5 F6V 2.2 H / - - (e),(f)
References:(a)Greavesetal.(2004);(b)Chenetal.(2006);(c)Habingetal.(2001);(d)Mennessonetal.(2014);(e)Ko´spa´letal.
(2009);(f)Trillingetal.(2008);(g)G´asp´aretal.(2013);(h)Chenetal.(2014);(i)Suetal.(2006);(j)Gillett(1986);(k)Defr`ereetal.
(2011);(l)Chenetal.(2005);(m)Plavchanetal.(2009);(n)Riekeetal.(2005);(o)Stapelfeldtetal.(2004);(p)Suetal.(2013);
(q)Ackeetal.(2012);(r)Wyattetal.(2012);(s)Beichmanetal.(2006).Thedistancesarederivedfromparallaxmeasurements(van
Leeuwen2007).Stellartemperaturesandluminositiesareadoptedfrom(c),vanBelleetal.(2001),vanBelleetal.(2006),Wyattetal.
(2007b),Mu¨lleretal.(2010),Pepeetal.(2011),Zorec&Royer(2012),Boyajianetal.(2013),andPace(2013),spectralclassesand
stellaragesaretakenfromMamajek(2012),Vican(2012),Absiletal.(2013),Erteletal.(2014),andMamajek&Bell(2014).
2.2 Model description
Table2.ParameterspaceformodellingthesystemsfromTab.1.
TheaimofthestudyistofittheNIRfluxesofthehotexo-
zodiacal dust systems. Owing to a paucity of observational Parameter Range Number Grid
data, a simple disc model is adopted to keep the number of
Discringradius R [au] 0.01 −10 100 log.
free parameters small. Grainsize a [µm] 0.001−10/100 100 log.
Disc properties. The disc model represents a thin ring Inclination i 0◦,90◦,sphere 3 discr.
with an inner radius R and outer radius R =1.5R. The
out
number density decreases with n(r) ∝ r−1. The dust mass
M ischosenasascalingfactortomatchtheNIRfluxfor scatteringandreemissionsimulationsareperformedandthe
dust
each individual system. Taking into account scattered radi- SEDs are calculated using an enhanced version of the tool
ation, the inclination i of the disc has to be considered. We debris(Erteletal.2011).Allfreeparametersandtherange
examine three cases: a face-on (i=0◦) and an edge-on disc withinwhichtheyhavebeenvariedarepresentedinTable2.
(i = 90◦) with an half opening angle of 5◦, and a spherical
shellaroundthecentralstar.Thelattercaseismotivatedby
thescenarioofdustexpelledfromexo-Oortcloudcomets,or 2.3 Procedure
bystellarmagneticfieldswhichcompelchargeddustgrains
To illustrate the data modelling procedure, the SED of the
on orbits perpendicular to the disc plane.
NIR excess harbouring system HD 56537 is shown in Fig-
Dust properties. Each dust ring is composed of com- ure2.Obviously,manyappropriateparametersettingsexist
pact and spherical dust grains with a single grain radius which would allow one to reproduce the NIR excess. For-
a. The grains are assumed to consist of pure graphite tunately, there exist further observations which potentially
(ρ = 2.24gcm−3; Weingartner & Draine 2001), using the help to constrain the possible ranges for the grain size a
1/3−2/3 approximation (Draine & Malhotra 1993). andthediscringradiusR.Inparticular,theobservedMIR
Theopticalpropertiesofthegrainsarecalculatedwith andFIRfluxesprovidestrictupperlimitsonthetotalmass
thesoftwaretoolmiexwhichisbasedonthetheoryofMie- (for given dust properties and radial density distribution).
scattering (Mie 1908; Wolf & Voshchinnikov 2004). Single Furthermore,anunderestimationoftheobservedMIR and
MNRAS000,1–14(2016)
4 F. Kirchschlager et al.
2.4.2 MIR and FIR data
100 Stellar photosphere
Observation: Dust
The colours (Eq. 1) are analysed for the wavelengths
Observation: Star and dust
Simulated SED λ=24µmand70µmforallGroupIandII-targets.Table1
10
indicates which of the systems show a significant excess in
HD 56537 theMIRorFIR.Severalsystemshavenooronlyminorex-
1 cess at these wavelengths. To cope with the problem that
Jy] a determination of the flux emitted by the dust is affected
[
Fn mainly by the uncertainty of the stellar photospheric flux,
0.1 we use the measured flux which comprises the contribution
of both dust and stellar photosphere at λ = 24µm
MIR/FIR
and 70µm. Although this condition is weaker than Eq. (3),
0.01
thishelpstocircumventtheuncertaintyofthephotospheric
flux.
0.001 ForHD10700,weuseIRAS-fluxesat60µmand100µm
1 10 100
l [m m] (Greaves et al. 2004) to interpolate the excess flux at
λ=70µm since there exists no observation at this wave-
length.ForHD131156andHD187642,bothfluxesat24µm
Figure 2. SED of HD 56537. The dashed line represents the and 70µm are estimated from the stellar photosphere and
stellar photosphere (T(cid:63) =7932K, L(cid:63) =27.4L(cid:12)), the red points interpolation of observations of IRAS (Habing et al. 2001),
show the observed fluxes (star plus dust, including Spitzer/IRS
Akari, WISE, and Herschel/PACS at 100µm (Ga´spa´r et al.
spectrum; VizieR-catalogue) and the black points mark the ex-
2013).
cess of the dust (without stellar flux contribution). The flux at
λ=8.5µmisanupperlimit.AsimulatedSEDwhichreproduces Inaddition,weuseMIRdatafromKeckfortheGroupI-
the NIR flux without overestimating the observed fluxes in the targets(Mennessonetal.2014).Foreachofthesesystemswe
MIRandFIRisshownasthebluesolidline. calculatethefluxemittedfromthedustatλ=8.5µmusing
F ∼2.5F E (B.Mennesson,privatecommunication),
dust (cid:63) 8-9
whereE isthemeasuredexcessleakgivenintheirTable2.
