The Disk Wind in the Young Binaries and the Origin of the Cyclic Activity of Young Stars

Abstract

We present results of numerical modeling of the cyclic brightness modulation in the young binary systems with the eccentric orbits and low-mass secondary components. Brightness variations of the primary is due to the periodical extinction variations on the line-of-sight caused by the disk wind of the secondary and a common envelope it produces. A matter distribution in the envelope has been calculated in the ballistic approach. Calculations showed that for the young binaries with the elliptic orbits parameters of the photometric minima (their depth, duration and the shape of light curves) depend not only on the disk wind parameters and an inclination of the binary orbit to the line-of-sight but also on the longitude of the periastron. A modulation of the scattered radiation of the common envelope with a phase of the orbital period has been investigated in the single scattering approach. It is shown that an amplitude of the modulation is maximal when the system is seen edge-on and has also a non-zero value in the binaries observed pole-on. Possible applications of the theory to the young stellar objects are discussed. In particular, an attention is payed to a resemblance of the light curves in some models with light curves of the objects suspected as candidates to FUORs. Comment: 18 pages, 9 figures, accepted by Astronomy Letters

Full text

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arXiv:astro-ph/0407035v1 1 Jul 2004
The Disk Wind in the Young Binaries and the Origin
of the Cyclic Activity of Young Stars
V.P.Grinin1,2,3, L.V.Tambovtseva1, N.Ya.Sotnikova2
1 - Main Astronomical Observatory Pulkovo, 196140, St. Petersburg, Russia
2 - The Sobolev Astronomical Institute, St. Petersburg University, Russia
3 - Crimean Astrophysical Observatory, Crimea, Nauchny, Ukraine
Abstract
We present results of numerical modeling of the cyclic brightness modulation
in the young binary systems with the eccentric orbits and low-mass secondary
components. It is suggested that the system components accrete the matter from
the remnant of the protostellar cloud and, according to the current models, the
low-mass companion is the main accretor. Brightness variations of the primary is
due to the periodical extinction variations on the line-of-sight caused by the disk
wind of the secondary and a common envelope it produces. A matter distribution
in the envelope has been calculated in the ballistic approach.
When calculating the optical effects due to the dust component of the disk
wind, we adopt the dust to gas mass ratio 1:100 as in the interstellar medium
and the optical parameters of the circumstellar dust typical for the young stars.
Calculations showed that in the young binaries with the elliptic orbits theoretical
light curves demonstrated the more variety of shapes comparing with the case
of the circular orbits. In this case parameters of the photometric minima (their
depth, duration and the shape of light curves) depend not only on the disk wind
parameters and an inclination of the binary orbit to the line-of-sight but also on
the longitude of the periastron. A modulation of the scattered radiation of the
common envelope with a phase of the orbital period has been investigated in the
single scattering approach. It is shown that an amplitude of the modulation is
maximal when the system is seen edge-on and has also a non-zero value in the
binaries observed pole-on. Possible applications of the theory to the young stellar
objects are discussed. In particular, an attention is payed to a resemblance of the
light curves in some models with light curves of the objects suspected as candidates
to FUORs.
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1Introduction
Photometric observations of the last years show that among young stars one can find the
eclipsing systems with a rather long lasting eclipses. For example, in the binary system GW
Ori (P = 242d, Mathieu et al. 1991) where the primary is a T Tauri star (TTS), a duration
of the eclipses is about 1/10 of the period (Shevchenko et al. 1998). The duration of the
eclipses of the weak T Tauri star (WTTS) KH 15D (P = 48.36d, Kearns and Herbst 1998;
Hamilton et al. 2001; Herbst et al. 2002) is even more: one third of the period. In the
binary HD 200775, whose period is about of 3 years (Pogodin et al. 2004) and where the
main component is the Herbig Ae/Be star, the duration of the eclipses is comparable with
the orbital period (Ismailov 2003). Not long ago one more WTTS H 187 with the eclipse of
3.6 years has been discovered in the young cluster IC 348 (Cohen et al. 2003). To date only
one eclipse has been observed completely. Therefore, the period of this system is estimated
rather approximately and according to Cohen et al. is about of 4 years. An interpretation
of such eclipses by classical models developed for the eclipsing binaries, where either the
secondary itself or the gas and dust envelope filling in its Roshe lobe is ”an obscuring body”,
leads to the serious contradictions with the physics of the young stars; in some cases such
an interpretation is impossible in principle as in the case of KH 15D and H 187, since during
such long lasting eclipses the gas and dust envelope around the secondary must have sizes
comparable with the radius of the orbit. Such envelopes are unstable and are quickly to
destroy due to the tidal perturbations.
