Hubble Space Telescope observations of the host galaxy of GRB 970508

We report on observations of the field of GRB 970508 made in 1998 early August, 454 days after outburst, with the STIS CCD camera on board the Hubble Space Telescope (HST). The images, taken in open filter (50CCD) mode, clearly reveal the presence of a galaxy that was overwhelmed in earlier (1997 June) HST images by emission from the optical transient (OT). The galaxy is regular in shape: after correcting for the HST/STIS PSF, it is well fitted by an exponential disk with a scale length of 0."046 +/- 0."006 and an ellipticity of 0.70 +/- 0.07. All observations are marginally consistent with a continuous decline in OT emission as t(-1.3) beginning 2 days after outburst; however, we find no direct evidence in the late-time HST image for emission from the OT, and the surface brightness profile of the galaxy is most regular if we assume that the OT emission is negligible, suggesting that the OT may have faded more rapidly at late times than is predicted by the power-law decay. Due to the wide bandwidth of the STIS clear mode, the estimated magnitude of the galaxy is dependent on the galaxy spectrum that is assumed. Using colors obtained from late-time ground-based observations to constrain the spectrum, we find V = 25.4 +/- 0.15, a few tenths of a magnitude brighter than earlier ground-based estimates that were obtained by observing the total light of the galaxy and the OT and then subtracting the estimated OT brightness, assuming that it fades as a single power law. This again suggests that the OT may have faded faster at late time than the power law predicts. The position of the OT agrees with that of the isophotal center of the galaxy to which, at the galaxy redshift z = 0.83, corresponds to an offset from the 0."01, center of the host of pc. This remarkable agreement raises the possibility that the gamma-ray burst less than or similar to 70 may have been associated with either an active galactic nucleus or a nuclear starburst.