Long GRBs as a Tool to Investigate Star Formation in Dark Matter Halos

Jun-Jie Wei, Jing-Meng Hao, Xue-Feng Wu, Ye-Fei Yuan

Published 2015-11-14Version 1

First stars can only form in structures that are suitably dense, which can be parametrized by the minimum dark matter halo mass $M_{\rm min}$. $M_{\rm min}$ must plays 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 $M_{\rm min}$ 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 $(1+z)^{\alpha}$, where the CSFR model as a function of $M_{\rm min}$. Using the $\chi^{2}$ statistic, the contour constraints on the $M_{\rm min}$--$\alpha$ plane show that at the $1\sigma$ confidence level, we have $M_{\rm min}<10^{10.5}$ $\rm M_{\odot}$ from 118 LGRBs with redshift $z<4$ and luminosity $L_{\rm iso}>1.8\times10^{51}$ erg $\rm s^{-1}$. We also find that adding 12 high-\emph{z} $(4<z<5)$ LGRBs (consisting of 104 LGRBs with $z<5$ and $L_{\rm iso}>3.1\times10^{51}$ erg $\rm s^{-1}$) could result in much tighter constraints on $M_{\rm min}$, for which, $10^{7.7}\rm M_{\odot}<M_{\rm min}<10^{11.6}\rm M_{\odot}$ ($1\sigma$). Through Monte Carlo simulations, we estimate that future five years of Sino-French spacebased multiband astronomical variable objects monitor (\emph{SVOM}) observations would tighten these constraints to $10^{9.7}\rm M_{\odot}<M_{\rm min}<10^{11.3}\rm M_{\odot}$. The strong constraints on $M_{\rm min}$ indicate that LGRBs are a new promising tool for investigating star formation in dark matter halos.