## 2. The modelWe solved numerically the system of differential equations of motions in the Galactic potential, taken in the form (Paczynski 1990): with a quasi-spherical halo with a density distribution: Here The density in our model is constant in time. The local density is
calculated using data and formulae from Bochkarev (1992) and Zane et
al. (1995). For we assumed: For was assumed to be uniform: Of course, this is not accurate for small R, so for the very central part of the Galaxy our results are only a rough estimate (see Zane et al. (1996) for detailed calculation of the NS emission from the Galactic center region). For we assumed For we assumed , and being taken from Bochkarev (1992). The total gas density distribution in the
In our model we assumed that the birthrate of NS and BH is proportional to the square of the local density. Stars were assumed to be born in the Galactic plane (Z=0) with circular velocities plus additional isotropic kick velocities. For the kick velocity distribution we used the formula from Lipunov et al. (1996). This formula was constructed as an analytical approximation of the three-dimensional velocity distribution of radio pulsars from Lyne & Lorimer (1994).
For each star we computed the exact trajectory and the accretion luminosity. The accretion luminosity was calculated using Bondi's formula: . The sound velocity, , was taken to be 10 km/s everywhere. We used a mass for NS and for BH. is the density, being the mass of the hydrogen atom. The radii, , where the energy is liberated, were assumed to be equal to 10 km for NS and 90 km (i.e. , ) for BH. Calculations used a grid with a cell size 100 pc in the R-direction and 10 pc in the Z-direction. The luminosity is given on the figures in ergs per second per cubic parsec. For the normalization of our results we assumed that and in the considered volume of the Galaxy. For a Salpeter mass function with =2.35 the ratio of NS to BH is about 10 if NS are formed from stars with masses between and , and BH from stars with masses higher than . Motch et al. (1997) argued that can be ruled out, being a more probable value, but for the calculations of the distribution the total number is not so important, and for other numbers of compact objects the results (i.e. the value of the luminosity) can be easily scaled. It should be mentioned, as suggested by the unknown referee, that is required to explain that the present heavy element abundance in the Galaxy is about Z=0.02. © European Southern Observatory (ESO) 1998 Online publication: February 16, 1998 |