Recently it was shown (Grinin and Tambovtseva 2002 (Paper I)) that in the young binaries
which still continue to accrete the matter from the remnants of the protostellar cloud, a rather
unusual mechanism of eclipses can occur where the role of ”the obscuring body” belongs to
the disk wind of the secondary component, namely, to its dusty component. Because of
an extended structure of the disk wind, the eclipses evoked by it can be very prolonged.
Unlike the classical models of the eclipsing binaries, where the eclipses occur only when the
line-of-sight lies in the orbit plane or deviates from the latter at a small angle, the eclipses
by the disk wind are possible even at the large inclination angles. The more the inclination
angle the longer can be the eclipses. This allows us to suppose that a number of the eclipsing
binaries among the young pairs has to be i) larger in comparison with the binaries of the
Main Sequence, and ii) the number of the eclipsing systems with the long eclipses has to be
larger among the young pairs.
In connection with this, it is interesting to continue a study of the optical effects caused
by the disk wind in the young binaries. In the present paper which is continuation of the
Paper I we give the results of the numerical simulation of the cyclic phenomena due to
the disk wind of the low mass secondary during its motion on the orbit. We investigate a
dependence of the theoretical light curves on the disk wind parameters as well as parameters
of the binary including its orientation in the space. Unlike Paper I where a solution of such
a problem has been obtained for the systems with the circular orbits, here we consider a
common case of the binaries with the elliptic orbits.
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2 The problem
As in Paper I, we assume the model of the young binary proposed by Artymowizc and Lubow
(1996) (AL96) as the basic one, and restrict ourselves to the case when the mass of the
secondary companion is much less than that of the primary1. In the center of such a system
a cavity almost free of the matter is formed under the effect of the periodic gravitational
perturbation (Fig. 1). Its typical size depends on the eccentricity e and the mass ratio of the
components q = m2/m1and is approximately equal to (2−3)·a where a is a large semi-axis
of the orbit of the secondary (Artymowizc and Lubow 1994).
The components of the binary accrete the matter from the remnants of the protostel-
lar cloud which forms so-called circumbinary (CB) disk. In this case , the accretion rate
onto the low mass component can substantially exceed the accretion rate onto the pri-
mary(Artymowizc and Lubow 1994, Bate and Bonnel 1997; Rozyczka and Laughlin 1997).
Since the process of the disk accretion is accompanied with the matter outflow from the
accretion disk (the disk wind) then at such conditions, the low mass companion becomes
a powerful source of the matter which it ejects up (and down) the CB disk plane during
its motion along the orbit. Calculations showed that the dust presented in the wind2can
originate the long lasting eclipses of the primary (Paper I) and could be (at the certain
conditions) the source of the thermal radiation whose luminosity in the near infrared region
of the spectrum can be comparable with that of the CB disk itself (Grinin 2002).
2.1A structure of the CB-disk
As an example, a structure of the CB-disk of the young binary with the low mass component
is shown on Fig. 1. We calculated the matter distribution in the disk in the hydrodynamical
approach by SPH (smoothed particle hydrodynamics) method using a scheme close to that
described by Hernquist and Katz (1989) but with a constant smoothing length of the hydro-
dynamical parameters. In the projection on the sky plane one can see two streams of the
matter from the CB disk feeding the accretion disks around the components of the system.
In the CB disk itself the wave densities caused by the periodical gravitational perturbations
are seen. Such a matter distribution in the CB disk agrees well with results obtained by
AL96.
A special feature of the binaries with the elliptic orbits is a global asymmetry in the
azimuthal distribution of the CB disk matter that is clearly seen both pole-on and edge-on
as well as in the cross-section (Fig. 1). As it was shown by Artymowizc and Lubow (2000),
the asymmetric CB disk precesses slowly with a precession period significantly exceeding
the orbital one. In the cross-section (Fig. 1, middle panel) CB disk resembles a classical
accretion disk around a single young star in which a main part of the matter is concentrated
in the geometrically thin equatorial layer with a thickness H ≪ r.
