\documentstyle{spacekap}
\begin{opening}
\title{Spatial distribution of accreting isolated neutron stars in the
Galaxy}
\author{S.B.Popov and M.E.Prokhorov}
\institute{
Sternberg Astronomical Institute, Moscow State University,\\
119899, Universitetskii pr.13\\
e-mail: polar@xray.sai.msu.su, mike@sai.msu.su}
\date{}
 \end{opening}
 \begin{document}

\begin{abstract}

        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 $\approx 5 kpc$. 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.

\end{abstract}
\begin{thebibliography}{}
\book{Bochkarev, N.G.}{  1993}{Basics of the ISM physics}
{ Moscow Univ. Press}{}
\article{Paczynski, B.}{ 1990}{ ApJ} { 348}{ 485}
\article{Treves, A. and Colpi, M.}  {1991}{ A\& A} {241}{ 107}
\article{Zane, S., Turolla, R., Zampieri, L., Colpi, M.,
and Treves, A.}{ 1995}{ ApJ} {451}{ 739}
\end{thebibliography}{}
\noindent
Figure 1. Luminosity distribution in the R-Z plane for a Maxwellian kick
velocity (maximum of the velocity distribution at 150 km/s). Luminosity
is given in arbitrary units.

\end{document}

