Aims. We present a detailed analysis of the prompt and afterglow emission of ORB 050410 and GRB 050412 detected by Swift for which no optical counterpart was observed. Methods. We analysed data from the prompt emission detected by the Swift BAT and from the early phase of the afterglow obtained by the Swift narrow field instrument XRT. Results. The 15-150 keV energy distribution of the GRB 050410 prompt emission shows a peak energy at 53-21 +40 keV. The XRT light curve of this GRB decays as a power law with a slope of α = 1.06 ± 0.04. The spectrum is well reproduced by an absorbed power law with a spectral index Γx = 2.4 ± 0.4 and a low energy absorption NH = -2 +3 × 10 21 cm-2 which is higher than the Galactic value. The 15-150 keV prompt emission in GRB 050412 is modelled with a hard (Γ = 0.7 ± 0.2) power law. The XRT light curve follows a broken power law with the first slope αl = 0.7 ± 0.4, the break time T break = 254-41 +79 s and the second slope α2 = 2.8-0.8 +0.5. The spectrum is fitted by a power law with spectral index Γx = 1.3 ± 0.2 which is absorbed at low energies by the Galactic column. Conclusions. The GRB 050410 afterglow light curve reveals the expected characteristics of the third component of the canonical Swift light curve. Conversely, a complex phenomenology was detected in the GRB 050412 because of the presence of the very early break. The light curve in this case can be interpreted as being the last peak of the prompt emission. The two bursts present tight upper limits for the optical emission, however, neither of them can be clearly classified as dark. For GRB 050410, the suppression of the optical afterglow could be attributed to a low density interstellar medium surrounding the burst. For GRB 050412, the evaluation of the darkness is more difficult due to the ambiguity in the extrapolation of the X-ray afterglow light curve.
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