Long GRBs as a tool to investigate star formation in dark matter halos
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First stars can only form in structures that are suitably dense, which can be parametrized by the minimum dark matter halo mass the MathML source">Mmin. the MathML source">Mmin 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 the MathML source">Mmin 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 the MathML source">(1+z)α, where the CSFR model is a function of the MathML source">Mmin. Using the the MathML source">χ2 statistic, the contour constraints on the the MathML source">Mminα plane show that at the 1σ   confidence level, we have the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S2214404815000658&_mathId=si4.gif&_user=111111111&_pii=S2214404815000658&_rdoc=1&_issn=22144048&md5=679c96601d65dd7456745dea8a8f6444">View <font color=the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S2214404815000658-si4.gif"> from 118 LGRBs with redshift the MathML source">z<4 and luminosity the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S2214404815000658&_mathId=si6.gif&_user=111111111&_pii=S2214404815000658&_rdoc=1&_issn=22144048&md5=98623f2db2e2959679a0ce33bcdfb238">View <font color=the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S2214404815000658-si6.gif">. We also find that adding 12 high-z  the MathML source">(4<z<5) LGRBs (consisting of 104 LGRBs with the MathML source">z<5 and the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S2214404815000658&_mathId=si144.gif&_user=111111111&_pii=S2214404815000658&_rdoc=1&_issn=22144048&md5=435f550fdbd5fe8046816b99292f840d">View <font color=the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S2214404815000658-si144.gif">) could result in much tighter constraints on the MathML source">Mmin, for which, the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S2214404815000658&_mathId=si10.gif&_user=111111111&_pii=S2214404815000658&_rdoc=1&_issn=22144048&md5=6a8fb0330aa634e01369d1c54b2f524f">View <font color=the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S2214404815000658-si10.gif"> (1σ). Through Monte Carlo simulations, we estimate that future five years of Sino–French spacebased multiband astronomical variable objects monitor (SVOM  ) observations would tighten these constraints to the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S2214404815000658&_mathId=si11.gif&_user=111111111&_pii=S2214404815000658&_rdoc=1&_issn=22144048&md5=65c3e27d9257f8803959c22fb5e051c1">View <font color=the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S2214404815000658-si11.gif">. The strong constraints on the MathML source">Mmin indicate that LGRBs are a new promising tool for investigating star formation in dark matter halos.

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