On possible circumbinary configurations of the planetary systems of α Centauri and EZ Aquarii

Possible configurations of the planetary systems of the binary stars α Cen A–BandEZAqr A–C are analyzed. The P-type orbits—circumbinary ones, i.e., the orbits around both stars of the binary, are studied. The choice of these systems is dictated by the fact that α Cen is closest to us in the Galaxy, while EZ Aqr is the closest system whose circumbinary planets, as it turns out, may reside in the “habitability zone.” The analysis has been performed within the framework of the planar restricted three-body problem. The stability diagrams of circumbinary motion have been constructed: on representative sets of initial data (in the pericentric distance–eccentricity plane), we have computed the Lyapunov spectra of planetary motion and identified the domains of regular and chaotic motion through their statistical analysis. Based on present views of the dynamics and architecture of circumbinary planetary systems, we have determined the most probable planetary orbits to be at the centers of the main resonance cells, at the boundary of the dynamical chaos domain around the parent binary star, which allows the semimajor axes of the orbits to be predicted. In the case of EZ Aqr, the orbit of the circumbinary planet is near the habitability zone and, given that the boundary of this zone is uncertain, may belong to it.     

The mass ratio distribution of MBH binaries in the hierarchical model

We present different mass ratio distributions of massive black hole(MBH)binaries due to different mechanisms involved in binary evolution. A binary system of MBHs forms after the merger of two galaxies, which has three stages: the dynamical friction stage, the stellar scattering or circumbinary disk stage, and the gravitational radiation stage. The second stage was once believed to be the "final parsec problem"(FPP) as the binary stalled at this stage because of the depletion of stars. Now, the FPP has been shown to no longer be a problem. Here we get two different mass ratio distributions of MBH binaries under two mechanisms, stellar scattering and the circumbinary disk interaction. For the circumbinary disk mechanism, we assume that the binary shrinks by interaction with a circumbinary disk and the two black holes(BHs)have different accretion rates in the simulation. We apply this simple assumption to the hierarchical coevolution model of MBHs and dark matter halos, and we find that there will be more equal-mass MBH binaries in the final coalescence for the case where the circumbinary mechanism operates. This is mainly because the secondary BH in the circumbinary disk system accretes at a higher rate than the primary one.     

On the evolution of giant protoplanets forming in circumbinary discs

We present the results of hydrodynamic simulations of Jovian mass protoplanets that form in circumbinary discs. The simulations follow the orbital evolution of the binary plus protoplanet system acting under their mutual gravitational forces, and forces exerted by the viscous circumbinary disc. The evolution involves the clearing of the inner circumbinary disc initially, so that the binary plus protoplanet system orbits within a low density cavity. Continued interaction between disc and protoplanet causes inward migration of the planet towards the inner binary. Subsequent evolution can take three distinct paths: (i) the protoplanet enters the 4 : 1 mean motion resonance with the binary, but is gravitationally scattered through a close encounter with the secondary star; (ii) the protoplanet enters the 4 : 1 mean motion resonance, the resonance breaks, and the planet remains in a stable orbit just outside the resonance; (iii) when the binary has initial eccentricity   e _bin≥ 0.2  , the disc becomes eccentric, leading to a stalling of the planet migration, and the formation of a stable circumbinary planet.
These results have implications for a number of issues in the study of extrasolar planets. The ejection of protoplanets in close binary systems provides a source of 'free-floating planets', which have been discovered recently. The formation of a large, tidally truncated cavity may provide an observational signature of circumbinary planets during formation. The existence of protoplanets orbiting stably just outside a mean motion resonance (4 : 1) in the simulations indicate that such sites may harbour planets in binary star systems, and these could potentially be observed. Finally, the formation of stable circumbinary planets in eccentric binary systems indicates that circumbinary planets may not be uncommon.     

Near-infrared polarimetry of the GG Tauri A binary system

A high angular resolution near-infrared image that shows the intensity of polarization for the GG Tau A binary system was obtained with the Subaru Telescope.The image shows a circumbinary disk scattering the light from the central binary. The azimuthal profile of the intensity of polarization for the circumbinary disk is roughly reproduced by a simple disk model with the Henyey-Greenstein phase function and the Rayleigh function, indicating there are small dust grains at the surface of the disk.Combined with a previous observation of the circumbinary disk, our image indicates that the gap structure in the circumbinary disk orbits counterclockwise, but material in the disk orbits clockwise. We propose that there is a shadow caused by material located between the central binary and the circumbinary disk. The separations and position angles of the stellar components of the binary in the past 20 yr are consistent with the binary orbit with a = 33.4 AU and e = 0.34.     

