#### Date of Degree

9-2022

#### Document Type

Dissertation

#### Degree Name

Ph.D.

#### Program

Physics

#### Advisor

Efrain J. Ferrer

#### Committee Members

Vivian de la Incera

Daniel N. Kabat

Charles Liu

Mario Diaz

#### Subject Categories

Elementary Particles and Fields and String Theory | Nuclear

#### Keywords

Compact Stars, Nuclear Astrophysics, QCD Phase Diagram

#### Abstract

In the context of neutron stars (NS), dense-magnetized quark and hadron models have been well studied under the assumption that the system's pressures are isotropic. However, the pressures determined from semi-classical statistical averaging of the energy momentum tensor in the presence of a uniform background magnetic field are anisotropic with different pressures arising along and perpendicular to the magnetic field direction. Since large magnetic fields are expected to be present in the interior of NS, it is important to understand the roll the pressure anisotropy plays. While considering the pressure anisotropy, we revisit some important calculations in NS physics.

We start by investigating the effects of a magnetic field on the thermodynamics of a neutron system at finite density and temperature. Our main motivation is to deepen the understanding of the physics of a class of NS known as magnetars, which exhibit extremely strong magnetic fields. Taking into account that the quantum field theory contribution to the pressure is non-negligible, we show that the maximum value that the inner magnetic field of a star can reach while being in agreement with the magneto-hydrostatic equilibrium between the gravitational and matter pressures becomes 10^{17}G, an order of magnitude smaller than the previous value obtained through the scalar virial theorem; that the magnetic field has a negligible effect on the neutron system's equation of state (EOS); that the system's magnetic susceptibility increases with the temperature and that the specific heat C_{V} does not significantly change with the magnetic field in the range of temperatures characteristic of proto NS.

Next, we investigate the hadron-quark phase transition at finite density in the presence of a magnetic field taking into account the anisotropy created by a uniform magnetic field in the system's EOS. We find a new anisotropic equilibrium condition that drives the first-order phase transition along the boundary between the two phases. Fixing the magnetic field in the hadronic phase, the phase transition is realized by increasing the baryonic chemical potential at zero temperature. It is shown in the Maxwell construction that the magnetic field is mildly boosted after the system transitions from the hadronic to the quark phase. The magnetic-field discontinuity between the two phases is supported by a surface density of magnetic monopoles, which accumulate at the boundary separating the two phases. The mechanism responsible for the monopole charge density generation is discussed. Each phase is found to be paramagnetic with higher magnetic susceptibility in the quark phase.

Finally, it is well known that for a fermion system with an isotropic (EOS), the square of the speed of sound (SOS)^{2} is a measure of the stiffness of the equation of state (EOS). It is also known that in the presence of a magnetic field the EOS becomes anisotropic with two different pressures arising, one directed parallel to the field direction and one perpendicular to it. Since the SOS in a medium is created by pressure oscillations, the anisotropy in the pressure should be transferred to the SOS. We derive from first principles the anisotropic wavelike equation from where the expressions for the longitudinal and transverse SOS in the presence of a uniform magnetic field can be obtained. We also investigate the degree to which the magnetic field in the weak and the strong limit affects the two SOS of (i) a system of hadrons modeled by the nonlinear Walecka model and (ii) a system of quarks modeled by the MIT bag model. We find that for the systems considered, the effects of the magnetic field on the SOS anisotropy are mild up to 10^{18}G. Links to NS physics will be discussed throughout.

#### Recommended Citation

Hackebill, Aric A., "Magnetic Field Effects on the Physics of Neutron Stars" (2022). *CUNY Academic Works.*

https://academicworks.cuny.edu/gc_etds/5030