Constraints on an optical afterglow and on supernova light following the short burst GRB 050813

We report early follow-up observations of the error box of the short burst 050813 using the telescopes at Calar Alto and at Observatorio Sierra Nevada (OSN), followed by deep VLT/FORS2 I-band observations obtained under very good seeing conditions 5.7 and 11.7 days after the event. Neither a fading afterglow, nor a rising SN component was found, so the potential GRB host galaxy has not been identified based on a comparison of the two VLT images taken at different epoches. We discuss if any of the galaxies present in the original 10 arcsec XRT error circle could be the host. In any case, the optical afterglow of GRB 050813 was of very low luminosity. We conclude that all these properties are consistent with the binary compact merger hypothesis for the progenitor of GRB 050813.