GG Tau: the ringworld and beyond

In binary stellar systems, exoplanet searches have revealed planetary mass companions orbiting both in circumstellar and in circumbinary orbits. Modelling studies suggest increased dynamical complexity around the young stars that form such systems. Circumstellar and circumbinary disks likely exhibit different physical conditions for planet formation, which also depends on the stellar separation. Although binaries and higher order multiple stars are relatively common in nearby star-forming regions, surprisingly few systems with circumbinary distributions of proto-planetary material have been found. With its spectacular ring of dust and gas encircling the central triple star, one such system, GG Tau A, has become a unique laboratory for investigating the physics of circumsystem gas and dust evolution. We review here its physical properties.     

Enhanced Activity in Close T Tauri Binaries

The number of confirmed and suspected close T Tauri binaries (period days) is increasing. We discuss some systems with enhanced emission line activity and periodic line profile changes. Non-axisymmetric flows of plasma in the region between the circumbinary disk and the stars can be generated through the influence of the secondary component. Such enhanced activity is found around binaries with eccentric as well as circular orbits. We discuss our observations of the T Tauri stars RW Aurigae A and RU Lupi, which may host very close brown dwarf companions. Model simulations indicate that non-axisymmetric flows are generated around close binaries with circumbinary disks, also in systems with circular orbits.     

Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems.     

On the dynamics of the exoplanetary system Kepler-413

This study is concerned with the stability of motion of the circumbinary exoplanet Kepler-413b. The analysis is performed within the framework of a flat restricted three-body problem. The stability diagram is plotted in the plane of initial conditions “pericentric distance—eccentricity” using mass calculations of Lyapunov exponents. According to the diagram, the Kepler-413b planet is located in a stable resonance cell, confined by the mean-motion resonances 6: 1 and 7: 1 with a central binary star, which agrees with the conclusions of Kostov et al. (2014) based on calculations of the MEGNO parameter. It is shown that the value of the critical semimajor axis acquired from the empirical formula of Holman and Wiegert (1999) almost coincides with the value obtained directly from the stability diagram; at low and moderate eccentricities of the planetary orbit, the position of the calculated boundary of the chaos zone is in close agreement with the boundary predicted by Shevchenko’s theory (2015). If the planet were in the instability zone, its characteristic Lyapunov time would be only ~1 year. In accordance with the conclusions of Kostov et al. (2014), it has been shown that the planet Kepler-413b is outside the habitability zone of the system.     

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.     

On the stability of circumbinary planetary systems

The dynamics of circumbinary planetary systems (the systems in which the planets orbit a central binary) with a small binary mass ratio discovered to date is considered. The domains of chaotic motion have been revealed in the “pericentric distance–eccentricity” plane of initial conditions for the planetary orbits through numerical experiments. Based on an analytical criterion for the chaoticity of planetary orbits in binary star systems, we have constructed theoretical curves that describe the global boundary of the chaotic zone around the central binary for each of the systems. In addition, based on Mardling’s theory describing the separate resonance “teeth” (corresponding to integer resonances between the orbital periods of a planet and the binary), we have constructed the local boundaries of chaos. Both theoretical models are shown to describe adequately the boundaries of chaos on the numerically constructed stability diagrams, suggesting that these theories are efficient in providing analytical criteria for the chaoticity of planetary orbits.     

Variations of broad emission lines from periodicity QSOs under the interpretation of supermassive binary black holes with misaligned circumbinary broad line regions

Quasars with periodic light curves are considered as candidates of supermassive binary black hole(BBH) systems.One way for further confirmations may be searching for other characteristic signatures,such as those in their broad emission lines(BELs),if any,which require a thorough understanding on the response of BELs to the BBH systems.In Ji et al.(2021),we have investigated the response of circumbinary broad line region(BLR) to the central active secondary black hole under the relativistic Doppler boosting(BBH-DB) and intrinsic variation(BBH-IntDB) dominant mechanisms for continuum variation by assuming the middle plane of the BLR aligned with the BBH orbital plane.In this paper,we explore how the BEL profiles vary when the BLR is misaligned from the BBH orbital plane with different offset angles under both the BBH-DB and BBH-IntDB scenarios.Given a fixed inclination angle of the BBH orbital plane viewed in edge-on and similar continuum light curves produced by the two scenarios,increasing offset angles make the initial opening angle of the circumbinary BLR enlarged due to orbital precession caused by the BBH system,especially for clouds in the inner region,which result in Lorentzlike BEL profiles for the BBH-DB model but still Gaussion-like profiles for the BBH-IntDB model at the vertical BLR case.The amplitude of profile variations decreases with increasing offset angles for the BBHDB scenario,while keeps nearly constant for the BBH-IntDB scenario,since the Doppler boosting effect is motion direction preferred but the intrinsic variation is radiated isotropically.If the circumbinary BLR is composed of a coplanar and a vertical components with their number of clouds following the mass ratio of the BBHs,then the bi-BLR features are more significant for the BBH-IntDB model that requires larger mass ratio to generate similar continuum variation than the BBH-DB model.     

