Neutron Stars in Scalar-tensor Gravity with Quartic Order Scalar Potential

Abstract: In this work we investigate the effects of a non-minimally coupled quartic order scalar model on static neutron stars, with the non-minimal coupling in the Jordan frame being of the form $f(\phi ) = 1 + \xi\phi^2$. Particularly we derive the Einstein frame Tolman-Oppenheimer-Volkoff equations, and by numerically integrating them for both the interior and the exterior of the neutron star, using a double shooting python 3 based numerical code, we extract the masses and radii of the neutron stars evaluated finally in the Jordan frame, along with several other related physical quantities of interest. With regard to the equation of state for the neutron star, we use a piecewise polytropic equation of state with the central part being Skyrme-Lyon (SLy), Akmal-Pandharipande-Ravenhall (APR) or the Wiringa-Fiks-Fabrocini (WFF1) equations of state. The resulting $M-R$ graphs are compatible with the observational bounds imposed by the GW170817 event which require the radius of a static $M\sim 1.6 M_{\odot}$ neutron star to be larger than $R=10.68^{+15}_{-0.04}$km and the radius of a static neutron star corresponding to the maximum mass of the star to be larger than $R=9.6^{+0.14}_{-0.03}$km. Moreover, the WFF1 EoS, which was excluded for static neutron stars in the context of general relativity, for the a quartic order scalar model neutron star model provides realistic results compatible with the GW170817 event.