Pre-Phase A Report - Lisa - Nasa

1.1 Theory of gravitational radiation 15
terns of more complicated sources and detectors. For example, a binary star system will
emit circularly polarised radiation along its orbital angular momentum axis, since from
this direction its mass motions are circular. By contrast, it will emit linearly polarised
radiation along directions in the orbital plane, since from these directions the transverse
mass motions are simple linear oscillations.
By measuring the degree of circular polarization in a wave and its orientation,
LISA can determine the angle of inclination of a binary orbit, and even the
direction of this inclination projected on the sky (to within a 90 ◦ ambiguity).
This information cannot usually be obtained by conventional observations of binary systems,
and is crucial to determining stellar masses. Note also that we see that the frequency
of the gravitational radiation from a binary is twice the frequency of the orbital motion,
since after half an orbital period the two stars have replaced one another and the mass
distribution is the same as at the beginning. (This is true even if the stars have dissimilar
masses, at least for the quadrupole radiation described below.)
Similarly, LISA will be most sensitive to sources located along a line perpendicular to the
plane containing its spacecraft, but it will have some sensitivity to sources in its plane.
As LISA orbits the Sun, its orientation in space changes (see Chapter 3 and
especially Section 4.4). This produces an amplitude modulation in a signal
received from a long-lived source, which gives some information about its
direction. Further directional information comes from LISA’s changing orbital
velocity. This results in a Doppler-induced phase modulation that can, for
sufficiently high frequencies, give very accurate positions.
This is similar to the way radio astronomers determine precise pulsar positions using only
single radio antennas with very broad antenna patterns. These issues are discussed in
detail in Section 4.4 .
For frequencies above about 3 mHz, LISA’s arm length is long enough that it can measure
the differences between the arrival times of the gravitational wave at the different
corners. This can in principle be used to triangulate positions on the sky, provided the
telemetry returns enough information to extract these timing signals. Further study is required
to determine whether the added information justifies providing the extra telemetry
bandwidth.
1.1.3 Generation of gravitational waves
We mentioned above the different approximation methods that are used to decide how
much radiation to expect from a given source. The simplest approximation, and the one
that is used for most estimates, is the lowest-order post-Newtonian formula, called the
“quadrupole formula”. Recall that the quadrupole radiation is the dominant radiation,
because conservation of energy and momentum kill off monopole and dipole gravitational
radiation. The interested reader can find a derivation of the quadrupole formula, using
only the assumptions and mathematical level we have adopted here, in Reference [7].
Corrected version 2.08 3-3-1999 9:33