Gluon effects on the equation of state of color superconducting strange stars

Compact astrophysical objects are a window for the study of strongly interacting nuclear matter given the conditions in their interiors, which are not reproduced in a laboratory environment. Much has been debated about their composition with possibilities ranging from a simple mixture of mostly protons and neutrons to deconfined quark matter. Recent observations on the mass of two pulsars, PSR $\mathrm{J}1614-2230$ and PSR $\mathrm{J}0348+0432$, have posed a great restriction on their composition, since the equation of state must be hard enough to support masses of about at least two solar masses. The onset of quarks tends to soften the equation of state, but it can get substantially stiffer since in the high-dense medium a repulsive vector interaction channel is opened. Nevertheless, we show that once gluon effects are considered, the equation of state of strange stars formed by quark matter in the color-flavor-locked (CFL) phase of color superconductivity becomes softer decreasing the maximum stellar mass that can be reached. This may indicate that strange stars made entirely of CFL matter can only be favored if other interactions, as the one corresponding to the vector channel, are taken into consideration and are large enough.

Figure 1

Energy per baryon number of quark matter at zero pressure as a function of the vector coupling. The horizontal long dashed line indicates the limiting value of 930 MeV (energy per baryon number of the iron nucleus). The solid line is for CFL matter without gluons, and the dashed line, for CFL matter with gluons.

Figure 2

Equation of state for CFL matter with gluon contribution (right panel) and without it (left panel), for different values of the vector coupling $G_V$.

Figure 3

Sound speed as a function of the baryon density for CFL matter without the gluon term (left panel) and with it (right panel), for different values of the vector coupling strengths. The starting point to the left of each curve corresponds to the zero pressure point. The horizontal long dashed line determines the causality limit ($v_S=c$).

Figure 4

Mass-radius relationship of strange stars made of CFL matter with (right panel) and without (left panel) the gluon contribution. The softening of the EOS by the gluons significantly decreases the maximum mass of the sequence, which for vector interaction with $G_V/G_S<0.2$ remains below $2M_{\odot }$.