We find the distribution of coalescence times , birthrates , spatial velocities , and subsequent radial offsets of coalescing neutron stars ( NSs ) in various galactic potentials accounting for large asymmetric kicks introduced during a supernovae .
The birthrates of bound NS–NS binaries are quite sensitive to the magnitude of the kick velocities but are , nevertheless , similar ( \sim 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 merger time of \sim 10 ^ { 8 } yr , we find that compact binaries should closely trace the star formation rate in the Universe .
In a range of plausible galactic potentials ( with M _ { galaxy } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } % \hbox { $ > $ } } } 3 \times 10 ^ { 10 } M _ { \odot } ) the median radial offset of a NS–NS merger is less than 10 kpc .
At a redshift of z = 1 ( with H _ { 0 } = 65 km s ^ { -1 } Mpc ^ { -1 } and \Omega = 0.2 ) , this means that half the coalescences should occur within \sim 1.3 arcsec from the host galaxy .
In all but the most shallow potentials , 90 percent of NS–NS binaries merge within 30 kpc of the host .
We find that although the spatial distribution of coalescing neutron star binaries is consistent with the close spatial association of known optical afterglows of gamma-ray bursts ( GRBs ) with faint galaxies , a non-negligible fraction ( \sim 15 percent ) of GRBs should occur well outside ( \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 30 kpc ) dwarf galaxy hosts .
Extinction due to dust in the host , projection of offsets , and a range in interstellar medium densities confound the true distribution of NS–NS mergers around galaxies with an observable set of optical transients/galaxy offsets .