FIRfluxeswouldstillbeinagreementwiththeobservations 8-9
Thefactor2.5correspondstotheaveragetransmissionvalue
because of the potential presence of additional dust distri-
overtheregionextendingfromtheinnerandouterworking
butionslocatedatlargerdistancestothestar,similartothe
angle.Onlyonesystem(HD102647)showsasignificantex-
Kuiper belt in the solar system.
cess. For all the other systems we use the significance limit
The ratio of the simulated flux in the NIR to the sim-
as an upper limit for the flux at λ=8.5µm.
ulated flux in the MIR and FIR is determined for each pa-
rameter setting:
Ssimu = Fνsimu(λNIR) . (1) 2.5 Sublimation radius and habitable zone
λMIR/FIR Fsimu(λ )
ν MIR/FIR Dustsublimationinthevicinityofthestarsetstheminimum
The simulated colour Ssimu has to be compared to the distance at which the dust material can be located. Subse-
λMIR/FIR
observed colour, quentlytotheinvestigationoftheparameterspacepresented
inSection2.2,wedeterminethesublimationradiiasafunc-
Fobs(λ )
Sobs = ν NIR , (2) tionofgrainsizeainthermalequilibrium.Thesublimation
λMIR/FIR Fobs(λ )
ν MIR/FIR radius R of a particle with a sublimation temperature
sub
and must fulfill the condition Tsub amounts to
SinλsiMmorIuRd/eFrIRto≥reSprλoobMsdIRu/cFeIRthe NIR excess. In this study we (a3s)- Rsub = R2(cid:63)(cid:115)(cid:82)(cid:82)0∞0∞BBλλ(T(Tsu(cid:63)b))QQaabbss(a(a,,λλ))ddλλ, (4)
sume that the hot dust emission does not vary with time
(Backman & Paresce 1993), where B is the Planck func-
(see Sect. 3.6 for a discussion of the time variability of the λ
tion and Q is the dimensionless absorption efficiency.
NIR excess). abs
We assume a sublimation temperature of T = 2000K
sub
(e.g.Lamoreauxetal.1987)forgraphiteanddeterminethe
2.4 Observational data sublimationradiusforeachsystem.Itshouldbenotedthat
themodellingresultspresentedinSection3stronglydepend
2.4.1 NIR data on the exact choice of the sublimation temperature T .
sub
For an approximate estimation of the borders of the
Except for HD 216956 (Fomalhaut), the NIR fluxes of the
habitable zone we assume a temperature profile
dust around all Group I-targets as well as HD 131156 and
HD173667ofGroupIIaredeterminedbyFLUOR/CHARA (cid:18)L (cid:19)0.25(cid:18)1au(cid:19)0.5
(Absil et al. 2013). The data for HD 216956 are taken THZ =(278.3K) L(cid:63) R , (5)
with VLTI/VINCI (Absil et al. 2009), while HD 14412, (cid:12) HZ
HD 104731 and HD 108767 of Group II are observed with where T is the temperature at the radial distance R of
HZ HZ
VLTI/PIONIER (Ertel et al. 2014). For the remaining tar- the habitable zone. The temperature range is 210 to 320K,
getsofGroupII,theweightedmeanfluxratiosofErteletal. equivalenttothehabitablezonelocationinthesolarsystem
(2014, 2016) are used (PIONIER). (e.g. Kopparapu et al. 2013).
MNRAS000,1–14(2016)
Constraints on the structure of hot exozodiacal dust belts 5
2.6 Spatially resolved dust emission and 1.2
sensitivity dependency over the field of view
1
The circumstellar emission in the NIR is spatially resolved.
However, dust within an inner working angle θ does not
contributetotheNIRexcess,whichhastobeconsideredin %] 0.8 f
the modelling. [ar observation
The angular resolution of an interferometer is given by F/cst 0.6
s
di
θ=λ/(xB), (6) F
=
whereBistheprojectedbaselineandx∈{1, 2, 4, ...}.Since f’ 0.4
the correct value for x is contentious, we choose a different
0.2
approach.Weassumeauniformlybrightemissionring(face-
on)1 with an inner radius R and outer radius R =1.5R
out
and adopt the measured NIR flux ratio f of the 0
observation 0.0001 0.001 0.01 0.1 1
spatially resolved dust and the central star. By varying the q [as]
inner radius, we calculate the visibility function V
((cid:63)+disc) Stellar radius inner working angle
of the star in combination with the disc for this simplified
system.Subsequently,theratiof(cid:48) ofthesimulatedobserva-
tional date is derived via f(cid:48) = (V −V )/V , where Figure3.Ratiof(cid:48)=Fdisc/F(cid:63)forthesystemHD56537,derived
(cid:63) ((cid:63)+disc) (cid:63) fromthesimulatedvisibilityfunctionofauniformlybrightemis-
V denotes the stellar visibility alone (Di Folcoet al. 2004).
