A TEST OF THE GALACTIC ORIGIN OF GAMMA-RAY BURSTS

The distribution of old neutron stars in the Galaxy was calculated by integrating numerically ∼90,000 orbits in the Galactic gravitational potential for up to 1010 yr. Neutron stars were assumed to be born in a thin disk with the velocity distribution observed for radio pulsars. The calculated volume density within 0.5 kpc of the Sun may be approximated as nNS ≈ 0.0014 (pc-3) (R/8 kpc)(-3 + 4z/kpc) [1 + (z/0.2 kpc)2]-1, where R is a distance from the Galactic center, z is a distance from the Galactic plane, and assuming that the total number of neutron stars in the Galaxy is 109, or equivalently, that there were 1.4 × 106 kpc-2 neutron stars born near the Sun over the lifetime of the Galaxy. The dipole and quadrupole moments, as well as the average value of V/Vmax were calculated for the expected distribution of gamma-ray bursts, assuming that they originate on neutron stars, and assuming various radial depths and detection thresholds of the surveys. For all intrinsic luminosity functions that were considered, the quadrupole moment, i.e., the concentration of sources to the Galactic plane, should be the easiest to detect. If all the nearest neutron stars are detected as bursters than this concentration should be detectable at a 3 σ level when ∼ 4000 independent events have their positions measured with an accuracy of a few degrees. If only some neutron stars produce gamma-ray bursts during the observational period then a larger volume will be sampled with fewer bursts, and the quadrupole moment in their distribution will become measurable with fewer than 4000 events. Even fewer events will be needed if there is a deficiency in the number of weak bursts, as indicated by the balloon experiment of Meegan et al. The GRANAT and GRO missions should discover enough bursts in ∼ 1 yr of their operation to provide evidence for or against the association of gamma-ray bursts with the Galactic disk neutron stars. Models that require accretion from a cold circumstellar disk or from a close companion are only marginally consistent with the apparently isotropic distribution of the observed bursts. Models that require accretion of interstellar matter are ruled out as they should produce a very strong dipole anisotropy. Models that propose the Galactic halo origin of gamma-ray bursts are briefly discussed. If the GRANAT and GRO missions confirm the flattening of number-intensity relation for weak bursts, and if the distribution of weak bursts is isotropic, then the bursters are most likely at cosmological distances.