Quark-hybrid matter in the cores of massive neutron stars

Using a nonlocal extension of the SU(3) Nambu–Jona-Lasinio model, which reproduces several of the key features of quantum chromodynamics, we show that mixed phases of deconfined quarks and confined hadrons (quark-hybrid matter) may exist in the cores of neutron stars as massive as around $2.1M_{\odot }$. The radii of these objects are found to be in the canonical range of $\sim 12–13\mathrm{km}$. According to our study, the transition to pure quark matter does not occur in stable neutron stars, but is shifted to neutron stars which are unstable against radial oscillations. The implications of our study for the recently discovered, massive neutron star PSR J1614–2230, whose gravitational mass is $1.97\pm 0.04M_{\odot }$, are that this neutron star may contain an extended region of quark-hybrid matter at it center, but no pure quark matter.

Figure 1

Pressure, $P$ (solid lines), baryon chemical potential, ${\mu }_b$ (dashed lines), and electron chemical potential, ${\mu }_e$ (dotted lines) as a function of baryon number density, $\rho$, in units of the normal nuclear matter density, ${\rho }_0=0.16{\mathrm{fm}}^{-3}$. The hatched areas denote the mixed phase regions where confined hadronic matter and deconfined quark matter coexist. The solid dots indicate the central densities of the associated maximum-mass stars, shown in Fig. 3, and $\chi$ is the respective fraction of quark matter inside of them. The results are computed for three different values of the vector coupling constant, ranging from 0, to 0.05 $G_s$, to 0.1 $G_s$.

Figure 2

Volume fraction, $\chi$, of quark phase as a function of baryon number density, $\rho$, in units of normal nuclear matter density, ${\rho }_0=0.16{\mathrm{fm}}^{-3}$. The solid dots indicate the central densities of the respective maximum-mass stars shown in Fig. 3.

Figure 3

Depending on the strength of the vector repulsion ($G_V$) of the nonlocal NJL model, maximum masses up to $2.1M_{\odot }$ are obtained. With increasing stellar mass, the stellar core compositions consist of either only nucleons, nucleons and hyperons, a mixed phase of quarks and hadrons (MP), or a pure quark matter phase (QP). The latter, however, exists only in neutron stars which lie to the left of their respective mass peaks. Such stars are unstable against radial oscillations and thus cannot exist stably in the Universe. In contrast to this, all neutron stars on the MP branches up to the mass peaks are stable. The gray band denotes the $1\mathrm{\text{−}}\sigma$ error bar of the $M=(1.97\pm 0.04)M_{\odot }$ neutron star PSR J1614–2230 [6].