Anisotropic pressure effect on central EOS of PSR J0740+6620 in the light of dimensionless TOV equation

TL;DR

This paper investigates how pressure anisotropy, influenced by magnetic fields or superfluidity, affects the central equation of state of neutron star PSR J0740+6620 using a dimensionless TOV equation for anisotropic models.

Contribution

The study derives a dimensionless TOV equation for anisotropic neutron stars and analyzes how anisotropy impacts the central EOS and observable parameters, providing new insights into neutron star structure.

Findings

Maximum mass and radius are linearly related to central pressure and energy density.

Anisotropy parameter significantly alters the inferred central EOS values.

Results are consistent with observational data for different anisotropy models.

Abstract

It is generally agreed upon that the pressure inside a neutron star is isotropic. However, a strong magnetic field or superfluidity suggests that the pressure anisotropy may be a more realistic model. We derived the dimensionless TOV equation for anisotropic neutron stars based on two popular models, namely the BL model and the H model, to investigate the effect of anisotropy. Similar to the isotropic case, the maximum mass $M_{max}$ and its corresponding radius $R_{Mmax}$ can also be expressed linearly by a combination of radial central pressure $p_{rc}$ and central energy density $\varepsilon_{c}$, which is insensitive to the equation of state (EOS). We also found that the obtained central EOS would change with different values of $\lambda_{BL}$ ($\lambda_{H}$), which controls the magnitude of the difference between the transverse pressure and the radial pressure. Combining with observational data of PSR J0740+6620 and comparing to the extracted EOS based on isotropic neutron star, it is shown that in the BL model, for $\lambda_{BL}$ = 0.4, the extracted central energy density $\varepsilon_{c}$ changed from 546 -- 1056 MeV/fm$^{3}$ to 510 -- 1005 MeV/fm$^{3}$, and the extracted radial central pressure $p_{rc}$ changed from 87 -- 310 MeV/fm$^{3}$ to 76 -- 271 MeV/fm$^{3}$. For $\lambda_{BL}$ = 2, the extracted $\varepsilon_{c}$ and $p_{rc}$ changed to 412 -- 822 MeV/fm$^{3}$ and 50 -- 165 MeV/fm$^{3}$, respectively. In the H model, for $\lambda_{H}$ = 0.4, the extracted $\varepsilon_{c}$ changed to 626 -- 1164 MeV/fm$^{3}$, and the extracted $p_{rc}$ changed to 104 -- 409 MeV/fm$^{3}$. For $\lambda_{H}$ = 2, the extracted $\varepsilon_{c}$ decreased to 894 -- 995 MeV/fm$^{3}$, and the extracted $p_{rc}$ changed to 220 -- 301 MeV/fm$^{3}$.