6.2 Formation rate
An estimate of the rate of the collapse of SMSs can be derived from the quasar luminosity function.
Haehnelt [99] has used the quasar luminosity function to compute the rate of GW bursts from supermassive
black holes, assuming that each quasar emits one such burst during its lifetime (and that each quasar is a
supermassive black hole). If it is assumed that each of these bursts is due to the formation of
a supermassive black hole via the collapse of a SMS, then Haehnelt’s rate estimates can be
used as estimates of the rate of SMS collapse. This rate is likely an overestimate of the SMS
collapse rate because many SMBHs may have been formed via merger. Haehnelt predicts that the
integrated event rate through redshift
ranges from
for
objects to
for
objects. Thus, as in the case of Population III stars,
a reasonable occurrence rate can be determined for an observation (luminosity) distance of
.