A&A 448, 633-639 (2006)
DOI: 10.1051/0004-6361:20053884
L. V. Tambovtseva1,2 - V. P. Grinin1,2,3 - G. Weigelt2
1 - Main Astronomical Observatory Pulkovo, Pulkovskoe shosse 65, St. Petersburg 196140, Russia
2 -
Max-Planck-Institute für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
3 -
Crimean Astrophysical Observatory, Crimea, Nauchny, Ukraine
Received 22 July 2005 / Accepted 25 October 2005
Abstract
We investigate the formation of moving shadows on the
circumbinary (CB) disk of young binary systems. Moving shadows can
be created by a dusty disk wind of the secondary component. The
densest parts of the dusty disk wind and the associated common
envelope can be optically thick and may block the stellar
radiation inside a certain solid angle, resulting in the
appearance of a moving shadow zone. Its shape and size depends on
the mass loss rate, the disk wind velocity, and optical properties
of the dust. Our calculations show that the shadow zone is
observable if the mass loss rate
is greater than
10
per year. This shadow resembles a clock hand.
If the orbit is an elliptical, the properties of this clock hand
will change during the orbital motion of the secondary.
Key words: accretion, accretion disks - stars: formation - binaries: close - circumstellar matter - stars: pre-main sequence
During the last decade, high-resolution images of the dust environment of young stellar objects (YSOs) (e.g., Burrow et al. 1996; Koresko 1998; Padgett et al. 1999; Stapelfeldt et al. 1999) have stimulated numerous theoretical investigations. Most of the model images are calculated for the case of a single young star (e.g., Whitney & Hartmann 1992, 1993; Wolf et al. 2003; Grosso et al. 2003; Hodapp et al. 2004). The observed images show different types of asymmetries. For example, Duchêne et al. (2004), Krist et al. (2002), and Itoh et al. (2002) report on images of the circumbinary disk of GG Tau (HBC 54; IRAS 04296+1725). The images show a ring-shaped CB disk with a small gap that could be a shadow caused by material between the stars and the ring. Roberge et al. (2004) present the first spatially resolved spectrum of scattered light from the TW Hydrae protoplanetary disk. The radial profile of the integrated disk brightness showed an azimuthal asymmetry that was not seen in the previous coronagraphic images.
In this paper, we investigate the formation of moving shadows on the CB disks of young binaries. Our analysis is based on the results of our previous papers (Grinin & Tambovtseva 2002; GT2002; Grinin et al. 2004; GTS2004), in which we investigated the effect of a common envelope, created by a dusty disk wind of the secondary, on the optical variability of the system. It is shown that the densest part of the common envelope may be optically thick and may periodically obscure the main component. Furthermore, this dusty disk wind can cause a moving shadow on the surfaces of the CB disk. We calculated the CB disk images for several disk wind models, and the results are compared with observations of YSOs.
The accretion activity in young binaries is a periodic function of
time (AL96), and the accretion is maximum near the apoastron
passage. The amplitude of modulation of the mass accretion rate
onto components
depends on eccentricity e(AL96) and also on the viscosity (Rozyczka & Laughlin 1997).
One might expect that the mass loss rates caused by the disk winds
on the components will also vary periodically. However,
this is not the case. Due to the large hydrodynamic time scale
,
which is much greater than the orbital period, the
orbital variations of
will be very weak (GTS2004).
Therefore, we only consider systems with constant mass loss rates.
We consider the disk wind of the secondary to be an axially
symmetric bipolar outflow in its own coordinate
system. The outflow is
assumed to be isotropic within the wind ejection angle range from
to
,
where the wind ejection angle is
the angle between the disk symmetry axis and the direction in
which wind particles are ejected from the accretion disk of the
secondary. For simplicity, we assume that the wind density and
velocity do not depend on the latitude within the above angle
range. We assume that the ejection angle range lies between about 40 to 60 degrees. In this range the main part of the low-velocity
component of the disk wind is formed (Goodson et al. 1999).
According to the numerical results of these authors, the
low-velocity component provides the biggest contribution (about
80%) to the mass loss rate of the disk wind. Therefore, the
high-velocity component is not important in the models considered
below.
Safier (1993) introduced a generalized version of the Blandford
& Payne (1982) self-similar wind model and argued that the
disk-driven outflow had enough momentum to lift dust grains from
the disk surface. He showed that the largest (millimeter-sized)
dust grains are not lifted up by the outflow. Following Safier
(1993) and Garcia et al. (2001), we assume that the disk wind
contains both gas and dust components and that they have a
"standard'' proportion, as in the interstellar medium (100:1). We
also assume that the dust component of the wind consists of a
mixture of dust particles similar to those in the circumstellar
(CS) disks of TTSs (Men'shchikov et al. 1999). According to this
paper, the absorption coefficient of such a mixture is equal to
cm2 g-1 per unit of the dust mass at
the wavelength of 5500 Å (V band). In accordance, the absorption
coefficient per unit of the gas and dust mixture is
cm2 g-1.
