Brightness oscillations in models of young binary systems with low-mass secondary components

We consider a model for the cyclic brightness variations of a young star with a low-mass companion that accretes matter from the remnants of a protostellar cloud. At small inclinations of the binary orbit to the line of sight, the streams of matter and the density waves excited in the circumbinary disk can screen the primary component of the binary from the observer. To study these phenomena, we have computed grids of hydrodynamic models for binary systems by the SPH method based on which we have calculated the phase light curves for the different orientations of the orbit. The model parameters were varied within the following ranges: the component mass ratio q = 0.01–0.1 and the eccentricity e = 0–0.5. We adopted optical grain characteristics typical of circumstellar dust. Our computations have shown that the brightness oscillations with orbital phase can have a complex structure. The amplitudes and shapes of the light curves depend strongly on the inclination of the binary orbit and its orientation relative to the observer and on the accretion rate. The results of our computations are used to analyze the cyclic activity of UX Ori stars.     

Bimodal brightness oscillations in models of young binary systems

We consider a model for the cyclic activity of young binary stars that accrete matter from the remnants of a protostellar cloud. If the orbit of such a binary system is inclined at a small angle to the line of sight, then the streams of matter and the density waves excited in the circumbinary disk can screen the primary component of the binary from the observer. To study these phenomena by the SPH (smoothed particle hydrodynamics) method, we have computed grids of hydrodynamic models for binary systems based on which we have constructed the light curves as a function of the orbital phase. The main emphasis is on investigating the properties of the brightness oscillations. Therefore, the model parameters were varied within the following ranges: the component mass ratio q = M ₂: M ₁ = 0.2–0.5 and the eccentricity = 0–0.7. The parameter that defined the binary viscosity was also varied. We adopted optical grain characteristics typical of circumstellar dust. Our computations have shown that bimodal oscillations are excited in binaries with eccentric orbits, provided that the binary components do not differ too much in mass. In this case, the ratios of the periods and amplitudes of the bimodal oscillations and their shape depend strongly on the inclination of the binary plane and its orientation relative to the observer. Our analysis shows that the computed light curves can be used in interpreting the cyclic activity of UX Ori stars.     

Hydrodynamic processes in young binaries as a source of cyclic variations in circumstellar extinction

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 ^m at a mass accretion rate onto the binary components of 10.8^?8 M _⊙ 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 stars.     

On the origin of the azimuthal asymmetry in pole-on protoplanetary disks: The case of LkHα 101

The model of a protoplanetary disk around a star with a low-mass companion (M ₂: M ₁ ≤ 0.1) moving in a circular orbit inclined at a small angle to the disk plane (≤10°) is considered. The SPH method is used to calculate the hydrodynamic flows. The orbital motion of the companion leads to a nonuniform distribution of matter in the disk: a matter-free gap, density waves, and gas flows are formed in it. As a result of perturbations, the inner part of the disk is inclined relative to its periphery and does not coincide with the orbital plane of the companion either. This leads to an anisotropic illumination of the disk by the star and, as a consequence, to the appearance of a large-scale inhomogeneity in the disk image: it has a bright horseshoe-shaped region and a small shadow zone located asymmetrically relative to the line of nodes. An asymmetry of the disk image is clearly seen even when it is viewed pole-on. The orbital motion of the companion does not lead to any synchronous motion of the dark (shadow) and bright regions: they only execute small oscillations relative to some preferential direction. The asymmetric image of the disk around the star LkHα 101 seen nearly pole-on can be reproduced rather accurately within the proposed model. A study of such asymmetric disks opens up new opportunities for the search of massive bodies in the neighborhoods of young stars.     

SPH simulations of structures in protoplanetary disks

Using the GADGET-2 code modified by us, we have computed hydrodynamic models of a protoplanetary disk perturbed by a low-mass companion. We have considered the cases of circular and eccentric orbits coplanar with the disk and inclined relative to its midplane. During our simulations we computed the column density of test particles on the line of sight between the central star and observer. On this basis we computed the column density of circumstellar dust by assuming the dust and gas to be well mixed with a mass ratio of 1: 100. To study the influence of the disk orientation relative to the observer on the interstellar extinction, we performed our computations for four inclinations of the line of sight to the disk plane and eight azimuthal directions. The column densities in the circumstellar disk of the central star and the circumbinary disk were computed separately. Our computations have shown that periodic column density oscillations can arise in both inner and circumbinary disks. The amplitude and shape of these oscillations depend on the system’s parameters (the orbital eccentricity and inclination, the component mass ratio) and its orientation in space. The results of our simulations can be used to explain the cyclic brightness variations of young UX Ori stars.     

