On the migration-induced resonances in a system of two planets with masses in the Earth mass range

We investigate orbital resonances expected to arise when a system of two planets, with masses in the range 1-4 Earth masses, undergoes convergent migration while embedded in a section of gaseous disc where the flow is laminar. We consider surface densities corresponding to 0.5-4 times that expected for a minimum mass solar nebula at 5.2 AU. Using hydrodynamic simulations we find that when the configuration is such that convergent migration occurs the planets can become locked in a first order commensurability for which the period ratio is (p+1)/p with p being an integer and migrate together maintaining it for many orbits. Relatively rapid convergent migration as tends to occur for disparate masses, results in commensurabilities with p larger than 2. However, in these cases the dynamics is found to have a stochastic character. When the convergent migration is slower, such as occurs in the equal mass case, lower p commensurabilities such as 3:2 are attained which show much greater stability. In one already known example of a system with nearly equal masses in the several Earth mass range (planets around pulsar PSR B1257+12) the two largest planets are intriguingly close to a 3:2 commensurability. A very similar behaviour is obtained when the systems are modeled using an N body code with simple prescriptions for the disc planet interaction. Using that, we found that an 8:7 resonance established in a hydrodynamic simulation run for 10-100 thousand orbits could be maintained for more than million orbits. Resonant capture leads to a rise in eccentricities that can be predicted using a simple analytic model constructed in this paper. We find that the system with the 8:7 commensurability is fully consistent with this prediction.Comment: 26 pages with 19 low resolution Postscript figures, abstract abridged, accepted for publication in MNRA

Interlayer Exchange Coupling in (Ga,Mn)As-based Superlattices

The interlayer coupling between (Ga,Mn)As ferromagnetic layers in all-semiconductor superlattices is studied theoretically within a tight-binding model, which takes into account the crystal, band and magnetic structure of the constituent superlattice components. It is shown that the mechanism originally introduced to describe the spin correlations in antiferromagnetic EuTe/PbTe superlattices, explains the experimental results observed in ferromagnetic semiconductor structures, i.e., both the antiferromagnetic coupling between ferromagnetic layers in IV-VI (EuS/PbS and EuS/YbSe) superlattices as well as the ferromagnetic interlayer coupling in III-V ((Ga,Mn)As/GaAs) multilayer structures. The model allows also to predict (Ga,Mn)As-based structures, in which an antiferromagnetic interlayer coupling could be expected.Comment: 4 pages, 3 figure

Conditions for the occurrence of mean-motion resonances in a low mass planetary system

The dynamical interactions that occur in newly formed planetary systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital resonances by migrating planets in the terrestrial mass range. Migration time scales varying between millions of years and thousands of years are considered. In the former case, for which the migration time is comparable to the lifetime of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter, relatively rapid migration regime commensurabilities of high degree such as 8:7 or 11:10 may be formed. However, in any one large-scale migration several different commensurabilities may be formed sequentially, each being associated with significant orbital evolution. We also use a simple analytic theory to develop conditions for first order commensurabilities to be formed. These depend on the degree of the commensurability, the imposed migration and circularization rates, and the planet mass ratios. These conditions are found to be consistent with the results of our simulations.Comment: 11 pages with 4 figures, pdflatex, to appear in the proceedings of the conference "Extra-solar Planets in Multi-body Systems: Theory and Observations"; eds. K. Gozdziewski, A. Niedzielski and J. Schneider, EAS Publication Serie

Two-dimensional radiation-hydrodynamic model for limit-cycle oscillations of luminous accretion disks

We investigate the time evolution of luminous accretion disks around black holes, conducting the two-dimensional radiation-hydrodynamic simulations. We adopt the alpha prescription for the viscosity. The radial-azimuthal component of viscous stress tensor is assumed to be proportional to the total pressure in the optically thick region, while the gas pressure in the optically thin regime. The viscosity parameter, alpha, is taken to be 0.1. We find the limit-cycle variation in luminosity between high and low states. When we set the mass input rate from the outer disk boundary to be 100 L_E/c^2, the luminosity suddenly rises from 0.3L_E to 2L_E, where L_E is the Eddington luminosity. It decays after retaining high value for about 40 s. Our numerical results can explain the variation amplitude and duration of the recurrent outbursts observed in microquasar, GRS 1915+105. We show that the multi-dimensional effects play an important role in the high-luminosity state. In this state, the outflow is driven by the strong radiation force, and some part of radiation energy dissipated inside the disk is swallowed by the black hole due to the photon-trapping effects. This trapped luminosity is comparable to the disk luminosity. We also calculate two more cases: one with a much larger accretion rate than the critical value for the instability and the other with the viscous stress tensor being proportional to the gas pressure only even when the radiation pressure is dominant. We find no quasi-periodic light variations in these cases. This confirms that the limit-cycle behavior found in the simulations is caused by the disk instability.Comment: 6 pages, 4 figures, accepted for publication in ApJ (ApJ 01 April 2006, v640, 2 issue

