Gravitational wave search from compact binary coalescences


How efficiently can we detect gravitational waves observed compact binary coalescences? 
The gravitational wave signals from coalescing binaries leave their tiny imprints on the LIGO-Virgo interferometer's noise which is challenging to detect. These signals, if accurately modeled, can be picked out by matched filtering technique. In matched filtering, the detector's output is correlated with a modeled signal called a template waveform. The modeling of a template depends on several parameters corresponding to individual masses of the compact objects, their component spins, orbital eccentricities, and location with respect to the detector. Since the values of these parameters are a priori unknown, matched filtering-based search pipelines tend to correlate data with a "bank of templates."
Pictorial representation of matched filtering of data with a waveform (template) to obtain a SNR time series
The template bank is generally constructed so that the maximum loss in matched-filtered signal-to-noise ratio (SNR) is not more than 3%, equivalent to less than 10% loss in detecting astrophysical signals. Since the correlation process involves Fast Fourier Transform (FFT), for a uniformly sampled time-series data having millions of points, the number of FFT computation scales as NlogN for N being the number of data points. This number increases when the correlation iterates over a million templates, thereby insanely increasing the computation cost.
One way to reduce the computation cost of matched filtering is by performing it in multiple stages using multiple banks. Consider matched filtering of coarsely sampled data with a less dense bank called a coarse bank. The GW candidates identified in this step will have fewer SNRs, which can be improved if a finer search is performed in the signal's parameter space neighborhood. The finer search in the neighborhood will use few templates and, therefore, will effectively reduce the total matched filter cost. 
Pictorial representation of a two-stage hierarchical search

Publication:

1/ Hierarchical search for compact binary coalescences in the Advanced LIGO's first two observing runs [ads] [google scholar]
Kanchan Soni, Bhooshan Uday Gadre, Sanjit Mitra, and Sanjeev Dhurandhar
Phys. Rev. D 105, 064005 (2022)

2/ Obtaining statistical significance of gravitational wave signals in hierarchical search [google scholar]
Kanchan Soni, Sanjeev Dhurandhar, Sanjit Mitra 
Phys. Rev. D 109, 024046 (2024) 


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