Speed of sound and isothermal compressibility in a magnetized quark matter with anomalous magnetic moment of quarks

We study the characteristics of quark matter under the influence of a background magnetic field with anomalous magnetic moment (AMM) of quarks at finite temperature and quark chemical potential in the framework of Polyakov loop extended Nambu Jona-Lasinio (PNJL) model. In presence of a magnetic field, the speed of sound and isothermal compressibility become anisotropic with respect to the direction of the background magnetic field, splitting into parallel and perpendicular directions with respect to the magnetic field. Though the qualitative nature of parallel and perpendicular components of squared speed of sound appear similar, they differ in magnitude at lower values of temperature. The parallel and perpendicular components of isothermal compressibility decrease with increasing temperature, indicating a trend towards increased incompressible strongly interacting matter. On inclusion of the AMM of quarks, the perpendicular component of isothermal compressibility becomes greater than the parallel component. Additionally, we investigate the quark number susceptibility normalized by its value at zero magnetic field, which may indicate the presence of magnetic fields in the system.