Performance of an externally triggered gravitational-wave burst search

We present the performance of searches for gravitational-wave bursts associated with external astrophysical triggers as a function of the search sky region. We discuss both the case of Gaussian noise and real noise of gravitational wave detectors for arbitrary detector networks. We demonstrate the ability to reach Gaussian limited sensitivity in real non-Gaussian data, and show the conditions required to attain it. We find that a single sky position search is $\sim 20\%$ more sensitive than an all-sky search of the same data.

Figure 1

Strain noise spectra from the LIGO detectors used in this study. Note that H2 data are treated as if the detector was located at the Virgo site in order to simulate the gravitational wave detector network operated in 2009–2010.

Figure 2

Sky dependence of the penalty factor ${\lambda }_c/{\rho }_c$ [Eq. (22)] assuming that V1 is a factor 2 less sensitive than H1 and L1. From top to bottom the penalty factor for, respectively, the H1L1, L1V1, and H1L1V1 networks are shown. The coordinates used are the longitude and latitude in a Mollweid projection, as the detectors are fixed to the Earth. The location of the detectors in each network are marked by blue dots; for each detector the projection on the celestial sphere of the location (and its opposite) are the points of maximum antenna response. For the two detector networks the zero points of the penalty factor correspond to the null of the antenna response for one of the two detectors. The plus marks show the sky location of the fiducial triggers analyzed to produce Fig. 3, whereas the circles show the large sky regions used for the study shown in Fig. 5. We omit the map for the H1V1 network as it is very similar to the L1V1 map.

Figure 3

Values of ${\rho }_c$ and ${\lambda }_c$ corresponding to the detection sensitivity $d_{50\%}$ found when analyzing real and simulated Gaussian noise. Each marker represents a complete end-to-end analysis for one of the networks and sky positions indicated in Fig. 2. Plus marks are for real noise from the H1L1 network, cross marks for real noise from the L1V1 network, star marks for real noise from the H1L1V1 network, and circles are for simulated Gaussian noise from the H1L1V1 network. The analyzed sky position are shown as crosses on Fig. 2.

Figure 4

Cumulative distribution over the sky of the sensitive distance $d_{50\%}$ assuming that V1 is a factor 2 less sensitive than H1 and L1. The lines show the distribution when $d_{50\%}$ is assumed to be given by a threshold on ${\lambda }_c$ (real data analysis): blue dashed line for the H1L1 network, red dotted line for the L1V1 network, and black solid line for the H1L1V1 network. The marks show the distribution when $d_{50\%}$ is assumed to be given by a threshold on ${\rho }_c$ (Gaussian data analysis): blue pluses for the H1L1 network, red crosses for L1V1 network, and black stars for the H1L1V1 network.

Figure 5

Fractional value of $d_{50\%}$ for real detector noise as a function of the number of analyzed sky positions relative to the expectation based on the typical threshold ${\lambda }_c=7.5$, which we obtained in Fig. 3. Blue plus marks denote results for the H1L1 network, red cross marks for the L1V1 network, and black circle marks for the H1L1V1 network. The six marks around 100 sky positions correspond to search sensitivity over the sky patches represented as circles in Fig. 2. The two marks with sky position number $>1000$ correspond to search sensitivity over the full sky.