Symmetry energy dilemma within a relativistic quark model

We develop the equation of state of dense neutron star matter with nucleons, nucleons and hyperons, nucleons and delta, as well as including strange interactions through strange meson-hyperon couplings to assess the effect of both the soft and stiff symmetry energy, determined in the recent PREX-II experiment, on the properties of neutron stars. The macroscopic properties of neutron stars such as the mass, radius and tidal deformability are a direct consequence of the underlying equation of state of dense neutron star matter. Given the recent advances in constraining the above macroscopic observations from gravitational wave analysis, NICER and radio observations, we study here the effect of a variation in the symmetry energy on such observational properties of neutron stars with different possible compositions in a relativistic quark model. We observe that the stiff symmetry energy satisfies the current constraints on maximum mass and radius, but creates tension with tidal deformability values.

Figure 1

(a) Symmetry energy as a function of density for four different $J$ values and (b) the corresponding slope $L$. The shaded region shows the range of $L=106\pm 37$ suggested in Ref. [2].

Figure 2

Neutron star masses as a function of the radius computed for different compositions. Each figure shows the effect of the variation in the $J$ and the shaded region shows the mass range $2.08\pm 0.07{\mathrm{M}}_{\odot }$ of the pulsar PSR $\text{J0740}+6620$ determined from NICER observations.

Figure 3

Love number as a function of mass of star.

Figure 4

Tidal deformability as a function of neutron star mass for different compositions. The vertical line indicates the canonical mass while the horizontal lines indicate earlier [30] and revised [31] upper limits of the ${\mathrm{\Lambda }}_D$.

Figure 5

The square of the speed of sound as a function of density for various compositions at different $J$. The horizontal line indicates the conformal limit $c_s^2=1/3$.

Figure 6

The adiabatic index as a function of density for different compositions.