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

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 and H models, to investigate the effect of anisotropy. Similar to the isotropic case, the maximum mass and its corresponding radius can also be expressed linearly by a combination of radial central pressure and central energy density , which is insensitive to the equation of state (EOS). We also found that the obtained central EOS would change with different values of ( ), which controls the magnitude of the difference between the transverse pressure and radial pressure. Combining with observational data of PSR J0740+6620 and comparing to the extracted EOS based on an isotropic neutron star, it is shown that in the BL model, for = 0.4, the extracted central energy density changed from 546 − 1056 MeV/fm3 to 510 − 1005 MeV/fm3, and the extracted radial central pressure changed from 87 − 310 MeV/fm3 to 76 − 271 MeV/fm3. For = 2, the extracted and changed to 412 − 822 MeV/fm3 and 50 − 165 MeV/fm3, respectively. In the H model, for = 0.4, the extracted changed to 626 − 1164 MeV/fm3, and the extracted changed to 104 − 409 MeV/fm3. For = 2, the extracted decreased to 894 − 995 MeV/fm3, and the extracted changed to 220 − 301 MeV/fm3.