Hydrodynamic processes in young binaries as a source of cyclic variations in circumstellar extinction
ABSTRACT Hydrodynamic models of a young binary accreting matter from the remnants of a protostellar cloud have been calculated by the
SPH method. Periodic variations in column density in projection onto the primary component are shown to take place at low
inclinations of the binary plane to the line of sight. These can result in periodic extinction variations accompanied by brightness
variations in the primary. Generally, there can be three periodic components. The first component has a period equal to the
orbital one and is attributable to the streams of matter penetrating into the inner regions of the binary. The second component
has a period that is a factor of 5–8 longer than the orbital one and is related to the density waves generated in a circumbinary
(CB) disk. Finally, the third, longest period is attributable to the precession of the inner CB disk regions. The relationship
between the amplitudes of these cycles depends on the model parameters as well as on the inclination and orientation of the
binary in space. We show that at a dust-togas ratio of 1: 100 and amass extinction coefficient of 250 cm2 g−1, the amplitude of the V-band brightness variations in the primary component can reach 1
at a mass accretion rate onto the binary components of 10.8−8
⊙ yr−1 and a 10° inclination of the binary plane to the line of sight. We discuss possible applications of the model to young, pre-main-sequence
- [show abstract] [hide abstract]
ABSTRACT: The results of Herbig Be-star periodicity search are discussed. The cyclic phenomena can be roughly divided into the following three types:P0 - long-term periodic variability with periods of more than one year and amplitudes of 0 . m 4-4 . m 0V. The following stars show this type of variability (PO in years are presented in parenthesis): VX Cas (4.46), UX Ori (3.70), BF Ori (6.3), VV Ser (2.87), V517 Cyg (8.9-9.6), V373 Cep (7.7), and the others.P1 - middle-scale quasi-cyclic variability with periods of 10-100 days and amplitudes of 0 . m 05-0 . m 5V. Twenty-three stars show this type of cyclicity. 7 stars are suspected to have this type of variability.P2 - short-periodic and quasi-cyclic variability with amplitudes of 0 . m 05-0 . m 5V and periods of less than 10 days. In some cases the periodicity correlates with variations in strong emission line profiles. As an example, the properties of AB Aur are discussed. A total of 14 objects are suspected to have short-periodic quasi-cyclicity. Four of them show a high probability of periods (0.85 < ii="">The discovered cyclic phenomena are interpreted in terms of Keplerian rotation of various structures in accretion disks and formations. The hypothesis of giant protocomets is suggested to explain the periods P0. Short-period cyclicity is associated with the changing of hot compact shell shapes modulated by rotation.Astrophysics and Space Science 01/1993; 202(1):137-154. · 2.06 Impact Factor
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ABSTRACT: A new, general-purpose code for evolving three-dimensional, self-gravitating fluids in astrophyics, both with and without collisionless matter, is described. In this TREESPH code, hydrodynamic properties are determined using a Monte Carlo-like approach known as smoothed particle hydrodynamics (SPH). Unlike most previous implementations of SPH, gravitational forces are computed with a hierarchical tree algorithm. Multiple expansions are used to approximate the potential of distant groups of particles, reducing the cost per step. More significantly, the improvement in efficiency is achieved without the introduction of a grid. A unification of SPH with the hierarchical tree method is a natural way of allowing for larger N within a Lagrangian framework. The data structures used to manipulate the grouping of particles can be applied directly to certain aspects of the SPH calculation.The Astrophysical Journal Supplement Series 05/1989; 70:419-446. · 16.24 Impact Factor
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ABSTRACT: We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.The Astrophysical Journal 03/1994; · 6.73 Impact Factor
arXiv:0809.4434v1 [astro-ph] 25 Sep 2008
Journal-Ref: Astronomy Letters, 2007, v. 33, No 9, pp. 594-603
Hydrodynamic Processes in Young Binary
Systems as a Source of Cyclic Variations of
N.Ya. Sotnikova1, V.P. Grinin1,2
1 – Sobolev Astronomical Institute, St. Petersburg State University, Universitetskii pr. 28,
Petrodvorets, St. Petersburg, 198504 Russia,
2 – Pulkovo Astronomical Observatory, Russian Academy of Sciences, Pulkovskoe sh. 65,
St. Petersburg, 196140 Russia
Hydrodynamic models of a young binary system accreting matter from the remnants of
a protostellar cloud have been calculated by the SPH method. It is shown that periodic
variations in column density in projection onto the primary component take place at low
inclinations of the binary plane to the line of sight. They can result in periodic extinction
variations. Three periodic components can exist in general case. The first component has a
period equal to the orbital one and is attributable to the streams of matter penetrating into
the inner regions of the binary. The second component has a period that is a factor of 5-8
longer than the orbital one and is related to the density waves generated in a circumbinary
(CB) disk. The third, longest period is attributable to the precession of the inner asymmetric
region of CB disk. The relationship between the amplitudes of these cycles depends on
the model parameters as well as on the inclination and orientation of the binary in space.
