Neutron star matter as a relativistic Fermi liquid

The equation of state (EoS) of neutron star matter, constrained by the existence of two-solar-mass stars and gravitational wave signals from neutron star mergers, is analyzed using the Landau theory of relativistic Fermi liquids. While the phase diagram of dense and cold QCD matter is still open for scenarios ranging from hadronic to quark matter in the center of neutron stars, a Fermi-liquid treatment is motivated by a microscopic approach starting from a chiral nucleon-meson field theory combined with nonperturbative functional renormalization group methods. In this scheme effects of multipionic fluctuations and repulsive nuclear many-body correlations suggest that the transition to chiral symmetry restoration is shifted to densities above those typically encountered in the neutron star core. Under such conditions a Fermi-liquid description in terms of nucleon quasiparticles appears to be justified. The leading Landau parameters are derived and discussed. Our results are contrasted with a well-known Fermi liquid, namely liquid ${}^3\mathrm{He}$.

Figure 1

The equation of state of neutron star matter in beta equilibrium (pressure $P$ as a function of energy density $\mathcal{E}$) derived from chiral nucleon-meson field theory combined with functional renormalization group equations [19, 20]. The shaded band gives an uncertainty estimate when varying the symmetry energy in the range $30–34\mathrm{MeV}$. In the limit of very low densities ($\rho <0.3{\rho }_0$ corresponding to $\mathcal{E}<0.045\mathrm{GeV}/{\mathrm{fm}}^3$), the EoS is matched to the Skyrme-Lyon (SLy) parametrization [21].

Figure 2

The squared speed of sound, $c_1^2=\partial P\left(\mathcal{E}\right)/\partial \mathcal{E}$, derived from the neutron star matter equation of state, Fig. 1.

Figure 3

Pressure as a function of energy density for neutron star matter with constraints from perturbative QCD and nuclear EFT calculations at the upper and lower ends of the density scale, adapted from Refs. [32, 33]. The area between the upper and lower limits marks the range of acceptable equations of state subject to empirical conditions on neutron star maximum mass and tidal deformability, the latter from LIGO and Virgo gravitational wave analysis. The solid curve represents the chiral FRG equation of state $P\left(\mathcal{E}\right)$ as in Fig. 1.

Figure 4

Energy density of neutron star matter from chiral FRG calculations [19, 20] as a function of density given in units of ${\rho }_0=0.16 {\mathrm{fm}}^{-3}$.

Figure 5

Energy per particle deduced from the chiral FRG equation of state as a function of baryon density given in units of ${\rho }_0=0.16 {\mathrm{fm}}^{-3}$.

Figure 6

Chemical potential of neutron matter from ChNM-FRG calculations [19, 20] as a function of density given in units of ${\rho }_0=0.16 {\mathrm{fm}}^{-3}$.

Figure 7

Neutron quasiparticle mass $M\left(\rho \right)$ and effective potential $U\left(\rho \right)$ as functions of density. The effective mass is given in units of the vacuum neutron mass, $M_0=939.57$ MeV.

Figure 8

Landau effective mass $m^{*}\left(\rho \right)=\sqrt{p_F^2+M^2\left(\rho \right)}$ as a function of density in units of ${\rho }_0=0.16 {\mathrm{fm}}^{-3}$.

Figure 9

Landau Fermi liquid parameters $F_0$ and $F_1$ for neutron star matter as a function of density $\rho /{\rho }_0$ in units of ${\rho }_0=0.16 {\mathrm{fm}}^{-3}$.

Figure 10

The effective vector potential $V_0\left(\rho \right)$ and the ratio of Landau effective mass over chemical potential, $m^{*}/\mu$, for the limiting case $M\left(\rho \right)\equiv M_0$, as functions of baryon density in units of ${\rho }_0=0.16 {\mathrm{fm}}^{-3}$. The dashed line indicates the range of densities, where the ansatz (74) yields $V_0<0$, at variance with the model assumptions (see main text).

Figure 11

Landau parameters $F_0$ and $F_1$ as functions of baryon density in units of ${\rho }_0=0.16 {\mathrm{fm}}^{-3}$. The upper and lower bounds of the shaded areas correspond to the following limiting cases for choices of the baryon mass: (a) lower boundary lines: $M\left(\rho \right)/M_0=\langle \sigma \rangle \left(\rho \right)/f_{\pi }$ as in Fig. 9; (b) upper boundary lines: $M\left(\rho \right)\equiv M_0$ at all densities.

Figure 12

Velocity $c_0$ (in units of the speed of light) of the zero-sound collective mode, as a function of baryon density in units of ${\rho }_0=0.16 {\mathrm{fm}}^{-3}$. The two curves correspond to different choices of quasiparticle masses. Curve (a): baryon mass $M\left(\rho \right)\propto f_{\pi }^{*}\left(\rho \right)$; curve (b): using $M\left(\rho \right)\equiv M_0$. At densities below and above the end points indicated in curve (a) the zero-sound velocity is complex.