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$#%(*;3:?'6829 (*;3:?'6829
Revealing the Structure of the Outer Disks of Be
Stars
Robert Klement
European Southern Observatory
Anthony C. Carcio%
University of San Paulo
$omas Rivinius
European Southern Observatory
Lynn D. Ma&hews
MIT Haystack Observatory
Rodrigo G. Vieira
Instituto de Astronomia
See next page for additional authors
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Revealing the Structure of the Outer Disks of Be Stars
Copyright Statement
",786+;*,+=0:/7,84099065-8649:86564?9:867/?90*9A#
Creator(s)
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A&A 601, A74 (2017)
DOI: 10.1051/0004-6361/201629932
c
ESO 2017
Astronomy
&
Astrophysics
Revealing the structure of the outer disks of Be stars
⋆
R. Klement
1, 2
, A. C. Carciofi
3
, T. Rivinius
1
, L. D. Matthews
4
, R. G. Vieira
3
, R. Ignace
5
, J. E. Bjorkman
6
, B. C. Mota
3
,
D. M. Faes
3
, A. D. Bratcher
6
, M. Curé
7
, and S. Štefl
⋆⋆
1
European Southern Observatory, Alonso de Córdova 3107, Vitacura, Casilla 19001 Santiago, Chile
e-mail: robertklement@gmail.com
2
Astronomical Institute of Charles University, Charles University, V Holešovi
ˇ
ckách 2, 180 00 Prague 8, Troja, Czech Republic
3
Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão 1226, Cidade Universitária,
05508-090 São Paulo, SP, Brazil
4
MIT Haystack Observatory, off Route 40, Westford, MA 01886, USA
5
Department of Physics & Astronomy, East Tennessee State University, Johnson City, TN 37614, USA
6
Ritter Observatory, Department of Physics & Astronomy, University of Toledo, Toledo, OH 43606, USA
7
Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Casilla 5030 Valparaíso, Chile
Received 19 October 2016 / Accepted 16 March 2017
ABSTRACT
Context. The structure of the inner parts of Be star disks (.20 stellar radii) is well explained by the viscous decretion disk (VDD)
model, which is able to reproduce the observable properties of most of the objects studied so far. The outer parts, on the other hand,
are not observationally well-explored, as they are observable only at radio wavelengths. A steepening of the spectral slope somewhere
between infrared and radio wavelengths was reported for several Be stars that were previously detected in the radio, but a convincing
physical explanation for this trend has not yet been provided.
Aims. We test the VDD model predictions for the extended parts of a sample of six Be disks that have been observed in the radio to
address the question of whether the observed turndown in the spectral energy distribution (SED) can be explained in the framework
of the VDD model, including recent theoretical development for truncated Be disks in binary systems.
Methods. We combine new multi-wavelength radio observations from the Karl. G. Jansky Very Large Array (JVLA) and Atacama
Pathfinder Experiment (APEX) with previously published radio data and archival SED measurements at ultraviolet, visual, and in-
frared wavelengths. The density structure of the disks, including their outer parts, is constrained by radiative transfer modeling of the
observed spectrum using VDD model predictions. In the VDD model we include the presumed effects of possible tidal influence from
faint binary companions.
Results. For 5 out of 6 studied stars, the observed SED shows strong signs of SED turndown between far-IR and radio wavelengths.
A VDD model that extends to large distances closely reproduces the observed SEDs up to far IR wavelengths, but fails to reproduce
the radio SED. Using a truncated VDD model improves the fit, leading to a successful explanation of the SED turndown observed for
the stars in our sample. The slope of the observed SEDs in the radio is however not well reproduced by disks that are simply cut off at
a certain distance. Rather, some matter seems to extend beyond the truncation radius, where it still contributes to the observed SEDs,
making the spectral slope in the radio shallower. This finding is in agreement with our current understanding of binary truncation
from hydrodynamical simulations, in which the disk does extend past the truncation radius. Therefore, the most probable cause for
the SED turndown is the presence of binary companions that remain undetected for most of our sources.
Key words. stars: emission-line, Be – circumstellar matter – binaries: general – radio continuum: stars – submillimeter: stars
1. Introduction
Be stars offer unique possibilities for studying circumstellar
disks. Because they are common among the bright, nearby stars
– 17% of B-type stars are Be stars (
Zorec & Briot 1997) – their
disks are among typical targets for modern optical/near-infrared
interferometers that have resolved them at the milliarcsec level.
As a result, the structure of the inner parts of the disks is now
well understood in the framework of the viscous decretion disk
(VDD) model, first proposed by
Lee et al. (1991) and further
developed by, for example, Bjorkman (1997), Porter (1999),
Okazaki (2001), and Bjorkman & Carciofi (2005). The central
⋆
Based on observations from the Karl J. Jansky Very Large Array
collected via programme 10B-143, on observations from APEX col-
lected via CONICYT programmes C-092.F-9708A-2013 and C-095.F-
9709A-2015 and on observations from CARMA collected via pro-
gramme c1100-2013a.
