We compare our results with the GRANAT X-ray observations of the Galactic center (Churazov et al. 1994, Pavlinsky et al. 1994). Besides Sgr A, 11 more X-ray sources have been reported to be observed in the central region of the Galaxy ( across, which corresponds to the linear size of 750 pc 750 pc, assuming the 8.5 kpc distance to the Galactic center). Two of these sources were classified as BH-candidates by their hard power-law tails in the X-ray spectrum (similar to Cyg X-1), and the other 9 sources are X-ray transients probably containing NS.
As we noted above, the BH-candidates/X-ray transients ratio is a good indicator of the time passed after the beginning of the starburst. The number of X-ray sources containing NS increases with time and becomes approximately constant after 6 Myr. The number of binary systems with accreting BHs decreases approximately exponentially with a characteristic timescale of Myr. This is due to the fact that massive stars with as BH progenitors rapidly evolve and their number strongly decreases after several Myr. The computed BH/NS ratio is at the age of 7 Myr, which should be considered as a lower limit to the true ratio because we are not able to observe all the X-ray transients simultaneously.
As only a few BH-candidates have been found in the region so far (Churazov et al. 1994, Pavlinsky et al. 1994), some uncertainties in the estimated age of the starburst result from a poor statistics. Yet, they are partially reduced as we use relative numbers of the systems. In our calculations employing the metallicity, we used the solar abundance. As the metallicity at the Galactic center is, by a factor of two, above the solar one, it also can slightly change our results. Still, given the adopted assumptions, our calculations of the absolute numbers of the systems of different types have an accuracy of 20%; relative numbers have been calculated even with a better accuracy. Bearing in mind that not all of our assumptions are realistic, we feel that our absolute numbers are uncertain within a factor of 2-3 or so.
It is instructive to compare our results for the Galactic center starburst with what might be expected for a continuous star formation, with the average rate characteristic for the whole Galaxy. For this continuous star formation model, we would expect to observe in the region of around the Galactic center about 10% of the total number of X-ray sources in the Galaxy. Accounting for the projection effect, the fraction of the X-ray sources in the central 375 pc would be even smaller, 4 %. Meanwhile in the entire Galaxy we currently observe only one SS 433-type source (SS 433 itself), one Cyg X-1-type source (Cyg X-1 itself), and about 10 X-ray transients are being discovered every year. Hence for the Galactic center one would expect, after several years of observations with X-ray satellites, to reveal about 5 X-ray transients and, most likely, no SS 433-type or Cyg X-1-type sources at all (the probability of their appearance is very low). Therefore, the continuous star formation model is able to explain neither the absolute nor relative numbers of the X-ray sources actually observed in the Galactic center. In contrast, the starburst model presented above seems to be quite successful in this respect.
As for the the size of the starburst region, the situation seems to be less certain. Still, as we have shown in Sec. 3.2, the deepness of the central potential well does rule out a scenario in which the starburst occurs in the central 1 pc or so and then a `kick' during the stage of neutron star formation ejects the binary system till the distances 1 kpc within which the observed X-ray sources are concentrated. We have discussed another scenario according to which the starburst occurs on a scale pc as a result of collision of two molecular clouds (Ozernoy 1995). In this approach, the high velocities acquired by the infalling gas in the galactic potential well are kept by the forming massive stars, which enables them to be scattered up to 1 kpc or so. A potential problem with this scenario is that, in a contrast to the observed distribution of X-ray sources on a scale like this, the observed distribution of their progenitors, the massive stars, is apparently seen much more concentrated towards the central 1 pc. Yet it is not excluded that accounting for the unknown selection effects might weaken/remove this problem. However, even in this case, the very presence of several dozens of hot, massive stars in the central 1 pc needs to be explained. In the frame of Scenario II envisioned in Sec. 3.2, which involves the scale pc for the starburst, a possible explanation would be as follows: For the newborn stars forming as a result of collisions of the two GMCs, dispersion of their velocities increases, owing to the conservation of angular momentum, up to the free fall velocity in due course of the infall onto the center. A fraction of the material kept in the gaseous form after the dissipation might fall into the center and produce massive stars whose velocity dispersion would not exceed 100 km/s. Further numerical modelling to test this would be highly desirable. If successful, this scenario would combine formation of massive stars close to the center of the Galaxy with an opportunity to observe the massive binary successors, the X-ray systems, at very large distances from the center.
One may argue that the region of pc in size around the Galactic center is broad enough so as to be contaminated by X-ray binaries originating in the adjacent regions. However, the fraction of X-ray binaries of such type among the `field' stars (i.e. not associated with the starburst of interest) is much lower. Yet, one could imagine in the Galactic center another starburst of a similar age but on a much larger scale, compared to what is considered above, which would of course somewhat change our results; however, no evidence for such a burst is known so far (for a comprehensive review of available evidence for, and constraints to, possible recurrent starbursts in the cental regions of the Galaxy, see Hartmann 1995). We notice that the proposed scenario of the origin of X-ray sources in a comparatively compact starburst has a clear signature: the velocity of an X-ray source is (statistically) expected to be the larger the closer the source is located to the Galactic center.
The results of our modelling seem to be also relevant for studying the star formation regions in other galaxies, including starburst galaxies. In the latter, short episodes of violent star formation with a time scale of 10 Myr have been suggested to occur recurrently some billion years (Coziol & Demers 1994). As follows from our modelling of the population synthesis of X-ray sources, production of a few 10 stars in a starburst has to be accompanied by the formation of about 10 hard X-ray sources at the starburst age of 6-8 Myr (and a larger number of X-ray sources at earlier times).
To summarize, the statistics of X-ray binaries, especially the ratio of the number of systems containing a BH to the number of X-ray transients with a NS, is a sensitive function of the starburst age on a time scale of 2 to 10 Myrs. As an application, a relatively large fraction of accreting BH candidates among the observed X-ray sources at the Galactic center could be naturally explained if a starburst indeed occurred 6-8 Myr ago (Tamblyn & Rieke 1993).
Acknowledgements. This work was partly supported by a COSMION grant and by Grant No. JAP100 from the International Science Foundation and the Russian Government. V.L., S.P., K.P. and M.P. acknowledge useful discussions with I.E. Panchenko and S.N. Nazin. We are thankful to the anonymous referee whose comments helped us to improve the paper.