Pre-Phase A Report - Lisa - Nasa

104 Chapter 4 Measurement Sensitivity
4.4 Data analysis
The objective on data analysis for a gravitational wave detector is to reconstruct as far
as possible the incoming gravitational wave. From the reconstruction, it is possible to
make the kind of inferences about sources that we have described in Chapter 1 . The
parameters that describe the wave are:
• Its direction on the sky in, say, galactic coordinates (ℓ, b). These are constants
that must be maintained during the observation. Proper motion and parallax are
unlikely because the observations of Galactic objects are unlikely to attain better
than a few arcminutes directional accuracy. (A stochastic background will not have
a precise direction, but that caused by binaries may be anisotropic on the scale of
tens of degrees.)
• Its amplitude and polarisation, or alternatively the amplitudes of two independent
components h+ and h×, and their relative phase. For most LISA sources, these
are constant in time, or at least very slowly varying. Binary orbital precession will
cause an intrinsic amplitude modulation of the signal. As LISA orbits the Sun, the
projection of the wave on the detector will change, which also causes an apparent
amplitude modulation, even if the intrinsic amplitude and polarisation of the signal
remain constant.
• Signal phase Φ(t). Gravitational wave detectors are coherent detectors, because
their operating frequencies are low enough to allow them to track the phase of the
signal. The phase, as a function of time, contains interesting information if it is
not regular: binaries that chirp, or even coalesce, provide important clues to their
masses and distances in the phase function, and the phase function of a black-hole
binary allows LISA to track the orbit to test general relativity.
The extraction of this information from the LISA data will use the same principles that
have been developed for ground-based interferometers. But there are a number of important
differences from ground-based instruments:
• LISA’s data rate will be 103 times less than a ground-based detector, because LISA
operates at much lower frequencies. The massive data-handling problems faced by
ground-based interferometers [110] will not exist for LISA. All its data for one year
will fit on a single disc, and the computational demands of the analysis are modest.
In this section we will assume that the signal stream for LISA will consist of two
2-byte data samples per second. The actual data stream may be sampled more
rapidly, but there is no useful gravitational wave signal data above 1 Hz, so the data
stream will be anti-alias filtered and resampled at the Nyquist rate of 2 Hz.
• LISA’s 3 arms form 2 independent detectors, in the sense that they record two independent
components of the incoming gravitational wave. Ground-based detectors
will also operate in groups of 2 or more for joint detection, but signal reconstruction
and direction finding are very different, because the detectors are well-separated.
LISA can, in the unfortunate event of the failure of one spacecraft, still reliably detect
gravitational waves even operating as a single detector. This is possible because
of the next important difference.
3-3-1999 9:33 Corrected version 2.08