One of the manifestation of the CB disk global asymmetry mentioned above is a depen-
dence of its geometrical thickness H not only on the distance from the center r but also on
the azimuth. For this reason, the precession of the CB disk has to originate a long lasting
periodical variations of the extinction in the young binaries observed nearly edge-on when
the line-of-sight is tangent to ”the surface” of the disk. It is also obviously, that the global
1According to the statistics of the Main-Sequence binaries (Duquennoy and Mayor 1991; Mazeh et al. 2000) such mass
component ratios are typical for the systems with periods P ≥ 3 yrs but they can be also found in the systems with shorter
periods. In particular, it could be systems with the substellar companions whose number rapidly grows owing to the continuing
research programmes (Mayor and Urdy 2000).
2As Safier (1993) showed, due to collisions of the dust particles with gas atoms in the accretion disk, the former are carried
away by the latter and are present approximately in the same proportion in the disk wind.
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Figure 1: A matter distribution in the CB-disk of the young binary obtained with SPH-method; the view
”edge-on” in the projection on XZ plane (the upper panel), the cross-section of the CB-disk in the same
plane (the middle panel) and the view ”pole-on” (the bottom). The co-ordinates X,Y,Z are expressed in the
units of the large semi-axis of the secondary’s orbit. The model parameters are e = 0.5, mass ratio q = 0.22
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Figure 2: The matter distribution in the common envelope of the young binary created by the disk wind of
the secondary in the projection on the XZ-plane (top) and on the equatorial (XY ) plane (bottom). The
secondary is at the point with the coordinates X = 1,Y = 0. The coordinates of the primary in the XY -
plane are equal to (0,0). All coordinates are expresses in the units of the large semi-axis of the secondary’s
orbit. The model parameters are Vw= 3,Uw= 0.5,e = 0.5 (see Section 3.2)
.
asymmetry of the CB disk is one of the sources of the intrinsic polarization of the young
binaries.
3 Formation of the common envelope
The disk wind of the secondary essentially modifies the model of the young binary: during
the orbital motion of the secondary it creates a rather complex in its structure asymmetric
common envelope (Fig. 2) which partially dissipates in the surrounding space but partially
can be captured by the main component. As a result, a dust appears above (and under) the
binary system’s plane giving an additional extinction on the line-of-sight.
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3.1Inertial properties of the accretion disks
A special feature of the binaries with the elliptic orbits is that the accretion rate onto the
system components undergone a strong modulation with a period equaled to the orbital one
(AL96). Moreover, in the binaries with elongated orbits (e ≥ 0.3) a modulation amplitude
can be so large that the accretion rate in the apastron and in the periastron can differ by
ten and more times (AL96; Rozyczka and Laughflin 1997). The dependence of the accretion
rate ˙Maon the orbital period phase can lead to that the mass loss rate in the disk wind ˙Mw
can be also a periodic function of time. Nevertheless, due to an inertia of the accretion disk,
the modulation amplitude of˙Mwdepends on the ratio between the orbital period P and the
hydrodynamical time tg. The latter is a characteristic time of the accretion disk dissipation
without any feeding. If it is less compared to the orbital period P then the accretion disk has
a time to react to the changes on its outer boundary caused by the changes in the accretion
rate. In this case ˙Mw∝ ˙Ma. In the opposite case, a reaction of the disk to the changes of
˙Macan be strongly smoothed.
According to Shakura and Sunyaev (1973)
tg= R2/ν (1)
Here R is the outer radius of the accretion disk, ν is a coefficient of the turbulent viscosity:
ν = αvsH, where H is a geometrical thickness of the disk, vsis a sound speed and α is a
dimensionless parameter depending on the mechanism of the generation of turbulence in the
accretion disk. Taking into account that vs/vφ≈ H/R where vφis a Keplerian velocity on
the outer boundary of the disk and expressing tgin the units of the orbital period we obtain
tg= (2πα)−1(R/H)2(trot/P),(2)
where trotis a Keplerian period at the outer boundary of the disk of the low mass companion.
The expression (1) one can rewrite in the form
tg= (2πα)−1(R/H)2q−1/2(R/a)3/2
(3)
where a is the large semi-axis of the secondary, q = m2/m1is the mass ratio of the compo-
nents.
