An analytical expression for apsidal superhump precession and comparisons with numerical simulations and dwarf nova observations

We compare analytical expressions of precession rates from apsidal (positive) superhumps in close binary systems with numerical disc simulation results and observed values. In the analytical expressions, we include both the dynamical effects on the precession of the disc and effects caused by pressure forces that have been theorized to provide a retrograde effect (i.e. slowing) on the prograde disc precession. We establish new limits on density wave pitch angle to a normalized disc sound speed 60≥Ω_orb  d  tan  i / c >2.214 . Using average values for the density wave pitch angle i and speed of sound c , we find good correlation between numerical simulations and the analytical expression for the apsidal superhump period excess, which includes both the prograde and retrograde effects, for mass ratios of 0.025≤ q ≤0.33 . We also show good correlations with the four known eclipsing systems, OY Car, Z Cha, HT Cas, and WZ Sge. Our analytical expression for apsidal superhump period excess as a function of orbital period is consistent with the trend found in observed systems.     

The mass of the white dwarf in the recurrent nova U Scorpii

We present spectroscopy of the eclipsing recurrent nova U Sco. The radial velocity semi-amplitude of the primary star was found to be     from the motion of the wings of the He  ii λ 4686-Å emission line. By detecting weak absorption features from the secondary star, we find its radial velocity semi-amplitude to be     . From these parameters, we obtain a mass of     for the white dwarf primary star and a mass of     for the secondary star. The radius of the secondary is calculated to be     , confirming that it is evolved. The inclination of the system is calculated to be     , consistent with the deep eclipse seen in the light-curves. The helium emission lines are double-peaked, with the blueshifted regions of the disc being eclipsed prior to the redshifted regions, clearly indicating the presence of an accretion disc. The high mass of the white dwarf is consistent with the thermonuclear runaway model of recurrent nova outbursts, and confirms that U Sco is the best Type Ia supernova progenitor currently known. We predict that U Sco is likely to explode within ∼700 000 yr.     

A Unified Model for Black Hole X-Ray Binary Jets?

We have recently put forward a ‘unified’ semi-empirical model for the coupling between accretion and jet production in galactic black hole X-ray binaries. In this paper, we summarise this model and briefly discuss relevant considerations that have arisen since its publication.     

Forced oscillations in a hydrodynamical accretion disk and QPOs

This is the second of a series of papers aimed to look for an explanation on the generation of high frequency quasi-periodic oscillations (QPOs) in accretion disks around neutron star, black hole, and white dwarf binaries. The model is inspired by the general idea of a resonance mechanism in the accretion disk oscillations as was already pointed out by Abramowicz and Klu’zniak (2001). In a first paper (P'etri, 2005a, paper I), we showed that a rotating misaligned magnetic field of a neutron star gives rise to some resonances close to the inner edge of the accretion disk. In this second paper, we suggest that this process does also exist for an asymmetry in the gravitational potential of the compact object. We prove that the same physics applies, at least in the linear stage of the response to the disturbance in the system. This kind of asymmetry is well suited for neutron stars or white dwarfs possessing an inhomogeneous interior allowing for a deviation from a perfectly spherically symmetric gravitational field. After a discussion on the magnitude of this deformation applied to neutron stars, we show by a linear analysis that the disk initially in a cylindrically symmetric stationary state is subject to {three kinds of resonances: a corotation resonance, a Lindblad resonance due to a driven force and a parametric resonance}. In a second part, we focus on the linear response of a thin accretion disk in the 2D limit. {Waves are launched at the aforementioned resonance positions and propagate in some permitted regions inside the disk, according to the dispersion relation obtained by a WKB analysis}. In a last part, these results are confirmed and extended via non linear hydrodynamical numerical simulations performed with a pseudo-spectral code solving Euler's equations in a 2D cylindrical coordinate frame. {We found that for a weak potential perturbation, the Lindblad resonance is the only effective mechanism producing a significant density fluctuation}. In a last step, we replaced the Newtonian potential by the so called logarithmically modified pseudo-Newtonian potential in order to take into account some general-relativistic effects like the innermost stable circular orbit (ISCO). The latter potential is better suited to describe the close vicinity of a neutron star or a black hole. However, from a qualitative point of view, the resonance conditions remain the same. The highest kHz QPOs are then interpreted as the orbital frequency of the disk at locations where the response to the resonances are maximal. It is also found that strong gravity is not required to excite the resonances.     

黑洞吸积盘的演化及温度分布的热不稳定性

本文在Ｔｈｏｒｎｅ工作的基础上讨论了吸积盘中黑洞的有关参量的演化，以及由Ｓｃｈｗａｒｚｓｃｈｉｌｄ黑洞吸积盘向Ｋｅｒｒ黑洞吸积盘演化过程中对吸积盘辐射通量的影响，最后针对几个典型的辐射过程，分别讨论了黑洞吸积盘在牛顿框架中的温度分布方程与广义相对论的温度分布方程的热不稳定性，并给出此类问题的热不稳定性的判据。     

Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs

We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from 1 Earth mass (1 M_⊕) to 1 Jupiter mass (1 M_J) by using the zeus hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses   M _p≳ 0.1 M_J  produce significant perturbations in the surface density of the disc. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc mid-plane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the orbit of the planet. Much of the mass supply to the circumplanetary disc comes from non-coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 M_J and is highly efficient, occurring at the local viscous rate. The migration time-scales for planets of mass less than 0.1 M_J, based on torques from disc material outside the Roche lobes of the planets, are in excellent agreement with the linear theory of type I (non-gap) migration for three-dimensional discs. The transition from type I to type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few M_J with little migration. Planets with final masses of the order of 10 M_J would undergo large migration, which makes formation and survival difficult.