Stellar Wind as a Stimulator of Accretion Activity in Young Binary Systems

A young binary system is considered, having a mass ratio of components M ₂/M ₁ 1, in which the low-velocity part of the stellar wind of the low-mass component (the so-called disk wind) can be partially captured by the gravitation of the primary component. It is shown that a large-scale redistribution of matter and angular momentum between the inner and outer parts of the gas-dust disk surrounding the binary system occurs as a result, with a consequent increase in the rate of accretion onto the primary component. In cases in which the orbital eccentricity of the secondary component is nonzero, modulation of the rate of accretion onto the primary component should be observed with a period equal to the orbital period, while in the case of a highly elongated orbit the mass accretion acquires a pulsed character. Since dust may be present in the disk wind from the secondary component, the capture of stellar wind will result in an increase in the effective geometrical thickness of the gas-dust disk. For this reason, the infrared (IR) emission excesses of such stars (especially in the near-IR range) and their intrinsic polarization can be considerably greater than in the case of a single star surrounded by a circumstellar disk of the same mass, and a periodic component may also be present in their behavior with time. Moreover, because of disruption of the axial symmetry in the dust distribution in the vicinity of the young binary system, the orbital period may also be present in its brightness variations. The role of these effects in the physics of young stars is discussed.     

Accretion activity of young binary systems with low-mass secondary components

The accretion activity of young binaries with low-mass (q = M ₂/M ₁ ≤ 0.1) secondary components is studied. The source of accreted matter is a common disk surrounding the binary system and coplanar with its orbit. Gas dynamic models of these systems are used to calculate the rates of accretion to the components and their dependence on the phase of the orbital period is studied. It is shown that, despite its low mass, the secondary accretes matter at a relatively higher rate than the primary. This result can be regarded as an extension of the work of Artymowicz and Lubow for young binaries with components that have unequal masses. Possible astrophysical applications of the theory are discussed.     

Anisotropic illumination of a circumbinary disk in the presence of a low-mass companion

The model of a young star with a protoplanetary disk and a low-mass companion (q ≤ 0.1) moving in a circular orbit inclined to the disk plane is considered. Hydrodynamic models of such a system have been calculated by the SPH method. The perturbations in the disk caused by the orbital motion of the companion are shown to lead to a strong dependence of the disk illumination conditions on azimuth (because of extinction variations between the star and the disk surface) and, as a result, to the appearance of a large-scale asymmetry in the disk images. Calculations show that the dependence of the disk illumination on azimuth is stronger in the central part of the disk than on the periphery. The bright and dark (shadow) regions are located asymmetrically relative to the line of nodes. The sizes of these regions and their positions on the disk depend on model parameters and orbital phase. During the orbital motion, the bright and dark regions do not follow the companion but execute small-amplitude oscillations relative to some direction. The model properties described above open up new possibilities for detecting low-mass companions in the vicinity of young stars. Stars with protoplanetary disks seen face-on or at low inclinations i are best suited for this purpose.     

Models for the formation of binary and millisecond radio pulsars

The peculiar combination of a relatively short pulse period and a relatively weak surface dipole magnetic field strength of binary radio pulsars finds a consistent explanation in terms of (i) decay of the surface dipole component of neutron-star magnetic fields on a timescale of (2–5) × 10⁶ yr, in combination with (ii) spin-up of the rotation of the neutron star during a subsequent mass-transfer phase. The four known binary radio pulsars appear to fall into two different categories. Two of them, PSR 0655 + 64 and PSR 1913 + 16, have short orbital periods (<25 h) and high mass functions, indicating companion masses 0.7M⊙ (∼1 (± 0.3) M⊙ and 1.4 M⊙, respectively). The other two, PSR 0820 + 02 and PSR 1953 + 29, have long orbital periods (117d), nearly circular orbits, and low, almost identical mass functions of about 3×10^-3 M⊙, suggesting companion masses of about 0.3M⊙. It is pointed out that these two classes of systems are expected to be formed by the later evolution of binaries consisting of a neutron star and a normal companion star, in which the companion was (considerably) more massive than the neutron star, or less massive than the neutron star, respectively. In the first case the companion of the neutron star in the final system will be a massive white dwarf, in a circular orbit, or a neutron star in an eccentric orbit. In the second case the final companion to the neutron star will be a low-mass (∼ 0.3 M⊙) helium white dwarf in a wide and nearly circular orbit. In systems of the second type the neutron star was most probably formed by the accretion-induced collapse of a white dwarf. This explains in a natural way why PSR 1953 + 29 has a millisecond rotation period and PSR 0820 + 02 has not. Among the binary models proposed for the formation of the 1.5-millisecond pulsar, the only ones that appear to be viable are those in which the companion disappeared by coalescence with the neutron star. In such models the companion may have been a red dwarf of mass 0.03M⊙, a neutron star, or a massive (>0.7M⊙) white dwarf. Only in the last-mentioned case is a position of the pulsar close to the galactic plane a natural consequence. In the first-mentioned case the progenitor system most probably was a cataclysmic-variable binary in which the white dwarf collapsed by accretion.     