According to Artymowizc and Lubow (1994), if the mass ratio q ≈ 0.1 the outer radius
of the secondary accretion disk R ≈ 0.1a. Assuming a ”standard” relation for the accretion
disks H /R = 0.05 and R = 0.1a, we obtain from Eq. (3) tg≈ 6.5α−1.
In the modern models (see the review by Stone et al. 2000 and the references therein)
the values of α are ranging from 0.005 to 0.5. Assuming the value α = 0.5 to estimate the
lower limit of tg, we obtain tg≥ 13.
Hence it follows, that even in the models with the high efficiency of the angular mo-
mentum transfer a typical hydrodynamical time of the accretion disk substantially exceeds
the orbital period. From this one can conclude that the disk wind forming mainly in the
central part of the disk is in no time ”to feel” the changes of the accretion rate at its outer
boundary. However, observations of the young binaries with the eccentric orbits testifies (see
e.g. Pogodin et al. 2004) that there is a modulation of some parameters of the emission
line Hα with the phase of the orbital period such as an equivalent width of the line and
parameters of its profile. This means, that physical conditions in the central part of the
accretion disk where this line is formed undergone the periodical variations connected with
the orbital motion of the system components. This variations can be caused by the tidal
perturbations and spiral shock waves forming in the accretion disks of the binaries (Sawada
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et al. 1986a,b; Bisikalo et al. 1995; Makita et al. 2000). As a result, the disk wind can
be strengthened near the orbit periastron. Therefore, further together with the conservative
model where ˙Mw= const, we also consider the model of the binary where the disk wind is
strengthening when the system components are approaching each other. For simplicity we
investigated the case when the mass loss rate is proportional to the accretion rate.
3.2Parameters of the disk wind
We remind briefly the main characteristics of the disk winds in the young stars. The nu-
merical modeling by Goodson et al. (1999) shows that the bulk of the matter (up to 80%)
is concentrated in the low velocity component of the wind and ejected from the accretion
disk in the angle range ω ≈ 40◦− 60◦where ω is the angle between the vector of the radial
velocity of the wind and the symmetry axis of the disk. Near the accretion disk, the disk
matter has not only the radial velocity component Vwbut also the azimuthal one Uw. At the
large distances from the accretion disk the latter decreases due to the angular momentum
conservation law and the radial velocity becomes the dominant component. Further, putting
the kinematic wind parameters, we shall mean the velocity components Vwand Uwas those
which the wind fragments have after completing the acceleration phase when the wind mo-
tion occurs inertly. Hartigan et al. (1995) and Hirth et al. (1997) estimated a typical low
velocity component of the wind from the observations of the forbidden lines in the spectra
of TTSs: few tens kilometers per second at the distances ≥ 1 AU.
Taking into account all mentioned above, we assume that all wind particles are ejected
with the same radial velocities Vw isotropically in the angle range 40◦≤ ω ≤ 60◦. It is
supposed that the disk wind possesses a mirror symmetry relatively to the orbit plane.
Since the radius of the accretion disk of the secondary is less compared to the large semi-
axis then, for simplification of calculations we adopt that the matter outflows from the point
source whose coordinates coincide with those of the secondary, and the mass center of the
system coincides with the primary location. The disk wind of the primary was not taking
into consideration when modeling because the accretion rate onto this component is much
less than that onto the secondary according to the problem condition.
It is also suggested that in the coordinate system of the secondary the disk wind has an
axial symmetry. This condition is fulfilled in those cases when one can neglect the tidal
perturbations due to the main companion. Since the radius of the accretion disk of the
secondary is less compared to the radius of the tidal interaction and the main contribution
to the disk wind is given by the internal layers of the accretion disk, such a suggestion seems
quite reasonable. An exclusion are binaries with a very large eccentricity. In such systems
the outer radius of the secondary accretion disk at the orbit periastron can turn out less
than the radius of the tidal interaction; as a result, the part of the matter from this disk can
be captured by the primary at the moment of the maximal approach. At these conditions
one can expect strong deviations from the azimuthal symmetry in the disk wind.