We show that at a dust-to-gas ratio of 1 : 100 and and a mass extinction coefficient of
250 cm2g−1, the amplitude of the brightness variations of the primary component in the
V-band can reach 1mat a mass accretion rate onto the binary components of 10−8M⊙yr−1
and a 10oinclination of the binary plane to the line of sight. We discuss possible applications
of the model to pre-main-sequence stars.
Key words: young binaries, accretion, hydrodynamics, variable extinction.
Binarity is widespread among stars, including young pre-main-sequence stars (see the
review by Mathieu et al. 2000). Such stars still continue accreting matter from the remnants
of a protostellar cloud. Numerical simulations by Artymowicz and Lubow (1994, 1996) of
hydrodynamic processes in young binaries show that periodic gravitational perturbations
and viscous forces produce a matter-free gap at the binary center into which two streams
of matter generally unequal in intensity from a circumbinary (CB) disk penetrate. These
streams maintain the accretion activity of the binary components.
The simulations by Artymowicz and Lubow (1996) showed that the accretion rate in
binaries with eccentric orbits depends on the orbital phase, reaching its maximum at the
time of periastron passage. For this reason, in binaries whose components are cool young T
Tauri stars (their luminosity depends sensitively on the accretion rate), periodic brightness
variations in their components can take place. This prediction of the theory was confirmed
by observations (Mathieu et al. 2000).
In this paper, we reproduce the Artymowicz–Lubow model by the SPH method and
show that another type of cyclic photometric variability of a young binary due to periodic
extinction variations on the line of sight is possible in this model. In contrast to periodic
modulation of the accretion rate, periodic extinction variations can be observed in binaries
with both elliptical and circular orbits, provided they are inclined at a small angle to the
line of sight.
FORMULATION OF THE PROBLEM
Following Artymowicz and Lubow (1994, 1996), we assume that the circumbinary disk is
coplanar with the binary. As in the papers of these authors, the hydrodynamic calculations
presented below were performed by the smoothed particle hydrodynamics (SPH) method
(Lucy 1977; Gingold and Monagan 1977) according to a scheme similar to that suggested
by Hernquist and Katz (1989), but with a constant smoothing length of hydrodynamic
quantities. No thermal balance was calculated. The system was assumed to be isothermal.
The SPH implementation used was described in detail previously (Sotnikova 1996).
The Hydrodynamic Model
The mass of the gaseous disk was assumed to be negligible compared to the total mass
of the stars in the binary. This allowed the disk self-gravity to be neglected. In the initial
scheme, we assumed free boundary conditions, i.e., neglected the pressure at the boundary of
the gas distribution. This approximation is justified if a flow of cold gas is modeled. During
our calculations, it emerged that the presence of a free boundary led to a slow outward
expansion of the disk, which deteriorated the statistics when the temporal variations in
disk column density were determined. Therefore, the scheme was slightly modified: an
artificial potential barrier on the far periphery of the disk was superimposed on the general
gravitational field of the binary1. The barrier parameters were chosen in such a way that, on
the one hand, the disk dissipation was slowed down and, on the other hand, no significant
distortions were introduced into the dynamics of density waves in the inner disk regions.
