星形成ゼミ
2017/11/10
SFN #297 #6-#10
長谷川哲夫（国立天文台）

1

iv:1708.02961v1 [astro-ph.SR] 9 Aug 2017

1

Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory,
Observatorievägen 90, 43992 Onsala, Sweden; e-mail: daria.dallolio@chalmers.se2
INAF–Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius, Italy
297
Methanol masers
revealthe17,
magnetic
fieldGermanyof the high-mass protostar IRAS
3
Max-Planck-Institutefor Astronomy,
Königstuhl
69117 Heidelberg,
4
JodrellBank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, M139PL Manchester, UK#618089-1732
D. Dall’Olio, W. H. T. Vlemmings, G. Surcis, H. Beuther, B. Lankhaar1, M. V. Persson, A. M. S. Richards, and E. Varenius
ReceivedarXiv:1708.02961v1
2 June 2017; accepted 9 August 2017
ABSTRACT
Context. The importance of the magnetic field in high-mass-star formation is not yet fully clear and there are still many open questions

concerning its role in the accretion processes and generation of jets and outflows. In the past few years, masers have been successfully
used to probe the magnetic field morphology and strength at scales of a few au around massive protostars, by measuring linear
polarisation angles and Zeeman splitting. The massive protostar IRAS 18089-1732 is a well studied high-mass-star forming region,
showing a hot core chemistry and a disc-outflow system. Previous SMA observations of polarised dust revealed an ordered magnetic
field oriented around the disc of IRAS 18089-1732.
Aims. We want to determine the magnetic field in the dense region probed by 6.7 GHz methanol maser observations and compare
it with observations in dust continuum polarisation, to investigate how the magnetic field in the compact maser region relates to thelarge-scale field around massive protostars.
Methods. We reduced MERLIN observations at 6.7 GHz of IRAS 18089-1732 and we analysed the polarised emission by methanol
masers.
Results. Our MERLIN observations show that the magnetic field in the 6.7 GHz methanol maser region is consistent with themagnetic field constrained by the SMA dust polarisation observations. A tentative detection of circularly polarised line emission is
also presented.
Conclusions. We found that the magnetic field in the maser region has the same orientation as in the disk. Thus the large-scale fieldcomponent, even at the au scale of the masers, dominates over any small-scale field fluctuations. We obtained, from the circularpolarisation tentative detection, a field strength along the line of sight of 5.5 mG which appeared to be consistent with the previous
estimates.
Key words. magnetic field – stars: formation – stars: massive – masers – polarization

大質量星形成領域 IRAS 18089-1732 (L = 12.89d, B = +0.50d)
観測• 距離 2.34 kpc, L = 1.3E4 L_sun, M_gas ~ 1E3 M_sun
6.7 GHz
CH3OH
maser
1. Introduction
netic braking which removes
mostof theangular momentum• Disk + ouMlow（南北方向）
MERLIN
from the circumstellar gas. This is the so-called magnetic brakSMAでの観測（Beuther+
2008年3月,
4月, 7月The roleof magnetic fields 2010）
during the formation of high-mass ing catastrophe in disc formation(Mestel& Spitzer 1956; Allen•
Diskのdust
conTnuum偏波→diskに沿った磁場（Chandrasekhar-Fermi法でB_pos
~
11
mG）
Beam
0.18”
x
0.03”
stars is not yet fully understood. As in the case of low-mass star et al. 2003; Mellon & Li 2008; Li et al.
2011, 2013). Only by• OuMlowのCO3-2でGoldreich-Kylaﬁs効果（P~ 8%） field apformation,
simulations
have shown that the magnetic
inserting non-ideal MHD e↵ects such as Ohmic dissipation or
CH3OH
6.7 GHzmaserのモニター（Goedhart+2009）→29.5日周期の強度変動
pears toprevent
fragmentation
around massive
protostars (Pe-ters et al. 2011, Myers et al. 2013) to influence accretion and todrive feedback phenomena such as collimated outflows and jets
(Seifried et al. 2011, 2012). Both the core accretion model (e.g.

ambipolar di↵usion, or the combined action of both, is it possible to overcome the apparent conflict between observations andsimulations (Machida et al. 2014, Zhao et al. 2016). Moreover,A&A proofs: manuscript no. IRAS15

1

Guido De Marchi1 , Nino Panagia2,3,4, and Giacomo Beccari5

European Space Research and Technology Centre, Keplerlaan 1, 2200 AG Noordwijk, Netherlands; gdemarchi@esa.int

2
297 Photometric
Determinationof SantheMartin
Massofpanagia@stsci.edu
Pre-main-sequence
Space Telescope
Science Institute, 3700
Drive,Accretion
Baltimore, MD Rates
21218, USA;3
INAF-NA, Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131 Napoli, Italy#7 Stars. V. 4RecentStar Formationin theRd.,
30Virgin
DorGorda
NebulaSupernova Limited,
OYV #131, Northsound
VG1150, Virgin Islands, UK

Guido 5De
Marchi,Southern
Nino Panagia,
and Giacomo
Beccari
EuropeanObservatory,Karl-Schwarzschild-Str.
2, D-85748 Garching, Germany; gbeccari@eso.org
ApJ 846, 110(2017)2017 May 1; revised 2017 July 27; accepted 2017 August 9; published 2017 September 7
Received

Abstract
We report on the properties of the low-mass stars that recently formed in the central ~2.7
¢ ´ 2.7¢ of 30 Dor,
including the R136 cluster. Using the photometric catalog of De Marchi et al., based on observations with the
Hubble Space Telescope, and the most recent extinction law for this ﬁeld, we identify 1035 bona ﬁde pre-mainsequence (PMS) stars showing Ha excess emission at the 4s level with an Ha equivalent width of 20 Å or more.
We ﬁnd a wide spread in age spanning the range ~0.1–50 Myr . We also ﬁnd that the older PMS objects are placedin front of the R136 cluster and are separated from it by a conspicuous amount of absorbing material, indicatingthat star formation has proceeded from the periphery into the interior of the region. We derive physical parameters
for all PMS stars, including masses m, ages t, and mass accretion rates Ṁacc . To identify reliable correlations
between these parameters, which are intertwined, we use a multivariate linear regression ﬁt of the typelog Ṁacc = a ´ log t + b ´ log m + c . The values of a and b for 30 Dor are compatible with those found in
NGC 346 and NGC 602. We extend the ﬁt to a uniform sample of 1307 PMS stars with 0.5 < m /M:<1.5 andt < 16 Myr in six star-forming regions in the Large and Small Magellanic Clouds and Milky Way withmetallicities in the range of 0.1–1.0 Z:. We ﬁnd a = -0.59 0.02 and b = 0.78 0.08. The residuals are
systematically different between the six regions and reveal a strong correlation with metallicity Z, of the typec = (-3.69 0.02) - (0.30 0.04) ´ log Z Z:. A possible interpretation of this trend is that when themetallicity is higher so is the radiation pressure, and this limits the accretion process, in both its rate and duration.
Key words: galaxies: star clusters: general – galaxies: star clusters: individual (30 Dor) – galaxies: stellar content –Magellanic Clouds – stars: formation – stars: pre-main sequence

