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Article overview
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Evolution of Compact-Binary Populations in Globular Clusters: A Boltzmann Study II. Introducing Stochasticity | | Sambaran Banerjee
; Pranab Ghosh
; | | Date: |
18 Feb 2008 | | 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.
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 $Gamma$ and
$gamma$, which we called Verbunt parameters in Paper I. 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. (abridged) | | Source: | arXiv, 0802.2446 | | Services: | Forum | Review | PDF | Favorites | |
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