⋆⋆
Deceased.
stars rotate close to break-up velocities, and an uncertain mecha-
nism – the so-called Be phenomenon – acts in addition to ro-
tation, leading to episodic or continuous mass ejection from
the stellar equator. Subsequently, outflowing, ionised, purely
gaseous disks, rotating in a nearly Keplerian way are formed (see
Rivinius et al. 2013, for a recent review). In the VDD model, it
is the turbulent viscosity that is responsible for the transport of
the angular momentum outwards, and therefore for the growth
of the disk.
In the last decades, observational techniques such as spec-
troscopy, linear polarimetry, and optical/near-IR interferometry
have been used to constrain the physical structure of VDDs.
Combining polarimetric and interferometric measurements, the
disk-like structure of the circumstellar matter was unambiguosly
confirmed (Quirrenbach et al. 1997) and the rotation law was
subsequently confirmed to be nearly Keplerian (Meilland et al.
2007; Wheelwright et al. 2012; Kraus et al. 2012). However, it
Article published by EDP Sciences A74, page 1 of 20
A&A 601, A74 (2017)
is important to note that these results apply to the inner parts of
VDDs only (.20 stellar radii,
Vieira et al. 2015), that are respon-
sible for the bulk of the disk emission in the optical and infrared
(IR), as well as for the Balmer lines (Carciofi 2011). At larger
radii, the disks are detectable only at radio wavelengths.
In this work, we are interested in the overall density structure
of VDDs, focusing on the parts outwards of ∼20 stellar radii. We
constrain the density structure by compiling the observed spec-
tral energy distribution (SED) from ultraviolet (UV) up to radio
wavelengths. Due to the nature of the disk continuum emission
– bound-free and free-free emission from the ionized hydrogen
in the disk – fluxes at longer wavelengths originate from pro-
gressively larger areas of the disk. At the UV wavelengths, the
SED usually consists of the stellar photospheric flux only, al-
though in shell stars (Be stars seen close to edge-on), the UV
photospheric spectrum can be dimmed by the surrounding disk
and also strongly blanketed by the disk line absorption (mostly
Fe). At longer wavelengths, the disk contribution to the SED be-
comes more significant until it dominates the SED in the mid-IR
to radio domains. This is well explained in terms of the gas in
the disk forming an optically thick pseudo-photosphere, whose
size grows with increasing wavelength (see
Vieira et al. 2015,
for more details on the pseudo-photosphere concept applied to
the continuum emission of Be disks).
Radio observations longwards of sub-mm wavelengths are
of special interest for studying the outer parts of VDDs, as the
disk pseudo-photospheres are larger at these wavelengths. In this
work, we revisit the Be stars that were detected by the Very Large
Array (VLA) observations at 2 cm by
Taylor et al. (1990, six de-
tected stars) and subsequently observed at mm wavelengths us-
ing the James Clerk Maxwell Telescope (JCMT) by Waters et al.
(1991). The main outcome of the radio measurements was the
discovery of an SED turndown, that is, a steepening of the spec-
tral slope somewhere between mid-IR (10–60 µm, as measured
by the IRAS satellite) and radio wavelengths, in the studied
stars. Using a simple wedge-shaped disk model seen pole-on,
Waters et al. (1991) were able to reproduce the observed SEDs
with the disks having power-law density structure in the form
ρ ∝ r
−n
, with the exponent n ranging from 2.0 to 3.5. However,
to reproduce the SED turndowns, disks truncated at a certain ra-
dius (ranging from 26 to 108 stellar radii) had to be used. Al-
though the VDD model was not yet established at that time, it
was already suspected that Be envelopes have disk-like shapes
that originate from the central star and flow outwards. If the
disks are dominated by rotation rather than outflow (as in the
VDD model), it would follow that the most likely reason for
the disk truncation is the presence of an (unseen) binary com-
panion. However, because
Waters et al. (1991) assumed wind-
like outflows rather than disks dominated by rotation, they found
truncation to be an unlikely explanation for the SED turndown,
favoring other possibilities, such as changes in the disk geom-
etry or additional acceleration of the disk material in the outer
disk.
In the last decade or so, the VDD model has been firmly
established as the framework in which most of the observable
properties of Be disks can be explained (at least in their inner
parts). Successful VDD reproductions of multi-technique and
multi-wavelength observations of individual objects include, for
example, ζ Tauri (
Carciofi et al. 2009), β CMi (Klement et al.
2015
, 2017) and 48 Lib (Silaj et al. 2016). This allows us to in-
terpret the radio observations on a firm physical basis and there-
fore distinguish between the suggested scenarios to explain the
SED turndown.
The goal of the present work is to carefully model the com-
piled SEDs of the Be stars detected in the radio by
Taylor et al.
(1990) using the VDD model implemented in the Monte
Carlo radiative transfer code HDUST (Carciofi & Bjorkman 2006,
2008). For four of these stars, we have obtained new multi-band
measurements in the cm domain, allowing us to study the proper-
ties of the SED turndown in detail. With the results of this study
we address the question of the origin of the SED turndown, that
is, whether it can be explained in the framework of the VDD
model, which may be truncated by a binary companion, or if
further physical ingredients in the model are needed.
In the following section we focus on the theoretical predic-
tions concerning the structure of the outer disks of Be stars. In
Sect. 3 we describe the observations used, and in Sect. 4 we ex-
plain the VDD model and the modeling procedure. The follow-
ing section details the results for the six individual objects and
the conclusions follow.
2. The outer parts of Be star disks
In an isolated VDD, the outflow velocity in the inner disk is
highly subsonic and grows linearly with the distance from the
central star (
Okazaki 2001). At a certain point, sometimes called
the critical or photo-evaporation radius, the outflow velocity
reaches the local sound speed, which marks the transition be-
tween a subsonic inner part and a supersonic outer part of the
disk. Outwards from this point, it is no longer viscosity but rather
the gas pressure that drives the outflow, and the disk becomes
angular momentum conserving. This transition may offer an ex-
planation for the SED turndown, as the density decreases much
more rapidly past the transonic part. However, the transition is
only expected to occur at very large distances from the central
star. An approximate relation for the critical radius R
c
was de-
rived by
Krti
ˇ
cka et al. (2011) for isothermal disks:
R
c
R
e
=
3
10
v
orb
c
s
!
2
, (1)
where R
e
is the stellar equatorial radius, v
orb
is the disk orbital
speed above the stellar equator and c
s
is the speed of sound.
The typical values of R
c
are approximately 350 and 430 R
∗
for
spectral types B0 and B9, respectively. According to the pseudo-
photosphere model of
Vieira et al. (2015), for typical disk den-
sities, the pseudo-photosphere radius attains such large values
only at wavelengths longer than 10 cm. Unless the disk is ex-
tremely dense, this means that only wavelengths longwards of
10 cm can probe the transonic regions. So far, no detections of
Be disk emission at these wavelengths have been reported. It fol-
lows that the SED turndown is likely unrelated to the existence
of a transonic regime in Be disks.
The only known physical mechanism that can truncate the
disk at a closer distance to the central star is the tidal influence
from an orbiting secondary companion. The effects of such a
scenario on the VDD of the primary have recently been explored
by smoothed particle hydrodynamics (SPH) simulations, under
the assumption that the orbit of the secondary is aligned with
the disk (
Panoglou et al. 2016). For circular orbits, the influence
of the secondary has two important effects on the Be disk. The
first is the truncation of the disk at a distance close to the 3:1
resonance radius, which is much smaller than the orbital sepa-
ration. Outwards of the truncation radius, the density starts to
decrease much more rapidly, but these parts can still contribute
to the emergent spectrum. The second is the so-called accumu-
lation effect, which causes the parts of the disk inwards of the
A74, page 2 of
20
R. Klement et al.: Revealing the structure of the outer disks of Be stars
Table 1. Details of the IR, sub-mm, and radio observations.
Mission/Telescope Epoch of observations λ
central
/phot. band Reference
IRAS 1–11/1983 12, 25, 60, 100 µm Helou & Walker (1988)
VLA 12/1987–9/1988, 2/1990, 8/1991 2, 3.6, 6 cm Taylor et al. (1987, 1990),
Apparao et al. (1990),
Dougherty et al. (1991b),
Dougherty & Taylor (1992)
RAO/NOAO/MKO 4/1988–3/1991 JHKLMN bands Dougherty et al. (1991a)
JCMT 8/1988, 8/1989 0.76, 1.1 mm Waters et al. (1989, 1991)
IRAM 3/1991, 12/1992 1.2 mm Wendker et al. (2000)
MSX 1996–1997 4.29, 4.35, 8.88, 12.13, 14.65, 21.3 µm Egan et al. (2003)
AKARI 5/2006–8/2007 9, 18, 65, 90, 140, 160 µm Ishihara et al. (2010)
WISE 1/2010–11/2010 3.3, 4.6, 12 and 22 µm Cutri & et al. (2014)
JVLA 10/2010 0.7, 1.3, 3.5 and 6.0 cm this work
CARMA 9/2013 3 mm Klement et al. (2015)
APEX/LABOCA 9/2013, 7–8/2015 0.87 mm this work
truncation radius to have a slower density fall-off (i.e., a smaller
radial power law exponent). The accumulation effect has a larger
impact with decreasing orbital period, decreasing viscosity, and
increasing binary mass ratio. Considering the possibility that the
orbit of the secondary is misaligned with respect to the equa-
torial plane of the disk, both the truncation and accumulation
effects become much weaker (
Cyr et al. 2017).