(cid:63) sion ring (face-on) for different inner radii R (see Sect. 2.6 for
Forlargeinnerradii(right inFigure3),theentirediscis
details). The inner working angle of the simulated NIR observa-
spatially resolved, and the derived ratio f(cid:48) equals the given tionisdefinedasthesmallestvalueθforwhichtheratiof(cid:48)isstill
ratio fobservation. Decreasing the inner radius, the emission withintheintervalfobservation±σf,whereσf istheuncertainty
getslessresolved,resultinginamodulationoff(cid:48) andanin- oftherealNIRobservation.
creaseofthedifferencebetweenf(cid:48) andf .Forsmall
observation
innerradii(Fig.3,left),theentirediscisunresolvedandf(cid:48)
is never resolved by the case of edge-on discs and spherical
convergesto0.Wedefinetheinnerworkingangleofthesim-
dust shells. In particular, a strong forward-scattering peak
ulatedNIRobservationasthesmallestvalueθforwhichthe
is invisible if scattered light is considered.
derived ratio f(cid:48) is still within the interval f ±σ ,
observation f Inadditiontotheinnerworkingangle,thesensitivityof
where σ is the uncertainty of the real NIR observation.
f anoptical,singlemodefiberinterferometersuchasFLUOR,
This is the most conservative approach for the adoption of
PIONIER,orVINCIisnotuniformoverthefieldofview.In-
an inner working angle, since we want to avoid assuming a
stead,itcanbeapproximatedasaGaussianfunctionwitha
toolargeinnerworkingangleandthusconstrainingthedust
FWHMof0.8as,0.4as,and1.6as,respectively(Absiletal.
distributioninawrongway.FortheFLUORobservationof
2013; Ertel et al. 2014; Absil et al. 2009). This disparity is
the system HD 56537 in Figure 3, a value of θ = 0.0034as
takenintoaccountinourNIRsimulations,sothatemission
is derived. Using Eq. 6, this is equivalent to x = 3.97. For
furtherawayfromthestarisweakerthanemissioncloserin.
comparison, Absil et al. (2013) assumed a value of 4 when
examining the resolution of the sublimation radius. In our
study, x is between 3.4 and 4.1 for all observations with
FLUOR, PIONIER and VINCI of the systems in Table 1. 3 RESULTS
Thesmallvariabilityinxistheresultoftheuncertaintyσ
f In this section the results of the disc modelling process are
of the individual observations.
presented. For each parameter setting in Table 2 the colour
Additionally to the interferometric data in the NIR, Ssimu iscalculatedandcomparedtoSobs .Atfirst
MIR nulling data obtained with the Keck Interferometer λMIR/FIR λMIR/FIR
we demonstrate the key results of the modelling for the
areusedfortheGroupI-targets.Theinnerworkinganglefor
exozodiacal dust system HD 56537 as a representative of
theseobservationsis6mas(Mennessonetal.2014).Thesig-
Group I in detail (Sect. 3.1). Subsequently, we discuss the
nalforsourcesatprojectedseparationslargerthan200mas
entire samples of Group I and II (Sect. 3.2 - 3.4). In Sec-
isstronglyattenuatedorevencompletelymissed,settingan
tion 3.5 - 3.7 the uncertainty and the time variability of
outer working angle of the instrument.
theNIRexcessaswellasconstraintsbyspectrallydispersed
After the determination of the inner working angle for data are discussed.
each system and NIR and MIR observation, it is used as
a strong limiting condition for the simulations: radiation
which is scattered or reemitted within the inner working 3.1 HD 56537
angle(oroutsidetheouterworkingangle)iscompletelyne-
HD56537(λGem)isa5×108yearoldsystem(Vican2012)
glected. While in the face-on case only discs with small in-
with a significant K band excess (0.74% ± 0.17% of the
ner radii R are affected, a significant fraction of radiation
stellar flux), but with no significant excess at λ = 8.5µm,
24µm or 70µm. This suggests that the NIR excess stems
1 Similarly, a uniformly bright emission is also adopted in the solely from the hot exozodiacal dust, with no contribution
wholefieldofviewbyAbsiletal.(2009),Absiletal.(2013)and from other potential disc components. The results of the
Ertel et al. (2014) to derive the NIR flux of the dust from the modelling are shown in Figure 4. Each panel represents a
observations. selectedrangeoftheparameterspaceconsistingofthegrain
MNRAS000,1–14(2016)
