Constraining hadron-quark phase transition parameters within the quark-mean-field model using multimessenger observations of neutron stars

We extend the quark mean-field (QMF) model for nuclear matter and study the possible presence of quark matter inside the cores of neutron stars. A sharp first-order hadron-quark phase transition is implemented combining the QMF for the hadronic phase with "constant-speed-of-sound" parametrization for the high-density quark phase. The interplay of the nuclear symmetry energy slope parameter, $L$, and the dimensionless phase transition parameters (the transition density $n_{\rm trans}/n_0$, the transition strength $\Delta\varepsilon/\varepsilon_{\rm trans}$, and the sound speed squared in quark matter $c^2_{\rm QM}$) are then systematically explored for the hybrid star proprieties, especially the maximum mass $M_{\rm max}$ and the radius and the tidal deformability of a typical $1.4 \,M_{\odot}$ star. We show the strong correlation between the symmetry energy slope $L$ and the typical stellar radius $R_{1.4}$, similar to that previously found for neutron stars without a phase transition. With the inclusion of phase transition, we obtain robust limits on the maximum mass ($M_{\rm max}< 3.6 \,M_{\odot}$) and the radius of $1.4 \,M_{\odot}$ stars ($R_{1.4}\gtrsim 9.6~\rm km$), and we find that a too-weak ($\Delta\varepsilon/\varepsilon_{\rm trans}\lesssim 0.2$) phase transition taking place at low densities $\lesssim 1.3-1.5 \, n_0$ is strongly disfavored. We also demonstrate that future measurements of the radius and tidal deformability of $\sim 1.4 \,M_{\odot}$ stars, as well as the mass measurement of very massive pulsars, can help reveal the presence and amount of quark matter in compact objects.