Analytical solution for the three-dimensional motion of a circumbinary planet around a binary star

By using the method of separating rapid and slow subsystem, we obtain an analytical solution for a stable three-dimensional motion of a circumbinary planet around a binary star. We show that the motion of the planet is more complicated than it was obtained for this situation analytically by Farago and Laskar (2010). Namely, in addition to the precession of the orbital plane of the planet around the angular momentum of the binary (found by Farago and Laskar (2010)), there is simultaneously the precession of the orbital plane of the planet within the orbital plane. We show that the frequency of this additional precession is different from the frequency of the precession of the orbital plane around the angular momentum of the binary. We demonstrate that this problem is mathematically equivalent both to the problem of the motion of a satellite around an oblate planet and to the problem of a hydrogen Rydberg atom in the field of a high-frequency linearly-polarized laser radiation, thus discovering yet another connection between astrophysics and atomic physics. We point out that all of the above physical systems have a higher than geometrical symmetry, which is a counterintuitive result. In particular, it is manifested by the fact that, while the elliptical orbit of the circumbinary planet (around a binary star) or of the satellite (around an oblate planet) or of the Rydberg electron (in the laser field) undergoes simultaneously two types of the precession, the shape of the orbit does not change. The fact that a system, consisting of a circumbinary planet around a binary star, possesses the hidden symmetry should be of a general physical interest. Our analytical results could be used for benchmarking future simulations.     

Interpretation of the light curve for the young binary (?) system UY Aur

Using visual, photographic, and photoelectric measurements, we have constructed a historical light curve for the young binary system UY Aur on an interval longer than 100 yr. About a quarter of all magnitude estimates have been obtained for the first time from photographic plates of the Sternberg Astronomical Institute and Harvard College Observatory Astronomical Plate Stacks. Analysis of the light curve and the magnitude dependences of the polarization and color has led us to the following conclusions. Cyclic variations in the seasonally mean brightness of the binary’s primary component UY Aur A with a period of ≃16.3 yr occurred from the mid-1920s to the mid-1940s and after 1986. The variations are caused by the change in the rate of disk accretion onto the star attributable to the motion of the hypothetical companion UY Aur C around the primary star in an orbit with a semimajor axis of ≃ 6 AU. From the early 1950s to the mid-1980s, the periodicity of the seasonally mean variations was not noticeable due to nonperiodic eclipses of UY Aur A by gas-dust clouds. Between 1945 and 1974, another gas-dust cloud obscured and still obscures the component UY Aur B, causing its mean optical brightness to drop by several magnitudes. The role of the clouds that caused an almost simultaneous eclipse of the stars, whose separation in projection onto the celestial sphere exceeds 100 AU, is played by the denser and puffed-up regions of their accretion disks. These regions are the result of a dynamical interaction between the binary’s stars and the outer circumbinary accretion disk. The extinction variations with time are attributable to orbital motion of the binary’s stars and azimuthal inhomogeneity of the clump regions in the disks. A number of observational tests are suggested to verify our conclusions.     

