[Paper Review] Effects of anisotropy on strongly magnetized neutron and strange quark stars in general relativity

Debabrata Deb, Banibrata Mukhopadhyay+1 more|arXiv (Cornell University)|Aug 27, 2021

Pulsars and Gravitational Waves Research152 references75 citations

TL;DR

This study investigates anisotropic, strongly magnetized neutron and strange quark stars in general relativity using the Tolman-Oppenheimer-Volkoff (TOV) equations with anisotropic pressure. It finds that transverse magnetic fields enhance mass and radius via repulsive anisotropic forces, while radial fields reduce them due to attractive forces, and hydrostatic equilibrium requires accounting for both local fluid anisotropy and magnetic field-induced anisotropy.

ABSTRACT

We investigate the properties of anisotropic, spherically symmetric compact stars, especially neutron stars and strange quark stars, made of strongly magnetized matter. The neutron stars are described by SLy equation of state, the strange quark stars by an equation of state based on the MIT Bag model. The stellar models are based on an a priori assumed density dependence of the magnetic field and thus anisotropy. Our study shows that not only the presence of a strong magnetic field and anisotropy, but also the orientation of the magnetic field itself, have an important influence on the physical properties of stars. Two possible magnetic field orientations are considered, a radial orientation, where the local magnetic fields point in the radial direction, and a transverse orientation, where the local magnetic fields are perpendicular to the radial direction. Interestingly, we find that for a transverse orientation of the magnetic field, the stars become more massive with increasing anisotropy and magnetic field strength and increase in size, since the repulsive, effective anisotropic force increases in this case. In the case of a radially orientated magnetic field, however, the masses and radii of the stars decrease with increasing magnetic field strength, because of the decreasing effective anisotropic force. Importantly, we also show that in order to achieve hydrostatic equilibrium configurations of magnetized matter, it is essential to account for both the local anisotropy effects as well as the anisotropy effects caused by a strong magnetic field. Otherwise, hydrostatic equilibrium is not achieved for magnetized stellar models.

Motivation & Objective

• To investigate how strong magnetic fields and anisotropy affect the structure of compact stars in general relativity.
• To determine the influence of magnetic field orientation (radial vs. transverse) on stellar mass, radius, and stability.
• To resolve the long-standing question of whether magnetic fields increase or decrease compact star masses.
• To ensure hydrostatic equilibrium by accounting for both local fluid anisotropy and magnetic field-induced anisotropy.
• To validate the physical consistency of magnetized anisotropic stellar models through magneto-hydrostatic stability analysis.

Proposed method

• Modeling neutron stars using the SLy equation of state and strange quark stars using the MIT bag model equation of state.
• Assuming a density-dependent magnetic field profile with two distinct orientations: radial and transverse to the radial direction.
• Solving the generalized Tolman-Oppenheimer-Volkoff (TOV) equations that include both local fluid anisotropy and magnetic field-induced anisotropy.
• Calculating physical parameters such as central density, pressure, mass, radius, surface redshift, and gravitational binding energy.
• Evaluating the effective anisotropic force and its role in hydrostatic equilibrium, particularly at the stellar center.
• Performing magneto-hydrostatic stability analysis to confirm physical validity of the models.

Experimental results

Research questions

• RQ1 How does the orientation of a strong magnetic field (radial vs. transverse) affect the mass and radius of anisotropic compact stars?
• RQ2 What is the combined effect of local fluid anisotropy and magnetic field-induced anisotropy on stellar equilibrium?
• RQ3 Can hydrostatic equilibrium be achieved in magnetized compact stars if only one type of anisotropy is considered?
• RQ4 How do magnetic fields and anisotropy modify the equation of state and physical parameters like surface redshift and compactness?
• RQ5 What is the role of the effective anisotropic force in determining the stability and structure of strongly magnetized neutron and strange quark stars?

Key findings

• For transverse magnetic fields, increasing anisotropy and magnetic field strength lead to larger masses and radii due to a repulsive effective anisotropic force.
• For radial magnetic fields, increasing magnetic field strength reduces both mass and radius due to a decreasing effective anisotropic force.
• The maximum mass of magnetized compact stars can be enhanced or reduced depending on the magnetic field orientation, resolving a longstanding ambiguity.
• Hydrostatic equilibrium in magnetized stars is only achieved when both local fluid anisotropy and magnetic field-induced anisotropy are simultaneously accounted for.
• The effective anisotropic force at the stellar center is non-zero and must be considered to avoid force imbalance and instability.
• The model remains consistent with spherical symmetry, as anisotropy-induced deviations are negligible (up to 80–81% lower than central pressure) even at high magnetic fields.