ar X iv : a st ro - p h / 97 06 06 8 v 1 7 J un 1 99 7 What is the redshift of gamma - ray burst 970508 ?

A Bayesian likelihood analysis is used to constrain the redshift of the optical transient associated with gamma-ray burst 970508, under the assumption that the absorption at redshift 0.835 is not physically associated with the transient. The maximum-likelihood, expectation value and 95-percent upper limit on the OT redshift are 0.835, 1.3 and 1.9 respectively. Subject headings: methods: statistical — quasars: absorption lines — gamma rays: bursts — X-rays: bursts Gamma-ray bursts are among the most fascinating mysteries in astrophysics, with their immense fluences, isotropic distribution on the sky, and number-flux relation that is not consistent with homogeneity. The holy grail in the study of gamma-ray bursts is the determination of their distances from the Earth; unfortunately, for lack of solid evidence, distance estimates range from the outskirts of our Solar System to the edge of the Universe. The strongest constraints on models are the intrinsic energies of the bursts, so accurate distance determination is crucial. A breakthrough occurred this year with observations of an optical transient (OT), apparently associated with an X-ray flare apparently associated with gamma-ray burst 970508 (Bond 1997; Djorgovski et al 1997; Metzger et al 1997), which show that the OT, and therefore probably the gamma-ray burst, is at a cosmological distance. The OT spectrum, taken near maximum light, shows a strong Mg II absorption system at redshift z = 0.835 (Metzger et al 1997). The absorption system could be associated with the OT itself or else the OT is further away and the gas cloud is between us and the OT. If the absorption is associated, the redshift of the OT is zOT = 0.835. There are several reasons to believe that the absorption is associated: The absorption is strong (equivalent width roughly 1.5 Å) and therefore the line-of-sight is not typical (Steidel & Sargent 1992). Furthermore, the relative strengths of the lines in the absorption suggests a line-of-sight through or at least very near the center of a galaxy (Steidel, private communication), which again makes the line-of-sight atypical. However, if the absorption system is unrelated, zOT is not known but can only be constrained. In this Letter we make the constraint quantitative with a Bayesian likelihood analysis. The