Characterizing the gravitational wave signature from cosmic string cusps

Cosmic strings are predicted to form kinks that travel along the string, and cusps, where a small region of the string moves at close to the speed of light. These disturbances are radiated away as highly beamed gravitational waves that produce a burst like pulse as the cone of emission sweeps past an observer. Gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA) and the Laser Interferometer Gravitational wave Observatory (LIGO) will be capable of detecting these bursts for a wide class of string models. Such a detection would illuminate the fields of string theory, cosmology, and relativity. Here, we develop template based Markov chain Monte Carlo (MCMC) techniques that can efficiently detect and characterize the signals from cosmic string cusps. We estimate how well the signal parameters can be recovered by the advanced LIGO-Virgo network and the LISA detector using a combination of MCMC and Fisher matrix techniques. We also consider joint detections by the ground- and space-based instruments. We show that a parallel tempered MCMC approach can detect and characterize the signals from cosmic string cusps, and we demonstrate the utility of this approach on simulated data from the third round of mock LISA data challenges.

Figure 1

The SNR as a function of observation time for three different sets of parameter values for cosmic string cusp bursts of gravitational waves from the MLDC.

Figure 2

The low frequency approximation to the LISA response compared to the full response for the same source.

Figure 3

Reflection in the plane of the detector gives a degenerate set of parameter values. Rotations in the plane of the detector give two sets of secondary maxima.

Figure 4

A sky location histogram of a parallel tempered MCMC search for MLDC source 3.4.2 on the full sky with quartile contours and a Fisher matrix approximation for the source location below for comparison (marginalized over the other source parameters). The all-sky figures use the HEALPix pixelization of the sky (http://healpix.jpl.nasa.gov).

Figure 5

A sky location histogram of a parallel tempered MCMC search for MLDC source 3.4.4 on the full sky with quartile contours and a Fisher matrix approximation for the source location below for comparison (marginalized over the other source parameters).

Figure 6

An MCMC search for an MLDC training data source with high SNR but a maximum frequency cutoff below the LISA transfer frequency.

Figure 7

An MCMC search for a source with the same parameter values as Fig. 6, except for a maximum frequency above the LISA transfer frequency.

Figure 8

The distribution of recovered parameter values for an MCMC search for MLDC training source 3.4.3 using simulated LISA data. The Fisher matrix Gaussian approximation is shown in blue for comparison.

Figure 9

The distribution of parameter values for an MCMC search of simulated data using the parameters for MLDC training source 3.4.0 (with $f_{\max }$ boosted to 500 Hz) for the advanced ground based detector network. The Gaussian Fisher matrix approximation is included in blue for comparison.

Figure 10

The distribution of parameter values for an MCMC search of simulated data using the parameters for MLDC training source 3.4.3 (with $f_{\max }$ boosted to 500 Hz) for the advanced ground based detector network. The Gaussian Fisher matrix approximation is included in blue for comparison.