Thermal Evolution and Light Curves of Young Bare Strange Stars

We study numerically the cooling of a young bare strange star and show that its thermal luminosity, mostly due to $e^{+}{e}^{-}$ pair production from the quark surface, may be much higher than the Eddington limit. The mean energy of photons far from the strange star is $\sim {10}^2\mathrm{k}\mathrm{e}\mathrm{V}$ or even more. This differs both qualitatively and quantitatively from the thermal emission from neutron stars and provides a definite observational signature for bare strange stars. It is shown that the energy gap of superconducting quark matter may be estimated from the light curves if it is in the range from $\sim 0.5\mathrm{M}\mathrm{e}\mathrm{V}$ to a few MeV.

Figure 1

Upper panel: luminosities in neutrinos, $L_{\nu }$, and photons plus $e^{+}{e}^{-}$ pairs, $L_{\mathrm{t}\mathrm{h}}$, for a strange star in the normal phase (solid lines) and in the 2SC phase (dashed lines). Lower panel: temperature in the center, $T_{\mathrm{c}}$, at the surface, $T_{\mathrm{s}}$, and 1 m below the surface, $T_{\mathrm{s}\mathrm{-}\mathrm{1}\mathrm{m}}$, of the strange star in the normal phase. The large difference between $T_{\mathrm{s}}$ and $T_{\mathrm{s}\mathrm{-}\mathrm{1}\mathrm{m}}$ at early times illustrates the enormous temperature gradient present just below the surface because of the large $L_{\mathrm{t}\mathrm{h}}$.

Figure 2

The thermal luminosity of the strange star in the 2SC phase with secondary pairing of the $u_3$-$d_3$ and $s$ quarks for three different scenarios of pairing [A], [B], and [C] as described in the text (solid lines). Arrows on curves [B] and [C] point to the time at which $L_{\nu }$ becomes lower than $L_{\mathrm{t}\mathrm{h}}$; in case [A] $L_{\nu }\gg L_{\mathrm{t}\mathrm{h}}$ at all times. The dotted line shows the evolution of $L_{\mathrm{t}\mathrm{h}}$ without any pairing for comparison (from Fig. 1).

Figure 3

The thermal luminosity for the same scenarios as in Fig. 2. It is assumed that the star is isothermal due to either convection or superfluid counterflow. The dotted curve shows the evolution of $L_{\mathrm{t}\mathrm{h}}$ without any pairing for comparison.