Novae ejecta as colliding shells

Following on our initial absorption-line analysis of fifteen novae spectra we present additional evidence for the existence of two distinct components of novae ejecta having different origins. As argued in Paper I one component is the rapidly expanding gas ejected from the outer layers of the white dwarf by the outburst. The second component is pre-existing outer, more slowly expanding circumbinary gas that represents ejecta from the secondary star or accretion disk. We present measurements of the emission-line widths that show them to be significantly narrower than the broad P Cygni profiles that immediately precede them. The emission profiles of novae in the nebular phase are distinctly rectangular, i.e., strongly suggestive of emission from a relatively thin, roughly spherical shell. We thus interpret novae spectral evolution in terms of the collision between the two components of ejecta, which converts the early absorption spectrum to an emission-line spectrum within weeks of the outburst. The narrow emission widths require the outer circumbinary gas to be much more massive than the white dwarf ejecta, thereby slowing the latter’s expansion upon collision. The presence of a large reservoir of circumbinary gas at the time of outburst is suggestive that novae outbursts may sometime be triggered by collapse of gas onto the white dwarf, as occurs for dwarf novae, rather than steady mass transfer through the inner Lagrangian point.     

Predicting the properties of binary stellar systems: the evolution of accreting protobinary systems

We investigate the formation of binary stellar systems. We consider a model where a 'seed' protobinary system forms, via fragmentation, within a collapsing molecular cloud core and evolves to its final mass by accreting material from an infalling gaseous envelope. This accretion alters the mass ratio and orbit of the binary, and is largely responsible for forming the circumstellar and/or circumbinary discs.
Given this model for binary formation, we predict the properties of binary systems and how they depend on the initial conditions within the molecular cloud core. We predict that there should be a continuous trend such that closer binaries are more likely to have equal-mass components and are more likely to have circumbinary discs than wider systems. Comparing our results with observations, we find that the observed mass-ratio distributions of binaries and the frequency of circumbinary discs as a function of separation are most easily reproduced if the progenitor molecular cloud cores have radial density profiles between uniform and 1/ r (e.g., Gaussian) with near-uniform rotation. This is in good agreement with the observed properties of pre-stellar cores. Conversely, we find that the observed properties of binaries cannot be reproduced if the cloud cores are in solid-body rotation and have initial density profiles which are strongly centrally condensed. Finally, in agreement with the radial-velocity searches for extrasolar planets, we find that it is very difficult to form a brown dwarf companion to a solar-type star with a separation ≲10 au, but that the frequency of brown dwarf companions should increase with larger separations or lower mass primaries.     

On the ephemeris of the eclipsing polar HU Aquarii

The magnetic cataclysmic variable HU Aquarii displayed pronounced quasi‐periodic modulations of its eclipse timing. These were interpreted in terms of the light‐travel time (LTT) effect caused by a circumbinary planet or planetary system. We report new photometric observations that revealed another precise eclipse timing for the October 2013 epoch, the first obtained in a high accretion state after many years in low or intermediate states. The eclipse was observed to occur earlier by 95.3 ± 2.0 s or 62.8 ± 2.0 s than expected for an assumed linear or quadratic ephemeris, respectively. The implied apparent strong evolution of the orbital period calls for a revision of the current planetary model or the planetary parameters. The object deserves further monitoring to uncover the true nature of the observed variability and to constrain the properties of the proposed planet or planetary system. The new observations prove that advanced amateur equipment can successfully be used in the growing field of planet search in wide circumbinary orbits via the LTT effect. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Factors affecting the motion of interplanetary dust particles

In this paper the dynamics of individual dust particles and the effects on their motion caused by insolation and consequent evaporation is considered. Evaporation rates and the radii of dust-free zones have been computed using thermodynamic data from various sources. Some doubt is thrown on the validity of the process of matching observed thermal emission peaks with theoretical evaporation zone radii.     