HST mulTband photometric catalog (De Marchi+ 2011)
1. Introduction
ages in excess of ∼10 Myr and are preferentially located to the• Concentrate on F555W (V), F814W (I), and F656N
east of(H-alpha)R136. This bands
indicates that formation of low-mass stars in

The Tarantula Nebula (30 Dor) in the Large Magellanic
Cloud (LMC) is the nearest extragalactic region of extended
star formation. It is energized by the OB association
NGC 2070, which hosts at its center the Radcliffe 136 (R136)
cluster, the closest example of a massive extragalactic starburst

this ﬁeld has proceeded over a period of time longer than thatassociated with the birth of the massive stars of R136 some
~2–3 Myr ago (e.g., De Marchi et al. 1993; Hunter et al. 1995;
de Koter et al. 1998; Massey & Hunter 1998; Walborn et al.

reddening caused by the circumstellar disk. Therefore, theeffect is negligible.
4. Searching for PMS Stars
As mentioned above, differential reddening makes it
impossible to identify bona ﬁde PMS stars based on theirbroadband photometry alone. Instead, we search for stars with astrong Ha excess emission. This feature is characteristic of
low-mass star formation and is attributed to the gravitationalenergy released by infalling matter that ionizes and excites thesurrounding gas (e.g., Königl 1991; Shu et al. 1994). A reliable
method to detect these objects using multicolor photometry isaddressed in a series of papers by De Marchi et al. (2010,2011a, 2011b, 2011c, 2013a), to which we refer the reader.
Brieﬂy, the median V−I and V - Ha colors of stars withsmall (<0.05 mag) photometric uncertainties in the V , I , andHa bands deﬁne an empirical reference template against which
we identify objects with excess Ha emission. Even before
correction for reddening, the color–color diagram V - Ha,V−I provides a robust identiﬁcation of stars with Ha excess,since in these bands the reddening vector runs almost parallel tothe median photospheric colors of normal stars (De Marchi
et al. 2010).
Following this procedure, we identiﬁed stars with V - Hacolor exceeding the V - Ha color of normal stars with noexcess and with the same V−I by at least 0.1 mag or by threetimes the photometric uncertainty on the V - Ha color (i.e.,

are typically older MS stars and do not have appreciable Ha
excess. For comparison, the thin dotted line shows the model
atmospheres of Bessell et al. (1998) for stars with effective
temperatures in the range 3500 K - Teff - 40000 K , surface
gravity log g = 4.5, and a metallicity index [M H ] = -0.5, asappropriate for the LMC (Dufour 1984). The theoretical colors,
calculated for the speciﬁc WFC 3 ﬁlters, already include atypical reddening value of E (V - I ) = 0.5, made up of
E (V - I ) = 0.1 owing to intervening MW absorption along
the line of sight and E (V - I ) = 0.4 owing to LMC absorption
in front of and within 30 Dor. As we will see later, this is a
representative average reddening value for this ﬁeld.
Objects with Ha excess emission are shown as thicksymbols in Figure 3. Following De Marchi et al. (2011c), we
will consider their positions in the CMD in relation to their
spatial distribution in order to determine how to correct theirphotometry for reddening using neighboring reference UMS
stars. All these objects with Ha excess emission are candidate
PMS stars and as such are relatively young. We used atheoretical PMS isochrone for a rough preliminary separationof younger and older PMS stars. A more accurate age
determination will be possible after correction for reddening.
The thin short-dashed line is the theoretical isochrone for a
PMS age of 5 Myr and metallicity Z=0.007 from the modelsof Tognelli et al. (2011), translated into the WFC 3 bands forthe assumed distance modulus and a combined reddeningAV=1.22. Using the 5 Myr PMS isochrone as a reference, wehave marked as thick ﬁlled circles and crosses, respectively, theobjects above and below that line, and hence approximately

The Astrophysical Journal, 846:110 (16pp), 2017 September 10

De Marchi, Panagia, & Beccari

The Astrophysical Journal, 846:110 (16pp), 2017 September 10

Figure 6. Histograms of the mass distribution for the 1035 bona ﬁde PMS
stars. Different line types correspond to different AV choices for the older PMS
objects: AV=1.22 (solid line), AV=0.72 (long-dashed line), and AV=0.22(short-dashed line). For completeness, the dotted line shows the mass
Ha excess foremission
hotterbona
than ﬁde
10,000K thatof ofthethestars
withdistribution
Figure 6.distribution
Histogramsmass
the 1035
PMS
we do line
not consider
in this work.
stars. Different
types correspondto different AV choices for the older PMS

objects: AV=1.22 (solid line), AV=0.72 (long-dashed line), and AV=0.22(short-dashed line). For completeness, the dotted line shows the mass
Hacells
excessemission
hotterthan 10,000
K that its
distribution
the stars all
withtheweofidentify
thatthat starcrossesthroughout
we do notevolution.
consider in thisFor work.
each cell, we compute the crossing time

(difference between the times of exit and entrance) andcharacteristic age (average of exit and entrance times). We
we identify
the processcells thatthroughout
its therepeatallthis
forthatall star
the crosses
tracks resulting
fromevolution.
For eachcell, weabove.
compute the crossing timeinterpolation
mentioned(differenceThebetween
the fourtimesmatrices
of exitand entrance)
andresults arecontaining
all the relevant
information
associatedofwith
evolutionary
tracks crossing
characteristicage (average
exittheandentrance times).
We
namely,of permanence
the cell,
repeat that
this cell,processformass,
all age,the time
tracksresulting infrom
theandmultiplicity
for thatabove.
cell (number of possible solutions). Given
interpolation
mentioned
observed
cell of thegrid to whichthat relevantstar belongs
The anresultsare star,four thematrices
containing
all thegives associatedus the mostwith
likelythe
mass
and age of tracks
the objects.
If moreinformation
evolutionary
crossing
one solution
is possiblethat cell, in
becausemorethat cell,thannamely,mass, age,time of forpermanence
the cell,andthanone trackcrossesthe cell of
orpossible
the same
track crosses
multiplicity
for thatcell (number
solutions).
Givenit atdifferent times, we assign an appropriate weight to eachan observedstar, the cell of the grid to which that star belongs
solution. As a zeroth-order approximation, assuming a constantgives usbirth
the rate,
mostthelikelymass
and age of tothetheobjects.
moretrack
weightis proportionaltime a If
given
than onespends
solutionispossible
for
that
cell,
becausemorethan forin that cell. Although this is typically sufﬁcient
one trackcrossesthe PMScell orthesubsequent
same track
crosses
at torapidly
evolving
stars,
iterations
areituseddifferenttake
times,
we assign
anrealistic
appropriate
weight history.
to eachinto accounta morestar formation
solution. As
zeroth-ordera constant
Thea largest
source approximation,of uncertainty onassuming
the derived
masses andbirth rate,
weightis theproportional
the time For
a giventrack
agesthecomes
fromreddening tocorrection.
younger
PMS
spends stars,
in thatcell.theAlthoughis typically
sufﬁcientfor
where
reddeningthis
correction
is applied
individually
the nearest-neighbors
method,iterations
the typicalare
uncertainty
rapidly using
evolving
PMS stars, subsequent
used to on
about realistic
0.1 mag, staras mentioned
Section 4. ThisV - I ) isa moretake intoE (accountformation inhistory.
translates
into aoftypicaluncertaintyof ∼6%
on masses
the massandand of
The largest
sourceuncertainty
on thederived∼18%fromon theFor older
PMS objects,
all PMSstars areages comestheage.
reddeningcorrection.
For where
younger
we measured
how individuallyvarying AV overassignedsame AV value,stars, wherethethereddeningcorrection
is applied
thenearest-neighbors
full range from 0.22
to 1.22theaffects
theuncertainty
individual masses
using themethod,typicalon
and ages. Objects appear more massive when AV grows, and the