Test calculations showed that introducing a barrier reduced the dissipation rate of the CB
disk approximately twofold. In the models presented below, the dissipation is attributable
mainly to mass accretion onto the binary components: through this process, the number of
particles in the CB disk decreases approximately twofold after 600 binary revolutions. In
the case without a barrier, the same result is obtained after 300 revolutions.
1Note that a similar barrier was used with the same goal by Artymowicz and Lubow (1994, 1996).
The SPH equations of motion for particle i that represents an element of gas in are very
similar to those described in (Hernquist and Katz 1989)
∇iW(ri− rj;h) − ∇ϕ(ri),
where Pi, Pj , ρi, ρj are the pressure and density at the position riand rj of particles i
and j; for the isothermal case under consideration, the equation of state is P = c2ρ, where
c is the speed of sound; ϕ is a variable gravitationalpotential produced by the binary; m
is the mass of the SPH particles (we considered equal-mass particles); W is the kernel for
smoothing hydrodynamicquantities (it was chosen in the form of a spline; seeMonaghan and
Gingold 1983); h is the smoothing length.
The contribution from the artificial viscosity to the pressure gradient is described by
the tensor Qij. There are various representations of Qij. We used its expression suggested
by Monaghan and Gingold (1983). For advantages and disadvantages of this choice, see
Hernquist and Katz (1989).
As in the papers by Artymowicz and Lubow, we took into account the contribution from
the viscous terms in the cases where the SPH particles approached each other and recede
from each other, i.e., in the form
Qij= (−αcµij+ βµ2
where µij= h(vi− vj) · (ri− rj)/(r2
parameters α and β are analogues of the viscosity coefficients in the Navier-Stokes equation.
Following Artymowicz and Lubow (1994), we assumed for most of the models that α ≃ 1
and β = 0.
The choice of parameter c, an isothermal speed of sound, is critical for our models. It
defines the effective viscosity of the gaseous disk: ν ∼ αch. Following Artymowicz and
Lubow (1994), we chose this parameter in units of the velocity of a test particle in a circular
orbit with a radius equal to the semimajor axis of the binary a moving around a point mass
m1+ m2, where m1 and m2 are the masses of the binary components. The parameter c
in these units was varied in the range from 0.01 to 0.08. Reducing the viscous properties
of the disk reduced the contribution from hydrodynamic effects and the behavior of the
system was similar to that of a celestial-mechanical system. Below, we call gaseous disks
with c ≈ 0.01 − 0.02 and c = 0.05 “cold” and “warm” CB disks, respectively.
The smoothing length was fixed at h = 0.1a, where a is the orbital semimajor axis of
the secondary component. This allowed the hydrodynamic quantities to be smoothed over
40-60 neighboring particles at a typical number of particles N ∼ 60000.
To integrate the SPH equations, we used the standard explicit leapfrog scheme; the time
step dt was controlled by the Courant condition.
ij+ η2), ρij= (ρi+ ρj)/2, rij= |ri− rj|, η ≃ 0.1h. The
Initial Conditions and Binary Parameters
The number of test particles modeling the CB disk was chosen to be from 50000 to
75000. The particles were distributed in accordance with a surface density profile ∼ 1/r.
The radius of the matter-free gap at the initial time was taken to be rin= 2a. After several
binary revolutions, it virtually ceased to change and did not differ much from its initial value.
We put the outer boundary of the disk at the initial time at a distance rout= 5.8a. Thus, we
modeled more extended disks than Artymowicz and Lubow (1994). The periodic variations
in gravitational potential produced no perturbations in this region of the gaseous disk and
the existence of a boundary (in particular, the presence of a barrier) had no effect on the
inner disk regions. The vertical particle distribution followed a barometric law.
