Low mass strange stars and the compact star 1E1207.4-5209 in the field correlator method

Abstract

We investigate the possible existence of anomalous mass defects in the low mass region of stellar sequences of strange stars. We employ the nonperturbative equation of state derived in the framework of the field correlator method to describe the hydrostatic equilibrium of the strange matter. The large distance static $Q\overline{Q}$ potential ${V}_{1}$ and the gluon condensate ${G}_{2}$ are the main parameters of the model. We use the surface gravitational redshift measurements as a probe to determine the ratio $(\mathcal{P}/\mathcal{E}{)}_{C}$ at the center of strange stars. For ${V}_{1}=0$ and ${G}_{2}\ensuremath{\gtrsim}0.035\text{ }\text{ }{\mathrm{GeV}}^{4}$, we show that $(\mathcal{P}/\mathcal{E}{)}_{C}\ensuremath{\simeq}0.262$ and the corresponding redshift ${z}_{S}\ensuremath{\simeq}0.47$ are limiting values at the maximum mass of the highest mass stellar sequence. As a direct application of our study, we try to determine the values of ${V}_{1}$ and ${G}_{2}$ from astrophysical observations of the compact star 1E 1207.4-5209. Due to the uncertainties in the surface redshift determination, we made two attempts to obtain the model parameters. Our findings show that $(\mathcal{P}/\mathcal{E}{)}_{C}=0.07{3}_{+0.024}^{+0.029}$ at 68% confidence, ${V}_{1}=0.44\ifmmode\pm\else\textpm\fi{}0.10\text{ }\text{ }\mathrm{GeV}$ at 90% confidence and ${G}_{2}=0.008\ifmmode\pm\else\textpm\fi{}0.001\text{ }\text{ }{\mathrm{GeV}}^{4}$ at 95% confidence in the first attempt; and $(\mathcal{P}/\mathcal{E}{)}_{C}=0.087\ifmmode\pm\else\textpm\fi{}0.028$ at 71% confidence, ${V}_{1}=0.43\ifmmode\pm\else\textpm\fi{}0.085\text{ }\text{ }\mathrm{GeV}$ at 94% confidence and ${G}_{2}=0.0093\ifmmode\pm\else\textpm\fi{}0.00092\text{ }\text{ }{\mathrm{GeV}}^{4}$ at 94% confidence in the second attempt. These values of ${V}_{1}$ and ${G}_{2}$ are in reasonable agreement with the lattice and QCD sum rules calculations. As a consequence of the high values of ${V}_{1}$ and ${G}_{2}$, the anomalous mass defects of 1E 1207.4-5209 are $|{\mathrm{\ensuremath{\Delta}}}_{2}M|\ensuremath{\simeq}2.56\ifmmode\times\else\texttimes\fi{}{10}^{53}\text{ }\text{ }\mathrm{erg}$ in the first attempt and $|{\mathrm{\ensuremath{\Delta}}}_{2}M|\ensuremath{\simeq}2.94\ifmmode\times\else\texttimes\fi{}{10}^{53}\text{ }\text{ }\mathrm{erg}$ in the second attempt.