A SHORT GAMMA-RAY BURST NO-HOST PROBLEM? INVESTIGATING LARGE PROGENITOR OFFSETS FOR SHORT GRBs WITH OPTICAL AFTERGLOWS

We investigate the afterglow properties and large-scale environments of several short-duration gamma-ray bursts (GRBs) with subarcsecond optical afterglow positions but no bright coincident host galaxies. The purpose of this joint study is to robustly assess the possibility of significant offsets, a hallmark of the compact object binary merger model. Five such events exist in the current sample of 20 short bursts with optical afterglows, and we find that their optical, X-ray, and gamma-ray emission are systematically fainter. These differences may be due to lower circumburst densities (by about an order of magnitude), to higher redshifts (by Delta z approximate to 0.5-1), or to lower energies (by about a factor of 3), although in the standard GRB model the smaller gamma-ray fluences cannot be explained by lower densities. To study the large-scale environments, we use deep optical observations to place limits on underlying hosts and to determine probabilities of chance coincidence for galaxies near each burst. In four of the five cases, the lowest probabilities of chance coincidence (P(< delta R) similar to 0.1) are associated with bright galaxies at separations of delta R similar to 10 '', while somewhat higher probabilities of chance coincidence are associated with faint galaxies at separations of similar to 2 ''. By measuring redshifts for the brighter galaxies in three cases (z = 0.111, 0.473, 0.403), we find physical offsets of approximate to 30-75 kpc, while for the faint hosts the assumption of z greater than or similar to 1 leads to offsets of similar to 15 kpc. Alternatively, the limits at the burst positions (greater than or similar to 26 mag) can be explained by typical short GRB host galaxies (L approximate to 0.1-1 L*) at z greater than or similar to 2-3. Thus, two possibilities exist: (1) similar to 1/4 of short GRBs explode similar to 50 kpc or similar to 15 kpc from the centers of z >= 0.3 or z greater than or similar to 1 galaxies, respectively, and have fainter afterglows due to the resulting lower densities; or (2) similar to 1/4 of short GRBs occur at z greater than or similar to 2 and have fainter afterglows due to their higher redshifts. The high-redshift scenario leads to a bimodal redshift distribution, with peaks at z similar to 0.5 and z similar to 3. The large offset scenario leads to an offset distribution that is well matched by theoretical predictions of NS-NS/NS-BH binary kicks, or by a hybrid population with globular cluster NS-NS binaries at large offsets and primordial binaries at offsets of less than or similar to 10 kpc (indicative of negligible kicks). Deeper constraints on any coincident galaxies to greater than or similar to 28 mag (using the Hubble Space Telescope) will allow us to better exclude the high-redshift scenario.