Dispersion properties of neutron star magnetospheric plasmas with relativistic kappa distribution

Abstract

The various distribution functions can encompass the diverse characteristics of the magnetospheric plasma of surrounding neutron stars in both hot and cold environments; however, the Maxwell-J\"uttner distribution is so far widely used to characterize these plasmas. We aim to analyze the linear dispersion properties yielded from the relativistic kinetic dispersion relation for the neutron star magnetospheric plasmas. We developed a numerical dispersion solver to investigate plasmas with arbitrary velocity distributions and focus on the comparison of relativistic kappa and Maxwell-J\"uttner distribution functions as analytical representatives. By considering different kappa distribution indices and using analytical and numerical approaches, the dispersion properties of the kappa and Maxwell-J\"uttner distributions approach each other for high wave numbers and low temperatures, indicating that the choice of distribution functions has little effect on high wave numbers $ck/\omega_p \gg 1$ and high inverse temperatures $\rho=100$. However, each distribution function exhibits unique yet complementary properties in semi-relativistic to relativistic inverse temperatures $\rho \leq 10^{-1}$ and at lower wave numbers $ck/\omega_p\leq 1$. This highlights the necessity of utilizing such a dispersion solver for these wave numbers to properly comprehend the dispersion properties of the neutron star magnetospheric plasmas.