Modifying two-body relaxation in N-body systems by gas accretion

We consider the effects that accretion from the interstellar medium on to 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- dependences 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. Secondly, 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.