5 research outputs found
Algebraic approach to time-delay data analysis for LISA
Cancellation of laser frequency noise in interferometers is crucial for
attaining the requisite sensitivity of the triangular 3-spacecraft LISA
configuration. Raw laser noise is several orders of magnitude above the other
noises and thus it is essential to bring it down to the level of other noises
such as shot, acceleration, etc. Since it is impossible to maintain equal
distances between spacecrafts, laser noise cancellation must be achieved by
appropriately combining the six beams with appropriate time-delays. It has been
shown in several recent papers that such combinations are possible. In this
paper, we present a rigorous and systematic formalism based on algebraic
geometrical methods involving computational commutative algebra, which
generates in principle {\it all} the data combinations cancelling the laser
frequency noise. The relevant data combinations form the first module of
syzygies, as it is called in the literature of algebraic geometry. The module
is over a polynomial ring in three variables, the three variables corresponding
to the three time-delays around the LISA triangle. Specifically, we list
several sets of generators for the module whose linear combinations with
polynomial coefficients generate the entire module. We find that this formalism
can also be extended in a straight forward way to cancel Doppler shifts due to
optical bench motions. The two modules are infact isomorphic.
We use our formalism to obtain the transfer functions for the six beams and
for the generators. We specifically investigate monochromatic gravitational
wave sources in the LISA band and carry out the maximisiation over linear
combinations of the generators of the signal-to-noise ratios with the frequency
and source direction angles as parameters.Comment: 27 Pages, 6 figure
Studying the anisotropy of the gravitational wave stochastic background with LISA
A plethora of gravitational wave stochastic backgrounds populate the
sensitivity window of the Laser Interferometer Space Antenna. We show that LISA
can detect the anisotropy of the background corresponding to the multipole
moments of order l=2 and 4. The signal-to-noise ratio generated by galactic
white dwarf binary systems could be as high as 60 for 3 yrs of integration, and
LISA could provide valuable information on the spatial distribution of a
variety of galactic sources. We also show that the cross-correlation of the
data sets from two interferometers could marginally lead to meaningful
upper-limits on the degree of isotropy of the primordial gravitational wave
background.Comment: 4 pages, uses RevTe