Pre-Phase A Report - Lisa - Nasa

1.2 Low-frequency sources of gravitational radiation 31
for this frequency range. This is done in order for give some basis for considering the
S/N ratio for the case of 10 6 M⊙ MBH masses.
It is clear that the integrated S/N ratio for some time interval cannot be obtained by
taking the ratio of two curve heights in Figure 1.4 . This is because the instrumental and
confusion noise curves correspond to 1 year of observation, and the signals of interest
sweep through quite a frequency range during this time. Instead, the S/N ratio has to
be integrated over time as the frequency changes, and the results are given in Figure 1.5 .
Here each symbol starting at the bottom left for each curve gives the integrated S/N ratio
after 1 week, 2 weeks, etc., from the beginning of the last year before coalescence. The
last symbol on each curve gives the total integrated S/N ratio up to roughly the last
stable circular orbit, but is plotted at the frequency corresponding to 0.5 weeks before
coalescence.
Signal−to−Noise Ratio
104.0 4
103.0 3
Log (S/N Ratio)
102.0 2
101.0 1
10 6 /10 6 M ⁄
10 6 −10 6 M •O
10 5 /10 5 M ⁄
10 5 −10 5 M •O
10 4 /10 4 M ⁄
MBH-MBH Binaries at z=1; Sum of
Binary Confusion Noise Estimate
plus LISA Instrumental Noise
500/500 500−500 M M ⁄ •O
S/N=5
0.0
-5.0
10
-4.5 -4.0 -3.5 -3.0
Log Frequency (Hz)
-2.5 -2.0 -1.5 -1.0
−5
10 −4
10 −3
10 −2
10 −1
10 0
Frequency (Hz)
10 4 −10 4 M •O
Figure 1.5 Cumulative weekly S/N ratios during the last year before
MBH-MBH coalescence.
Moreover, by combining the amplitude, polarisation, and chirp-rate information from
LISA’s observations, we will be able to deduce (as in Section 1.1.3) the distance to the
event. In cosmological terms, the distance measured will be the luminosity distance.
The extremely high signal-to-noise ratios that are expected in some cases are remarkable.
They mean that LISA will not just detect such events; it will be able to study them in
detail. The frequency modulation of the observed signal over a period of 3 months or more
will locate the event on the sky, and the amplitude modulation as the plane containing
LISA rotates will determine the signal’s polarisation (see Section 4.4). The scientific payoff
of observing such events will be great:
• Detection will confirm the existence of black holes, and details of the orbital evolution
will test general relativity.
Corrected version 2.08 3-3-1999 9:33