Hubble Space Telescope imaging of the optical transient associated with GRB 970508

We report on Hubble Space Telescope observations of the optical transient (OT) discovered in the error box of the gamma-ray burst GRB 970508. The object was imaged on 1997 June 2 with the Space Telescope Imaging Spectrograph and Near-Infrared Camera and Multiobject Spectrometer. The observations reveal a pointlike source with R = 23.1 +/- 0.2 and H = 20.6 +/- 0.3, in agreement with the power-law temporal decay seen in groundbased monitoring. Unlike the case of GRB 970228, no nebulosity is detected surrounding the OT of GRB 970508. We set very conservative upper limits of R similar to 24.5 and H similar to 22.2 on the brightness of any underlying extended source. If this subtends a substantial fraction of an arcsecond, then the R-band limit is similar to 25.5. In combination with Keck spectra that show Mg I absorption and [O II] emission at a redshift of z = 0.835, om observations suggest that the OT is located in a star-forming galaxy with total luminosity 1 order of magnitude lower than the knee of the galaxy luminosity function, L-*. Such galaxies are now thought to harbor the majority of star formation at z similar to 1; therefore, these observations may provide support for a link between GRBs and star formation.