Neutron stars in the large-$N_c$ limit

Abstract

We study the phase transition from dense baryonic matter to dense quark matter within the large-$N_c$ limit. By using simple constant speed of sound equations of state for the two phases, we derive the scaling with $N_c$ of the critical quark chemical potential ${\mu }_c^{\mathrm{crit}}$ for this phase transition. While quark matter is strongly suppressed at large $N_c$, the phase transition at a large but finite density could nevertheless be important to determine the maximum mass of compact stars. In particular, in the range $3\le N_c\lesssim 5.5$ the quark phase would take place in compact stars and would lead to the formation of an unstable branch of hybrid stars. As a consequence, the maximum mass is restricted to the range $2.1M_{\odot }<M_{max}<3M_{\odot }$. For larger value of $N_c$, the phase transition would occur at densities too high to be reached in the core of compact stars. However, the very requirement that it occurs (although at a very large density) translates into interesting constraints on the stiffness of the baryonic phase: its speed of sound must exceed $\sqrt{1/3}$.

8 pages, 1 figure

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Cited by in corpus (4)

• Remarks on nuclear matter: how an ${\omega }_0$ condensate can spike the speed of sound, and a model of $Z(3)$ baryons
• The fate of the critical endpoint at large $N_c$
• Building models of quarks and gluons with an arbitrary number of colors using Cartan-Polyakov loops
• Wheeler-DeWitt Universe Wave Function in the presence of stiff matter