4 Method of calculation
As in Paper I we suppose that the disk wind consists of the weakly interacting fragments
which are treated as independent (probe) particles. When going to the coordinate system of
the primary the velocity vector of the particle Vw+ Uwis summed with the velocity vector
of the secondary orbital motion Vk. As a result the disk wind becomes anisotropic:
V0= Vw+ Uw+ Vk.(4)
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In this case the part of the matter (ejected in the directions opposite to that of the orbital
motion of the secondary) can get the velocity less than the escape one and can be captured
by the main component.
The calculation of the trajectories of the particles motion in the gravitational field of the
primary3was carried out in the ballistic approach. The particle velocity V0 determined
by Eq. (4) and its coordinates at the moment of ejection are put as initial conditions in
calculation of its trajectory. In the computing process an orbit of the secondary was divided
by n fragments in such a way that its motion along each part of the orbit took the same time
∆t = P/n. We put n = 72 or 180 (that in the case of the circular orbit corresponded to the
orbit step equal to 5◦or 2◦correspondingly). The same algorithm of the common envelope
modeling as in Paper I has been used. Model simulations of the disk wind was carried out
via ejection of the probe particles on each step isotropically within the range of solid angles
mentioned above into the upper and lower semi-space.
Thus, the model parameters of the problem are:
• an eccentricity of the orbit e; for model simulations it is adopted e = 0.5;
• the radial Vwand azimuthal Uwvelocity components of the disk wind of the secondary
(the Keplerian velocity of the secondary in the periastron is assumed to be equal to the
unity: Vk= 1);
• the mass loss rate from the accretion disk of the secondary ˙Mw.
In calculations of the optical characteristics of the dust component in the disk wind we
adopted the same dust to gas ratio as in the interstellar medium 1:100. For simplicity we
consider a mono-dispersed graphite and silicate mixture of the dust particles whose chemical
composition is analogous to that in the interstellar medium (Mathis et al. 1977). We used
so-called astrosilicate in our calculations. The radius of the particles s = 0.1µm, the average
density is equal to 3 g cm−3. The optical characteristics of such particles were calculated
with the Mie theory in Paper I.
5Results
We calculated a series of the common envelope models for the different phases of the orbital
period with the help of the method described above. As an example, one of them is presented
in Fig. 2. In the binaries with the elliptic orbits a concentration of the particles on the line-of-
sight in the direction towards the primary (hereafter we shall call this parameter as a column
density of the probe particles N) depends not only on the phase of the orbital period φ and
an inclination of the orbit plane to the line-of-sight θ but also on an orientation of the orbit
relatively to an observer. Fig 3. shows four variants of the orientation of the secondary’s
orbit relatively to the observer for which the column densities N were calculated as a function
of φ as well as corresponded optical depths τ. A transition from N to the column density
of the real particles Ndwas fulfilled using re-scaling when the ratio of the total number of
the dust particles ejected by the wind over one revolution to the corresponded number of
the probe particles was taking into consideration (see Paper I for details). Also we took into
account a difference in the cross-sections of the columns: the column density of the probe
particles was calculated per the section σ (see below), while that of the dust grains Ndwas
normalized to the cross-section of 1 cm2.
3Masses of the circumstellar (CS) disks of the young stars usually do not exceed 0.1 M⊙ (see, e.g. Natta et al. 2000) and
their self-gravity can be neglected.
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Figure 3: The orbit of the low mass secondary companion of the binary with an eccentricity e = 0.5. Arrows
point out the four different directions to the observer for which the phase dependence of the column density
in Fig. 4 and the light curves in Figs. 5-7 have been calculated.
As an example, Fig. 4 demonstrates a dependence of N on φ for one of the model
considered. The integer values of the phase correspond to the moments when the secondary
passes the periastron. Calculations were made for the different angles of the inclination of
the orbit plane θ and the different orientations of the orbit relatively to the observer. The
cross-section of the column σ was adopted to be equal to 0.1a x 0.2a, where a is the large
semi-axis of the secondary’s orbit. The test calculations showed that for less values of σ
the statistic fluctuations increased because of the low number of the probe particles in the
column while for larger values of σ smoothing of the details on the light curves took place.
5.1Amplitudes and shapes of the light curves
As in Paper I, when calculating a dilution of the light of the binary due to the variations of
the extinction on the line-of-sight, we adopted that the main source of the radiation was the
main component which was treated as a point source. The radiation flux from it decreases
when going through the dust component of the disk wind by e−τtimes. When τ ≫ 1,
that means a strong dilution of the direct radiation of the primary, the radiation flux is
determined by the scattered radiation of the CS dust included that of the CS and CB disks
as well as the common envelope. Taking this into account we can write
Fobs=
L∗
4πD2e−τ+ Fsc,(5)
where D is a distance from the observer.
