Reduced Basis Catalogs for Gravitational Wave Templates

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for nonspinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about $10–{10}^5$ fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.

Figure 1

Error in approximating the space of waveforms by a discrete catalog for BNS inspirals with Initial LIGO. For reduced basis, the error is the square of the greedy error (3) while for metric placement the error is ($1-MM$) with $MM$ the minimal match. The lower panel shows the extrapolation of the maximum number of RBs generated for an infinitely large training space. The fit shown (red) excludes the two points with largest $x$, which change the asymptotic value by 0.2.

Figure 2

The points show the parameter values chosen for the catalog of BNS and Initial LIGO. The density of parameter values is shown using a coloramp as well as histograms.