Region of the anomalous compression under Bondi-Hoyle accretion

We investigate the properties of an axisymmetric non-magnetized gas flow without angular momentum on a small compact object, in particular, on a Schwarzschild black hole in the supersonic region near the object; the velocity of the object itself is assumed to be low compared to the speed of sound at infinity. First of all, we see that the streamlines intersect (i.e., a caustic forms) on the symmetry axis at a certain distance $r_x$ from the center on the front side if the pressure gradient is neglected. The characteristic radial size of the region, in which the streamlines emerging from the sonic surface at an angle no larger than $\theta_0$ to the axis intersect, is $\Delta r= r_x\theta^2_0/3.$ To refine the flow structure in this region, we numerically compute the system in the adiabatic approximation without ignoring the pressure. We estimate the parameters of the inferred region with anomalously high matter temperature and density accompanied by anomalously high energy release.Comment: 10 pages, 2 figure

Limit theorems for random point measures generated by cooperative sequential adsorption

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity of the model is that the probability distribution of a point depends on previously allocated points. We assume that the dependence vanishes as the concentration of points tends to infinity. Under this assumption the law of large numbers, the central limit theorem and Poisson approximation are proved for the generated sequence of random point measures.Comment: 17 page

Prompt emission from tidal disruptions of white dwarfs by intermediate mass black holes

We present a qualitative picture of prompt emission from tidal disruptions of white dwarfs (WD) by intermediate mass black holes (IMBH). The smaller size of an IMBH compared to a supermassive black hole and a smaller tidal radius of a WD disruption lead to a very fast event with high peak luminosity. Magnetic field is generated in situ following the tidal disruption, which leads to effective accretion. Since large-scale magnetic field is also produced, geometrically thick super-Eddington inflow leads to a relativistic jet. The dense jet possesses a photosphere, which emits quasi-thermal radiation in soft X-rays. The source can be classified as a long low-luminosity gamma-ray burst (ll-GRB). Tidal compression of a WD causes nuclear ignition, which is observable as an accompanying supernova. We suggest that GRB060218 and SN2006aj is such a pair of ll-GRB and supernova. We argue that in a flux-limited sample the disruptions of WDs by IMBHs are more frequent then the disruptions of other stars by IMBHs