At the initial time, the particles were placed in circular orbits around the center of mass
of the binary with a Keplerian velocity corresponding to the orbital radius.
We varied the orbital eccentricity of the binary within the range from e = 0 to e = 0.7
and the component mass ratio q = m2/m1within the range from 0.1 to 1.0. The evolution
of the CB disk was traced on time scales up to 300 binary revolutions (in some cases, up to
600 revolutions). The orbital parameters of the binary in this time interval were assumed to
Determining the Column Density in the Disk
Simultaneously with the calculation of the dynamical evolution of the gaseous disk in the
binary’s periodically varying potential, we determined the mass accretion rate from the disk
onto both components. We assumed that if a particle fell into a region less than 0.3 of the
radius of the corresponding Roche lobe, then it was captured by the star and contributed
to the accretion rate. Subsequently, such particles were eliminated from our calculations.
The derived accretion rates of test particles onto the binary components were then used to
determine the particle mass when calculating the circumstellar extinction.
The particle column density was determined for various orbital phases and various in-
clinations of the line of sight to the binary plane. Let us denote the binary inclination to
the line of sight by θ. To calculate the particle column density n(θ, t) as a function of time,
we chose a column with a cross section σ = 0.1a × 0.2a. Test calculations showed that the
statistical fluctuations due to a small number of test particles in the column increase at lower
values of σ, while the features on the t dependences of n are smoothed at higher values of σ.
RESULTS OF SIMULATIONS
As an example, Fig. 1 shows the particle distribution in the binary after 60 revolutions
from the beginning of our calculation. The models with warm (a) and cold (b) disks are
shown. The model parameters are: e = 0.5, m2: m1= 0.7 : 2, c = 0.02 for the cold disk;
c = 0.05 for the warm disk.
In the model with a warm disk (Fig. 1a), we clearly see two streams of matter unequal
in intensity from the CB disk, which feed the accretion disks of the binary components and
which are extensions of the spiral density waves (the second stream is more pronounced at
other intermediate orbital phases). The more intense stream accretes onto the less massive
binary component. This peculiarity was first pointed out by Artymowicz and Lubow (1996)
and, as the calculations by Bate and Bonnell (1997) showed, is obtained even in the models
with a component mass ratio of 1 : 10. This is because the low-mass companion moves in
its orbit not far from the inner boundary of the CB disk — the main reservoir of the matter
that it “pulls” on itself, while the primary component of the binary is located near its center,
in a matter-free zone. The characteristic size of this zone depends on orbital eccentricity e
and component mass ratio q and is equal to ≈ (2−3)a (Artymowicz and Lubow (1994). On
the whole, the disk more likely resembles a wide ring.
In the “cold” model (Fig. 1b), the spiral pattern on the CB disk appears more fragmentary
and is represented by several short remnants of the spiral density waves near the inner disk
boundary. The accretion streams are less pronounced.
The disk itself is geometrically
The Global Asymmetry of CB disk
We see from Figs. 1a and 1b that the distribution of matter in the CB disk is characterized by
a global asymmetry seen in both projections of the binary. The asymmetry manifests itself
particularly clearly in the inner disk region — the inner boundary of the ring has a noticeable
eccentricity and its center is shifted relative to the binary center of mass. According to Lubow
and Artymowicz (2000), such an eccentricity is the result of instability. It arises when there
is a 3 : 1 resonance in the gaseous disk. This instability manifests itself even in binaries
with circular orbits. For this instability to operate, the mass ratio of components q must be
Figure 1: Binary models with warm (a) and cold (b) disks and a low-mass (m2: m1= 0.7 : 2)
secondary component in an eccentric (e = 0.5) orbit. The figure shows the following: view
from the pole (upper panels), projection onto the xz plane (middle panels), and section
(lower panels) passing through the center of mass in this plane. The binary is displayed
in revolution 61 at phase 3/8. The strenght of the image blackening corresponds to the
logarithm of the particle number per pixel.
greater than 0.2. On the other hand, the component masses must differ, q cannot be close
to unity, or the instability will be damped by viscosity.