As a rule, a scattered light gives only a weak deposit to the direct radiation of the young
star and its main function is to restrict the amplitude of the minima in those cases when
the direct radiation of the star is strongly diluted due to the absorbtion in the CS medium.
Such limiting functions of the scattered radiation of the CS disks of the young stars are the
well known phenomenon in the case of UX Ori type stars whose brightness undergoes strong
decreases due to the variable CS extinction (Grinin 1988).
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Figure 4: A dependence of the column density of the probe particles N on the phase of the orbital period
φ in the model with Vw = 1,Uw = 0,e = 0.5 for four orientations of the binary system relatively to the
observer. The angle θ between the line-of-sight and the equatorial plane of the system is given on the right
side.
In Figs. 5-7 a series of the light curves calculated for the different models is presented.
For simplicity it is adopted that the flux of the scattered radiation does not depend on the
phase of the orbital period and is equal to 0.1F∗. Calculations are made for the wavelength
5500˚ A centered to the V-band.
Like in the models with the circular orbits (Paper I), the light curves in Figs. 5-7 have
an asymmetric two-component shape caused by a conic structure of the disk wind. At some
system orientations the two-component shape of the minima is not revealed due to the low
resolution because of the column cross-section σ adopted in calculation of N(φ). Since the
stellar disk of the main companion has finite sizes, a similar smoothing of the light curves
can also occur in the real situations.
One sees from Figs. 5-7 that at the same other conditions, the longest minima take place
in the systems whose eclipses are happened at the moment of passing the apastron by the
secondary, and to the contrary, the shortest eclipses has to be observed from the side of
the periastron. It is easy to show that a ratio of the eclipse durations at these opposite
orientations of the binary is
∆ta/∆tp= (1 + e)/(1 − e).(6)
Hence it follows, that when e = 0.5 durations of eclipses differ by 3 times.
In the most models considered at the orbit orientation b (Fig. 3) (when an eclipse occurs
after a passage of the periastron), the light curve is characterized by the steep descent and
a slow ascent while in the same models but in the position d (when an eclipse occurs before
a passage of the periastron) the result is the opposite: a decrease of the brightness is slower
compared to its increase.
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Figure 5: Theoretical light curves of the main system component for the orbit orientations shown in Fig.
3. Model parameters are e = 0.5,Vw = 1,Uw = 0, the mass loss rate of the disk wind of the secondary
˙
Mw= 10−8M⊙yr−1(solid line) and 3 · 10−9M⊙yr−1(dashed line). The angle θ between the line-of-sight
and the plane of the double system is given on the right side.
At the small inclination angles of the orbit a duration of the eclipses is less compared to
the period of the orbital motion. An exception are the systems oriented with the apastron to
the observer (the variant c in Figs. 5-7): in such cases, even under a small θ an eclipse can
last for a rather long time. With increase of the orbit inclination a duration of the eclipses
increases and for θ ≥ 30◦can be compared with the system period.
As it is seen from Fig. 5, in the models with the low velocities of the disk wind one
can see a weaker minimum preceding the main one. A similar feature is also present in the
models with circular orbits. As shown in Paper I, its origin is caused by the wind particles
ejected during the previous passage of the secondary component on the orbit and captured
by the main component. In the models with the high mass loss rate (˙Mw≥ 10−7M⊙yr−1)
and the large inclination angles of the orbit a boundary between the main minimum and its
predecessor vanishes resulting the more extended two-component structure of the minima.
In the models with larger wind velocity (Fig. 6) a portion of the matter captured by the
primary decreases resulting only one main minimum on the light curves.
Calculations show that taking into account a rotation of the disk wind yields a more
rapid expansion of the wind in the horizontal directions in comparison with the models
where Uw= 0. As a result, the depth of the minima decreases but their duration increases
(Grinin and Tambovtseva 2003). The minima parameters and their shape depend also
on the geometry of the disk wind. Fig. 6 demonstrates results of calculations for two
models differing only with open angle of the wind; in one case it is the same as in Fig. 5
(40 ≤ α ≤ 60◦), in another case it is 45◦. It is seen that in the last case the minima are
shorter and have a more symmetric shape.