6 F. Kirchschlager et al.
3 3 3
Face−on disc Edge−on disc Spherical Shell
20 20 20
1 1 1
15R) 15R) 15R)
MI MI MI
R [au] 0.3 Sublimation R [au] 0.3FR)/(nSublimation R [au] 0.3FR)/(nSublimation FR)/(n
10NI 10NI 10NI
( ( (
Fn Fn Fn
0.1 0.1 0.1
5 5 5
0.03 0. 003 0. 003 0
10−3 10−2 10−1 100 101 10−3 10−2 10−1 100 101 10−3 10−2 10−1 100 101
a [mm] a [mm] a [mm]
3 1325 1325 125
’Colorbox_horo.jpg’ binary filetype=jpg
120 120 120
%] %] %]
1 1115n [ 1115n [ 115n [
o o o
110diati 110diati 110diati
a a a
R [au] 0.3 Sublimation R [au] 0 1.305Total rSublimation R [au] 0 1.305Total rSublimation 105Total r
100on/ 100on/ 100on/
si si si
s s s
0.1 0 9.15mi 0 9.15mi 95mi
e e e
e e e
99 % 90 % 90 % R 99 % 90 % 90 % R 99 % 90 % 90 % R
90 90 90
0.03 0. 0835 0. 0835 85
10−3 10−2 10−1 100 101 10−3 10−2 10−1 100 101 10−3 10−2 10−1 100 101
a [mm] a [mm] a [mm]
3 73 73 7
Figure 4. Explored parameter space for the system HD 56537. The dust material is pure graphite. The disc inclination is i=0◦ (left
column) and 90◦ (middle column), and the resu l6ts for the case of a spherical dust distributio 6n are shown in the right column. In the 6
first1row thecalculationsconsideringtheobservati1onsatλ=2.2µm,8.5µm,24µmand70µma1reshown.Theblueregionsinthepanels
5 5 5
correspondtoparametersettingswhichcanreproducetheobservationaldata,whiletheparametersettingsoftheredregionsfail.The
sublimationradius(whitedashedline)andtheupperblue-redbordercomprisetheregionofsuitableparametersettings(dashedarea).
4 4 4
RIu [au]npt0th.o3e1s0e0co%nd(arpowrictohte).rBatlaiockofctohnetorueremlinisessiosnhotR [au]owtt0h h3.e3Pe [%]t9o0ta%lraanddiat9i9on%isleivlleul.strated.ThecolourR [au]sca0 l3.e3P [%]islinear,rangingfrom84%(turquoise) 3P [%]
2 2 2
size0.1aandthedustringradiusR.Inthefollo0w.1ing,weinves- thecorrespondingpar0a.1metersettingsreproducetheNIRex-
tigate potential constraints which can be derived for these 0.1 %c1e %ss5w %ithout overestimating the fluxes at these three wave-
1 1 1
quantities and determine the contribution of scattered and lengths, while in the red-coloured regions the simulated
po0l.0a3rised radiation of the NIR flux. 0. 003 fluxes of at least o0n. e003of them is too large. Models with 0
10−3 10−2 10−1 100 101 10−3 10−2 10i−n1ner ra10d0ii R (cid:46)1010.081a0u−3fail b1e0−c2ause o10f−1the in1n0e0r work1-01
a [mm] a [mm] a [mm]
3 1325 ing angle of the simu3la3ted NIR observations. On the other 125
3.1.1 Constraints on grain size and dust location Edge−ohna nddis,cmodels with inner radii 0.08au(cid:46)R (cid:46)0.14au repro-
120 duce the observations because of the larger inner working 120
RTaSiMtdt [au]shinmoothIede00nRewa..s131flohfrlrnroafieadorccSsrdithtuaffutiicdblahaoetloitrrinesmanieeotantsofdinotrpcofiuoirehnbonresenuadfrtbdrtiiotoeffecihamtatetetwhlroieeoleddintenguduhtnhsesefttptdrtoohleisossbmncehccsasdeaeetedilrttnltnveuehccderaslreidtrinefneouegcflafrlpuotogttirpxhsheoeet)oeensirmecastsR [au]naoasce(ltwatwlite00tyra hd91111..tey131=y50011etel.l0505hri(emission/Total radiation [%]Inseainw0tndsa◦FhacNrtidiahocgI(dshreuRweirtfsd9hreaio0oeaincx◦en4cdhs)--,. alttdttciihhhonmioueeergnrsalsespeitnusaiaopfnniorotnodeafarnrmbrttdalahrheeliadlnteeedpigguruisaruspipramssaappiinmruseaRaR [au]lrceamssetptib(ez00ee120ali..retd.131us.t6se−91MMie10 []s,raedustearthe-MasSvlritulteautfyI)odiblR.nudrlirmgaebFemsoptaosuebtioiri(rcdondsldttnveihesamefrreosvdtuhrrachmmetobeedimoyoaarmncapenhtsr,rihd.enisaessimSeyum)i.NsbnatutTlhxIceimRmeemihmiarstluoeiathmbmgaineosirdioneetdsnrautuvrfhobaiaosnert---f 91111500110505emission/Total radiation [%]
e e
not change the observe99d %flu90x %ei9t0h %er, due to t9h0eRsensitivity 0.1 %r1i n%g5r a%dius,grainsize,andmassarederiv9e9d %.F9o0 r%H90D %56537, 90R
of the optical single mode fiber) depend on the dust distri- the maximum disc ring radius is R = 0.65au (0.68au;
max
bu0t.0i3on geometry. The results for the spheri0c.a 083l5shell can be 0.68au) for the face-0o.0n3 disc (edge-on disc; sphere). The to- 85
inter1p0r−e3tedqu1a0−l2itativae1 l[0ym−m1a]sinte1r0m0ediate1b01etwee1n0−3theres1u0−l2ts a1 [0mt−ma1]l dust100mass r1e0q1uired10−t3o repr1o0d−2uce tah1 [0em−m1N] IR fl1u00x is be1-01
for the face-on and the edge-on disc. tween 0.5×10−9M (0.9×10−9M ; 0.6×10−9M ) and
⊕ ⊕ ⊕
In the upper row of Figure 4 the calculations con- 22×10−9M (52×10−9M ; 33×10−9M ). The grain
⊕ ⊕ ⊕
sidering the observations at the wavelengths λ = 8.5µm, sizes for this system are not limited by our study, and both
24µm and 70µm are shown. In the blue-coloured regions
MNRAS000,1–14(2016)
Constraints on the structure of hot exozodiacal dust belts 7
3 7
Photosphere Astro Sili MgFe Pyro Graphite
Observ.: Dust Olivine MgFe Oliv AC
100
6
1 10
5
u] 4%] [Jy] 1
R [a 0.3 P [ Fn
3 0.1
2
0.1 0.01
0.1 % 1 % 5 %
1
0.001
1 10
l [m m]
0.03 0
10−3 10−2 10−1 100 101
a [m m]
Figure6.SEDconsideringdifferentdustmaterials(seetext)ina
discwithringradiusR=0.4auanddustgrainsofsizea=0.1µm
around HD 56537. The dust mass M is chosen as a scaling
Figure 5. Polarisation degree P of the total radiation for the dust
factor to match the flux at λ = 2.2µm for each material. All
system HD 56537. The dashed white line indicates the sublima-
silicates (green) show the characteristic spectral feature around
tionradiusandtheregionofsuitableparametersettingsishigh-
λ∼10µmwhichcausesanoverestimationofthefluxat8.5µm,
lightedasdashedarea(seeFig.4).Theblackcontourlinesshow
contrary to the observations. In contrast, carbonaceous grains
the 0.1%, 1% and 5% level. The dust material is graphite and
theinclinationis90◦. (blue)reproducetheobservations.
