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Calculation of binary NS coalescence rates next up previous
Next: Effect of sources evolution Up: Evolution of the double Previous: Introduction

Calculation of binary NS coalescence rates

We have calculated the binary coalescence rate with time using the ``Scenario Machine'' code, which allows us to simulate evolution of large ensembles of binary stars in an artificial galaxy using a Monte Carlo method (see Lipunov 1992, Lipunov et al 1994, 1995 and references therein).

It is reasonable to expect a priori that the evolution of events is strongly time dependent, so the star formation history tex2html_wrap_inline211 in a galaxy is another important parameter. Therefore, by calculating the evolution of events after a tex2html_wrap_inline213 -function like star formation burst, one gets a Green function tex2html_wrap_inline215 for any arbitrary star formation history.

At the one extreme we assume instantaneous star formation at a particular redshift resulting in a stellar system which we call ``elliptical'' since stars in elliptical galaxies to a good approximation can be assumed to be old and little if any additional star formation is occuring today. Thus the event rates in ``ellipticals'' can be described by the computed Green function. At the other extreme, constant star formation ( tex2html_wrap_inline217 ) would result in ``spiral''-like stellar systems. Irregular galaxies have probably also an irregular star formation history, but their contribution to the overall event rate hardly exceeds their fraction among all galaxies, that is tex2html_wrap_inline219 , so we neglect them in this context.

The source evolution in a galaxy with given star formation rate tex2html_wrap_inline211 is thus calculated as tex2html_wrap_inline223 , where tex2html_wrap_inline225 is the redshift at the turn-on of star formation, which is the second important parameter of the model. Assuming to the zero approximation tex2html_wrap_inline227 , we get tex2html_wrap_inline229 .

We parametrize the star formation history in the Universe by the fractional part of the luminous baryonic matter entering into elliptical galaxies, tex2html_wrap_inline231 , where E and S refer to ``elliptical'' galaxies (i.e. without additional star formation) and ``spiral'' galaxies (with a constant star formation rate). In fact, this parameter must be higher than the presently observed fraction of elliptical galaxies, as any galaxy must have had more violent star formation at earlier time. The galaxies are supposed to be formed at the moment tex2html_wrap_inline225 with the initial star formation during first 500 million years. The mean number of galaxies each of tex2html_wrap_inline239 was taken tex2html_wrap_inline241 per cubic megaparsec (this roughly corresponds to a density of baryonic matter in galaxies without hidden mass of tex2html_wrap_inline243 ).

We assumed an initial distributions of binary stars similar to those presently observed in our Galaxy (a Salpeter function for mass tex2html_wrap_inline245 of the primary component, tex2html_wrap_inline247 and a flat distribution of the initial binary separations A: f(log A) = const). Based on findings by the ``Scenario Machine'' analysis of the evolutionary scenario by Lipunov et al. (1995), we take the initial mass ratio distribution in a power-law form tex2html_wrap_inline253 and the efficiency coefficient of angular momentum removal at the common envelope stage tex2html_wrap_inline255 (as defined by van den Heuvel 1994).


next up previous
Next: Effect of sources evolution Up: Evolution of the double Previous: Introduction

Mike E. Prokhorov
Tue Aug 20 18:36:42 MSD 1996