## 4. Collision rate and X-ray fluxLet us now estimate the number of HNS and their consequent X-ray luminosity. We assume a number of neutron stars spherically distributed in the galaxy (up to the radius kpc) and a number of dark clusters (assumed for simplicity of the same mass ). Here is the fraction of dark matter in the form of molecular clouds. According to the standard halo model (see e.g. De Paolis, Ingrosso & Jetzer 1996d ), the dark cluster number density is given by where pc As regard the spatial distribution of the neutron stars, for the
sake of simplicity, we assume the same distribution law as for the
dark matter in Eq. (1), but with a different core radius The collision rate , i.e. the number of HNS colliding (per second) with dark clusters, is given by where is the effective cross-section for the collision and the relative velocity between neutron stars and dark clusters. The obtained values of are in the range correspondingly to the extreme cases of kpc and kpc, respectively. The crossing time of a HNS in a dark cluster is
yr, so that the total number of HNS crossing
today dark clusters
From Eq. (2) and the definition of , it is straightforward to obtain the radial dependence of the HNS number density as where the local number density of HNS is given by
and results to be in the range
pc The instantaneous accretion rate into the surface of a neutron star is described by the Bondi formula (Shapiro & Teukolsky 1983 ) where (in the range 0.1-10 km
s where km is the radius of the neutron star. Therefore, according to we have and in the range and , respectively. The luminosity in Eq. (6) strongly depends
on the value of which enters with the inverse
cube power. Thus, for the same values of the density
, slower neutron stars have higher X-ray
luminosities. In the framework of our scenario, we expect in
particular that for the DCNS is of the order of
the velocity dispersion ( km s The effective temperature of the emitting
region on the surface of the neutron star can be estimated (assuming a
black body emission) by using the relation ,
where which implies substantial emission in the X-ray band, for a large
range of values of and © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |