Limits on Runaway Growth of Intermediate Mass Black Holes from Advanced
  LIGO
  There is growing evidence that intermediate-mass black holes (IMBHs), defined
here as having a mass in the range M=500-10^5 Msun, are present in the dense
centers of certain globular clusters (GCs). Gravitational waves (GWs) from
their mergers with other IMBHs or with stellar BHs in the cluster are mostly
emitted in frequencies <10 Hz, which unfortunately is out of reach for current
ground-based observatories such as advanced LIGO (aLIGO). Nevertheless, we show
that aLIGO measurements can be used to efficiently probe one of the possible
formation mechanisms of IMBHs in GCs, namely a runaway merger process of
stellar seed BHs. In this case, aLIGO will be sensitive to the lower-mass rungs
of the merger ladder, ranging from the seed BH mass to masses >~50-300 Msun,
where the background from standard mergers is expected to be very low. Assuming
this generic IMBH formation scenario, we calculate the mass functions that
correspond to the limiting cases of possible merger trees. Based on estimates
for the number density of GCs and taking into account the instrumental
sensitivity, we show that current observations do not effectively limit the
occupation fraction f_occ of IMBHs formed by runaway mergers of stellar BHs in
GCs. However, we find that a six-year run of aLIGO at design sensitivity will
be able to probe down to f_occ<3% at a 99.9% confidence level, either finding
evidence for this formation mechanism, or necessitating others if the fraction
of GCs that harbor IMBHs is higher.
