Feedback Effects of First Supernovae on the Neighboring Dark Matter Halos

The first-generation stars in the $\Lambda$CDM universe are considered to have formed in dark halos with total masses in the range $\sim 10^{5}-10^{7}M_sun$ at $z \sim 20-50$. These stars expected to be very massive and in some cases they end their lives as the first supernovae (SNe). We explore the problem of whether star formation in low mass dark halos (< 10^{7} M_sun) was triggered or suppressed by the SN feedback from neighboring star-forming halos. We take into consideration mainly two effects by the SN shock: one is the evacuation of gas components from the halos and the other is the promotion of H_2 formation because of the enhanced ionization degree by shock heating. Combining above effects, we find that the star formation activities in the neighboring dark matter halos (M < 10^{7} M_sun) are basically suppressed in case they are located close to the SN center, because of the gas evacuation effect. The critical distance within which the gas is blown away falls within the range $\sim 0.3-1.5$kpc depending on the SN energy and the halo mass. In addition, we find there is very little window in the parameter space where star formation activities in dark halos are induced or promoted by neighboring SN.