Supermassive neutron stars rule out twin stars

We investigate the implications of a hypothetical $2.5{\mathrm{M}}_{\odot }$ neutron star in regard to the possibility of a first order phase transition to quark matter. We use equations of state (EoS) of varying stiffness provided by a parametrizable relativistic mean field model transitioning to a constant speed of sound EoS. We find a strong connection between the discontinuity in energy density and the maximal neutron star mass. We demonstrate, that high maximal masses cannot be realized for large discontinuities. As a result visible mass gaps, i.e., twin stars, and masses of $M_{\max }\gtrsim 2.2M_{\odot }$ are mutually exclusive.

Figure 1

Examples for category I (black dashed line), II (red dashed line), III (blue continuous lines) and IV (orange line) phase transitions for a hadronic base EoS with $m^{*}/m=0.65$. As well as the pure hadronic case (purple line) and an example of a connected second branch (dashed blue line). The values in parenthesis indicate the transitional pressure and the jump in energy density in units of $\mathrm{MeV}/{\mathrm{fm}}^3$ respectively. The point, where the first branch ends is indicated by a dot in the color corresponding to the category. Additionally the NICER constraints [6, 7] (black shaded area), pulsar mass limit [4] (green shaded area) and the mass of the unknown compact object of GW190814 [20] (blue shaded area) were added.

Figure 2

The $m^{*}/m=0.55$ case of the maximal hybrid star mass as a function of the jump in energy density for different transitional pressures. The dashed black line indicates $\mathrm{\Delta }\epsilon =350\mathrm{MeV}/{\mathrm{fm}}^3$, which is the lowest value of $\mathrm{\Delta }\epsilon$ that generates a mass gap of $\mathrm{\Delta }M=\pm 0.1M_{\odot }$ for all transitional pressures. The hypothetical neutron star participant of GW190814 (shaded blue) is only realizable for smaller values of $\mathrm{\Delta }\epsilon$, implying no viable mass gap. The solid horizontal black line represents the $2.14M_{\odot }$ of $\mathrm{J}0740+6620$ [4]. Only the $p_{\text{trans}}=10\mathrm{MeV}/{\mathrm{fm}}^3$ case reaches this value at $\mathrm{\Delta }\epsilon \le 350\mathrm{MeV}/{\mathrm{fm}}^3$, suggesting, that only this case can support twin stars and a maximal hybrid star mass of $M_2\ge 2.14M_{\odot }$. However, when considering the error bar of the stated mass (red shaded area) all cases reach the limit.

Figure 3

Most transitional pressures of category III in the $m^{*}/m=0.65$ case do not reach the pulsar mass limit of $\mathrm{J}0740+6620$ at $\mathrm{\Delta }\epsilon \ge 350\mathrm{MeV}/{\mathrm{fm}}^3$. Therefore only the cases where $p_{\text{trans}}\le 24\mathrm{MeV}/{\mathrm{fm}}^3$ have a mass gap of $0.1M_{\odot }$ and generate a mass value compatible with Cromartie et al. [4] at the $1\sigma$ interval.