nanometer-sized grains and those larger than ∼ 10µm can even below 1% for grains smaller than 0.24µm. Only for
reproduce the observed excesses. The reason for the possi- grain radii between 0.3µm and ∼ 0.5µm, the polarisation
ble presence of the large particles is that the sublimation islargerthan2%.Becauseofsymmetryconstraints,thein-
radius of this system is not spatially resolved by the MIR tegrated polarisation equals zero in the case of the face-on
observationatλ=8.5µm.Apile-upoflargegrainsnearthe disc and the spherical shell. The results are consistent with
sublimation radius would cause a detectable excess in the polarisationmeasurementsofhotduststarswiththeinstru-
NIR,whichcouldnotbeobservedbytheMIRobservations. mentHIPPIattheAnglo-AustralianTelescopeintheoptical
In contrast, the theoretical approach of an infinitely small wavelength range, which have shown that the detected po-
resolution of both the NIR or MIR observations would rule larised emission does not exceed 1% (Marshall et al. 2016).
out large grains in this system due to small observed fluxes
at λ=8.5µm compared to the NIR.
Ingeneral,ahighersublimationtemperaturewouldde- 3.1.3 Different dust materials
crease the minimum radius and minimum dust mass and
To investigate the impact of different dust materials on the
increase the maximum grain size.
discmodelling,appropriatesimulationsoftheSEDareper-
formed for an exemplary disc with ring radius R = 0.4au
anddustgrainsofsizea=0.1µm(Fig.6).Besidesgraphite
3.1.2 Scattered and polarised radiation
(optical data from Weingartner & Draine 2001) from the
The contribution of scattered radiation to the NIR flux is previous section, we also consider:
still an open question, although previously published stud-
• Astronomicalsilicate(AstroSili;Weingartner&Draine
iestendedtofavourasmallcontribution(e.g.vanLieshout
2001),
etal.2014;Riekeetal.2016).Theratioofthethermalree-
• Natural (terrestrial) olivine from San Carlos, Arizona
mission radiation to the total radiation is illustrated in the
(Olivine; data for 928 K; Zeidler et al. 2011, 2015),
second row of Figure 4. We find that for suitable param-
• Glassy magnesium-iron silicates with pyroxene compo-
eter settings thermal reemission is the dominating source.
sition,Mg Fe SiO (MgFePyro;Dorschneretal.1995),
0.5 0.5 3
The lowest ratio of the thermal reemission to the total ra-
• Glassy magnesium-iron silicates with olivine composi-
diation for all three disc geometries amounts to 84%. For
tion, MgFeSiO (MgFe Oliv; Dorschner et al. 1995),
grain radii below 0.2µm the ratio is larger than 99%. Con- 4
• Amorphous carbonaceous dust analogues produced by
sequently, the contribution of scattered radiation and thus
pyrolysis of cellulose at 1000◦C (AC; J¨ager et al. 1998).
the influence of the disc inclination are negligible for these
smallgrains.Onlyforgrainswithradiibetween0.2µmand The first four materials are silicates and the last one is a
∼1µm, the fraction of scattered radiation is larger. carbon. The silicates show the characteristic broad spectral
Moreover, the polarisation degree P of the total radi- featurearoundλ∼10µm.Regardingthethermalreemission
ation in the NIR is determined (Fig. 5). According to the asthedominatingsourceofradiation,thefluxatλ=8.5µm
low contribution of scattered radiation for the suitable pa- is expected to be larger than the NIR flux in most cases.
