Modifying two-body relaxation in N-body systems by gas accretion
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abstract
We consider the effects that accretion from the interstellar medium onto the
particles of an N-body system has on the rate of two-body relaxation. To this
end, we derive an accretion-modified relaxation time by adapting Spitzer's
two-component model to include the damping effects of accretion. We consider
several different mass-dependencies and efficiency factors for the accretion
rate, as well as different mass ratios for the two components of the model.
The net effect of accretion is to accelerate mass segregation by increasing
the average mass $\bar{m}$, since the relaxation time is inversely proportional
to $\bar{m}$. Under the assumption that the accretion rate increases with the
accretor mass, there are two additional effects that accelerate mass
segregation. First, accretion acts to increase the range of any initial mass
spectrum, quickly driving the heaviest members to even higher masses. Second,
accretion acts to reduce the velocities of the accretors due to conservation of
momentum, and it is the heaviest members that are affected the most. Using our
two-component model, we quantify these effects as a function of the accretion
rate, the total cluster mass, and the component masses. We conclude by
discussing the implications of our results for the dynamical evolution of
primordial globular clusters, primarily in the context of black holes formed
from the most massive stellar progenitors.
