Supercritically charged objects and electron-positron pair creation

We investigate the stability and ${e}^{+}{e}^{\ensuremath{-}}$ pair creation of supercritically charged superheavy nuclei, $ud\mathrm{QM}$ nuggets, strangelets, and strangeon nuggets based on the Thomas-Fermi approximation. The model parameters are fixed by reproducing masses and charge properties of these supercritically charged objects reported in earlier publications. It is found that $ud\mathrm{QM}$ nuggets, strangelets, and strangeon nuggets may be more stable than $^{56}\mathrm{Fe}$ at the baryon number $A\ensuremath{\gtrsim}315$, $5\ifmmode\times\else\texttimes\fi{}{10}^{4}$, and $1.2\ifmmode\times\else\texttimes\fi{}{10}^{8}$, respectively. For those stable against neutron emission, the most massive superheavy element has a baryon number $\ensuremath{\sim}965$, while $ud\mathrm{QM}$ nuggets, strangelets, and strangeon nuggets need to have baryon numbers larger than 39, 433, and $2.7\ifmmode\times\else\texttimes\fi{}{10}^{5}$. The ${e}^{+}{e}^{\ensuremath{-}}$ pair creation will inevitably start for superheavy nuclei with charge numbers $Z\ensuremath{\ge}177$, for $ud\mathrm{QM}$ nuggets with $Z\ensuremath{\ge}163$, for strangelets with $Z\ensuremath{\ge}192$, and for strangeon nuggets with $Z\ensuremath{\ge}212$. A universal relation $Q/{R}_{e}=({m}_{e}\ensuremath{-}{\overline{\ensuremath{\mu}}}_{e})/\ensuremath{\alpha}$ is obtained at a given electron chemical potential ${\overline{\ensuremath{\mu}}}_{e}$, where $Q$ is the total charge and ${R}_{e}$ the radius of electron cloud. The maximum number of $Q$ without causing ${e}^{+}{e}^{\ensuremath{-}}$ pair creation is then fixed by taking ${\overline{\ensuremath{\mu}}}_{e}=\ensuremath{-}{m}_{e}$. For supercritically charged objects with ${\overline{\ensuremath{\mu}}}_{e}l\ensuremath{-}{m}_{e}$, the decay rate for ${e}^{+}{e}^{\ensuremath{-}}$ pair production is estimated based on the Jeffreys-Wentzel-Kramers-Brillouin (JWKB) approximation. It is found that most positrons are emitted at $t\ensuremath{\lesssim}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{s}$, while a long lasting positron emission can be observed for large objects with $R\ensuremath{\gtrsim}1000\text{ }\text{ }\mathrm{fm}$. The emission of positrons and electron-positron annihilation from supercritically charged objects may be partially responsible for the short $\ensuremath{\gamma}$-ray burst during the merger of binary compact stars, the 511 keV continuum emission, as well as the narrow faint emission lines in x-ray spectra from galaxies and galaxy clusters.