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Figure 1: Illustration of the geometry of the model. An asterisk indicates the location of the primary. The secondary is not seen because of the disk wind above and below the circumsecondary disk. The drawing is not to scale. |
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Figure 2: Disk geometry (see text for details). |
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Figure 2 shows that
Equation (1) can be rewritten as:
The scattered radiation from the disk surface is assumed to be
proportional to .
This is a good approximation if the
free-path length of photons in the disk is small compared to the
size of the shadow. In the CS disks of the pre-main-sequence
stars, this condition holds everywhere except at the periphery of
the disks. We did not take the forward scattering of the stellar
radiation by the disk wind into account since the albedo of dust
particles is low,
0.4-0.5 (Natta & Whitney 2000). In
order to demonstrate its possible effect on the contrast in the
shadow, we calculated the scattered light for one of the wind
models in the single scattering approximation.
Using this approach for accretion disks and the phase-dependent density distribution obtained earlier for the common envelopes (GT2002; GTS2004), we calculated disk images seen face-on for several disk wind models.
Table 1: The model's parameters.
Figure 3 shows, as an example, the matter distribution in the common envelope for model 1. Deviations from the axial symmetry, which are caused by the vector summing of the wind and orbital velocities mentioned above, are clearly seen in the XZ and YZ images, as well as the asymmetric spiral structure of the pole-on (XY) image. The secondary is at the point X = 0.5 and Y = 0. All distances are given in the units of the semimajor axis.
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Figure 3: Matter distribution in the common envelope in the XZ and XY plane for model 1. The semimajor axis of the binary coincides with the X-axis. The low-mass companion is at point with coordinates X = 0.5; Y = 0. |
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In Figs. 4-7, we present our calculated intensity distributions
for models 2-4 in the assumption that the disk surface
isotropically irradiates an incident light. All brightness
contours are given in arbitrary units (the contours are spaced by
a factor of 0.2). The coordinates X and Y are expressed in
units of the orbital semimajor axis. Figure 4 shows the isophotes
computed for model 2. The disk flaring parameter
.
We
plotted three maps with different mass loss rates:
,
10-8, and
per year. One
can see that a noticeable shadow appears on the disk surface if
the mass loss rate is significant enough (
per year). Figure 5 shows the pole-on view of the disk with a
shadow for two different parameters
.
Evidently, more
flared disks show wider shadows at the disk periphery. The centers
of the images are masked with filled circles since the central
regions of the common envelopes can cause additional scattering
(GTS2004), which is not taken into consideration in the present
paper; but this scattering does not influence the shadow
formation.
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Figure 4:
Theoretical brightness map for model 2:
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Figure 5:
Theoretical brightness maps for model 2:
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A more interesting situation is obtained in binary systems with elliptic orbits (Figs. 6 and 7 corresponding to models 3 and 4). In this case, the shape of the shadow on the disk will change during the orbital motion: at the moment of the apoastron passage, the shadow will be narrower and fainter than in the periastron. In the periastron, the shadow can be much more extended (right columns of Figs. 6, 7); in Figs. 6 and 7, we show the disk with a cut outer region to represent its inner part better.
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Figure 6:
Theoretical brightness maps for model 3:
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Figure 7: Same as Fig. 6 but for model 4. |
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As an example, Fig. 8a illustrates the decrease in the shadow's
intensity with the distance from the star calculated for model 3.
Both intensity profiles are given at the distances of 30 and 300
AU. The mass loss rate due to the wind is
yr-1. This case is shown when the secondary component is in
the apoastron. Intensities are normalized to their maximum values
calculated out of the shadow (in the bright regions). The shadow
profile has a double-peaked form, which is also seen on the most
images presented in Figs. 4-7. It is caused by a specific wind
geometry: the particles are ejected within a cone limited by
angles of 40 and 60 degrees.
Since the dust opacity depends on the wavelength, the contrast is
also sensitive to the wavelength. Figure 8b shows an azimuthal
intensity profiles of the CB disk for the disk wind model 3 in the
two bands: V and H. The cut is made at the distance of 30 AU from
the star. Opacity in the H band is less than in the V band by
about one order of magnitude. Therefore, a contrast between
shadowed and bright parts of the CB disk dramatically decreases to
the longer wavelengths. This means that in the near infrared the
wind shadow can be detected for greater mass loss rates (
yr-1).
