OPTIMAL SOLUTION TO THE INVERSE PROBLEM FOR THE GRAVITATIONAL-WAVE SIGNAL OF A COALESCING COMPACT BINARY

Coalescing compact binaries are the most promising sources of the gravitational waves to be detected by planned long-arm laser interferometers. Estimation of the parameters of such a binary, such as the masses of its members, distance to the binary, and their distribution in the sky, will provide a wealth of astrophysical information. An important problem, called the inverse problem, is to determine the astrophysically interesting parameters of the binary (such as the distance to the binary and its position in the sky) from the parameters of the detector's response function to the gravitational wave signal of the binary. To solve the problem one needs the network of at least three detectors. We present the solution of the problem that gives the maximum likelihood estimators of the astrophysically interesting parameters with the least possible errors. This involves solving a complicated set of algebraic equations. We find that for the network of the three planned advanced LIGO and/or VIRGO detectors and for a binary consisting of two neutron stars of 1.4 solar masses each at a distance of 100 Mpc we can expect to determine its distance to an accuracy of the order of 10%, its mass parameter to an accuracy of the order of 10(-6) solar masses, and its position in the sky to an accuracy of the order of 10(-4) sr.