The incidence of binarity among Be stars remains an impor-
tant open issue. The presence of a close binary companion was,
in the past, believed to be the cause of the Be phenomenon, al-
though that is not likely the case (
Oudmaijer & Parr 2010). How-
ever, the evolution of a mass-transferring binary may produce a
low-mass subdwarf O or B star (sdO/sdB, the mass donor that
was originally the more massive component and is now stripped
of its outer layers) and a fast-spinning star (the mass and an-
gular momentum gainer, that is now the primary star). It is ex-
pected that at least some Be stars may have formed in this fash-
ion. Owing to their lower luminosity, sdO/sdB companions are
difficult to detect and only five Be+sdO/sdB systems have been
reported so far: ϕ Per (
Gies et al. 1998), FY CMa (Peters et al.
2008), 59 Cyg (Peters et al. 2013), o Pup (Koubský et al. 2012),
and HR 2142 (Peters et al. 2016). They were revealed by pe-
riodic signatures in the UV spectra and by traveling emission
components in the emission lines of the Be star caused by ra-
diative interaction of the hot sdO/sdB star with the outer disk of
the Be star. Other common companions of Be stars are neutron
stars, which may emit X-rays as they accrete some of the mat-
ter from the disk of the Be primary. Other compact companions
should include black holes and white dwarfs, although only one
such system has been confirmed (Be star + black hole system
HD 215227;
Casares & Jonker 2014). The companions that are
hardest to detect, though they are possibly common, are low-
mass main-sequence stars.
Searching for binary companions using radial velocity (RV)
shifts of spectral lines is complicated by their large rotational
broadening. The exceptions from this rule are shell stars, which
have narrow absorption lines in the centers of broad emission
lines formed in the disk and thus orbiting companions are more
easily detectable. Searches for binary companions of Be stars us-
ing speckle interferometry (
Mason et al. 1997) and direct imag-
ing with adaptive optics (
Roberts et al. 2007; Oudmaijer & Parr
2010) led to the conclusion that the incidence of binaries among
Be stars is around 30%. However, these results apply only for
companions that are farther than 0.1 arcsec (∼20 au for the
most nearby targets), with a maximum magnitude difference of
10 mag in the I and K-bands. That means that Be companions
such as main sequence objects of spectral classes F and cooler or
sdO/sdB stars are not detectable with these techniques. Such bi-
nary companions would remain invisible, but could, in principle,
be revealed through their influence on the density structure of the
disk of the primary. If prevalent, the truncation of Be disks by
such companions could be the cause of the observed turndown
in the SEDs. Considering additional indirect evidence, line emis-
sion in the IR Ca triplet has been suggested to indicate binarity in
Be stars (see, e.g., discussion by
Koubský et al. 2011). Also, in
known Be binaries in a close orbit (e.g., γ Cas), the Hα line often
shows no clear peaks or symmetry, which is thought to indicate
disturbances in the disk due to the orbiting companion.
3. Observations
The primary dataset used for the modeling is the SED measure-
ments, namely the absolutely calibrated UV spectra and pho-
tometric measurements from visual to radio wavelengths. The
secondary dataset contains visual spectra and polarimetry. The
spectra were used to search for RV variations that could be as-
signed to the presence of an orbiting companion. The emission
line profiles and the polarimetry were used to check for variabil-
ity in the disk throughout the last decades.
The epochs, wavelengths, and references of the IR, sub-mm,
and radio photometric measurements are given in Table
1. The
epochs of the observations span over three decades. Since Be
disks are often highly variable, this may introduce errors in our
solutions. Nevertheless, the data for each target were still com-
bined into a single dataset, which then represents average prop-
erties of the disk over the last decades. For more details on the
variability of individual targets, and how it affects the solution,
we refer to Sect.
5.
3.1. Ultraviolet spectra
For the UV part of the spectrum, data from the Interna-
tional Ultraviolet Explorer (IUE)
1
and the Wisconsin Ultra-
violet Photo-Polarimeter Experiment (WUPPE)
2
were used. For
the IUE spectra, large aperture measurements were used in all
cases due to the problems with absolute flux calibration of the
1
https://archive.stsci.edu/iue/
2
https://archive.stsci.edu/wuppe/
A74, page 3 of 20