Searching for periodic sources with LIGO

Patrick R. Brady, Teviet Creighton, Curt Cutler, and Bernard F. Schutz
Phys. Rev. D 57, 2101 – Published 15 February 1998
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Abstract

We investigate the computational requirements for all-sky, all-frequency searches for gravitational waves from spinning neutron stars, using archived data from interferometric gravitational wave detectors such as LIGO. These sources are expected to be weak, so the optimal strategy involves coherent accumulation of signal-to-noise using Fourier transforms of long stretches of data (months to years). Earth-motion-induced Doppler shifts, and intrinsic pulsar spindown, will reduce the narrow-band signal-to-noise by spreading power across many frequency bins; therefore, it is necessary to correct for these effects before performing the Fourier transform. The corrections can be implemented by a parametrized model, in which one does a search over a discrete set of parameter values (points in the parameter space of corrections). We define a metric on this parameter space, which can be used to determine the optimal spacing between points in a search; the metric is used to compute the number of independent parameter-space points Np that must be searched, as a function of observation time T. This method accounts automatically for correlations between the spindown and Doppler corrections. The number Np(T) depends on the maximum gravitational wave frequency and the minimum spindown age τ=f/ that the search can detect. The signal-to-noise ratio required, in order to have 99% confidence of a detection, also depends on Np(T). We find that for an all-sky, all-frequency search lasting T=107s, this detection threshold is hc(45)h3/yr, where h3/yr is the corresponding 99% confidence threshold if one knows in advance the pulsar position and spin period. We define a coherent search, over some data stream of length T, to be one where we apply a correction, followed by a fast Fourier transform of the data, for every independent point in the parameter space. Given realistic limits on computing power, and assuming that data analysis proceeds at the same rate as data acquisition (e.g., 10 days of data gets analyzed in 10days), we can place limitations on how much data can be searched coherently. In an all-sky search for pulsars having gravity-wave frequencies f<~200Hz and spindown ages τ>~1000yr, one can coherently search 18days of data on a teraflops computer. In contrast, a teraflops computer can only perform a 0.8-day coherent search for pulsars with frequencies f<~1kHz and spindown ages as low as 40 yr. In addition to all-sky searches we consider coherent directed searches, where one knows in advance the source position but not the period. (Nearby supernova remnants and the galactic center are obvious places to look.) We show that for such a search, one gains a factor of 10 in observation time over the case of an all-sky search, given a 1 Tflops computer. The enormous computational burden involved in coherent searches indicates the need for alternative data analysis strategies. As an example we briefly discuss the implementation of a simple hierarchical search in the last section of the paper. Further work is required to determine the optimal approach.

  • Received 27 February 1997

DOI:https://doi.org/10.1103/PhysRevD.57.2101

©1998 American Physical Society

Authors & Affiliations

Patrick R. Brady1, Teviet Creighton1, Curt Cutler2,3, and Bernard F. Schutz3

  • 1Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125
  • 2Center for Gravitational Physics and Geometry, Pennsylvania State University, University Park, Pennsylvania 16802
  • 3Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Schlaatzweg 1, D-14473 Potsdam, Germany

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Issue

Vol. 57, Iss. 4 — 15 February 1998

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