6.1 Enhancement of the detection rate for binary BH mergers
Coalescing binaries emit gravitational wave signals with a well known time-dependence (waveform) (see
Section 3.1 above). This allows one to use the technique of matched filtering [399
]. The signal-to-noise ratio
for a particular detector, which is characterized by the dimensionless noise rms amplitude
at a given frequency
, depends mostly on the “chirp” mass of the binary system
and its distance
. Here, we will use the simplified version for
([399]; see also [106]):
At a fixed level of
, the detection volume is proportional to
and therefore it is proportional to
. The detection rate
for binaries of a given class (NS + NS, NS + BH or BH + BH) is the
product of their coalescence rate
with the detector’s registration volume
for these
binaries.
It is seen from Table 4 that the model Galactic rate
of NS + NS coalescences is typically higher
than the rate of NS + BH and BH + BH coalescences. However, the BH mass can be significantly larger than
the NS mass. So a binary involving one or two black holes, placed at the same distance as a NS + NS binary,
produces a significantly larger amplitude of gravitational waves. With the given sensitivity of the
detector (fixed
ratio), a BH + BH binary can be seen at a greater distance than a NS + NS
binary. Hence, the registration volume for such bright binaries is significantly larger than the
registration volume for relatively weak binaries. The detection rate of a given detector depends on the
interplay between the coalescence rate and the detector’s response to the sources of one or another
kind.
If we assign some characteristic (mean) chirp mass to different types of double NS and BH systems, the
expected ratio of their detection rates by a given detector is
where
and
refer to BH + BH and NS + NS pairs, respectively. Here, we discuss the
ratio of the detection rates, rather than their absolute values. The derivation of absolute values
requires detailed evolutionary calculations, as we discussed above. Taking
(for
) and
(for
), Equation (60) yields
As
is typically 0.1 – 0.01 (see Table 4), this relation suggests that the registration rate of BH mergers
can be higher than that of NS mergers. This estimate is, of course, very rough, but it can serve as an
indication of what one can expect from detailed calculations. We stress that the effect of an enhanced
detection rate of BH binaries is independent of the desired
and other characteristics of the detector;
it was discussed, for example, in [420, 228, 124
].