Formation of Massive Black Holes in Dense Star Clusters. II. IMF and
  Primordial Mass Segregation
  A promising mechanism to form intermediate-mass black holes (IMBHs) is the
runaway merger in dense star clusters, where main-sequence stars collide and
form a very massive star (VMS), which then collapses to a black hole. In this
paper we study the effects of primordial mass segregation and the importance of
the stellar initial mass function (IMF) on the runaway growth of VMSs using a
dynamical Monte Carlo code for N-body systems with N as high as 10^6 stars. Our
code now includes an explicit treatment of all stellar collisions. We place
special emphasis on the possibility of top-heavy IMFs, as observed in some very
young massive clusters. We find that both primordial mass segregation and the
shape of the IMF affect the rate of core collapse of star clusters and thus the
time of the runaway. When we include primordial mass segregation we generally
see a decrease in core collapse time (tcc). Moreover, primordial mass
segregation increases the average mass in the core, thus reducing the central
relaxation time, which also decreases tcc. The final mass of the VMS formed is
always close to \sim 10^-3 of the total cluster mass, in agreement with the
previous studies and is reminiscent of the observed correlation between the
central black hole mass and the bulge mass of the galaxies. As the degree of
primordial mass segregation is increased, the mass of the VMS increases at most
by a factor of 3. Flatter IMFs generally increase the average mass in the whole
cluster, which increases tcc. For the range of IMFs investigated in this paper,
this increase in tcc is to some degree balanced by stellar collisions, which
accelerate core collapse. Thus there is no significant change in tcc for the
somewhat flatter global IMFs observed in very young massive clusters.
