Can Gamma-Ray Burst Jets Break Out the First Stars?

We show that a relativistic gamma-ray burst (GRB) jet can potentially pierce the envelope of very massive first generation star (Population III; Pop III) by using the stellar density profile to estimate both the jet luminosity (via accretion) and its penetrability. The jet breakout is possible even if the Pop III star has a supergiant hydrogen envelope without mass loss, thanks to the long-lived powerful accretion of the envelope itself. While the Pop III GRB is estimated to be energetic, E_{gamma,iso} ~ 10^{55} erg, the supergiant envelope hides the initial bright phase into the cocoon component, leading to a GRB with a long duration ~ 1000(1+z) sec and an ordinary isotropic luminosity ~ 10^{52} erg s^{-1} (~ 10^{-9} erg cm^{-2} s^{-1} at redshift z ~ 20). The neutrino-annihilation is not effective for Pop III GRBs because of a low central temperature, while the magnetic mechanism is viable. We also derive analytic estimates of the breakout conditions, which are applicable to various progenitor models. The GRB luminosity and duration are found to be very sensitive to the core and envelope mass, providing possible probes of the first luminous objects at the end of the high redshift dark ages.