Ab initio constraints on thermal effects of the nuclear equation of state

We exploit the many-body self-consistent Green's function method to analyze finite-temperature properties of infinite nuclear matter and to explore the behavior of the thermal index used to simulate thermal effects in equations of state for astrophysical applications. We show how the thermal index is both density and temperature dependent, unlike often considered, and we provide an error estimate based on our ab initio calculations. The inclusion of three-body forces is found to be critical for the density dependence of the thermal index. We also compare our results to a parametrization in terms of the density dependence of the nucleon effective mass. Our findings point to possible shortcomings of predictions made for the gravitational-wave signal from neutron-star merger simulations with a constant thermal index.

Figure 1

Energy per nucleon (at $T=0$, black dots/lines) and free energy per nucleon for $T=20,30,40$, and 50 MeV as function of density for SNM (left) and PNM (right), obtained from SCGF calculations with the 2.0/2.0 (EM) chiral two- and three-nucleon interactions. Symbols correspond to calculated data, solid lines represent the fits of the free-energy (see text for details).

Figure 2

Pressure for $T=0,20,30,40$, and 50 MeV as function of density for SNM (left) and PNM (right), obtained from SCGF calculations with the 2.0/2.0 (EM) chiral two- and three-nucleon interactions.

Figure 3

Thermal energy (first row), thermal pressure (second row), and thermal index (third row) for $T=20,30,40$, and 50 MeV as function of density, for SNM (left panels) and PNM (right panels), obtained from SCGF calculations with the 2.0/2.0 (EM) chiral two- and three-nucleon interactions.

Figure 4

Thermal energy (first row), thermal pressure (second row), and thermal index (third row) for $T=30$ MeV as function of density for SNM (left panels) and PNM (right panels), using six different chiral two- and three-nucleon interactions (see text for details). Note that the $2N$ N3LO (EM) results are for two-nucleon interactions only.

Figure 5

Thermal index for $T=30$ MeV as function of density for SNM (left) and PNM (right). The black solid lines are extractions of the thermal index from the thermal energy and thermal pressure using Eq. (10) while the green dashed lines are for ${\mathrm{\Gamma }}_{\mathrm{th}}$ based on the density dependence of the effective nucleon mass, Eq. (11). Results are shown for the $2N$ N3LO (EM) and $2N$ N3LO (EM) $+ 3N$ N2LO chiral interactions.

Figure 6

Effective mass for $T=30$ MeV as function of density for SNM (left) and PNM (right), extracted from the single-particle energy at the chemical potential [see Eq. (12)] using six different chiral two- and three-nucleon interactions.

Figure 7

Effective mass for $T=30$ MeV as function of density for SNM (left panels) and PNM (right panels) using the $2N$ N3LO (EM) $+ 3N$ N2LO (upper row) and $2N$ N3LO (EM) (lower row) chiral interactions. The full $m^{*}$ as well as $m^{\omega }$ and $m^k$ are shown, extracted from the single-particle energy at the chemical potential, $m\left(p_{\mu }\right)$, or at the Fermi momentum, $m\left(p_{\mathrm{F}}\right)$.