First stars can only form in structures that are suitably dense, which can be parametrized by the minimum dark matter halo mass M_min. M_min 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 M_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 is a function of M_min. In Fig. 1, we show the CSFR obtained from the self-consistency models as a function of M_min. The observational CSFR taken from Hopkins (2004, 2007) and Li (2008), which are based on the observations of other authors who are listed in these publications, are also shown for comparison. One can see from this plot that CSFR is very sensitive to the minimum mass M_min, especially at high-z. In addition, all of these models have good agreement with observational data at z<6.
Using the chi^2 statistic, the contour constraints on the M_min -- alpha plane show that at the 1 sigma confidence level, we have M_min <10^10.5 M_sun from 118 LGRBs with redshift z<4 and luminosity L_iso>1.8×10^51 erg s^-1. We also find that adding 12 high-z (4<z<5) LGRBs (consisting of 104 LGRBs with z<5 and L_iso>3.1×10^51 erg s^-1) could result in much tighter constraints on M_min, for which, 10^7.7 M_sun< M_min<10^11.6 M_sun (1 sigma). Through Monte Carlo simulations, we estimate that future five years of Sino-French space-based multiband astronomical variable objects monitor (SVOM) observations would tighten these constraints to 10^9.7 M_sun< M_min < 10^11.3 M_sun. The strong constraints on M_min indicate that LGRBs are a new promising tool for investigating star formation in dark matter halos. 
BY with WEI Junjie Figure 1. The CSFR derived from the self-consistency models compared to the observational data taken from Hopkins (2004, 2007) (dots) and Li (2008) (circles). The curves represent models with a minimum halo mass M_min =10^7.5 M_sun, 10^8.0 M_sun, 10^8.5 M_sun, and 10^9.0 M_sun, respectively. The work by Jun-Jie Wei, Jing-Meng Hao, Xue-Feng Wu, and Ye-Fei Yuan has been published in Journal of High Energy Astrophysics. Please see JHEAp 9-10 (2016) 1-8 for more details.(http://www.sciencedirect.com/science/article/pii/S2214404815000658) |