We remind that all model presented above are calculated in suggestion of a constant
mass loss rate. For comparison we also considered the models with a variable mass loss rate:
˙Mw∝˙Main which a dependence of˙Maon φ has been taken from AL96. Calculations showed
(Fig. 7) that in the models with the variable ˙Mwan amplitude of the minima depended on
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Figure 6: The light curves for the model with parameters: Vw= 2,Uw= 0,e = 0.5 with the mass loss rate
˙Mw= 3 · 10−9M⊙yr−1(dashed line), ˙Mw= 3 · 10−8M⊙yr−1(solid line) and ˙Mw= 10−7M⊙yr−1(dots).
The angle θ = 20◦. Top: 40 ≤ α ≤ 60◦, bottom: α = 45◦
the orientation of the orbit of the secondary relatively to the observer that is quite natural:
it was maximal in the systems whose periastron was between the observer and the primary
(the variant a in Fig. 3) and minimal in the case of the opposite orbit orientation (the
variant c in Fig. 3). As for a shape of the light curves, the difference between these two
models is not so essential.
5.2Modulation of the scattered radiation with the phase of the orbital period
When calculating light curves, we adopted for simplicity that an intensity of the scattered
radiation did not depend on the phase of the orbital period. Such a situation is possible if
the CB disk is a main source of the scattered radiation. In our case the part of the scattered
radiation originates from the disk wind of the secondary and the common envelope created
by it, and this part undergoes a periodical modulation. Let us consider a simple example
that demonstrates how the phase dependence of the scattered radiation can influence the
light curves of the binary.
For this purpose, the intensity of the scattered radiation for two of models considered has
been calculated in a single scattering approach. (An analysis showed that this approach was
valid for the mayor part of the common envelope at ˙Mw≤ 10−8M⊙ per year). The flux of
the scattered radiation in this approach is
Fsc=
L∗
4πD2πs2Qsc
?
Vn(r)r−2f(γ)e−τ1−τ2dr
(7)
Here n(r) is a concentration of the particles at the point r, Qsc is a scattering efficiency
factor of the dust grain, s is its radius, τ1is an optical depth between the point r and the
primary, τ2is an optical depth between the point r and the observer. The integration in Eq.
(7) is carried out over all volume V of the common envelope.
As in the previous section, we assume that the dust consists of the mixture with equal
amounts of the graphite and astrosilicate particles with the radius s = 0.1µm. A scattering
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Figure 7: Light curves for the model with a variable mass loss rate (˙Mw∝˙Ma). The solid line corresponds
to ˙Mw= 3·10−8M⊙yr−1in the periastron and the dashed line to ˙Mw= 3·10−9M⊙yr−1in the periastron.
The model parameters are Vw = 2,Uw = 0,e = 0.5. The angle θ between the line-of-site and the double
system plane is given on the right side.
process is described with the Henyey-Greenstein phase function
f(γ) =
1
4π
1 − g2
(1 + g2− 2g cosγ)3/2
(8)
where γ is a scattering angle, the asymmetry factor g is assumed to be equal to 0.5.
Fig. 8a demonstrates the results of calculations for the two system orientations: almost
edge-on (θ = 5◦) and pole-on. In both cases an integer value of the phase φ corresponds
to the moment of the periastron passage by the low-mass companion. In the first case the
periastron is between the primary and the observer. It is seen that the flux of the scattered
radiation Fscreaches its maximum namely in this phase. When observing the system edge-
on, this takes place due to the forward elongated scattering phase function. When observing
the system pole-on, a maximum of Fscis reached due to that a dilution coefficient weighted
over all envelope is maximal at the moment of the periastron passage by the low-mass
companion.
One can see from Fig. 8a that a dependence of Fscon the orbital period phase is asym-
metric and characterized with a steep growth when the secondary approaches the periastron
and a slower decrease when the secondary moves away from it. Calculations show that a
degree of asymmetry depends both on the value of the dimensionless velocity of the disk
wind Vwand on the eccentricity of the orbit e and its inclination to the line-of-sight. In the
model considered above (Fig. 8a) a maximal asymmetry of Fscis reached if the system is
observed pole-on.
