Hot neutron stars and their equation of state

A set of microscopic, covariant density-functional, and nonrelativistic Skyrme-type equations of state is employed to study the structure of purely nucleonic neutron stars at finite temperature. After examining the agreement with presently available astrophysical observational constraints, we find that the magnitude of thermal effects depends on the nucleon effective mass as well as on the stiffness of the cold equation of state. We evidence a fairly small but model-dependent effect of finite temperature on stellar stability that is correlated with the relative thermal pressure inside the star.

Figure 1

Energy per nucleon of $\beta$-stable matter $E_{\beta }$ (top panel) and symmetry energy $E_{\mathrm{sym}}$ (bottom panel) at $T=0$ for the different EOSs. All curves end at the central density of their respective $M_{\max }$ configuration.

Figure 2

Mass-radius relations obtained with different EOSs. The mass of the most heavy pulsar PSR $\text{J0740}+6620$ [48] observed until now is also shown, together with the constraints from the GW170817 event [2] and the mass-radius constraints on the pulsars $\text{J0030}+0451$ and $\text{J0740}+6620$ of the NICER mission [3, 4, 5, 6]. The black bars indicate the limits on $R_{2.08}$ and $R_{1.4}$ obtained in the combined data analyses in Refs. [6, 49, 50].

Figure 3

Upper panel: The temperature profiles corresponding to $\beta$-stable matter with $S/A=2$. Lower panel: Proton fractions in $\beta$-stable matter for $T=0$ (broken curves) and $S/A=2$ (solid curves). Markers indicate the $M_{\max }$ configurations for each EOS.

Figure 4

Neutron and proton effective masses in cold $\beta$-stable matter as a function of the nucleon density for some EOSs considered in this work.

Figure 5

Nucleon and lepton contributions to the thermal pressure of $\beta$-stable matter, Eq. (12), at $S/A=2$ for the different EOSs. The dot-dashed curves show the pressure caused by composition change only, Eq. (13). The vertical lines indicate the central density of the $M_{\max }$ configurations. The SRO(APR) and TNTYST results in the last panel are scaled down by a factor of 2.

Figure 6

Ratio of thermal pressure to cold pressure of $\beta$-stable matter, Eq. (15), as a function of density for different EOSs. All curves end at the central density of their respective $M_{\max }$ configuration.

Figure 7

NS gravitational mass vs central density for cold and hot stars and the different EOSs.

Figure 8

Correlation between relative change of the maximum gravitational mass, Eq. (16), and the pressure ratio at the center of the star, Eq. (15), for different EOSs. Full symbols indicate EOSs respecting the constraint $2.1<M_{\text{max}}/M_{\odot }<2.4$.