Matched filtering of gravitational waves from inspiraling compact binaries: Computational cost and template placement

Abstract

We estimate the number of templates, computational power, and storage required for a one-step matched filtering search for gravitational waves from inspiraling compact binaries. Our estimates for the one-step search strategy should serve as benchmarks for the evaluation of more sophisticated strategies such as hierarchical searches. We use a discrete family of two-parameter wave form templates based on the second post-Newtonian approximation for binaries composed of nonspinning compact bodies in circular orbits. We present estimates for all of the large- and mid-scale interferometers now under construction: LIGO (three configurations), VIRGO, GEO600, and TAMA. To search for binaries with components more massive than ${m}_{\mathrm{min}}{=0.2M}_{\ensuremath{\bigodot}}$ while losing no more than $10%$ of events due to coarseness of template spacing, the initial LIGO interferometers will require about $1.0\ifmmode\times\else\texttimes\fi{}{10}^{11}$ flops (floating point operations per second) for data analysis to keep up with data acquisition. This is several times higher than estimated in previous work by Owen, in part because of the improved family of templates and in part because we use more realistic (higher) sampling rates. Enhanced LIGO, GEO600, and TAMA will require computational power similar to initial LIGO. Advanced LIGO will require $7.8\ifmmode\times\else\texttimes\fi{}{10}^{11}$ flops, and VIRGO will require $4.8\ifmmode\times\else\texttimes\fi{}{10}^{12}$ flops to take full advantage of its broad target noise spectrum. If the templates are stored rather than generated as needed, storage requirements range from $1.5\ifmmode\times\else\texttimes\fi{}{10}^{11}$ real numbers for TAMA to $6.2\ifmmode\times\else\texttimes\fi{}{10}^{14}$ for VIRGO. The computational power required scales roughly as ${m}_{\mathrm{min}}^{\ensuremath{-}8/3}$ and the storage as ${m}_{\mathrm{min}}^{\ensuremath{-}13/3}.$ Since these scalings are perturbed by the curvature of the parameter space at second post-Newtonian order, we also provide estimates for a search with ${m}_{\mathrm{min}}{=1M}_{\ensuremath{\bigodot}}.$ Finally, we sketch and discuss an algorithm for placing the templates in the parameter space.