Impact of the equation-of-state-gravity degeneracy on constraining the nuclear symmetry energy from astrophysical observables

There is a degeneracy between the equation of state (EOS) of superdense neutron-rich nuclear matter and the strong-field gravity in understanding properties of neutron stars. While the EOS is still poorly known, there are also longstanding ambiguities in choosing Einstein's general relativity (GR) or alternative gravity theories in the not-so-well-tested strong-field regime. Besides the possible appearance of hyperons and new phases, the most uncertain part of the nucleonic EOS is currently the density dependence of nuclear symmetry energy especially at suprasaturation densities. At the same time, the EOS of symmetric nuclear matter (SNM) has been significantly constrained at saturation and suprasaturation densities. To provide information that may help break the EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy within its uncertain range determined by recent terrestrial nuclear laboratory experiments on the gravitational binding energy and space-time curvature of neutron stars within GR and the scalar-tensor subset of alternative gravity models, constrained by recent measurements of the relativistic binary pulsars J1738+0333 and J0348+0432. In particular, we focus on effects of the following three parameters characterizing the EOS of superdense neutron-rich nucleonic matter: (1) the incompressibility K-0 of SNM, (2) the slope L of nuclear symmetry energy at saturation density, and (3) the high-density behavior of nuclear symmetry energy. We find that the variation of either the density slope L or the high-density behavior of nuclear symmetry energy leads to large changes in both the binding energy and the curvature of neutron stars while effects of varying the more constrained K-0 are negligibly small. The difference in predictions using the GR and the scalar-tensor theory appears only for massive neutron stars, and even then it is significantly smaller than the differences resulting from variations in the symmetry energy. We conclude that, within the scalar-tensor subset of gravity models, the EOS-gravity degeneracy has been broken by the recent relativistic pulsar measurements and that measurements of neutron-star properties sensitive to the compactness constrain mainly the density dependence of the symmetry energy at saturation and suprasaturation densities.