PROSPECTS FOR DETECTING THE CHRISTODOULOU MEMORY OF GRAVITATIONAL-WAVES FROM A COALESCING COMPACT BINARY AND USING IT TO MEASURE NEUTRON-STAR RADII

A coalescing compact binary, during its last tenth of a second of life, emits a burst of gravitational waves consisting of a high-frequency ''chirp,'' with the frequencies much greater than 100 Hz, superimposed on a gradually growing memory, known as the Christodoulou memory. Most of the memory's growth occurs over the last few hundredths of a second, so its signal has strong Fourier components at f similar to 100 Hz. The planned LIGO and/or VIRGO broadband gravitational-wave detectors have optimal performance at frequencies around 100 Hz and should be well suited, in terms of frequencies, to detect the growth of the memory amidst the chirp. If one or both of the binary's components is a neutron star (the other being either a neutron star or a black hole), then the growth of the memory will be cut off by the star's tidal disruption. The larger the neutron star's radius the sooner the cutoff and correspondingly the weaker the total memory. Therefore, from a LIGO and/or VIRGO measurement of the memory's strength, one could hope to infer the neutron-star radius. The prospects for such measurements to succeed are evaluated quantitatively and found to be poor because of the weakness of the memory. Even under optimistic circumstances the memory is so weak that only for a black-hole-black-hole binary is there much chance of detecting it, and then the prospects are only marginal.