Constraints on Obscured Star Formation in Host Galaxies of Gamma-ray Bursts

We present the results of the 16-cm-waveband continuum observations of four host galaxies of gamma-ray bursts (GRBs) 990705, 021211, 041006, and 051022 using the Australia Telescope Compact Array. Radio emission was not detected in any of the host galaxies. The 2sigma upper limits on star-formation rates derived from the radio observations of the host galaxies are 23, 45, 27, and 26 Msun/yr, respectively, which are less than about 10 times those derived from UV/optical observations, suggesting that they have no significant dust-obscured star formation. GRBs 021211 and 051022 are known as the so-called "dark GRBs" and our results imply that dark GRBs do not always occur in galaxies enshrouded by dust. Because large dust extinction was not observed in the afterglow of GRB021211, our result {\bf suggests the possibility} that the cause of the dark GRB is the intrinsic faintness of the optical afterglow. On the other hand, by considering the high column density observed in the afterglow of GRB051022, the likely cause of the dark GRB is the dust extinction in the line of sight of the GRB.