The ever challenging emission‐line binary β Lyrae

A brief history of investigations of Lyr, an emission‐line binary and one of the first ever discovered Be stars is presented. A rather fast progress in the understanding of this enigmatic object during the past fifteen years is then discussed in some detail. The current picture of β Lyr is that it is an eclipsing binary in a stage of mass transfer between the components. The mass‐losing star is a B6‐8II object, with a mass of about 3 M_⊙, which is filling the Roche lobe and sending material towards its more massive companion at a rate of about 2 × 10^—5 M_⊙ yr^—1. This leads to the observed rapid increase of the orbital period at a rate of 19 s per year. The mass‐gaining star is as early B star with a mass of about 13 M_⊙. It is completely hidden inside an opaque accretion disk, jet‐like structures, perpendicular to the orbital plane and a light‐scattering halo above the poles of the star. The observed radiation of the disk corresponds to an effective temperature which is much lower than what would correspond to an early B star. The disk shields the radiation of the central star in the directions along the orbital plane and redistributes it in the directions perpendicular to it. That is why the mass‐losing star appears brighter of the two in the optical region of the spectrum. At present, rather reliable estimates of all basic properties of the binary and its components are available. However, in spite of great progress in understanding the system in recent years, some disagreement between the existing models and observed phase variations still remains, both for continuum and line spectrum, which deserves further effort.     

Disk wind in young binaries and the origin of the cyclic activity of young stars

We present the results of our numerical simulations of the cyclic brightness modulation in young binary systems with eccentric orbits and low-mass secondary components. We suggest that the binary components accrete matter from the remnants of the protostellar cloud, with the main accretor (according to current models) being the low-mass component. The brightness variations of the primary are attributable to the periodic extinction variations on the line of sight caused by the disk wind from the secondary and by the common envelope produced by this wind. The distribution of matter in the envelope was calculated in the ballistic approximation. When calculating the optical effects produced by the dust component of the disk wind, we adopted the dust-to-gas mass ratio of 1:100 characteristic of the interstellar medium and the optical parameters of the circumstellar dust typical of young stars. Our calculations show that the theoretical light curves for binaries with elliptical orbits exhibit a wider variety of shapes than those for binaries with circular orbits. In this case, the parameters of the photometric minima (their depth, duration, and shape of the light curve) depend not only on the disk-wind parameters and the orbital inclination of the binary to the line of sight, but also on the longitude of the periastron. We investigate the modulation of the scattered radiation from the common envelope with orbital phase in the single-scattering approximation. The modulation amplitude is shown to be at a maximum when the system is seen edge-on and to be also nonzero in binaries seen pole-on. We discuss possible applications of the theory to young stellar objects. In particular, several model light curves have been found to be similar to those of candidate FU Orionis stars (FUORs).     

A new light‐time effect study of AR Aurigae

A period study of the young binary AR Aur based on the extensive series of published photoelectric/ccd minima times indicates the cyclic (O – C) variation for the system. This continuous oscillatory variation covers almost three cycles, about 6000 orbital periods, by the present observational data. It can be attributed to the light‐time effect due to a third body with a period of 23.68 ± 0.17 years in the system. The analysis yields a light‐time semi‐amplitude of 0.0084 ± 0.0002 day and an orbital eccentricity of 0.20 ± 0.04. Adopting the total mass of AR Aur, the mass of the third body assumed in the co‐planar orbit with the binary is M₃ = 0.54 ± 0.03 M_⊙ and the semimajor axis of its orbit is a₃ = 13.0 + 0.2 AU. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The orbit of the visual binary ADS 8630 (γ Vir)

We present a new orbit for the visual binary ADS 8630 = γ Vir. Although it is one of the first visual double stars discovered, its orbital elements were still poorly known. Indeed the very high eccentricity of the orbit and the difficulty of observing the pair at periastron passage in 1836 has meant that it is only now that sufficient measures of the recent close approach in 2005 have allowed an orbital analysis which predicts the angular motion to an acceptable degree of accuracy. We present a series of 35 speckle measurements of ADS 8630 obtained with PISCO in Merate between 2004 and 2006. Those measures have been crucial for determining the new orbital elements since they cover an arc of 130 degrees in the apparent orbit and include the periastron passage of 2005. The masses of the individual F0V components of the binary are found to be 1.40 M_⊙ with an accuracy of about 3%. We also investigate in detail the possibility of the presence of a third body in the system, that was proposed by other authors. The high‐angular resolution infra‐red image of γ Vir that we obtained in June 2006 with the LuckyCam instrument on the ESO NTT shows the absence of any companion as faint as a M0V star at a distance larger than 0.4″. Combined with the analysis of the residuals of our orbit, the values found for the masses of the individual components and the radial velocity measurements, this observation rules out the presence in the system of a third companion with a mass larger than 0.3 M_⊙. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Astrometric study of the triple star ADS 9173

