Negative feedback effects on star formation history and cosmic   reionization
  After considering the effects of negative feedback on the process of star formation, we explore the relationship between star formation process and the associated feedback, by investigating how the mechanical feedback from supernovae(SNe) and radiative feedback from luminous objects regulate the star formation rate and therefore affect the cosmic reionization.Based on our present knowledge of the negative feedback theory and some numerical simulations, we construct an analytic model in the framework of the Lambda cold dark matter model. In certain parameter regions, our model can explain some observational results properly. In large halos(T_vir>10000 K), both mechanical and radiative feedback have a similar behavior: the relative strength of negative feedback reduces as the redshift decreases. In contrast, in small halos (T_vir<10000 K$) that are thought to breed the first stars at early time, the radiative feedback gets stronger when the redshift decreases. And the star formation rate in these small halos depends very weakly on the star-formation efficiency. Our results show that the radiative feedback is important for the early generation stars. It can suppress the star formation rate considerably. But the mechanical feedback from the SNe explosions is not able to affect the early star formation significantly. The early star formation in small-halo objects is likely to be self-regulated. The radiative and mechanical feedback dominates the star formation rate of the PopII/I stars all along. The feedback from first generation stars is very strong and should not be neglected. However, their effects on the cosmic reionization are not significant, which results in a small contribution to the optical depth of Thomson scattering. 
Lei Wang, Jirong Mao, Shouping Xiang, Ye-Fei Yuan