## 2. Model propertiesIn this paper the model presented in Paper I has been improved
in different respects. A mass distribution for the stars has been
introduced as well as a star radius distribution. A more realistic
description of star collisions has been also developed by introducing:
i) the angle (between the direction
of motion of one star and the trajectory of the other one,
with
corresponding to the case of equal star velocities); ii) the impact
parameter As a first step, mass segregation has not been taken into account
in the expression for the star density distribution
(stars/pc In this expression The presence of stars of different masses has important consequences on the energetics of stellar collisions since the energy released in each collision is strictly linked to the amount of the involved mass. In fact, the energy available for emission in the collision between stars and (star masses in terms of ) is the star kinetic energy relative to the center of mass: In this expression is the mass center velocity, and is the star keplerian velocity around the central mass, .
is composed of the black hole mass
and the sum of all stellar masses
inside the sphere of radius where cm is the Schwarschild radius. The introduction of a more realistic geometry for star collisions takes into account that the relative velocity of the two stars, , is related to the angle: and that the cross section for a collision is . Since a collision can occur only if the distance between the two star centers is less or equal to the sum of the two star radii, the impact parameter is limited by the condition where Star radii, , are defined in terms of star masses by the following the relationship (Foellmi 1998) obtained from a fit over the results of stellar evolutionary models by Schaller et al. 1992. Assuming an isotropic distribution of stars, the collision rate
within a shell at a distance
Some of the parameters entering the collision description can not
be fixed from outside, these are: the distance The other parameters present in the above description have been chosen following the physical considerations described hereafter. © European Southern Observatory (ESO) 2000 Online publication: June 26, 2000 |