Impact of Rastall gravity on mass, radius and sound speed of the pulsar PSR J0740+6620

Abstract: Millisecond pulsars are perfect laboratories to test possible matter-geometry coupling and its physical implications in light of recent Neutron Star Interior Composition Explorer (NICER) observations. We apply Rastall field equations of gravity, where matter and geometry are nonminimally coupled, to Krori-Barua interior spacetime whereas the matter source is assumed to be anisotropic fluid. We show that all physical quantities inside the star can be expressed in terms of Rastall, $\epsilon$, and compactness, $C=2GM/Rc^2$, parameters. Using NICER and X-ray Multi-Mirror X-ray observational constraints on the mass and radius of the pulsar PSR J0740+6620 we determine Rastall parameter to be at most $\epsilon=0.041$ in the positive range. The obtained solution provides a stable compact object; in addition the squared sound speed does not violate the conjectured sound speed $c_s^2\leq c^2/3$ unlike the general relativistic treatment. We note that no equations of state are assumed; the model however fits well with linear patterns with bag constants. In general, for $\epsilon>0$, the theory predicts a slightly larger size star in comparison to general relativity for the same mass. This has been explained as an additional force, due to matter-geometry coupling, in the hydrodynamic equilibrium equation, which contributes to partially diminish the gravitational force effect. Consequently, we calculate the maximal compactness as allowed by the strong energy condition to be $C = 0.735$ which is $\sim 2\%$ higher than general relativity prediction. Moreover, for the surface density at saturation nuclear density $\rho_{\text{nuc}} = 2.7\times 10^{14}$ g/cm$^3$ we estimate the maximum mass $M=4 M_\odot$ at radius $R=16$ km.