Bayesian Inference of dense matter equation of state of neutron star with antikaon condensation

In this paper, we employ the Density Dependent Relativistic Hadron (DDRH) field theoretical Model in a Bayesian analysis to investigate the equation of state (EOS) of dense matter featuring antikaon condensation for $K^-$ and $\bar{K}^0$ inside neutron stars. The vector coupling parameters within the kaonic sector are determined through the iso-spin counting rule and quark model. Our study integrates various constraints, including $\chi$EFT calculations, nuclear saturation properties, and astrophysical observations from pulsars PSR J0030+0451 and PSR J0740+66 and from the GW170817 event. We present posterior distributions of model parameters derived from these constraints, enabling us to explore the distributions of nuclear matter properties and neutron star (NS) characteristics such as radii, tidal deformabilities, central energy densities, and speed of sound. The antikaon potential at the 68(90)\% confidence intervals is determined to be $-129.36^{+12.53(+32.617)}_{-3.837(-5.696)}$ MeV. This aligns with several studies providing estimates within the range of $-120$ to $-150$ MeV. We find that the maximum neutron star mass is constrained to around 2M$_\odot$ due to the significant softening of the EOS caused by antikaon condensation. This softening results in a considerable decrease in the speed of sound. Although antikaon condensation for $K^-$ is not feasible inside the canonical neutron stars, it becomes feasible for higher NS masses. The condensation of both $K^-$ and $\bar{K}^0$ is probably present in the interior of neutron star with mass greater than 2M$_\odot$. We also discuss the interconnections among input variables, isoscalar and isovector aspects of the EOS, and specific NS properties in the context of antikaon condensation.