Twin stars within the SU(3) chiral quark-meson model

We present new stable solutions of the Tolman-Oppenheimer-Volkoff equations for quark stars using a quark matter equation of state based on the SU(3) quark-meson model that exhibits the onset of the chiral phase transition. These new solutions appear as two stable branches in the mass-radius relation allowing for so-called twin stars, i.e., two stable quark star solutions with the same mass, but distinctly different radii. We find solutions which are compatible with causality, the stability conditions of dense matter, the astrophysical constraints of the rotation of the millisecond pulsar PSR J1748-2446ad and the $2M_{\odot }$ pulsar mass constraint.

Figure 1

The EoS (upper plot) as well as the nonstrange and strange scalar fields (lower plot) as a function of the energy density for the parameter set $m_q=300\mathrm{MeV}$, $m_{\sigma }=600\mathrm{MeV}$, $g_{\omega }=4$ and different values of the vacuum pressure $B^{1/4}$.

Figure 2

The mass-radius relation for the parameter set $m_q=300\mathrm{MeV}$, $m_{\sigma }=600\mathrm{MeV}$, $g_{\omega }=4$ and different values of the vacuum pressure $B^{1/4}$. The upper-left shaded region is excluded due to causality whereas the lower shaded area on the right-hand side is forbidden by the rotation of the millisecond pulsar PSR J1748-2446ad. The horizontal line indicates the $2M_{\odot }$ limit. Thick lines in the mass-radius relation represent stable configurations, whereas thin ones correspond to unstable solutions.

Figure 3

The speed of sound $c_s^2$ as a function of the energy density for the parameter set $m_q=300\mathrm{MeV}$, $m_{\sigma }=600\mathrm{MeV}$, $g_{\omega }=4$. The speed of sound is independent of the value of the bag constant. Vertical lines indicate the first maximum in the mass-radius relation in Fig. 2, where the mass-radius relation becomes unstable.

Figure 4

The baryon number $N_B$ as a function of the energy density for the parameter set $m_q=300\mathrm{MeV}$, $m_{\sigma }=600\mathrm{MeV}$, $g_{\omega }=4$ and various values of the vacuum pressure $B^{1/4}$. Thick lines represent stable configurations, whereas thin lines correspond to unstable solutions.

Figure 5

Contour lines in the $g_{\omega }$ versus $B^{1/4}$ plane indicating TSS. Two stable branches with maxima $M_1^{\max }<M_2^{\max }$ appear when crossing the upper line from above. The middle line indicates stars with $M_1^{\max }\simeq M_2^{\max }$. The lower line shows the limit where $M_1^{\max }>M_2^{\max }$. Above the upper line and below the lower line no twin stars are possible. The vertical line $g_{\omega }=g_n$ indicates the approximate boundary between first order and crossover phase transitions. The two- and three-flavor lines provide the stability conditions for dense matter. Twin stars within the shaded area fulfill the stability constraints.

Figure 6

Same contour lines in the $g_{\omega }$ versus $B^{1/4}$ plane indicating TSS, as in Fig. 5, but including the two-flavor line, the $2M_{\odot }$ limit and also showing the region excluded by the rotation of the millisecond pulsar PSR J1748-2446ad. twin stars within the shaded area fulfill all these constraints.