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Figure 8:
a) Azimuthal profile intensity of the
circumbinary disk in the V band at distances of 30 AU (solid) and
300 AU (dashed) (model 3). b) V band (solid) and H band
(dashed) azimuthal profile intensity of the circumbinary disk in
the same model at 30 AU from the star. The mass loss rate
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Figure 9:
Azimuthal variability of the CB disk intensity profile at
300 AU from the star for the two positions of the secondary
companion in model 3: a periastron (solid line) and an apoastron
(dashed line). The mass loss rate
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Figure 9 demonstrates changes in the shadow's shape and depth
during the orbital period depending on the position of the
secondary on the orbit. For a better representation we combine
shadow profiles for the periastron and the apoastron positions.
One can see that the "periastron shadow'' is wider and deeper than
the "apoastron'' one, which is due to the fact that the particle
concentration in the disk wind decreases with the distance from
the source of the wind. For the same reason a contrast of the
shadow from the disk wind will decrease with increase in the
semimajor axis of the orbit. The results show that a shadow on the
CB disk of a young binary system resembles a clock hand. In the
case of an elliptical orbit, the properties of this clock hand,
including its shape, can change during the orbital motion of a
secondary (Fig. 10). If the masses (and luminosity) of the
companions are similar, their disk winds can form two shadows that
are located opposite each other.
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Figure 10: Shadow motion. a) periastron, c) apoastron, b), d) phasesbetween periastron and apoastron. |
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For model 3 we calculated a radiation scattered by the disk wind
for the optically semi-transparent case (
yr-1). In the single scattering approximation
that is valid if the optical depth of the wind is small compared
to unity (
), the flux of the scattered radiation
from the whole disk wind falling on the disk surface at
a given point can be written as
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(5) |
In some cases, CS disks around companions may produce their own
shadows on the outer CB disk. But accretion disks are
geometrically thin (). Besides, they are rather compact
(Artymowicz & Lubow 1994). The noticeable shadows they cause may
be seen only under specific conditions, such as when the primary
is an AA Tau-like star. The inner part of the accretion disk
around this star is warped due to interaction with the stellar
magnetosphere formed by an inclined magnetic dipole (Bouvier et
al. 2003; Terquem & Papaloizou 2000). The shadows from such a
warped disk will also be moving but with a period close to that of
the star rotation.
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Figure 11:
Azimuthal profile of the CB disk intensity without
(solid) and with (dashed) radiation scattered by the disk wind for
model 3 at the distances of 30 AU a) and 150 AU
b) from the star. The secondary is in the periastron.
The mass loss rate
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Another possibility is that the gap is the shadow of an opaque CS dust cloud. Such clouds exist in the vicinity of young stars and can be responsible for their brightness variability. This mechanism can explain the variability of the UX Ori type stars (e.g., Grinin 2000). However, if this mechanism were the cause of GG Tau A's disk gap, then the gap position should change during the orbital motion of the CS dust cloud. Since GG Tau A's disk gap did not change for several years, the origin of GG Tau A's disk gap is still a mystery.
HH 30. One of the most spectacular asymmetric objects is the reflection nebula of the jet object HH 30 (Stapelfeldt et al. 1999). Asymmetry was present in 1998, but was absent in the 1994 and 1995 images. Wood & Whitney (1998) consider the possibility that such asymmetry could be caused by a variable, asymmetric illumination of the CS disk by a rotating T Tauri star with spots on its surface. Cool spots could be the result of a large-scale magnetic field, and hot spots could be caused by accretion activity controlled by the stellar magnetic field. If the spots are asymmetrically distributed around the stellar axis, the rotation of the star leads to a variable illumination of the surrounding CS matter and can produce the changing asymmetric image shapes. Stapelfeld et al. (1999) consider this model for the interpretation of HH 30's variable asymmetry. Another possible explanation discussed by Stapelfeldt et al. (1999) is a variable CS extinction of the direct stellar radiation caused by opaque dust clouds. If HH 30 is a close binary, a dusty disk wind of the secondary could play the role of such an eclipsing cloud. Other young objects with very asymmetric inner disk-outflow environments are, for example, R Mon (e.g., Weigelt et al. 2002) and S 140 IRS 3 (Preibisch et al. 2001).
Acknowledgements
V.G. and L.T. acknowledge the kind hospitality of the Max-Planck-Institute für Radioastronomie, where part of this work has been done. We are grateful to the anonymous referee for useful comments and suggestions. This project was supported in part by the grant of the Russian Academy of Sciences "Non-stationary phenomena in Astronomy'' and the grant INTAS 03-51-6311.