Spatial Distribution of Accreting Isolated Neutron Stars in the Galaxy

In the last few years, the spatial distribution of old, isolated neutron stars has become of great interest (see, for example, Treves and Colpi (1991)). Several sources of this size have been observed by ROSAT. We present here a computer model of the distribution of the luminosity produced by old, isolated neutron stars accreting from the interstellar medium.We use direct calculations of trajectories in the Galaxy potential, taken in the form given by Paczynski (1990). The system of differential equations was solved numerically. We made calculations on a grid with cell size 100 pc in the R direction and 10 pc in the Z direction (centered at R=50 pc, Z=5 pc and so on). Stars were born in the Galactic plane with a specified velocity distribution corresponding to non-symmetrical supernova explosions.In our model, we assumed that the birth rate of neutron stars is proportional to the square of the local density. The local density was calculated using the data and formulas of Bochkarev (1993) and Zane et al. (1995). We then calculated the luminosity using the Bondi formula (in the inner kiloparsec our results are only a rough estimate).We show that for various mean velocities for the old isolated neutron stars, the distribution of the luminosity has a torus-like structure, with the maximum at 5kpc. Since we made very general assumptions, we argue that this type of distribution is not unique to our Galaxy, and all spiral galaxies should have such a distribution of the luminosity density, associated with accreting old, isolated neutron stars.