Lyα and ultraviolet emission from high-redshift gamma-ray burst hosts:: to what extent do gamma-ray bursts trace star formation?

We report the result of a search for Ly alpha emission from the host galaxies of the gamma-ray bursts (GRBs) 030226 (z = 1.986), 021004 (z = 2.335) and 020124 (z = 3.198). We find that the host galaxy of GRB 021004 is an extended (around 8 kpc) strong Ly alpha emitter with a rest-frame equivalent width (EW) of 68(-11)(+12) angstrom, and a star formation rate of 10.6 +/- 2.0 M-circle dot yr(-1). We do not detect the hosts of GRB 030226 and GRB 020424, but the upper limits on their Lya fluxes do not rule out large rest-frame EWs. In the fields of GRB 021004 and GRB 030226 we find seven and five other galaxies, respectively, with excess emission in the narrow-band filter. These galaxies are candidate Ly alpha-emitting galaxies in the environment of the host galaxies. We have also compiled a list of all z greater than or similar to 2 GRB hosts, and demonstrate that a scenario where they trace star formation in an unbiased way is compatible with current observational constraints. Fitting the z = 3 luminosity function (LF) under this assumption results in a characteristic luminosity of R* = 24.6 and a faint-end slope of alpha = 1.55, consistent with the LF measured for Lyman-break galaxies.