A ROSAT Deep Survey of Four Small Gamma-Ray Burst Error Boxes

We have used the ROSAT High Resolution Imager to search for quiescent X-ray counterparts to four gamma-ray bursts which were localized to small (< 10 sq. arcmin.) error boxes with the Interplanetary Network. The observations took place years after the bursts, and the effective exposure times for each target varied from ~16 - 23 ks. We have not found any X-ray sources inside any of the error boxes. The 0.1 - 2.4 keV 3 sigma flux upper limits range from around 5 x 10^-14 erg cm^-2 s^-1 to 6 x 10^-13 erg cm^-2 s^-1 depending on the burst and the assumed shape of the quiescent spectrum. We consider four types of X-ray emitting galaxies (normal, AGN, faint, and star-forming) and use the flux upper limits to constrain their redshifts. We then use the GRB fluences to constrain the total energies of the bursts.