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Star Formation Rate and Normalization of Stellar Populations

We have assumed a constant in time star formation rate and the total number of stars in the Galaxy, tex2html_wrap_inline10361 , to be such that the total mass of the galaxy is tex2html_wrap_inline10363 ; assuming the Salpeter mass function  tex2html_wrap_inline10365 , we get


where tex2html_wrap_inline10367 stands for the minimum possible mass of the main sequence star. With tex2html_wrap_inline10369 , tex2html_wrap_inline10371 and tex2html_wrap_inline10373 , we obtain tex2html_wrap_inline10375 2.6 tex2html_wrap_inline8845 tex2html_wrap_inline8911 stars in such a galaxy. This number agrees with a standard estimation of the galactic star formation rate of order of tex2html_wrap_inline10381 per year. In each run of calculations, we trace the evolution of tex2html_wrap_inline10383 binaries with initial parameters randomly distributed according to the chosen initial laws. The evolution of each binary is calculated until either it comes to the stage where both components remain unchanged (say, double BH or BH with NS in a wide enough orbit that the orbital evolution due to the GR can be neglected), or until the time of evolution reaches a maximum value, tex2html_wrap_inline10385 tex2html_wrap_inline8845 tex2html_wrap_inline9463 yr.

We calculate the total number of systems, tex2html_wrap_inline10391 , passed through a given evolutionary stage ``i'', and calculate the sum of the stage durations, tex2html_wrap_inline10395 . Then the total number of systems tex2html_wrap_inline10397 at the given evolutionary stage simultaneously existing in the Milky Way is estimated as


The number of the initial binaries was taken high enough (typically 1 million each run) to produce a significant statistics ( tex2html_wrap_inline10399 ) for every stage of interest.

Mike E. Prokhorov
Sat Feb 22 18:38:13 MSK 1997