Additional effects arise in the case of eccentric orbits. The presence of an one-armed bar
potential with (m, l) = (1, 0) results in lopsided structure of a disk. The disk disturbance
produced by a variable gravitational potential follows the apsidal motion of the binary. The
disk eccentricity varies periodically and the rate of these variations depends on the angle
between the major axes of the binary orbit and the elliptical disk itself. The effects of disk
precession due to the quadrupole moment from the binary are added to this. The precession
rate is low and the entire eccentric disk turns in a time interval that is hundreds of times
longer than the orbital period.
If we look at the disk edge-on, then its significant asymmetry is also noticeable in the
vertical direction: on the one side, it is considerably thicker than on the other side (Fig. 1,
central panels). We are probably the first to point out this peculiarity of CB disks. The part
of the disk whose inner boundary is located farther from the center of mass turns out to be
thicker. The thickening may be caused by a weakening of the gravitational forces from the
binary, which is known to result in an increase in the geometrical thickness of the disk in an
external gravitational field.
Figure 2 demonstrates the vertical asymmetry and the overall turn of the warm disk on
time scales of the order of one precession period (≈ 200P, where P is the orbital period
of the binary). The parameters of the presented model are e = 0.5, m2: m1= 1 : 2, and
c = 0.05. As we will show below, the existence of a global asymmetry in the CB disk is one
of the reasons why the optical properties of a young binary at low inclinations to the line of
sight depend significantly on its orientation in space.
The global asymmetry in the cold disk on time scales of several hundred binary revolutions
is more pronounced than that in the warm disk. This is particularly clearly seen if we look at
the disk edge-on. Its precession time is approximately twice that for the warm disk. Figure 3
shows the projections of the cold disk onto the xz and yz planes at various times. In a time
of about 200 orbital periods, the disk in the yz projection turns approximately through
180o, while in the “warm” model the CB disk made an almost complete turn. The CB disk
precession and asymmetry, which is particularly clearly seen in the vertical direction, are
common properties of such disks and take place not only in the models with eccentric orbits,
but also in those with circular orbits. Moreover, we found no significant dependence of the
precession period on eccentricity.
The Behavior of the Column Density
Our calculations showed that the particle column density in binaries with elliptical or-
bits toward the primary component depends not only on the orbital phase and the orbital
inclination to the line of sight θ, but also on the orientation of the orbit relative to the ob-
server. Figure 4 shows the behavior of the column density n(θ, t) for two angles, θ = 0oand
θ = 10o, and one of the orbital orientations relative to the observer at which the azimuth
angle between the direction from the primary component to the apoastron of the secondary
star and the observer’s direction is zero. In this case, the orbital apoastron of the secondary
component lies between the observer and the primary component.
We see from Fig. 4 that two cycles are present in the column density variations. One of
them has a period equal to the orbital period. Its amplitude is larger in the case with an
Figure 2: Precession of the warm disk in projections onto the xz and yz planes at various
times. The time is given in units of the orbital period. The model parameters are m2: m1=
1 : 2 and e = 0.5. The strenght of the image blackening corresponds to the logarithm of the
particle number per pixel.
Figure 3: Same as Figure 2 for the cold disk. The binary parameters are m2: m1= 0.7 : 2
and e = 0.5. The strenght of the image blackening corresponds to the logarithm of the
particle number per pixel.
inclination of 10oand is barely noticeable in the case with θ = 0o. This cycle originates from
the streams of matter accreting onto the binary components and periodically crossing the
line of sight. The second component in the dependence on model parameters has a period
that is approximately a factor of 6-8 longer than the orbital one. It owes its origin to the
motion of density waves in the inner CB disk region. Comparison of the solutions obtained
at the same θ, but at different binary orientations relative to the observer shows that the
relationship between these two components depends sensitively on the observer’s direction.