De Marchi, Panagia, & Beccari

Figure 7. Histograms of the age distribution of PMS stars. A constantlogarithmic step is used (factor of 2). The solid line provides the number ofstars inside each age bin, while the dashed line shows the apparent starformation rate in units of Myr−1.

Figure 7. Histograms of the age distribution of PMS stars. A constantlogarithmic step is used (factor of 2). The solid line provides the number ofstarstimes
insidewider
each thanage bin,while thedashed lineonshows
the apparent
star
the typicaluncertainty
the mass.
Different−1.
formation
rate inunits of Myrline types
correspondto different
A choices for the older PMS

Figure 8. Histograms of the mass accretion rate values of the bona ﬁde PMS
stars. As before, different line types correspond to different AV choices for theolder PMS objects: AV=1.22 (solid line), AV=0.72 (long-dashed line), andAV=0.22 (short-dashed line).

V

objects as mentioned above: AV=1.22 (solid line), AV=0.72
=0.22 (short-dashedThe(long-dashedand AVuncertainty
times
wider thanline),
the typicalon the mass.line).
Different
histograms show a larger number of more massive stars whenline types correspond to different AV choices for the older PMS
the value of AV is higher, and correspondingly a smaller(solid ofline),
objects
as mentioned
V=1.22
lower.
numberof massiveabove:stars Awhen
the value
AV AisV=0.72
=0.22(short-dashedline). andThe(long-dashedline),andA
V
However, the three mass distributions are rather similar,
histogramsshow
a largerdifferences
number of(~4moremassivestarsinwhens ) areonly seen
thestatisticallysigniﬁcanthigher,and correspondingly a smaller
themassvalueof 0.7–1.0
AV is Mrange:.
is range
lower.
numbermassive show
stars awhen
the broadvalue peakof AinV the
The ofhistograms
relatively
However,massthat,
distributions
aremeasurements
rather similar,
andWethreeunderline
while theseshow
1–2 M:.the~4s )stars,
the relative
mass distributionof (PMSthey seencannotin set
are onlythestatisticallysigniﬁcantdifferences
constraints
on the shapemassrange 0.7–1.0
M:. of the mass function, since we are only
the rangetime
considering
PMS showstars that
had Ha excess
The
histogramsa relatively
broademission
peak inatthe
observations
and
we
are
also
not
accounting
for
the
.
We
underline
that,
while
these
measurementsshow
1–2ofMthe:photometricincompleteness,
whichtheyis moreseveretheunavoidable
relative mass
distributionof PMS stars,
cannotset
at low masses.
constraints
on the shape of the mass function, since we are only
The histogramsin Figure7 show
the ageemission
distribution
for time
theHa excessat theconsidering
PMS stars
that had
PMS stars, for an adopted AV=0.72 for objects older thanof the observations and we are also not accounting for the
5 Myr. The solid line gives the number of stars in each age bin,unavoidable
which is morewhich we photometrichave selectedincompleteness,with a constant logarithmic
stepsevereof aat lowmasses.
factor of 2 to match the isochrones in Figure 5. The age bins are
Thehistogramsin Figureshow the age
distribution
for theseveraltimes wider
than the7uncertainty
on theage. The dashedfor objectsobtained
older thanPMS
adoptedrateAV=0.72
linestars,
givesfortheanapparentof star formation,by
5 Myr.
The thesolidline gives
theinnumber
in eachbin,
dividing
numberof starseach binof
bystars
the ageextentageof thewhichwith a compared
constant logarithmic
stepbin. we
Thehaveﬁgureselected
can be directlywith Figure 10
of of
De a
factorof 2 ettoal.
match
the isochronesin Figurewith
5. Theageapparent
bins areMarchi(2011c),and it is consistent
it: the−1, dashed
and itstar formation
ratethanin the2 Myr is ∼150
severaltimes wider
thepastuncertainty
on theMage.
The
: Myr
−1
Myr
between
20
and
30
Myr
ago.
drops
to
∼10
M
line gives the apparent
rate of star formation, obtained by:
These
necessarily
lower
limitsbin
to bythethestarageformation
rate,
dividing
thearenumberof starsin eachextent oftheHa10excess
we only
considerPMS stars
bin.because
The ﬁgurecan bedirectlyhere
compared
withwith
Figureof De
at the timewithof theit:observations.
emissionthe 4s level
Marchiet al.at (2011c),
andoritmore
is consistent
the apparent
−1
Hait
show
largeis ∼150
variationsin their, andstarMoreover,formation young
rate in stars
the past
2 Myr
M: Myremission over hours −1
or days (e.g., Fernandez et al. 1995; Smith

radius. However, since at low temperatures the reddening
vector crosses the evolutionary tracks, any unaccounted
extinction would lead to an underestimate of the stellar mass,
thus resulting in a systematically higher value of the R* M*
ratio. On the other hand, this effect is relatively small, and atypical uncertainty of 0.1 mag in E (V - I ), as relevant in ourcase, corresponds to an uncertainty of ∼6% on the R* M*
ratio. In summary, the combined statistical uncertainty on Ṁacc
amounts to ∼23%. When also the systematic uncertainties dueto the conversion between L (Ha) and L acc are considered, theﬁnal combined uncertainty on Ṁacc amounts to less than afactor of 2. This is important, because it allows us to make asolid comparison between the Ṁacc values for objects ofdifferent masses and ages across our sample.
6. Mass Accretion Rate and Stellar Parameters
The broad distribution of Ṁacc values seen in Figure 8
reﬂects the wide range of masses m and ages t covered by thissample. We will now explore how Ṁacc depends on both m andt for these stars, and later we will compare these results withother massive star-forming regions in the MCs and MW. The
large size of our samples of PMS stars will allow us to derive
statistically signiﬁcant conclusions.
We begin by combining information on the three parameters
in one graph, showing in Figure 9 the values of Ṁacc as afunction of t. The 30 Dor PMS stars are marked by diamonds,
and the size of the symbols is proportional to the mass (seelegend). As a representative value of the extinction for PMS
stars older than 5 Myr (unﬁlled diamonds) we have adopted
AV=0.72. Overall, the mass accretion rate of the 30 Dor
objects appears to decline with age as Ṁacc µ t -0.63, as shownby the best ﬁt to the data (dashed line). The other symbols, asconsistent withHartmann et al
The observ
agreement with
namely, NGC 3
NGC 602 (a =However, it is cpredicted by thCalvet et al. 20
consistent withBarentsen et alstars (<0.6 M:
Cepheus and T
Therefore, th
the Galaxy env
scales with age
we cannot simp
the mass spreadthe apparent sc
m. In the low-m
as m2 (Muzero
et al. 2004, 200(Fang et al. 20
based on rather
often with aaddress how
dependence of
Figure 10 sh
age t for four r
0.5–1.1 M:, 1.
given in each p

