Speed of Sound for Hadronic and Quark Phases in a Magnetic Field

TL;DR

This study calculates the speed of sound in different phases inside magnetized neutron stars, revealing non-monotonic behavior influenced by magnetic fields and phase transitions, with implications for understanding dense matter properties.

Contribution

It introduces a detailed analysis of the anisotropic speed of sound across hadronic, MDCDW, and quark phases in magnetic fields, including first-principles derivations and Landau level effects.

Findings

Speed of sound varies non-monotonically across phases.

Magnetic fields induce anisotropy in the speed of sound.

Lowest Landau level significantly impacts sound speed in magnetized phases.

Abstract

In this paper we calculate the speed of sound for three phases that may exist inside a magnetized hybrid neutron star at different density regions: A hadronic phase at low densities, quark-matter in the magnetic dual chiral density wave (MDCDW) phase at intermediate densities and a free-quark phase modeled by the MIT bag model at higher densities. It is found that the speed of sound exhibits a non-monotonic behavior, that goes from values smaller than the conformal limit ($c_s^2 < 1/3$) in the hadronic phase, to peak ($c_s^2 > 1/3$) in the MDCDW phase, to finally reach the conformal limit ($c_s^2 \sim 1/3$) at higher densities for quarks in the MIT bag model. Also, the anisotropic speed of sound in the presence of a magnetic field is derived from first principles. This is a consequence of the anisotropy in the system's pressures produced by the breaking of the rotational symmetry in the presence of a magnetic field. The role played by the lowest Landau level contribution in affecting the speed of sound in the magnetized phases is discussed.