This dependence originates from the global CB disk asymmetry discussed above. The slow
secular turn of an asymmetric disk changes the relationship between the amplitudes of the
short and longer periods of the column density variations at the same orbital inclination.
Figures 5 and 6 show the column density variations on a long time scale (300 orbital
periods) for four orbital orientations relative to the observer corresponding to azimuth angles
φ equal to 0o, 90o, 180o, and 270o(the angles are measured from the direction of the apoastron
of the secondary in the direction opposite to its orbital motion). As has already been noted
above, in the first of these cases, the orbital apoastron of the secondary component lies
between the observer and the primary component. In the third case, the binary is viewed
from the periastron. In addition, for each of the four listed cases, we considered two orbital
inclinations: θ = 0o(Figs. 5a and 6a) and θ = 10o(Figs. 5b and 6b).
50 55 60 65 70 75 80
ϕ = 0o
θ = 0o
θ = 10o
Figure 4: Variations in column density n(θ, t) for two orbital inclinations with respect to the
observer: θ = 0o(solid line) and θ = 10o(dotted line). The orbit is turned to the observer
in such a way that the apoastron of the secondary component lies between the observer and
the primary star. The model parameters are m2: m1= 1 : 2, e = 0.5, the warm disk. The
time is given in units of the orbital period.
Slow CB disk precession produces a long-period modulation of n(θ, t). As a result, apart
from the two periodic components discussed above, a secular period is also present in the
column density variations with time. There is also a slow decrease in column density with
time common to all models that is attributable to gradual CB disk dissipation due to mass
accretion onto the binary components. The secular period of the column density variations
is equal to the precession period of the inner region of an asymmetric CB disk and is ∼ 200P
for the models presented in Fig. 2. In observations at θ = 0o, the line of sight passes through
different parts of the asymmetric gaseous ring. As a result, the values of n in the global
modulation curve for the same time, but for different orbital orientations relative to the
observer are different (Figs. 5a and 6a). In the directions (along the line of sight) where the
disk is more extended, the column density is higher.
In observations at θ = 10o, the picture is significantly different (Figs. 5b and 6b). Over
fairly long time intervals, the column density decreases almost to zero. At these times, the
thin side of the disk is turned to the observer and the line of sight hardly touches it. The
small n variations in these time intervals stem from the fact that the line of sight periodically
crosses the stream of matter directed to the secondary component. Thus, because of the CB
disk precession, a young binary whose equatorial plane is slightly inclined to the line of sight
can be observable in certain time intervals and may turn out to be completely occulted from
the observer by its own CB disk after a lapse of time and this occultation can last very long.
In general case, the three different (in duration) periods of the column density variations
manifest themselves as follows. The secular (precession) period manifests itself clearly in the
models with both circular and eccentric orbits. A decrease in viscosity causes an increase in
precession period (for the models with e = 0.5 and m2: m1= 0.7 : 2, the secular period for
the cold disk increases by almost a factor of 2 compared to the warm model and is ∼ 400P).
For binaries with high eccentricities (e = 0.5,0.7), the period related to the motion of density
waves at the inner disk boundary (5-8 orbital periods, depending on the model parameters)
is superimposed on the secular period. This second period shows up particularly clearly at
the maxima of the secular n(θ, t) modulation amplitudes (Figs. 5 and 6). In this case, its
amplitude in “cold” binaries is smaller than that in “warm” ones.
Since apart from gas, there is also dust in the streams of matter penetrating from the
CB disk into the inner region of the binary, the periodic variations in column density will
be accompanied by periodic extinction variations. Taking the standard dust-to-gas ratio for
the model considered above to be 1 : 100 and the mass extinction coefficient to be 250 cm2
g−1, we estimated the photometric effect due to the periodic column density variations. The
amplitude of the V-band brightness variations in the primary component at a 10oinclination
of the binary plane to the line of sight turned out to be about 1mat an accretion rate of
10−8M⊙yr−1. In binaries with a higher accretion rate, an appreciable (in amplitude) cyclic
activity can be observed at a higher binary inclination to the line of sight.