Embedded Filaments in IRAS 05463+2652: Early Stage of Fragmentationand Star Formation Activities
1

2

3

3

L.
K. Dewangan, R. Devaraj, T. Baug, and
D. K.ofOjha
297 Embedded
Filaments
in IRAS05463+2652:
Early
Stage
Fragmentation and1
Physical Research Laboratory, Navrangpura, Ahmedabad—380 009, India; lokeshd@prl.res.in
2#8 StarFormation
Activities
Instituto
Nacional de Astrofísica,Óptica y Electrónica, Luis Enrique Erro # 1, Tonantzintla, Puebla, C.P. 72840, México
3

Departmentof Astronomy
and Astrophysics,of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
L. K. Dewangan, R. Devaraj, T. Baug ,Tata
andInstitute
D. K. Ojha
Received
2017
June
20;
revised2017
August31;
accepted 2017 September 1; published 2017 October 10
ApJ 848, 51 (2017)

Abstract
We present a multiwavelength data analysis of IRAS 05463+2652 (hereafter I05463+2652) to study starformation mechanisms. A shell-like structure around I05463+2652 is evident in the Herschel column density
map, which is not associated with any ionized emission. Based on the Herschel submillimeter images, several
parsec-scale ﬁlaments (including two elongated ﬁlaments, “s-ﬂ” and “nw-ﬂ” having lengths of ∼6.4 and∼8.8 pc, respectively) are investigated in the I05463+2652 site. The Herschel temperature map depicts all thesefeatures in a temperature range of ∼11–13 K. 39 clumps are identiﬁed and have masses between ~70–945 M:.
The majority of clumps (having Mclump 2 300 M:) are distributed toward the shell-like structure. 175 youngstellar objects (YSOs) are selected using the photometric 1–5 μm data and a majority of these YSOs are
distributed toward the four areas of high column density (25 ´ 10 21 cm−2; AV∼5.3 mag) in the shell-likestructure, where massive clumps and a spatial association with ﬁlament(s) are also observed. The knowledge of
observed masses per unit length of elongated ﬁlaments and critical mass length reveals that they are supercritical.
The ﬁlament “nw-ﬂ” is fragmented into ﬁve clumps (having Mclump ~ 100–545 M:) and contains noticeable
YSOs, while the other ﬁlament “s-ﬂ” is fragmented into two clumps (having Mclump ~ 170–215 M:) without
YSOs. Together, these observational results favor the role of ﬁlaments in the star formation process in I05480+2545. This study also reveals the ﬁlament “s-ﬂ,” containing two starless clumps, at an early stage offragmentation.
Key words: dust, extinction – ISM: clouds – ISM: individual objects (IRAS 05463+2652) – stars: formation –stars: pre-main sequence – stars: protostars

データ：+2652 site.Herschel
They found an extended molecular cloud associated
1. Introduction• 182.0-00.3,
Vlsr = -10.6 km/s, distance = 2.1 kpc
with I05463+2652
and referred
to as “182.0−00.3” cloud (ID
UKIRT UKIDSSGP survey
The investigationofﬁlaments
instar-forming
regionshas−1• dV = 1.7 km/s, R ~ 10 pc, Mcloud ~ 9000 Msun #70; Vlsr∼−10.6 km s ; line width=1.7 km s−1; radius
NRAO VLA Sky Survey
recently received much attention,c with the availabilityof the(Rc)∼
Herschel continuum data (e.g., André et al. 2010, 2016;
WISE,
Glimpse360
10 pc; Mass
(Mcloud) ~ 9000 M:) (see Table 1 and Figure 9(j)13CO 1-0 観測（Kawamura+ 1998）

Kainulainen et al. 2016, 2017; Li et al. 2016, and references
therein). There are several works of theoretical and observationalin Kawamura et al. 1998). Herschel far-infrared (FIR) andsubmillimeter (sub-mm) images are available toward the I05463

sources (e.g., Gutermuth et al. 2009). Using the 2MASS andGLIMPSE360 photometric data at 1–5 μm, we have examinedthe dereddened color–color space ([K−[3.6]]0 and[[3.6]−[4.5]]0). The dereddened colors were estimated using
the color excess ratios given in Flaherty et al. (2007).
Following the dereddened color conditions listed in Gutermuth
et al. (2009), we ﬁnd 134 (18 Class I and 116 Class II) YSOs in

help of previously known conditions (i.e., [3.6]0 < 15 mag forClass I and [3.6]0 < 14.5 mag for Class II; e.g., Gutermuth
et al. 2009). The dereddened 3.6 μm magnitudes werecomputed using the observed color and the reddening laws
(from Flaherty et al. 2007). Figure 5(a) shows the color–color
diagram ([K−[3.6]]0 versus [[3.6]−[4.5]]0). The red circles andblue triangles refer to ClassI and ClassII YSOs, respectively.

P. Elliott , A. Scholz , R. Jayawardhana , J. Eislö↵el , and E. M. Hébrard

1708.03711v2 [astro-ph.SR] 22 Aug 2017

1

Department of Physics and Astronomy, York University, Toronto, ON M3J 1P3, Canadae-mail:297
Apmelliott0@gmail.com
deep staring campaign in the σ Orionis cluster Variability in substellar
2
SUPA, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK
3#9members
Thüringer
Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenburg, Germany
P. Elliott, A. Scholz, R. Jayawardhana, J. Eislöﬀel, and E. M. Hébrard
Received
18/04/2017; accepted 09/08/2017
arXiv:1708.03711v2
ABSTRACT
Context. The young star cluster near

