Electron and positron pair production of compact stars

Neutral stellar core at or over nuclear densities is described by a positive charged baryon core and negative charged electron fluid since they possess different masses and interactions. Based on a simplified model of a gravitationally collapsing or pulsating baryon core, we approximately integrate the Einstein-Maxwell equations and the equations for the number and energy-momentum conservation of complete degenerate electron fluid. We show possible electric processes that lead to the production of electron-positron pairs in the boundary of a baryon core and calculate the number and energy of electron-positron pairs. This can be relevant for understanding the energetic sources of supernovae and gamma-ray bursts.

Figure 1

The space and time evolution of the electric field (left) and charge separation (right) around the boundary layer of the baryon core, $M=10M_{\odot }$, $R_c\approx {10}^7\mathrm{cm}$, and $v_p=0.2c$. The coordinate is $\xi \equiv r-R_c$.

Figure 2

Time evolution of electric fields at different radial positions around the boundary layer of the baryon core, $M=10M_{\odot }$, $R_c\approx {10}^7\mathrm{cm}$, and $v_p=0.2c$. The coordinate is $\xi \equiv r-R_c$.

Figure 3

The estimate of the core collapsing velocity $v_p\equiv {\dot{R}}_c=d{R}_c/dt$ at different collapsing radii $R_c$ for the baryon core of mass $M=10M_{\odot }$.

Figure 4

The energy (left) and number (right) densities of electron-positron pairs at selected values of collapsing radii $R_c$ for $M=10M_{\odot }$ and $N_p/N_B\approx 1/38(\mathrm{upper});1/380(\mathrm{lower})$. We select $R_c^{\max }\sim {10}^7\mathrm{cm}$ so that ${\overline{n}}_B\sim n_{\mathrm{nucl}}$.

Figure 5

The charge-mass ratio $Q/M$ averaged over oscillations of electric fields is plotted at different collapsing radii $R_c$ for the baryon core of mass $M=10M_{\odot }$.