Catching supermassive black hole binaries without a net

The gravitational wave signals from coalescing Supermassive Black Hole Binaries are prime targets for the Laser Interferometer Space Antenna (LISA). With optimal data processing techniques, the LISA observatory should be able to detect black hole mergers anywhere in the Universe. The challenge is to find ways to dig the signals out of a combination of instrument noise and the large foreground from stellar mass binaries in our own galaxy. The standard procedure of matched filtering against a grid of templates can be computationally prohibitive, especially when the black holes are spinning or the mass ratio is large. Here we develop an alternative approach based on Metropolis-Hastings sampling and simulated annealing that is orders of magnitude cheaper than a grid search. For the first time, we show that it is possible to detect and characterize the signals from binary systems of Schwarzschild Black Holes that are embedded in instrument noise and a foreground containing millions of galactic binaries. Our technique is computationally efficient, robust, and applicable to both high and low signal-to-noise ratio systems.

Figure 1

The strain spectral density in a single LISA channel. The gray line is the LISA response to a galactic background of $26\times {10}^6$ sources plus simulated instrumental noise. The solid black lines show the LISA response to the SMBHB signals alone. The dashed black line indicates the RMS instrument plus galactic confusion noise level.

Figure 2

A plot of the search chains for the five intrinsic parameters and the SNR. In all cases, the straight solid line represents the true values of the SMBHB parameters. After $N=N_c=10000$ steps the search becomes a standard MCMC exploration of the posterior distribution function.

Figure 3

Examples of the SNR evolution for three runs searching for the low SNR signal at redshift $z=5.5$. The chains typically found, then lost the signal on several occasions early in the runs due to the high temperature and low SNR. The chains usually locked on for good at around iteration $N\sim 12000$.