Abstract:
We discuss the statistical mechanics of rotating self-gravitating systems by allowing properly for the conservation of angular momentum. We study analytically the case of slowly rotating isothermal spheres by expanding the solutions of the Boltzmann-Poisson equation in a series of Legendre polynomials, adapting the procedure introduced by Chandrasekhar (1933) for distorted polytropes. We show how the classical spiral of Lynden-Bell & Wood (1967) in the temperature-energy plane is deformed by rotation. We find that gravitational instability occurs sooner in the microcanonical ensemble and later in the canonical ensemble. According to standard turning point arguments, the onset of the collapse coincides with the minimum energy or minimum temperature state in the series of equilibria. Interestingly, it happens to be close to the point of maximum flattening. We determine analytically the generalization of the singular isothermal solution to the case of a slowly rotating configuration. We also consider slowly rotating configurations of the self-gravitating Fermi gas at non zero temperature.

Abstract:
Quasi-spherical subsonic accretion onto slowly rotating magnetized NS is considered, when the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasi-static shell. The shell mediates the angular momentum transfer to/from the rotating NS magnetosphere by large-scale convective motions, which lead to an almost iso-angular-momentum rotation law inside the shell. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instability while taking cooling into account. The settling regime of accretion is possible for moderate X-ray luminosities L <4 10^36 erg/s. At higher luminosities a free-fall gap above the NS magnetosphere appears due to rapid Compton cooling, and accretion becomes highly non-stationary. From observations of spin-up/spin-down rates of wind accreting equilibrium XPSRs with known orbital periods (GX 301-2, Vela X-1), the main dimensionless parameters of the model and be determined and the NS magnetic field can be estimated. For equilibrium pulsars with independent measurements of the magnetic field the velocity of the stellar wind can be estimated without the use of complicated spectroscopic measurements. For non-equilibrium pulsars, a maximum possible value of the spin-down rate of the accreting neutron star exists. From observations of the spin-down rate and the X-ray luminosity in such pulsars (e. g. GX 1+4, SXP 1062 and 4U 2206+54) a lower limit on the neutron star magnetic field is obtained, which in all cases turns out to be close to the standard 10^12-10^13 G value, in agreement with cyclotron line measurements. The model explains both the spin-up/spin-down of the pulsar frequency on large time-scales and the irregular short-term frequency fluctuations, which may correlate or anti-correlate with the X-ray luminosity fluctuations.

Abstract:
In the present work, we consider the possibility of observationally testing Ho\v{r}ava gravity by using the accretion disk properties around slowly rotating black holes of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. The energy flux, temperature distribution, the emission spectrum as well as the energy conversion efficiency are obtained, and compared to the standard slowly rotating general relativistic Kerr solution. Comparing the mass accretion in a slowly rotating Kehagias-Sfetsos geometry in Ho\v{r}ava gravity with the one of a slowly rotating Kerr black hole, we verify that the intensity of the flux emerging from the disk surface is greater for the slowly rotating Kehagias-Sfetsos solution than for rotating black holes with the same geometrical mass and accretion rate. We also present the conversion efficiency of the accreting mass into radiation, and show that the rotating Kehagias-Sfetsos solution provides a much more efficient engine for the transformation of the accreting mass into radiation than the Kerr black holes. Thus, distinct signatures appear in the electromagnetic spectrum, leading to the possibility of directly testing Ho\v{r}ava gravity models by using astrophysical observations of the emission spectra from accretion disks.

Abstract:
Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.

Abstract:
We study nonaxisymmetric perturbations of rotating relativistic stars. modeled as perfect-fluid equilibria. Instability to a mode with angular dependence $\exp(im\phi)$ sets in when the frequency of the mode vanishes. The locations of these zero-frequency modes along sequences of rotating stars are computed in the framework of general relativity. We consider models of uniformly rotating stars with polytropic equations of state, finding that the relativistic models are unstable to nonaxisymmetric modes at significantly smaller values of rotation than in the Newtonian limit. Most strikingly, the m=2 bar mode can become unstable even for soft polytropes of index $N \leq 1.3$, while in Newtonian theory it becomes unstable only for stiff polytropes of index $N \leq 0.808$. If rapidly rotating neutron stars are formed by the accretion-induced collapse of white dwarfs, instability associated with these nonaxisymmetric, gravitational-wave driven modes may set an upper limit on neutron-star rotation. Consideration is restricted to perturbations that correspond to polar perturbations of a spherical star. A study of axial perturbations is in progress.