Orionis is one of the primary environments to study the properties of young brown dwarfs
down to masses comparable to those of giant planets.
Aims. Deep optical imaging is used to study time-domain properties of young brown dwarfs over typical rotational timescales and to
search for new substellar and planetary-mass cluster members.
Methods. We used the Visible Multi Object Spectrograph (VIMOS) at the Very Large Telescope (VLT) to monitor a 240 ⇥ 160 field in
the I-band. We stared at the same area over a total integration time of 21 hours, spanning three observing nights. Using the individual
images from this run we investigated the photometric time series of nine substellar cluster members with masses from 10 to 60 MJup .
The deep stacked image shows cluster members down to ⇡5 MJup . We searched for new planetary-mass objects by combining our
deep I-band photometry with public J-band magnitudes and by examining the nearby environment of known very low mass members
for possible companions.
Results. We find two brown dwarfs, with significantly variable, aperiodic light curves, both with masses around 50 MJup , one of which
was previously unknown to be variable. The physical mechanism responsible for the observed variability is likely to be di↵erent for
the two objects. The variability of the first object, a single-lined spectroscopic binary, is most likely linked to its accretion disc; thesecond may be caused by variable extinction by large grains. We find five new candidate members from the colour-magnitude diagram
and three from a search for companions within 2000 au. We rule all eight sources out as potential members based on non-stellar shape
and/or infrared colours. The I-band photometry is made available as a public dataset.
Conclusions. We present two variable brown dwarfs. One is consistent with ongoing accretion, the other exhibits apparent transientvariability without the presence of an accretion disc. Our analysis confirms the existing census of substellar cluster members down to⇡7 MJup . The zero result from our companion search agrees with the low occurrence rate of wide companions to brown dwarfs foundin other works.

1. Introduction
The discovery of brown dwarfs in 1995 (Nakajima et al. 1995;
Rebolo et al. 1995), in conjunction with the discovery of the first
exoplanet around a solar-type star in the same year (Mayor &Queloz 1995), has triggered a significant revision in our ideasof star and planet formation. In particular, instead of a bimodal
view where stars form from cores and planets in discs, our cur-regions (see review by Luhman 2012). For each star, about 0.20.5 brown dwarfs are formed, in all regions studied so far, with
only a minor, if any, dependence on environmental conditions(Scholz et al. 2013; Muzic et al. 2017). Brown dwarfs can hostmassive discs (Testi et al. 2016) and show signs of accretion,
just like young stars. The widely-accepted view we have today
is that most of the more massive brown dwarfs are an extensionof the stellar mass function and form in a way similar to low-t al.: A deep staring campaign in theMOS) at the veryof deep images toollowing the prel. (2004), Scholz

Orionis cluster

F. Ménard4 , M.R. Meyer1, 16 , J. Milli11 , D. Mouillet4 , J. Olofsson17, 7, 20 , A. Pavlov7 , J. Pragt18 , P. Puget4 ,S.P. Quanz1 , R. Roelfsema18 , B. Salasnich3 , R. Siebenmorgen12 , E. Sissa3 , M. Suarez12 , J. Szulagyi1 , M. Turatto3 ,S. Udry19 , and F. Wildi19

iv:1709.00417v2 [astro-ph.EP] 7 Sep 2017297 The HIP 79977 debris disk in polarized lightEngler, H.M. Schmid, Ch. Thalmann, A. Boccaletti, A. Bazzon, A. Baruﬀolo, J.L. Beuzit, R. Claudi, A. Costille, S.
#10 N.
(Affiliations
can be foundafter thereferences)
Desidera, K. Dohlen, C. Dominik, M.
Feldt, T. Fusco,
C. Ginski,
D. Gisler,
J.H. Girard, R. Gratton, T. Henning, N. Hubin,
M. Janson, M. Kasper, Q. Kral, M. Langlois, Received
E. Lagadec,
F. Ménard,...; accepted... M.R. Meyer, J. Milli, D. Mouillet, J. Olofsson, A.
Pavlov, J. Pragt, P. Puget, S.P. Quanz, R. Roelfsema, B. Salasnich, R. Siebenmorgen, E. Sissa, M. Suarez, J. Szulagyi,
M. Turatto, S. Udry, and F. Wildi
ABSTRACT
arXiv:1709.00417v2
Context. Debris disks are observed around 10 to 20 % of FGK main-sequence stars as infrared excess emission. They areimportant signposts for the presence of colliding planetesimals and therefore provide important information about the evolutionof planetary systems. Direct imaging of such disks reveals their geometric structure and constrains their dust-particle properties.
Aims. We present observations of the known edge-on debris disk around HIP 79977 (HD 146897) taken with the ZIMPOL
di↵erential polarimeter of the SPHERE instrument. We measure the observed polarization signal and investigate the diagnostic
potential of such data with model simulations.
Methods. SPHERE-ZIMPOL polarimetric data of the 15 Myr-old F star HIP 79977 (Upper Sco, 123 pc) were taken in the VeryBroad Band (VBB) filter ( c = 735 nm,= 290 nm) with a spatial resolution of about 25 mas. Imaging polarimetry efficiently
suppresses the residual speckle noise from the AO system and provides a di↵erential signal with relatively small systematic
measuring uncertainties. We measure the polarization flux along and perpendicular to the disk spine of the highly inclined disk
for projected separations between 0.200 (25 AU) and 1.600 (200 AU). We perform model calculations for the polarized flux of an
optically thin debris disk which are used to determine or constrain the disk parameters of HIP 79977.
Results. We measure a polarized flux contrast ratio for the disk of (Fpol )disk /F⇤ = (5.5 ± 0.9) · 10 4 in the VBB filter. The
surface brightness of the polarized flux reaches a maximum of SBmax = 16.2 mag arcsec 2 at a separation of 0.200 0.500 along
the disk spine with a maximum surface brightness contrast of 7.64 mag arcsec 2 . The polarized flux has a minimum near thestar < 0.200 because no or only little polarization is produced by forward or backward scattering in the disk section lying in frontof or behind the star. The width of the disk perpendicular to the spine shows a systematic increase in FWHM from 0.100 (12AU) to 0.300 0.500 , when going from a separation of 0.200 to > 100 . This can be explained by a radial blow-out of small grains.
The data are modelled as a circular dust belt with a well defined disk inclination i = 85(±1.5) and a radius between r0 = 60
and 90 AU. The radial density dependence is described by (r/r0 )↵ with a steep (positive) power law index ↵ = 5 inside r0 anda more shallow (negative) index ↵ = 2.5 outside r0 . The scattering asymmetry factor lies between g = 0.2 and 0.6 (forward
scattering) adopting a scattering-angle dependence for the fractional polarization such as that for Rayleigh scattering.
Conclusions. Polarimetric imaging with SPHERE-ZIMPOL of the edge-on debris disk around HIP 79977 provides accurate
profiles for the polarized flux. Our data are qualitatively very similar to the case of AU Mic and they confirm that edge-on
debris disks have a polarization minimum at a position near the star and a maximum near the projected separation of the main
debris belt. The comparison of the polarized flux contrast ratio (Fpol )disk /F⇤ with the fractional infrared excess provides strong
constraints on the scattering albedo of the dust.
Key words. Planetary systems – Scattering – Stars: individual object: HIP 79977, HD 146897 – Techniques: high angularresolution, polarimetricEngler et al.: HIP79977 debris disk in polarized light

N

E

0.5
’’