rameter settings, the polarisation degree is below 5% and However, the flux observed at λ = 8.5µm in systems with
MNRAS000,1–14(2016)
8 F. Kirchschlager et al.
hot exozodiacal dust is one order of magnitude below the Stellar luminosity / L
⊙
measured NIR flux. We cannot reproduce the observational 0.4 6 3.0 6 1 0.2 1 3.2 5 1 6.6 1 9.9 7 2 7.4 3 6.5 6 3 7
constraints under the assumption of dust grains consisting
ofanyoftheconsideredsilicates.Morespecifically,onlydisc 1 Habitable
ringradiibelowthesublimationradiusincombinationwith
thedominanceoflargegrains(wherethespectralfeatureis
less pronounced) would result in fluxes which are in agree- u]
a
mentwiththeobservations.Althoughthemodellingcannot R [ 0.1
exclude the presence of large particles due to the limited
resolution of the observation at λ=8.5µm, we expect that Rmax
they do not occur in the disc. Therefore, large amounts of Rmin
silicatesinthematerialoftheexozodiacaldustareexcluded. 0.01
1000
Incontrast,thecrystallinegraphiteandtheamorphous
carbon can reproduce the observations, so that we focus on
] 100
graphite in the following sections. M¯
9
− 10
0
1
[ust 1
3.2 Survey: Group I-targets d
M 0.1 Mmax
We now perform the calculations of the SED for each tar- Mmin
get of Group I and determine the parameter settings which 10
reproduce the observational data. The results are shown in Edge on
Figure 7. Sphere
The minimum disc ring radius Rmin varies between m] Face on
∼0.01au and ∼0.2au and increases in a rough trend with
thestellarluminosity.Thisisofcourseexpected,sinceRmin m [ax 1
m
isinmostcasesdeterminedbythesublimationradiusRsub. a
ThemaximumdiscringradiusR isbelow∼1aufor
max
allsystems,withaminimumvalueof0.06auforHD10700.
Interestingly, it also appears to increase with the stellar lu-
0.1
minosity. In contrast to the minimum radius, this trend is 0 4 42 47 56 80 7 24 67
0 8 6 6 9 2 3 7 1
notobvious,sincewedonotknowwhichphysicalprocesses 07 24 87 02 16 03 65 77 72
1 2 1 1 2 2 5 1 1
set the location of the exozodiacal dust and whether or not D D D D D D D D D
H H H H H H H H H
theseare,forinstance,temperature-dependent.Accordingly,
atentativetrendmightbeimportant,andwenowundertake
a basic statistical analysis. Figure 7. Results of the disc modelling of the Group I-targets
(Tab. 1). The stellar luminosity increases from left to right.
The Pearson correlation coefficient between logL and
logR amounts to R = 0.70, and the Spearman(cid:63)rank Top:Minimum and maximum disc ring radius, Rmin and Rmax,
max p within which the hot zodiacal dust is located. An approximate
correlation coefficient, which is more robust and does not
habitable zone between 210 and 320K is marked for HD 10700
require linearity, is R = 0.65. If two apparent outliers,
s and HD 22484 as green boxes. For the other systems, the cor-
HD 22484 and HD 102647, are dropped from the analysis, responding habitable zone is outside of the displayed radii.
the correlation gets even stronger (Rp = 0.85, Rs = 0.94), Middle:Minimum and maximum dust mass, Mmin and Mmax,
indicating a high significance. respectively. Bottom: Maximum grain size for discs with face-on
Sincethetrendissignificant,wecanmakeapower-law oredge-onorientationandforthesphericalshell.
fit.Theresultstronglydependsonhowwetreattheoutliers
(Fig. 8). For the full sample of nine stars, i.e. not excluding
anyoutliers,theresultisR ∝L0.5±0.3.Withouttwoob- HD 22484 only, the best fit for the remaining eight systems
max (cid:63)
viousoutliersmentionedabovewefindR ∝L1.4±0.4.Fig- is R ∝L0.7±0.5.
max (cid:63) max (cid:63)
ure 8 suggests that HD 172167 (Vega) may be another out- Since we are interested in the most likely distance at
lier.ExcludingallthreesystemsresultsinR ∝L1.8±0.2. whichthehotdustislocated,wemayalsochoosetoanalyse
max (cid:63)
Trying to understand which of these relations can be more the geometrical mean of the minimum and maximum radii,
√
trustable,wecanlookatallthreepotentialoutliers.Indeed, i.e. R = R R instead of R . Doing this with-
mean min max max
HD 22484 has the relatively small ratio of the measured outtheoutlierHD22848leadstoanevenflatterdependence,
NIRfluxtothefluxat8.5µm,whichresultsinweakercon- R ∝L0.6±0.2.Infact,thedustlocationmayscaleasthe
mean (cid:63)
straints for the model parameters (see Sect. 3.3). Thus we squarerootofthestellarluminosity,whichwouldimplythat
deemdiscardingthissystemreasonable.HD102647(β Leo) allexozodiacaldustdiscshaveapproximatelythesametem-
is the only system with a significantly high flux at 8.5µm, perature.Iftrue,thiscouldmeanthatthehotdustlocation
and this system reveals some differences to other resolved isdrivenbytemperature-dependentprocesses.Alternatively,
cases (see notes on this system in Sect. 3.3). As for Vega, this may be a chance coincidence. For instance, if the hot
thereissomeuncertaintyaboutitsluminosity(seeSect.3.3 dust is trapped by stellar magnetic fields (see Sect. 4), a
for this star, too). Yet we do not see any justifiable reason similar trend may possibly arise if the Lorentz force scales
for excluding β Leo and Vega from the analysis. Discarding withthestellarluminosityinasimilarway.Onanyaccount,
MNRAS000,1–14(2016)
Constraints on the structure of hot exozodiacal dust belts 9
1000
1.4 6 systems 9 systems
1.2 7 systems Observation
] 100
1 M¯
R [au]max 00..68 −9 [10 ust 1 10
d
0.4 M
0.1
0.2
Mmax Mmin
0
0 5 10 15 20 25 30 35 40 0.1 1 10
L [L ] t [109 yr]
⊙
Figure8.MaximumdiscringradiusRmaxasafunctionofstellar Figure 9. Minimum and maximum dust mass as a function of
luminosityL(cid:63)forthenineGroupI-targets(bluetriangles),fitted stellaragefortheGroupI-targets(Tab.1).
