Pre-Phase A Report - Lisa - Nasa

22 Chapter 1 Scientific Objectives
that the performance of LISA could in principle turn out to be significantly better
than shown.
2. LISA is likely to have a significantly longer lifetime than one year. The mission is
planned for 2 years, but it could last up to 10 years without exhausting on-board
supplies. As described above, its sensitivity to long-lived sources improves as the
square root of the mission duration. Not only would this lower the noise and threshold
curves, but it would also lower any gravitational-wave noise from white-dwarf
binaries, since LISA would resolve more of those sources and remove them from this
confusion-limited background.
3. LISA will actually have three arms, not two. LISA’s third arm provides necessary
redundancy for the success of the mission, but it also has an important scientific
benefit: it allows LISA to detect two distinct gravitational wave observables, which
can be thought of as formed from the signals of two different interferometers, with
on arm common to both. This improves both the sensitivity of LISA and its ability
to measure parameters, particularly the polarisation of the waves. The sensitivity
shown in Figure 1.3 is only for a single interferometer.
The two interferometers are not perfectly orthogonal, since they are not oriented at 45◦ to each other. But they are oriented differently enough so that two distinct, linearly independent
gravitational-wave observables can be formed, with similar signal-to-noise ratios.
One is the difference in arm length for the two arms of the “primary” interferometer. The
other is the length of the third arm minus the average of the lengths of the other two
arms.
The fact that the two interfermometers share a common arm means that they will have
common noise. Most of the signals in Figure 1.3 have signal-to-noise ratios that are so
large that the likelihood that the signal is caused by noise will be negligible; in this case,
the information from the two interferometers can be used to obtain extra polarization
and direction information. This will be particularly helpful for observations of relatively
short-lived sources, such as the coalescences of 10 6 M⊙ black holes, where the signal does
not last long enough to take full advantage of the amplitude and frequency modulation
produced by LISA’s orbital motion.
For signals nearer the noise limit, the second observable will still provide some increase
in the confidence of detection. Using three arms could increase the effective signal-tonoise
ratio by perhaps 20 %. And for stochastic backgrounds, the third arm will help
to discriminate such backgrounds as produced by binaries and cosmological effects from
anomalous instrumental noise. This will be considered in detail in Section 4.4 below.
The frequency of radiation emitted by a source of mass M and size R will normally be
of the same order as its natural gravitational dynamical frequency, as in Equation 1.12,
recalling that the gravitational wave frequency is twice the orbital frequency1 :
f GW = 1
2π ω GW = 1
π
GM
R 3
1/2
=3.7×10 −3
1/2
M
R
1 M⊙ 1×108 m
−3/2
Hz. (1.16)
1 An exception is a system which is emitting much less radiation than the upper limit in Equation 1.9,
such as a slowly rotating neutron star with a small lump on it. We do not expect any such sources to be
prominent at low frequencies.
3-3-1999 9:33 Corrected version 2.08