Deep Ly alpha imaging of two z=2.04 GRB host galaxy fields

We report on the results of deep narrow-band Ly-alpha, U and I imaging of the fields of two GRBs at z=2.04 (GRB 000301C and GRB 000926). We find that the host galaxy of GRB 000926 is an extended, strong Ly-alpha emitter with a rest-frame equivalent width of 71+20-15 AA. The galaxy consists of two main components and several fainter knots. GRB 000926 occurred in the western component, whereas most of the Ly-alpha luminosity (about 65%) originates in the eastern component. Using archival HST images of the host galaxy we measure the spectral slopes (f_lambda prop. to lambda^beta) of the two components to beta = -2.4+-0.3 (east) and -1.4+-0.2 (west). This implies that both components contain at most small amounts of dust, consistent with the observed strong Ly-alpha emission. The western component has a slightly redder V-I colour than the eastern component, suggesting the presence of at least some dust. We do not detect the host galaxy of GRB 000301C in neither Ly-alpha emission nor in U and I-band images. We infer a limit of U(AB)>27.7 (2-sigma limit per arcsec^2). The upper limits on the Ly-alpha flux implies a Ly-alpha equivalent width upper limit of 150AA. We find 11 and 8 other galaxies with excess emission in the narrow filter in the fields of GRB 000301C and GRB 000926 respectively. Based on these detections we conclude that GRB 000926 occurred in one of the strongest centres of star formation within several Mpc, whereas GRB 000301C occurred in an intrinsically very faint galaxy far from being the strongest centre of star formation in its galactic environment. Under the hypothesis that GRBs trace star formation, the wide range of GRB host galaxy luminosities implies a very steep faint end slope of the high redshift galaxy luminosity function.