The results of our hydrodynamic calculations presented above show that cyclic variations
in the column density of matter accreting onto the binary components can take place in
young binaries inclined at a small angle to the line of sight. The fundamental period of these
variations is equal to the orbital one and is attributable to the streams of matter in the inner
parts of the binary that are periodically projected onto the primary component. The second
period is produced by the motion of spiral density waves in the CB disk and is a factor of
5-8 longer than the orbital one. At low inclinations of the binary, both n(θ, t) oscillation
modes can be present simultaneously. The relationship between them depends both on the
inclination of the binary plane and on its orientation in space.
Apart from these two cycles, there is also a secular cycle with a duration of the order
of several hundred orbital periods in the behavior of the column density. This cycle is
attributable to the precession of the inner parts of an asymmetric CB disk. The lower the
viscosity, the longer its duration. The characteristics of the two shorter cycles (primarily
their amplitude) depend significantly on the phase of the secular cycle (Figs. 5 and 6). Note
also that the existence of a global asymmetry in the distribution of matter in the inner CB
disk region must be taken into account when the intrinsic polarization in young binary stars
The periodic variations in column density can be accompanied by noticeable extinc-
tion and brightness variations in the binary. Such variations are observed in UX Ori stars
(Shevchenko et al. 1993; Grinin et al. 1998; Rostopchina et al. 2000; Bertout 2000). The
brightness of these stars is known to undergo great variations attributable to extinction vari-
ations in circumstellar disks inclined at a small angle to the line of sight (see the review by
Grinin (2000) and references therein). Both “rapid” variability on time scales of the order
of several days with an irregular (unpredictable) pattern and slow variability on a time scale
from several to twenty years or more are observed. In a number of stars, the slow com-
ponent is cyclic in pattern. In two cases, SV Cep (Rostopchina et al. 2000) and CQ Tau
(Shakhovskoi et al. 2005), the cyclic activity is described by two oscillation modes with a
period ratio close to that obtained above (5-8). Therefore, the idea that the cyclic activity
of UX Ori stars can be the result of their latent binarity seems quite plausible.
Other objects of application of the theory considered above can be such young binaries
with abnormally long occultations as KH 15D (Winn et al. 2006), H 187 (Grinin et al. 2006;
Nordhagen et al. 2006), and GW Ori (Shevchenko et al. 1998). There are the reasons to
assume that the equatorial planes of these binaries are inclined at a small angle to the line
of sight and, hence, periodic variations in column density can take place. We are going to
return to a discussion of these questions in the next papers.
We thank Pawel Artymowicz for a helpful discussion of the questions touched upon in
the paper. This work was performed as part of the “Origin and Evolution of Stars and
Galaxies” Program of the Presidium of the Russian Academy of Sciences under support of
INTAS grant no. 03-51-6311 and grant no. NSh-8542.2006.2.
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Translated by V. Astakhov
Figure 5: Variations in column density n(θ, t) for two orbital inclinations with respect to
the observer: (a) θ = 0oand (b) θ = 10o. The variations in column density with time are
shown in each plot for one of the four orbital orientations with respect to the observer (from
the bottom upward: the angles φ between the directions of the apoastron of the secondary
component and the observer as viewed from the primary star are, respectively, 0o, 90o,
180o, and 270o). For convenience, the upper and lower plots were displaced with respect to
one another by 100 and 50 units along the y axis, respectively. The model parameters are
m2: m1= 0.7 : 2 and e = 0.5, the warm CB disk. The time is given in units of the orbital
Figure 6: Same as Figure 5 for m2: m1= 1 : 2.