Can life survive Gamma-Ray Bursts in high-redshift universe?

Nearby Gamma-Ray Bursts (GRBs) have been proposed as a threat to life on Earth and the cause of some of the Earth mass extinction events such as the one in late Ordovician. Due to the higher event rate of GRBs at higher redshifts, it has been speculated that life as we know of may not survive above a certain redshift (e.g. z > 0.5). We examine the duty cycle of lethal GRBs in the solar neighborhood and within other galaxies using the observed Sloan Digital Sky Survey (SDSS) galaxy samples, the GRB host galaxy sample, and through Monte Carlo (MC) simulations. The dependence of the long GRB rate on star formation rate and metallicity are properly taken into account. We find that the number of lethal GRBs attacking Earth within the past ~ 500 Myr (close to the epoch of Ordovician mass extinction) is 0.93. The number of lethal GRBs at the scale length of a galaxy increases with redshift, due to the higher GRB rate resulting from higher star formation rate and lower metallicity. Taking 1 per 500 Myr as a conservative duty cycle for life to survive, as evidenced by our existence, we find that there are still a good fraction of galaxies up to z=1 where the GRB rate is lower than this value. Through extrapolating SDSS galaxies to higher redshifts and MC simulations, we derive the fraction of survival galaxies as a function of redshift, and find that the fraction is ~ 50\% at z ~ 1.5 and ~ 10\% even at z ~ 3. In all redshifts, the highest probability to find life is from Milky-Way-mass galaxies due to their large mass and relatively low star formation rate. GRB host galaxies are among the most dangerous galaxies for life.