Pre-Phase A Report - Lisa - Nasa

4.4 Data analysis 117
LISA’s distance determination accuracy ∆DL/DL for MBH mergers will be roughly in
the range 0.1 % – 30 %, with ∼ 1 % being typical. This is much worse than the naive
guess of ∆DL/DL ≈ (S/N) −1 , due to correlations between DL and the various angles
describing the source. Large values of ∆DL/DL have a strong positive correlation with
large uncertainties ∆ΩL in the binary’s orientation. However LISA should determine the
masses of the two BH’s to very good accuracy indeed: typically ∆Mi/Mi ∼ 0.1%–1%.
From the simplified calculation we have described, it is clear that LISA will not have
sufficient angular resolution to determine the location of the the merging MBH binary
from the gravitational waveform alone. This is because one square degree contains of
order 104 L∗ galaxies. However, LISA could have sufficient angular resolution to facilitate
simultaneous detections in the electromagnetic spectrum. This is because for events with
S/N ∼ 103 − 104 , LISA should detect the inspiral several weeks before the final merger
phase, and LISA’s one-degree error box will be available more than a day before the final
merger. Thus the source position will be known in time to train a battery of optical,
radio, and X-ray telescopes at the roughly the right location on the sky, at precisely the
right time. One can hope that some electromagnetic flare accompanies the MBH merger
(due to the remnants of an accretion disk that one or both holes might carry with them),
which would then identify the source. Clearly this would revive the possibility of using
LISA to measure the cosmological parameters.
4.4.5 Estimation of background signals
Several types of background signals which either will or may be observable have been
discussed previously. These are:
• a confusion-limited background due to unresolved galactic binaries;
• a similar background due to extragalactic binaries;
• possible cosmic backgrounds due to phase transitions in the early universe; and
• a possible primordial cosmic background due to quantum fluctuations before inflation.
An important issue for LISA is how well we can expect to do in identifying, separating,
and quantifying these types of backgrounds.
As described earlier, backgrounds due to galactic neutron star binaries and white dwarf
binaries will be observed at frequencies up to about 1 mHz. Hundreds to thousands of
binaries of these kinds also will be observed as resolved signals, which are considerably
stronger than the background or instrumental noise. Most of these will be at frequencies
of roughly 1 mHz and higher. Their distribution in different parts of the galaxy such as the
disk and the bulge will be determined from the measured directions and the statistics of the
signal strengths. With this information, the galactic backgrounds can be modeled quite
well, and fitted to the observations. The galactic backgrounds will be quite anisotropic
because of the geometry of the galaxy.
The unresolved background due to extragalactic binaries will be quite different in nature.
A few individual binaries from the LMC and other nearby galaxies probably will be resolvable.
However, the universal background will have comparable contributions from equal
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