Can average speed of sound and thermodynamic response functions signal the exotic phases in neutron star cores?

Abstract

The speed of sound in dense nuclear matter is crucial for understanding neutron star structure and constraining the EOS. We have discussed in details the decomposition of speed of sound via the average speed of sound and its logarithmic derivative and have connected it to the other two decomposition schemes via slope and curvature of the energy per particle or through the normalized trace anomaly and its derivative. These thermodynamic variables provide important diagnostic tools for the composition of the inner core of the compact stars. We discuss a new method of understanding phase transition and the microphysics of dense matter through the thermodynamic response functions like isothermal compressibility, baryon number susceptibility and bulk modulus in order to distinguish between local (sharp interface) and global charge (mixed phase) neutrality conditions, thereby revealing the signatures of the phase transition. The corresponding neutron-star mass--radius relations demonstrate that all considered equations of state satisfy current astrophysical constraints, while the most massive stable configurations contain either an extended mixed phase or a quark core depending on the phase-transition construction.