An approximate orbit of the wide visual binary star ADS 9173 A(Bb) with a period of ～6000 yr has been determined for the first time by the method of apparent motion parameters. The orbit was computed using a short (1982–2004) arc of photographic observations obtained with the 26-inch Pulkovo Observatory refractor and the Hipparcos parallax. Agreement of the new orbit with the observations from the WDS catalog beginning in 1832 serves as a check. The errors in the orbital elements are large, but the orientation elements of the orbital plane (i and Ω) were estimated reliably. Component B has an invisible spectroscopic companion with a period of 4.9 yr. An astrometric orbit of Bb consistent with radial velocity measurements was determined from the residuals to the relative orbital motion of A(Bb). The orbital planes are nearly coplanar. If the mass of component B is taken in accordance with the mass—luminosity relation, 1.5 M _⊙, and the parallax is 0.″021, then the mass of the secondary component is no less than 0.5M _⊙. Component A may also be a long-period binary system.     

Dynamical friction on a satellite of a disk galaxy: The circular orbit

In a previous paper, we have studied dynamical friction during a parabolic passage of a companion galaxy past a disk galaxy. This paper continues with the study of satellites in circular orbits around the disk galaxy. Simulations of orbit decay in a self gravitating disk are compared with estimates based on two-body scattering theories; the theories are found to give a satisfactory explanation of the orbital changes. The disk friction is strongly dependent on the sense of rotation of the companion relative to the rotation of the disk galaxy as well as on the amount of mass in a spherical halo. The greatest amount of dynamical friction occurs in direct motion if no spherical halo is present. Then the infall time from the edge of the disk is about one half of the orbital period of the disk edge. A halo twice as massive as the disk increases the infall time four fold. The results of Quinn and Goodman, obtained with a non-self-gravitating method, agree well with our experiments with massive halos (Q ₀ 1.5), but are not usable in a more general case. We give analytic expressions for calculating the disk friction in galaxies of different disk/halo mass ratios.     

Dusty disk wind in young binary systems viewed pole-on

A model of a young binary system with companions of unequal mass whose orbital plane is inclined at a large angle to the line of sight is examined. The system components are assumed to accrete matter from the remains of the protostellar cloud. It is found that eclipsing of the primary component by the disk wind of the secondary can be observed when the plane of the orbit is inclined at a large angle to the line of sight or even when the binary system is observed pole-on. __________ Translated from Astrofizika, Vol. 51, No. 2, pp. 267–275 (May 2008).     

Stability of a planet in the HD 41004 binary system

The Hill stability criterion is applied to analyse the stability of a planet in the binary star system of HD 41004 AB, with the primary and secondary separated by 22 AU, and masses of 0.7 M_⊙ and 0.4 M_⊙, respectively. The primary hosts one planet in an S‐type orbit, and the secondary hosts a brown dwarf (18.64 M_J) on a relatively close orbit, 0.0177 AU, thereby forming another binary pair within this binary system. This star‐brown dwarf pair (HD 41004 B+Bb) is considered a single body during our numerical calculations, while the dynamics of the planet around the primary, HD 41004 Ab, is studied in different phase‐spaces. HD 41004 Ab is a 2.6 M_J planet orbiting at the distance of 1.7 AU with orbital eccentricity 0.39. For the purpose of this study, the system is reduced to a three‐body problem and is solved numerically as the elliptic restricted three‐body problem (ERTBP). The Hill stability function is used as a chaos indicator to configure and analyse the orbital stability of the planet, HD 41004 Ab. The indicator has been effective in measuring the planet's orbital perturbation due to the secondary star during its periastron passage. The calculated Hill stability time series of the planet for the coplanar case shows the stable and quasi‐periodic orbits for at least ten million years. For the reduced ERTBP the stability of the system is also studied for different values of planet's orbital inclination with the binary plane. Also, by recording the planet's ejection time from the system or collision time with a star during the integration period, stability of the system is analysed in a bigger phase‐space of the planet's orbital inclination, ≤ 90°, and its semimajor axis, 1.65–1.75 AU. Based on our analysis it is found that the system can maintain a stable configuration for the planet's orbital inclination as high as 65° relative to the binary plane. The results from the Hill stability criterion and the planet's dynamical lifetime map are found to be consistent with each other. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)