Long GRBs as a tool to investigate star formation in dark matter halos

First stars can only form in structures that are suitably dense, which can be parametrized by the minimum dark matter halo mass MminMmin. MminMmin must play an important role in star formation. The connection of long gamma-ray bursts (LGRBs) with the collapse of massive stars has provided a good opportunity for probing star formation in dark matter halos. We place some constraints on MminMmin using the latest Swift   LGRB data. We conservatively consider that LGRB rate is proportional to the cosmic star formation rate (CSFR) and an additional evolution parametrized as (1+z)α(1+z)α, where the CSFR model is a function of MminMmin. Using the χ2χ2 statistic, the contour constraints on the MminMmin–α plane show that at the 1σ   confidence level, we have Mmin<1010.5M⊙ from 118 LGRBs with redshift z<4z<4 and luminosity Liso>1.8×1051 ergs−1. We also find that adding 12 high-z  (43.1×1051 ergs−1) could result in much tighter constraints on MminMmin, for which, 107.7M⊙