Abstract:
We analyze the temporal evolution of accretion onto rotating black holes subject to large-scale magnetic torques. Wind torques alone drive a disk towards collapse in a finite time $\sim t_{ff} E_k/E_B$, where $t_{ff}$ is the initial free-fall time and $E_k/E_B$ is the ratio of kinetic-to-poloidal magnetic energy. Additional spin-up torques from a rapidly rotating black hole can arrest the disk's inflow. We associate short/long gamma-ray bursts with hyperaccretion/suspended-accretion onto slowly/rapidly spinning black holes. This model predicts afterglow emission from short bursts, and may be tested by HETE-II.

Abstract:
We present our numerical results of two-dimensional magnetohydrodynamic (MHD) simulations of the collapse of rotating massive stars in light of the collapsar model of gamma-ray bursts (GRBs). Pushed by recent evolution calculations of GRB progenitors, we focus on lower angular momentum of the central core than the ones taken mostly in previous studies. By performing special relativistic simulations including both realistic equation of state and neutrino coolings, we follow a unprecedentedly long-term evolution of the slowly rotating collapsars up to $\sim$ 10 s, accompanied by the formation of jets and accretion disks. Our results show that for the GRB progenitors to function as collapsars, there is a critical initial angular momentum, below which matter is quickly swallowed to the central objects, no accretion disks and no MHD outflows are formed. When larger than the criteria, we find the launch of the MHD jets in the following two ways. For models with stronger initial magnetic fields, the magnetic pressure amplified inside the accretion disk can drive the MHD outflows, which makes the strong magnetic explosions like a 'magnetic tower' (type II). For the models with weaker initial magnetic fields, the magnetic tower stalls first and the subsequent MHD outflows are produced by some eventual inflows of the accreting material from the equator to the polar regions (type I). Regardless of type I or II, the jets can attain only mildly relativistic speeds with the explosion energy less than $10^{49} \erg$, which could possibly be related to the X-ray flashes. Due to high opacity for neutrinos inside the disk, we find that the luminosities of $\nu_e$ and $\bar{\nu}_e$ become almost comparable, which is advantageous for making the energy deposition rate larger.

Abstract:
The internal structure of a slowly rotating, charged black hole that is undergoing mass inflation at its inner horizon is derived. The equations governing the angular behavior decouple from the radial behavior, so all conclusions regarding inflation in a spherical charged black hole carry through unchanged for a slowly-rotating black hole. Quantities inflate only in the radial direction, not in the angular direction. Exact self-similar solutions are obtained. For sufficiently small accretion rates, the instantaneous angular motion of the accretion flow has negligible effect on the angular spacetime structure of the black hole, even if the instantaneous angular momentum of the accretion flow is large and arbitrarily oriented.

Abstract:
(Abridged.) The accretion-induced collapse (AIC) of a white dwarf (WD) may lead to the formation of a protoneutron star and a collapse-driven supernova explosion. This process represents a path alternative to thermonuclear disruption of accreting white dwarfs in Type Ia supernovae. Neutrino and gravitational-wave (GW) observations may provide crucial information necessary to reveal a potential AIC. Motivated by the need for systematic predictions of the GW signature of AIC, we present results from an extensive set of general-relativistic AIC simulations using a microphysical finite-temperature equation of state and an approximate treatment of deleptonization during collapse. Investigating a set of 114 progenitor models in rotational equilibrium, with a wide range of rotational configurations, temperatures and central densities, we extend previous Newtonian studies and find that the GW signal has a generic shape akin to what is known as a "Type III" signal in the literature. We discuss the detectability of the emitted GWs, showing that the signal-to-noise ratio for current or next-generation interferometer detectors could be high enough to detect such events in our Galaxy. Some of our AIC models form massive quasi-Keplerian accretion disks after bounce. In rapidly differentially rotating models, the disk mass can be as large as ~0.8-Msun. Slowly and/or uniformly rotating models produce much smaller disks. Finally, we find that the postbounce cores of rapidly spinning white dwarfs can reach sufficiently rapid rotation to develop a nonaxisymmetric rotational instability.

Abstract:
We investigate properties of r-modes characterized by regular eigenvalue problem in slowly rotating relativistic polytropes. Our numerical results suggest that discrete r-mode solutions for the regular eigenvalue problem exist only for restricted polytropic models. In particular the r-mode associated with l=m=2, which is considered to be the most important for gravitational radiation driven instability, do not have a discrete mode as solutions of the regular eigenvalue problem for polytropes having the polytropic index N > 1.18 even in the post-Newtonian order. Furthermore for a N=1 polytrope, which is employed as a typical neutron star model, discrete r-mode solutions for regular eigenvalue problem do not exist for stars whose relativistic factor M/R is larger than about 0.1. Here M and R are stellar mass and stellar radius, respectively.