Studies of Thermally Unstable Accretion Disks around Black Holes with Adaptive Pseudo-Spectral Domain Decomposition Method I. Limit-Cycle Behavior in the Case of Moderate Viscosity

We present a numerical method for spatially 1.5-dimensional and time-dependent studies of accretion disks around black holes, that is originated from a combination of the standard pseudo-spectral method and the adaptive domain decomposition method existing in the literature, but with a number of improvements in both the numerical and physical senses. In particular, we introduce a new treatment for the connection at the interfaces of decomposed subdomains, construct an adaptive function for the mapping between the Chebyshev-Gauss-Lobatto collocation points and the physical collocation points in each subdomain, and modify the over-simplified 1-dimensional basic equations of accretion flows to account for the effects of viscous stresses in both the azimuthal and radial directions. Our method is verified by reproducing the best results obtained previously by Szuszkiewicz & Miller on the limit-cycle behavior of thermally unstable accretion disks with moderate viscosity. A new finding is that, according to our computations, the Bernoulli function of the matter in such disks is always and everywhere negative, so that outflows are unlikely to originate from these disks. We are encouraged to study the more difficult case of thermally unstable accretion disks with strong viscosity, and wish to report our results in a subsequent paper.Comment: 29 pages, 8 figures, accepted by Ap

Why Low-Mass Black-Hole Binaries Are Transient

We consider transient behavior in low-mass X-ray binaries. In short-period neutron-star systems (orbital period less than ~ 1d) irradiation of the accretion disk by the central source suppresses this except at very low mass transfer rates. Formation constraints however imply that a significant fraction of these neutron star systems have nuclear-evolved main-sequence secondaries and thus mass transfer rates low enough to be transient. But most short-period low-mass black-hole systems will form with unevolved main-sequence companions and have much higher mass transfer rates. The fact that essentially all of them are nevertheless transient shows that irradiation is weaker, as a direct consequence of the fundamental black-hole property - the lack of a hard stellar surface.Comment: 13 pages (including 3 figures); accepted for publication in Ap

Radiation pressure instability driven variability in the accreting black holes

The time dependent evolution of the accretion disk around black hole is computed. The classical description of the $\alpha$-viscosity is adopted so the evolution is driven by the instability operating in the innermost radiation-pressure dominated part of the accretion disk. We assume that the optically thick disk always extends down to the marginally stable orbit so it is never evacuated completely. We include the effect of the advection, coronal dissipation and vertical outflow. We show that the presence of the corona and/or the outflow reduce the amplitude of the outburst. If only about half of the energy is dissipated in the disk (with the other half dissipated in the corona and carried away by the outflow) the outburst amplitude and duration are consistent with observations of the microquasar GRS 1915+105. Viscous evolution explains in a natural way the lack of direct transitions from the state C to the state B in color-color diagram of this source. Further reduction of the fraction of energy dissipated in the optically thick disk switches off the outbursts which may explain why they are not seen in all high accretion rate sources being in the Very High State.Comment: 31 pages, 14 figures; accepted to Ap

A Note on Bimodal Accretion Disks

The existence of bimodal disks is investigated. Following a simple argument based on energetic considerations we show that stationary, bimodal accretion disk models in which a Shakura--Sunyaev disk (SSD) at large radii matches an advection dominated accretion flow (ADAF) at smaller radii are never possible using the standard slim disk approach, unless some extra energy flux is present. The same argument, however, predicts the possibility of a transition from an outer Shapiro--Lightman--Eardley (SLE) disk to an ADAF, and from a SLE disk to a SSD. Both types of solutions have been found.Comment: 9 pages including 9 figures, accepted for publication in The Astrophysical Journa

Dissipation Instability in the Accretion Disk

The model of a geometrically thin gaseous disk in the external gravitational potential is considered. The dinamics of small nonaxisymmetric perturbations in the plane of the accretion disk with dissipative effects is investigated. It is showed, that conditions of development and parameters of unstable oscillation modes in the opticaly thick accretion disk are strongly depended on the models of viscosity and opacity.Comment: Plain TeX, 6 pages, 2 figures (GIF), Submitted to Astron. Astrophys. Transaction