The functions Fscof φ given in Fig. 8a were calculated for the model with˙Mw= const. In
the models with˙Mw∝˙Maa total picture is qualitatively the same. As earlier, a maximum of
the scattered radiation is reached in the periastron of the orbit and has even larger amplitude.
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Figure 8: a: An example of the phase dependence of the scattered radiation flux for two system orientations
θ = 5◦(solid line) and θ = 90◦(dashed line). The model parameters are Vw= 1,Uw= 0,e = 0.5; b: The
model of the eclipse of the main companion in the binary system with the account of the phase dependence
of the scattered radiation for the same model: in the periastron (left) and apastron (right). The dots indicate
to the light curves without the scattered radiation. The dashed line shows a behavior of the scattered light
flux with phase.
If to use the values of Fscobtained above in Eq. (5), then asymmetric low-amplitude
brightening appears on the light curve on going and/or outgoing the star from the minimum
(Fig. 8b). A similar details are observed from time to time on the light curves of some
eclipsing young objects (see, e.g. G¨ urtler et al. 1999; Herbst et al. 2002) and can occur
due to scattering the radiation of the primary by those dust particles who have a forward
scattering phase function. It is also obviously that taking into account a phase dependence
of the scattered light one can expect a brightness increase in the central part of the deep
minima whose amplitude is restricted from below to a scattering radiation.
5.3FUOR-like light curves
As calculations showed, in the models with the large mass loss rate a common envelope
formed by the disk wind of the secondary can be so powerful that during a substantial part
of the orbital cycle the main component can be obscured from an observer. In such cases the
light curve looks like a series of the subsequent flares; the latter, in fact, represents a short
time intervals corresponding to the minimal values of the extinction on the line-of-sight (Fig.
9).
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Figure 9: The light curves for the mass loss rate
Vw= 3,Uw= 0.5,e = 0.5 and θ = 20◦
˙ Mw = 10−7M⊙ yr−1in the model with parameters
This result can be interesting in connection with the debates on the nature of FUORs
(see Herbig et al. 2003 and the literature cited there). According to Hartmann and Kenyon
(1985) the outbursts of these objects are caused by the repeated ”outbursts” of the accretion
rate onto the young stars resulting an increase of the luminosity of the accretion disk that is
associated with the FUOR flare. According to another hypothesis (Herbig et al. 2003), the
FUORs outbursts are caused by the changes in the star luminosity. Both hypotheses are not
free of difficulties. Therefore, as an alternation, it is interesting to consider a possibility to
interpret the light curves of some FUOR-like objects on the base of the young binary model,
in which the primary (a star of a high luminosity) is periodically screened by the gas and
dust common envelope formed by the disk wind of the secondary.
6 Discussion
Thus, the theoretical light curves of the young binaries in which the eclipses of the main
component are caused by the disk wind of the secondary companion are characterized with
a large variety of the shapes, and in many cases absolutely do not resemble the classical light
curves observed in the usual eclipsing binaries. If the mass loss rate by the accretion disk of
the secondary ˙Mw≥ 310−8, the eclipses can be observed even if its orbital plane is strongly
inclined to the line-of-sight. The duration of such eclipses can be compared with a period
of the orbital motion. Taking into consideration this fact as well as a large number of the
double and multiple systems among the young stars (see the review by Mathieu et al. 2000),
one can expect an existence of the large-scaled cyclic brightness variability in many young
stars. Therefore, it is reasonable to suppose, that several young eclipsing systems with the
long lasting eclipses discovered not long ago is, in fact, a rather wide-spread population of the
young stars whose number will be rapidly increase with an accumulation of the photometric
data on the young clusters. We suppose that the UX Ori type stars also belong to such
eclipsing systems; the cyclic activity of these stars have been interpreted in assumption of
their binarity by Grinin et al. (1998), Rostopchina et al. (1999) and Bertout (2000).
There is one more feature in the model of eclipse considered here which is necessary to
take into account for an analysis of the continuous photometric observations of the young
stars. As mentioned in Section 2, in the binaries with the eccentric orbits the CB disk is
characterized with the global asymmetry and slowly precesses. Observations of such systems
under a small inclination to their equatorial plane have to reveal slow (secular) variations of
the extinction and, hence, the brightness of the primary. Theoretically a situation is possible,
when a direct radiation of the companions will be completely blocked by the CB disk during
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