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 model and the H model, to investigate the effect of anisotropy. Similar to the isotropic case, the maximum mass Mₘₐₓ and its corresponding radius RMmax can also be expressed linearly by a combination of radial central pressure prc and central energy density εc, which is insensitive to the equation of state (EOS). We also found that the obtained central EOS would change with different values of λBL (λH), 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 λBL = 0.4, the extracted central energy density εc changed from 546 -- 1056 MeV/fm³ to 510 -- 1005 MeV/fm³, and the extracted radial central pressure prc changed from 87 -- 310 MeV/fm³ to 76 -- 271 MeV/fm³. For λBL = 2, the extracted εc and prc changed to 412 -- 822 MeV/fm³ and 50 -- 165 MeV/fm³, respectively. In the H model, for λH = 0.4, the extracted εc changed to 626 -- 1164 MeV/fm³, and the extracted prc changed to 104 -- 409 MeV/fm³. For λH = 2, the extracted εc decreased to 894 -- 995 MeV/fm³, and the extracted prc changed to 220 -- 301 MeV/fm³.