Pair luminosity and cooling of newborn strange star: unpaired quarks

TL;DR

This study analyzes the thermal evolution of a newborn strange star composed of unpaired strange quark matter, focusing on the electrosphere Schwinger pair production and the limited quark thermal conductivity. By solving the hydrostatic structure with a bag-model EOS, modeling the electrosphere via Poisson and Vlasov-Maxwell equations, and performing both neutrino-transparent and neutrino-opaque heat-transfer calculations, it shows that a surface temperature gradient forms rapidly and the surface temperature plummets well before the interior cools, yielding surface luminosities around $10^{43}$ erg s$^{-1}$ within $\sim 10^{2}$ s. The results imply that such stars cannot maintain extreme pair luminosities for long, challenging scenarios that rely on prolonged high surface temperatures, and they highlight the potential impact of color superconductivity on thermal transport as a future avenue.

Abstract

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.

Figures (8)

• Figure 1: Total mass vs. central density for stable quark stars.
• Figure 2: Chemical potentials as functions of radius of the star with $M=1.4M_\odot$: $\mu_s=\mu_d$ (orange), $\mu_u$ (green), $10\mu_e$ (blue).
• Figure 3: Exact solution of Poisson equation \ref{['poissoneq']} for $k_BT=m_ec^2$: as function of distance we show chemical potential (top), electric field (middle) and particle density (bottom). Since the chemical potential decreases to zero at $z\simeq21\lambda_e$ the electric field vanishes at this distance. The density of electrons does not vanish here.
• Figure 4: Normalized pair rate \ref{['ndotschwinger']} (blue) with the corresponding normalized electric field (red) for $k_BT=m_ec^2$.
• Figure 5: Stationary solution of Vlasov-Maxwell equations for electrosphere for $k_BT=2m_ec^2$ with dependence on distance of electric field (top), particle density (middle) and luminosity (bottom). Approximate electrostatic solution given by eq. (\ref{['poissoneq']}) is shown in black. Colors correspond to: electric field (red), electrons (blue) positrons (orange), and electrostatic solution (black).