Fig. 2. Composite image of debris disk around HIP 79977 with the VBB and I-band filters obtained with LOCI data reduction. The original
data were 3 ⇥ 3 binned to reduce the e↵ect of the noise. The position of the star is marked by an asterisk in orange. The white dotted line
et al.:
debrisdisk
in color-scalepolarized lightshows the position of the expected lines of Engler
nodes foran HIP79977
inclined disk
ring.
The
is given in arbitrary units.

pN
P = Q2 + U 2 . However,
P is a↵ected for low signal-tonoise data by a systematic bias e↵ect because of squaring ofφ poQ and U parameters.
Therefore we characterize the diskElarization pattern with a locally defined azimuthal / radial Qand U-parameter definition with respect to the central lightsource as discussed in Schmid et al. (2006). Single scatteringo↵ dust particles in optically thin debris disks generates linearly polarized light with the electric field vector azimuthallyoriented with respect to the star. Polarization in the azimuthal
direction is defined by the Stokes parameter Q' :Q

Q' = (Q cos 2' + U sin 2'),(3)where ' is the polar angle between north and the point of interest measured from the north over east. The Stokes parame0.5 ’’
ter U' :Engler et al.: HIP79977 debris disk in polarized lightUnoise level and large-scale systematic errors in our observations.
Veryφclose to the star, marked by a white circle with ar ' 0.1200 (Figs. 3 and 4), the data are unreliable because ofstrongly variable wings of the PSF peak. Also visible are thefaint features at r & 0.1200 above and below the disk which arenegative in the Q and U images, and appear as positive signal in the Q' and U' images. These features are much fainter(factor < 0.1) than the disk signal and originate most likely
from poorly corrected instrumental e↵ects because an intrinsic signal is expected to produce no U' signal.

4. Data analysis
4.1. Disk position angle

We measured the position angle of the disk in the Q' -image
by the determination of the orientation of the mirror line
defines the polarization pattern in the directions ±45 with through the central star perpendicular to the disk. The best
angle was 16
found by searchingwithrespect-5to the Q' -2
direction. 1
4
7
10position 13
19
22 an angle
25 increFigure 4 shows the final Q' and U' . The Q' image clearly ment of 0.1 the orientation of the mirror line which produces
reveals the nearly edge-on disk structure down to a projected the smallest residuals if one side is subtracted from the otherseparation of ⇠ 0.100 . Polarized light is detected across the side.
The results from the polarimetric and imaging data sets
entire width of the image of ⇠ 3.600 . The peak of the surface
brightness appears here as a narrow stripe below the expected agree. After including ZIMPOL’s True North o↵set of 2
axis to be ✓disk =major axis of ESE
an inclined circular ring (white dotted line) we obtain the position angle of the disk
WNW
114.5 ± 0.6 . This value is in good agreement with PA =with a flux minimum near the position of the star.
114 reported by Thalmann et al. (2013) for the scattered light
By contrast, the U' image contains no structural features images in H-band and with PA = 115 measured by Liemanfrom the disk. Assuming azimuthal polarization of light gen- Sifry et al. (2016) in the sub-mm range.
erated in single scattering processes and no multiple scatterWe define an x y disk coordinate system where the staring (see Canovas et al. 2015), we do not expect to find any is at the origin, +x is the coordinate along the major axis inastrophysical signal in the U' image. Therefore, this image roughly WNW-direction (✓disk +180 ), x towards ESE (✓disk ),can be used for an estimation of the statistical pixel to pixel and y perpendicular to this with the positive axis towards NNE
U' = Q sin 2' + U cos 2'(4)

0.5 ’’

Article number, page 5 of 20

61 AU

Fig. 4. Polarimetric di↵erential imaging data of HIP 79977 with the VBB filter (590-880 nm). The original data were 3 ⇥ 3 binned to reduce
the noise. The position of the star is marked by an asterisk in red. The upper panel shows Q' (left) and U' (right) images. Lower panel:
Isophotal contours of polarized light overlying Q' image. The contours were measured from the Q' image smoothed via a Gaussian kernel
with = 1.5 px. Contour levels are given for 3 (blue line), 9 (light blue), 15 (orange) and 21 (red) counts per frame per binned pixel.
The white dotted line shows the position of the expected ring axis. The region inside the white stellarcentric circle with radius ⇠ 0.1200 is
dominated by strong speckles variations. The color-bars show the counts per binned pixel.

and fit for x . 0.600 because the Mo↵at profile cannot fit correctly negative flux values at small angular separations which
originate from the systematic e↵ects described above.
The vertical o↵set y0 (x) of the disk spine is shown iny0 ⇡ 50 mas, and also in the outskirts (|x| & 100 ) the y0 -o↵set
is even more than 50 mas. In comparison, the o↵set y0 (x) of
the disk spine measured in the imaging data (Fig. 2) is approximately 60 ± 5 mas (⇡7.5 AU) at |x| < 0.300 . For larger
separations, the y0 -o↵set in intensity is smaller and achieves

Fig. 6. HIP 79977 debris disk properties along the axis x. The individual points give parameters of the Mo↵at profile of the vertical crosssection as shown in Fig. 5 and described in Sect. 4.2. From the top to the bottom: (a) the profile peak SBpeak (x), (b) FWHM, (c) verticallyintegrated flux P(xA&A proofs: manuscript no. HIP_79977_arch

et al.: HIP79977 debris disk in polarized lightrees of freedom

use the noise isresent flux intenferred from theich look essencalized spurious
disk. The fitting
model convolul, the key proprized flux alongle.
to fit the hP|x|ihe profile fitting
e range [60, 86]e maximum. Of
by 9 parameters
que solution forl defined ranges

mined by the 2model. This apl noise is larger
are much harderk models whichg to the Q' imdel parameters.
distribution of
he 2D image fit
distribution are
eir uncertainties
calculated frommeters together
le 3 (Col. 5 andthetic image ofconvolved imFig. 9(d)) well.
me PSF-shapedd below the disk
m the disk flux.
he spine at small

pth in the disk isimate a ⌧ ⇡ 0.5
plane (⇥ = 0 ),ering, a photon
we see the diskng allows an asem where many
he data. In par-A&A proofs: manuscript no. HIP_79977_arch

