we use a simple Thomas-Fermi model considered by @Al86 and take into account the finite temperature effects as discussed by @Ke95.

This model can be solved exactly, and all physical quantities of interest (chemical potential, electric field etc.) can be expressed in an exact analytical form [@ChHa03; @Us05]. The chemical equilibrium in the electrosphere implies that the electron chemical potential $\mu _e$ satisfies the condition $-V\left(\infty \right)+\mu _e\left(\infty \right)=-V+\mu _{e}$, where $V$ is the electrostatic potential per unit charge and $V\left(\infty \right)$ and $ \mu _e\left(\infty \right)$ are the values of the electrostatic potential and of the electron’s chemical potential at infinity, respectively. Since far outside the star both $V\left(\infty \right)$ and $ \mu _e\left(\infty
\right)$ tend to zero, it follows that $\mu _{e}=V$ [@Al86].

The structure of the electrosphere and the corresponding radiation processes essentially depends on the value of $V_q$, the electric charge density inside the quark star. When the temperature of the quark star core drops below $10^{9}$ K, the strange matter becomes superfluid. At this temperature quarks can form colored Cooper pairs near the Fermi surface and become superconducting. From the BCS theory it follows that the critical temperature $T_{c}$ at which the transition to the 