withafunctionRmax=c1Lc(cid:63)2.Excludingnosystem,orexcluding
HD 22484 and HD 102647, or excluding HD 22484, HD 102647
andVega,theresultisRmax∝L0(cid:63).5±0.3(dots),Rmax∝L1(cid:63).4±0.4 as a function of stellar age in Figure 9. With the Pearson
(dashedline),andRmax∝L1(cid:63).8±0.2 (solidline),respectively. correlationcoefficientRp =0.29andtheSpearmanrankco-
efficientR =0.11(neglectingofHD22484andHD102647:
s
R = −0.10, R = 0.04), no strong correlation exists be-
p s
tween the maximum mass of the hot exozodiacal dust and
no definite conclusions can be made, given a small sample
the age of the system.
size and rather large uncertainties with which the dust ring
radii are estimated.
In addition, we note that for all systems the location 3.3 Individual targets of Group I
of the habitable zone defined in Sect. 2.5 is outside of the
In this section, individual sources of Group I are discussed
location of the hot dust.
briefly.
The range of grain sizes depends on whether the subli-
mationradiusisresolvedbytheobservationatλ=8.5µmor
not(HD10700,HD22484,HD56537).Ifitisnot,wearenot
HD 10700 (τ Cet)
abletoputanyconstraintsontheparticlesize.Sincelarger
dust grains are not excluded in these systems, scattered ra- HD10700isoneofthebrightestsun-likestarsinourneigh-
diationhasahigherimpactontheNIRflux.HD102647and bourhood(G8V,K =1.7mag)andwith∼1010yrtheoldest
HD177724aremarginallyresolvedbytheMIRobservation, of the sample. The K band excess was first reported by Di
resulting in a large maximum grain radius a for at least Folco et al. (2007). While there is no significant excess at
max
oneofthethreediscgeometries.Fortheremainingsystems λ = 8.5µm or 24µm, Habing et al. (2001) reported excess
of Group I, the maximum grain sizes are constrained to be at 60µm and 100µm and Greaves et al. (2004) and Lawler
between 0.2µm and 0.5µm and the deviations for different etal.(2014)presentedresolvedimagesat70µm,160µmand
disc inclinations are below 10%. Thermal reemission is the 850µm.
dominating source of the excess in the NIR. Consequently, We find that the hot dust has to be located between
the polarisation degree is below 5%, and for grain sizes be- 0.013au and 0.06au. The minimum dust mass is about
low ∼0.2µm even below 1%. The ratio of the scattered to 0.03×10−9M⊕.Themaximumdustmasstakesvaluesfrom
total radiation amounts to values up to 35%. However, the 1.2×10−9M⊕ (face-on) to 2.4×10−9M⊕ (edge-on). Since
modelling results in a lower limit of the minimum particle the sublimation radius of the large particles is resolved for
sizeforthesystemsHD10700,HD187642andHD216956. the NIR observation but not for the MIR observation, the
The maximum dust mass M shows the same be- maximum grain size is not constrained. Particles smaller
max
haviourasthemaximumdiscringradiusR andisinthe than 1µm sublimate at larger distances than larger parti-
max
range(0.26−840)×10−9M ,whiletheminimumdustmass cles. For the face-on disc and the spherical dust sphere of
⊕
M amounts to (0.03−1.1)×10−9M . Again, the max- HD10700,thisconditionsetsalowerlimitforthegrainsizes
min ⊕
imum dust masses can be much better constrained for the (seeFig.10),andtheminimumparticleradiusis34nmand
systemswherethesublimationradiusisspatiallyresolvedby 22nm, respectively.
the MIR observation. In such systems, the maximum dust
mass amounts to (0.2−3.5)×10−9M .
⊕ HD 22484 (10 Tau)
A decay of the dust mass with the stellar age is a ro-
bust theoretical prediction for“classical”debris discs, i.e., Ko´spa´letal.(2009)showedthattheSEDexhibitsanexcess
Kuiper-belt analogues (e.g. Dominik & Decin 2003; Wyatt at 70µm for HD 22484, while there is no significant excess
et al. 2007b; L¨ohne et al. 2008). This trend has also been at24µm.TheratioofthemeasuredNIRfluxtothefluxat
confirmed observationally, especially for A-type stars (e.g. 8.5µm is relatively small (∼3.5).
Rieke et al. 2005; Su et al. 2006), although the dependence The scattered radiation contributes to the NIR flux up
is much weaker for solar-type stars (e.g. Eiroa et al. 2013; to∼30%(forgrainsbetween0.1µmand1µm),eventhough
Montesinos et al. 2016). However, it is not known whether thermal reemission is the dominant source for the NIR flux
thesameistrueforexozodiacaldustsystems.Tocheckthis, atawiderangeofthesuitableparametersettings.Thedisc
weplottedtheinferredminimumandmaximumdustmasses ring radii are not strongly affected by the disc inclination
MNRAS000,1–14(2016)