5.1. The scattering phase function for polarized lighta

The phase function (PF) f (✓) in Equation(7)polarimetriccharacterizes profile. Lieman-Sifry et al. (2016) also meathe
the angle dependence of scattered radiation. In the following,+3
sured
we disregard the wavelength dependence of
the PF.a disk inclination i > 84 and PA = 115 3 which are
A very popular way to describe the scattering
phase funcconsistent
with our and previous results.
tion is the Henyey-Greenstein (HG) function (Henyey &Greenstein 1941):f (✓) =b1
4⇡(1 + g2

g2,
2gcos✓)3/2

6.2. Diagnostic
potential of polarimetry(11)

scattered
where g is the average of the cosine ofThethe scatteringan- flux has been measured for more than 20 degle which characterizes the shape of the phaseForbris function.
disks, mainlywith the Hubble Space Telescope (HST)
isotropic scattering g = 0, forward scattering
have(e.g., grains
Schneider
et al. 2014, 2016). With ground-based ob0 < g  1, while for 1  g < 0 the scattering is peaked
servations the flux measurement for the scattered light frombackwards.
However, there exists also growing evidence
thatdisksa simpledebrisis very difficult because of the speckle noise inHG-function is a poor approximation for the modeling of thetroducedbytheatmospheric turbulence. The polarized flux of
scattered intensity from debris disks. This is nicely demon- Fig. 11. Comparison between alternative models of the HIP79977 debris disk: "Model 40" with the radius of the planetesimal belt r0 = 40
mucheasierto determine,
becausea parameters as specified in Table 3. From top to the bottom: (a)and "Model70" withthe radius of r0 = 70
AU (right) it
andis
fitting
strated for the bright disk HR 4796A (Millithe
et al.disk
2017),(Fwhichpol )diskAUis(left)
model of the dust distribution in the disk, (b) model of the polarized light, (c) model of the polarized light convolved with the instrumental
shows, for small phase angles ✓ < 30 , adi↵erential
strong di↵raction
quantity
which can be distinguished from the unPSF and (d) residuals left after subtraction of the PSF-convolved model image from the Q' image. Color-scales of images (a) and (b) are
peak and, for large phase angles ✓ > 30 , a scattering inten- Fig.
Scattering
phase
functionforthe (c)polarized
light (blue)
given8.inthe
arbitraryunits.
Color-bar
ofstarimagesand (d)fluxevenin forcounts at each pixel of the image.
brightcentral((F) shows⇡ 0),sity which is roughly angle-independent. polarized
Thus, a morelightgen- fromthree di↵erent asymmetry parameters gsca =pol0.2,⇤gsca = 0.4, anderal phase function, for example, a two-component(or dou- of
gsca strong= 0.6. Redlines show the corresponding
in the presence
atmosphericspeckles. Heyney-Greenstein0000ble) HG function seems to be required for the modeling of functions for f (✓, gsca ).
For HIP 79977 the disk profile in polarized flux reveals signala from the disk for separations from 0.3 to 1.5 , comthe scattered intensity of highly inclined debris disks
pared the polarization with the intensity profile and found a0cclear maximum which traces the radial location of the disk
fractional polarization of ⇠ 10 % (1 -range [5 %, 20 %]) at

5.2. Model fitting
Fig.
Ratio
0.500 and⇠ 4513.
% ([30%, 60of%])polarized
at 1.500 . Fromflux
their todata,theit scattered light luminosinformation is difficult to6 obtain from intensityw) · fring.
(✓, gsca )This,(12)
whetheror not theythin
see indebris
polarized
flux a maxiity for
opticallydisks
as a function of disk inclinaWe have calculated 5.28 · 10 models for a parameter grid asis not clear
00
imaging of edge-on disks, because the Stokes I disk profile
mum attion
a separationof around 0.6 asymmetry
and a flux decrease
inside.
and scatteringparameter
gsca (plotted for gsca =where the first term describes the strong di↵raction peak, the specified in Table 3 in order to find the set of model parame-Thalmann
et al. (2013) also fit the observations with model
thewhichforwardin front
ofimage.
the starbest fitscattering
the observed dust
polarized
intensity
second term represents the more isotropicis
anddominatedmuch less for-by ters
0.0, 0.2,
0.3,adopt..., 0.9).
Theisindependentof the disk geometry
calculations
but theya radiusof rratio
=
40
AU
for
the
For the fitting,
we extension
reduced the number
image
pixels byplanetesimal ring and do not investigate 0models with larger
ward scattering part (see also Min et al. 2010),
and w is thethe projected
and therefore
disk
may ofnot
be visible.
and follows from the scattering phase functions as shown in Fig. 8.
3 ⇥ 3 binning and selected a rectangular image area with ra .
scaling parameter, 0  w  1.
0
The diskfluxlength
Fdiskofand
polarized
contain
341 theand widthof 100 flux
binned(Fpixelscenteredandpol )disk
For the polarized scattered radiation from a debris
disk theThe new SPHERE - ZIMPOL observations presented into the diskabout
x and y the(majorscatteringand minor) axes
(see The
Fig.this work provide a very much improved polarimetric sensituation is slightly di↵erent. The strong complementary
forward peak seen aligned
information
dust.
in intensity, which can be ascribed to the light di↵raction by 9(d)). A round area with a radius of 16 pixels (0.1700 ) centeredsitivity whichThe
fractional
infraredexcessof HIP 79977 LIR /L⇤ =clearly
reveals a maximum
in thepolarizascattering angle dependence is strongly di↵erent because forlarge particles a, is expected to produce no significant on the star and the spurious features near the saturated regiontion profile
P(x)at 3a isprojected
separationof 0.60±0.0600et al. (2015). This yields
5.21
·
10
given
in
Jang-Condellward
andbackward
scattering
produces
no
or
only
very
littleareexcludedfromtheevaluation
of
the
fit
goodness.
Figurelight polarization. The scattering polarization is produced by(74±7 AU). This maximum location is not compatible withthering
double9 illustrates
the alsodi↵erent
in the image fitting
the smallradius ofratio
r0 = 40 AU adopted by Thalmann
the photons hitting the particle surface andpolarizedinteracting by
dif- Thisflux.
applies
to stepsthe di↵raction
peakprocedure.
(or forfuse reflection or/and refraction and transmission as described From the model dust distribution in the disk (a) the expectedet al. (2013), probably, because they only fit the intensity proward
scattering
peak)
from
large
particles
a
>
,
which
is
not
(Fno
)disk /Fthat
polfeatures⇤ could constrain the ring raabove by the second term f (✓, gsca ). But, in addition, the an- polarization flux is calculated (b), convolved with the instru-file which shows
Fig. 12.
Two-dimensional
constraints
on theradiusoftheresiduals
planetes- (e)= 0.11 ± 0.02,
dius. ⇤ =PSF(c), This
fitted tomeans
observation(d),andpolarizedtheonlyslightlypolarized.
that
the
flux
gle dependence of the linear polarization orLP(✓)
producedby ment
imal belt r0 and the asymmetry
parameter g sca for HIP 79977. The
L
/L
2
IR
⇤
are
then showused thefor68%
the andevaluation
offortheimage
fit.
Our best-fit model is in good agreement with results ofthe particle scattering needs to be taken into
account.
For
eximagecontours
95%
CLregionsthemodelsampleoriginates predominantly from scatterings with scattering anrecent observations of HIP 79977 with ALMA. Lieman-Sifry
ample, strict forward and backward scattering will produce and The
goodnessofthe
thelocations
fit was ofestimatedfor eachmodel
the dots
point out
the describedmodelsin thiswith
whereuncertainty
accounts
2
gles inrangethe45reduced
135
and the polarizedA&A
flux proofs:
produced
et al. (2016)
used
the
1240
µm continuumonly
visibilities
and de- for uncertainty in the
manuscript
no.theHIP_79977_arch
parameter
plain.
no polarization for randomly oriented particles
forthesymme-parameter:
rived basic
geometricalparametersof the disk. Theymodelled
try reasons. We adopt the Rayleigh scatteringfunction as a event can be approximated(F)/F-ratioderivedinthispaper. The double ratio ⇤per scatteringbyanaveragedparpol
disk
⇤
⇥
⇤
N
2
data
the surface density of the disk with a single power law r 1
X yi xi ( p)1
simple approximation for the angle dependence of the polar2 the induced
could
a goodthebetweenthe parameters
polarized oflu-twoticle parameterforscatteringpmresultingforthefor flux
extraction
for the intensity
extendingfrom bean inner
to an
outer
and
theyratio
derived=parameterse↵ects, 6 models
Table 3. Gridofself-subtraction
for
the
5.28
·polarization
10
andparametersfortheproxy
bestradius
fitformodel.
Also
given are thered
2ization fraction psca :+11
Ndataderived
N partheimage andRinner = 60
AU without detecting an outer cut-o↵ radius.
i=1intrinsic yiintensity slope for the diskf (✓, gdi↵ , gsca ) = w · f (✓, gdi↵ ) + (1deselected comparison
models70" and "Model 40").
the scattering
angle
of 90
(see("Model
Sect. 5.1).
along the major axis. In addition, they detected a polarimetric13
minosity
and the IR-excess luminosity of the disk

