Pair luminosity and cooling of newborn strange star: Unpaired quarks

It was shown that pair luminosity of the newborn strange star with temperature of $10^{11}$ K may be as high as $L_\pm\simeq 10^{52}$ erg/s. The question remains: can a strange star maintain such a high surface temperature for a long time? To answer this question we studied thermal evolution of newborn strange star made of unpaired quarks taking into account its thermal conductivity and neutrino emission by the URCA processes $d\rightarrow u + e + \barν_e$ and $u+e\rightarrow d+ν_e$. Our results show that extremely high luminosity due to the Schwinger process and insufficient thermal conductivity of quarks leads to development of steep temperature gradient at the surface of strange star. As a result, the temperature at the surface and hence its luminosity decreases, reaching $10^{43}$ erg/s already at $10^2$ seconds. This result holds even in the presence of neutrinosphere.