Pre-Phase A Report - Lisa - Nasa

4.4 Data analysis 107
for ground-based detectors, where an all-sky all-frequency search for unknown rotating
neutron stars in data sets of order one year in length will require a teraflop computer
to carry out to the sensitivity limit of the detectors. But in the low-frequency range of
LISA, the demands are considerably reduced. One year of data might occupy 250 MB of
storage. Given what is today an easily achieved computing speed of 1 Gflop and a memory
of 512 MB, a computer could perform a Fourier transform (the basis of the matched filter)
in a time of order one second. Searching up to 104 error boxes on the sky for binaries, or
104 different chirp masses between 1 M⊙ and 108 M⊙ for coalescing binary systems, could
be done in a day. By the time LISA is launched these will be even easier to do.
What is not trivial is searching for neutron stars and black holes falling into massive black
holes. Here the parameter space is considerably larger, since even in a few orbits the signal
can be dramatically affected by the spins of the objects and the amount of eccentricity
of the orbit. Work is underway to estimate the computational demands of this problem,
but we are confident that, by the time LISA is launched, even this filtering will not be
very difficult.
Other signals. The LISA data will also be searched for unexpected signals. By definition,
one cannot construct a matched filter for these. Instead, one implements a robust
filter that responds to a wide range of signals of a given type. Candidates for these
“discovery” filters are wavelets, fractional Fourier transforms, and nonlinear techniques
like adaptive filters. These will be developed and proved intensively on the ground-based
detectors, and LISA will benefit from that insight.
One source that is different from others is a possible random background of gravitational
waves. This appears as an extra component of the noise Sh. We will consider how to
recognise it and determine its origin in Section 4.4.5 below.
4.4.2 Angular resolution
Introduction. The LISA mission consists of 3 spacecraft forming a laser interferometric
antenna in a plane inclined 60◦ with respect to the ecliptic, the complete constellation
describing an Earth-like orbit at a distance of R =1AU from the sun and trailing the
earth in its orbit by 20◦ [111]. One spacecraft is placed at each corner of an equilateral
triangle with baselines of 5×109 m, as was sketched in Figure 2.5 .
As the LISA configuration orbits around the Sun, it appears to rotate clockwise around its
center, as viewed from the Sun, with a period of one year. This is indicated in Figure 4.8.
As a nonmoving detector would reveal no information about the directional parameters
of the source of the gravitational wave, all the information about the source parameters
is contained in the variation of the detector response that results from LISA’s orbital
motion.
Firstly, the detector’s sensitivity pattern is not isotropic; rather it projects a quadrupolar
beam pattern onto the sky, which rotates with the detector. This rotating beam pattern
modulates both the amplitude and phase of the measured waveform.
Secondly, the detector is moving relative to the source due to the periodic motion of its center
around the Sun. This Doppler-shifting of the measured gravitational wave frequency of
the results in a further phase modulation of the detector output. Both the beam-pattern
Corrected version 2.08 3-3-1999 9:33