This result confirms the large ring radius r0 found by us from

where Nis a numberof data may
points bewithobtained
measurementif
data dust
New constraints
onproperties
1 cos2 ✓(Fpol )disk /F⇤ Article(Lnumber,results yi which have uncertainties yi . Each data point
psca (✓) = pm
= pm LP(✓),
page 15 of 20
pol )disk
1 + cos2 ✓quantitative polarimetric
data
of
many
debrisdisks
can ofbe linear⇤=⇡, Model 70 Model 40
corresponds
the minimization
Parameterto a binned pixel within
Range
Step
Best model
L
/L
L
IR
⇤
IR
with the scaling factor pm , which defines the
maximumfracwindow
shown
in
Fig.
9(d).
N
denotesthenumberofcollected. The dust grain size distribution
thepar and therefore
samplingmean value 68% CL
tional polarization produced at a scattering angle of ✓ = 90 . free parameters p = (p1 , p2 , ..., pN par ) used to create a model
polarimetric properties
areexpected
to dependonthe spectral if the wavelength and inclination dependence of the
Figure 8 shows some examples of obtained phase function image
withofvalueslisted in Col.
1 of90]
Table 3.
Radiusbeltxirand
[30,
10
73
16
70
40⇤ dust scat0 (AU)type oftheof central
star and di↵erent
system ages may reveal tering can be neglected. It is emphasized,
for the polarized flux LP(✓) f (✓, gsca ) for di↵erent
cases
the
that
neglecting
the
⇤
⇤
Inner
radial
index↵inprocedure[1,
10]
1
5.0
2.8
2.0
2.0
To accelerate
thepolarimetricfitting
wehave made aof
preseHG function f (✓, gsca ). For isotropic scattering(gsca = 0) theprocesses
evolutionary
in theproperties
thewavelength dependence of the polarized flux of the disk may
maximum of scattered polarized flux occurs at ✓ = 90 . For lection of disk models using the mean disk profile hP|x|i along
Outer
index
↵out10. The[-6,
0.5 not be an -2.5
1.4
-3.0
-2.5 for examscattering dust. thePolarimetricparameterswhich
can bequanFig. 9. Comparison of the best-fitanmodel
withparameter
the Q' gimage.
(a) Imasymmetry
majorradial
axis shownin Fig.
mean-1]
profilehP|x|iconacceptable simplification
for some cases,
sca > 0 the maximum is shifted
00
00⇤
tified for theare ofscatteringcross-sectionor albedo,
to smaller
scatteringa corresponding
asym-dust
sisting
15 points|x| = 0.22
to |x|= 1.80for theage visualizing the dust distribution
in thedisk.angles(b) producing
Model image
sca
Scale
heightH0from
(AU)
[0.5,
3.5]
0.5 ple, for near-IR
2.3
0.7
1.5 around 0.5
polarimetryofdisks
A-stars,which
metry within the amountof polarizedreceived
the front ofobserved
disk polarizationscattering
is obtained byaveraging p
the P(x)andparameters
the polarimetricfunctionof the polarized light non-convolved
PSF. (c)Modellightimage
of fromm andof their radiation
spectralregion.
and back sides of the disk. So, for example, the value of po- data
points fromthe negative and positive
Verticalprofile[0.5, x-axes2.5] given in Fig.
0.5 emit most0.9
0.6 in the UV-visual
1.0
1.0
the polarized light convolved withthe flux
instrumental
PSF.
imgsca. Ahigher
betterthe dust
in debris
larizedPF (gsca = 0.6)
at ✓ (d)= 20Qis' 35
times
thanunderstanding
6(c). Thus the 2Dofmodelswere collapsed
to adisks
profile would
and fitTherefore,
observationalthat depends,
2
Flare
[0.5,
2.2 ⇤ is an 1.4
2.5parameter3.5
at ✓area= 160outlined.
ted
first index
to the hP|x|i profile
calculating
the4.5]and defining
a1
age from the data. The rectangularwith an orange box
be very useful forinterpretations
regardingthenatureof their

0.5’’

61 AU

like the scattering albedo, on the ratio between dust scatter-shows the minimization windowArticle
as describedin the body text. The
Inclinationi ( ) the observed[82,dust
87] in a colli1 ing cross-section
84.6
1.7
85.0
82.0⇤
parent bodies which
producednumber, page 12 of 20
sca and absorption , and parameters of theorange circle marks the central region of the image excluded fromsional cascade. HG parameter g sca[0.0, 0.9]
0.1 polarimetric
0.43phase function
0.25 pm and
0.20
0.20
gsca asthe 2 evaluation. (e) Residual image obtained after subtraction of
Scalingfactor
A
9.04
4.03
3.10
p
the PSF-convolved model image (c) from the Q' image (d). Colorsca ( )⇤/· f (pm ( ), gsca ( ), i) .
(13)
6.2.1. Polarized flux and infrared excess
scales of images (a) and (b) are given in arbitrary units. The color-bar
for images (c), (d) and (e) shows polarized flux in counts per binned Notes: ⇤ Parameter value lies outside the 68% confidence interval.
The reflectivity or scattering albedo of the dust in the deThe inclination dependence of (Fpol )disk is illustrated inpixel.

bris disk of HIP 79977 can be characterized by a comparisonof the scattered polarized flux with the IR excess luminosity
which is a good measure for the dust absorption.

Fig. 13, which shows the polarized flux (Fpol )disk (expressed
per steradian) with respect to the scattered light luminosity
is a steeper
fall-o↵ thana Gaussian
distribution,
indicatLsca This
excludingthe di↵racted
light.
The scattered
light inter-