10 F. Kirchschlager et al.
0.3 3 3 35
HD 10700 (t Cet) HD 102647 (b Leo) HD 172167 (Vega)
9
25
30
8
0.1 1 1
20 7 25
R) R) R)
MI 6MI MI
R [AU]0.03 R [AU]0 .135FNIR)/(nSublimation R [AU]0 45.F3NIR)/(n Sublimation 1250FNIR)/(n
Sublimation 10F(n 3F(n F(n
0.01 0.1 0.1 10
2
5
5
1
0.003 0.0 03 0. 003 0
10−3 10−2 10−1 100 101 10−3 10−2 10−1 100 101 10−3 10−2 10−1 100 101
a [mm] a [mm] a [mm]
Figure 10. Same as Figure 4, but for the systems HD 10700 (τ Cet), HD 102647 (β Leo), and HD 172167 (Vega), and only for the
face-on case. The dust material is pure graphite. For HD 10700, the sublimation radius and the upper blue-red border constrain the
minimum dust grain size, while for HD 102647 and HD 172167 the the maximum grain radii are constrained. HD 102647 is the only
systemofthesamplewithasignificantexcessat8.5µm(Mennessonetal.2014).
andtakevaluesbetween0.035auand0.52au.Theminimum etal.2006)whichmakesstellarparametersafunctionofthe
dust mass is about 0.2×10−9M and the maximum dust stellarlatitude.Consequently,theluminosityattheequator
⊕
massisintherange(150−840)×10−9M .Thegrainsizes andatthepolesderivedfromequatorialandpolarvaluesof
⊕
are not constrained. the stellar radius R and temperature T deviate between
(cid:63) (cid:63)
7900−10150K and 28−57L , respectively (Aufdenberg
(cid:12)
etal.2006).Inoursimulations,weadoptintermediatevalues
HD 56537 (λ Gem)
of T(cid:63) =9620K and 37L(cid:12) (Mu¨ller et al. 2010).
The system was discussed in detail in Section 3.1. Besides Wefindthatthedusthastobelocatedbetween0.15au
theKbandexcess,therewasnosignificantsignalabovethe and 0.68au and the dust mass amounts to (0.8−3.6)×
photosphere at 8.5µm, 24µm or 70µm (Ga´sp´ar et al. 2013; 10−9M⊕. The sublimation radius is resolved for all par-
Chen et al. 2014; Mennesson et al. 2014). ticle sizes by both the NIR and the MIR observation.
Consequently, the maximum grain size is well constrained
(< 0.35µm, Fig. 10). These values are comparable to the
HD 102647 (β Leo, Denebola) parameters found by Absil et al. (2006) and Defr`ere et al.
(2011),whoindicatedgrainsofsizessmallerthan0.2µmand
The K band excess of HD 102647 was first reported by
distances of R∼0.2−0.3au.
Akeson et al. (2009). It is the only system of the sample
with a significant excess at 8.5µm (Mennesson et al. 2014).
HD 102647 also has a significant excess at both 24µm and
70µm (Su et al. 2006) and is well studied (e.g. Stock et al. HD 177724 (ζ Cep), HD 187642 (α Aql, Altair),
and HD 203280 (α Cep, Alderamin)
2010;Churcheretal.2011),revealingarelativecompactdisc
at60−70auandwithfurtherdustcomponentslocatedclose ThesethreesystemsareallshowinganexcessintheKband
to 2au to the star. Herschel images show a nearly face-on but are free of excess at any longer wavelengths (Habing
disc (Matthews et al. 2010). et al. 2001; Chen et al. 2005; Plavchan et al. 2009; Ga´spa´r
In our disc modelling we derived the location of the et al. 2013; Mennesson et al. 2014).
hot exozodiacal dust to be between 0.07au and 1au. The For HD 177724, the minimum and maximum of the in-
minimum dust mass amounts to 0.3×10−9M⊕. The maxi- ner disc ring radius amount to about 0.12au and 1.1au,
mumdustmasstakesvaluesfrom5.8×10−9M⊕(face-on)to respectively. The minimum mass is between 1.1×10−9M⊕
8.1×10−9M⊕ (edge-on).Sincethesublimationradiusisre- and 1.3 × 10−9M⊕ and the maximum mass lies between
solved for all particle sizes by the NIR and also marginally 10×10−9M and 52×10−9M . For the edge-on case and
⊕ ⊕
by the MIR observation, the maximum grain size is con- thesphericaldustshell,thesublimationradiusisunresolved
strainedto0.74µm(face-on,Fig.10),7.6µm(edge-on)and forthelargedustgrains,andthusthemaximumdustgrain
1.0µm (sphere). size not constrained. For the face-on case, the maximum
grain size amounts to 0.46µm.
ForHD187644,thedustisstronglyconfinedtoarange
HD 172167 (α Lyr, Vega)
between0.09auand0.11auandthemassamountsto(0.8−
HD 172167 shows excess in H band (Defr`ere et al. 2011) 1.3)×10−9M . The minimum grain size is about 0.15µm
⊕
and K band (Absil et al. 2006), while the flux at 8.5µm is and the maximum grain size amounts to 0.22µm.
not significant but only slightly below the significance limit For HD 203280, the inner dust ring radius is located
(Mennesson et al. 2014). Su et al. (2006) reported a large between0.1auand0.45auwithadustmassof(0.47−2.4)×
excess at 70µm, which corresponds to a disc nearly face- 10−9M .Themaximumgrainsizeisconstrainedto0.35µm
⊕
on (Monnier et al. 2012). Vega is a rapid rotator (Peterson (face-on), 0.46µm (edge-on) and 0.42µm (sphere).
MNRAS000,1–14(2016)