The effect of Kelvin-Helmholtz instability on rising flux tubes in the convection zone

If the solar dynamo operates at the bottom of the convection zone, then the magnetic flux created there has to rise to the surface. When the convection zone is regarded as passive, the rising flux is deflected by the Coriolis force to emerge at rather high latitudes, poleward of typical sunspot zones (Choudhuri and Gilman, 1987; Choudhuri, 1989). Choudhuri and D'Silva (1990) included the effects of convective turbulence on the rising flux through (a) giant cell drag and (b) momentum exchange by small-scale turbulence. The momentum exchange mechanism could enable flux tubes of radii not more than a few hundred km to emerge radially at low latitudes, but the giant cell drag mechanism required unrealistically small flux tube radii (a few meters for a reasonable giant cell upflow) to counteract the Coriolis force. We now include the additional effect of Kelvin-Helmholtz instability in a symmetrical flux ring caused by the azimuthal flow induced during its rise. The azimuthal flow crosses the threshold for the instability only if there is a giant cell upflow to drag the flux tubes appreciably. In the absence of such a drag, as in the case of a passive convection zone or in the case of momentum exchange by small-scale turbulence, the azimuthal velocity never becomes large enough to cause the instability, leaving the results of the previous calculations unaltered. The giant cell drag, aided by Kelvin-Helmholtz instability, however, becomes now a viable mechanism for curbing the Coriolis force - 10⁴ G flux tubes with radii of a few hundred km being dragged radially by upflows of 70 m s^-1.     

Modulation of circumstellar extinction in a young binary system with a low-mass companion in a noncoplanar orbit

We consider a model of cyclic brightness variations in a young star with a low-mass (q = M ₂/M ₁ ≤ 0.1) companion that accretes matter from the remnants of a protostellar cloud (circumbinary disk). We assume that the orbit of the companion is circular and that its plane does not coincide with the disk plane. We have computed grids of hydrodynamic models for such a binary by the SPH method based on which we have investigated the circumstellar extinction variations produced by the streams of matter and density waves excited in the circumbinary disk by the orbital motion of the companion. We show that, depending on the inclination and orientation of the binary’s line of nodes relative to the observer, the brightness of the primary component can undergo various (in shape and depth) oscillations with a period equal to the orbital one. In contrast to the models with coplanar circular orbits, the accretion rate onto the components of a binary with a noncoplanar orbit depends on the orbital phase. The results of our computations can be used to study the cyclic activity of UX Ori stars and young eclipsing binaries with anomalously long eclipses.     

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.     

Orbital Evolution of Dust Particles in the Sublimation Zone near the Sun

We have performed the calculations of the orbital evolution of dust particles from volcanic glass (p-obsidian), basalt, astrosilicate, olivine, and pyroxene in the sublimation zone near the Sun. The sublimation (evaporation) rate is determined by the temperature of dust particles depending on their radius, material, and distance to the Sun. All practically important parameters that characterize the interaction of spherical dust particles with the radiation are calculated using the Mie theory. The influence of radiation and solar wind pressure, as well as the Poynting–Robertson drag force effects on the dust dynamics, are also taken into account. According to the observations (Shestakova and Demchenko, 2016), the boundary of the dust-free zone is 7.0–7.6 solar radii for standard particles of the zodiacal cloud and 9.1–9.2 solar radii for cometary particles. The closest agreement is obtained for basalt particles and certain kinds of olivine, pyroxene, and volcanic glass.     

On the rotation period of Capella

We present differential Hα and Hβ photometry of the very bright RS CVn‐binary α Aurigae (Capella)obtained with theVienna automatic photoelectric telescope in the years 1996 through 2000. Low‐level photometric variations of up to 0^m_.04 are detected in Hα. A multifrequency analysis suggests two real periods of 106 ± 3 days and 8.64 ± 0.09 days, that we interpret to be the rotation periods of the cool and the hot component of the Capella binary, respectively. These periods confirm that the hotter component of Capella rotates asynchronously, while the cooler component appears to be synchronized with the binary motion. The combined Hα data possibly contains an additional period of 80.4 days that we, however, believe is either spurious and was introduced due to seasonal amplitude variations or stems from a time‐variable circumbinary mass flow. The rotational periods result in stellar radii of 14.3 ± 4.6 R_⊙ and 8.5 ± 0.5 R_⊙ for the cool and hot component, respectively, and are in good agreement with previously published radii based on radiometric and interferometric techniques. The long‐period eclipsing binary Aurigae served as our check star, and we detected complex light variations outside of eclipse of up to 0^m_.15 in H α and 0^m_.20 in Hβ. Our frequency analysis suggests the existence of at least three significant periods of 132, 89, and 73 days. One of our comparison stars (HD 33167, F5V) was discovered to be a very‐low amplitude variable with a period of 2.6360 ± 0.0055 days.