The spatial distribution of coalescing neutron star binaries: implicationsfor gamma-ray bursts

We find the distribution of coalescence times, birth rates, spatial velocit ies, and subsequent radial offsets of coalescing neutron stars (NSs) in var ious galactic potentials accounting for large asymmetric kicks introduced d uring a supernova. The birth rates of bound NS-NS binaries are quite sensit ive to the magnitude of the kick velocities but are, nevertheless, similar (similar to 10 per galaxy per Myr) to previous population synthesis studies . The distribution of merger times since zero-age main sequence is, however , relatively insensitive to the choice of kick velocities. With a median me rger time of similar to 10(8) yr, we find that compact binaries should clos ely trace the star formation rate in the Universe. In a range of plausible galactic potentials (with M-galaxy greater than or similar to 3 x 10(10) M.) the median radial offset of a NS-NS merger is les s than 10 kpc. At a redshift of z = 1 (with H-0 = 65 km s(-1) Mpc(-1) and O hm = 0.2), this means that half the coalescences should occur within simila r to 1.3 arcsec from the host galaxy. In all but the most shallow potential s, 90 per cent of NS-NS binaries merge within 30 kpc of the host. We find t hat although the spatial distribution of coalescing neutron star binaries i s consistent with the close spatial association of known optical afterglows of gamma-ray bursts (GRBs) with faint galaxies, a non-negligible fraction (similar to 15 per cent) of GRBs should occur well outside (greater than or similar to 30 kpc) dwarf galaxy hosts. Extinction owing to dust in the hos t, projection of offsets, and a range in interstellar medium densities conf ound the true distribution of NS-NS mergers around galaxies with an observa ble set of optical transients/galaxy offsets.