SCYON Abstract

Received on February 21 2008

Evolution of Compact-Binary Populations in Globular Clusters: A Boltzmann Study II. Introducing Stochasticity

Authors	Sambaran Banerjee and Pranab Ghosh
Affiliation	Dept. of Astronomy & Astrophysics, Tata Institute of Fundamental Research, Mumbai, 400005, India
Accepted by	Astrophysical Journal
Contact	sambaran@tifr.res.in
	pranab@tifr.res.in
URL	http://arxiv.org/abs/0802.2446
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Abstract

We continue exploration of the Boltzmann scheme started in Banerjee and Ghosh (2007, henceforth Paper I) for studying the evolution of compact-binary populations of globular clusters, introducing in this paper an explicit method for describing the inherent stochasticity of the dynamical processes of binary formation, destruction and hardening in globular clusters due to stellar encounters. We describe the fluctuations in the rates of the above stochastic processes as a "Wiener process". The Boltzmann equation then becomes a stochastic partial differential equation, the solution of which involves the use of "Ito calculus" (this use being the first, to our knowledge, in this subject), in addition to ordinary calculus. As in Paper I, we focus on the evolution of (a) the number of X-ray sources N_XB in globular clusters, and (b) the orbital-period distribution of the X-ray binaries, showing explicitly the fluctuations in the results due to the stochasticity in the above processes. We show that, although the details of these fluctuations differ from one "realization" to another of the stochastic processes, the general trends of the full results follow those found in the continuous-limit study of Paper I. Indeed, the average result over many such realizations is very close to the continuous-limit result, showing the value of the latter for understanding overall trends. Extending the results of Paper I, we investigate the dependence of N_XB found by these full calculations on two essential globular-cluster properties, namely, the star-star and star-binary encounter-rate parameters Γ and γ, which we used extensively in Paper I, and which we called Verbunt parameters. We compare our computed results with those from CHANDRA observations of galactic globular clusters, showing that the expected scaling of N_XB with the Verbunt parameters is in good agreement with the observed one. We indicate how more complicated, time-dependent problems can be tackled with this scheme, and also what additional features are to be incorporated into the scheme in the future.