Enforcing causality in nonrelativistic equations of state at finite temperature

We present a thermodynamically consistent method by which equations of state based on nonrelativistic potential models can be modified so that they respect causality at high densities, both at zero and finite temperature (entropy). We illustrate the application of the method by using the high-density phase parametrization of the well-known Akmal–Pandharipande–Ravenhall model in its pure neutron matter configuration as an example. We also show that, for models with only contact interactions, the adiabatic speed of sound is independent of the temperature in the limit of very large temperature. This feature is approximately valid for models with finite-range interactions as well, insofar as the temperature dependence they introduce to the Landau effective mass is weak. In addition, our study reveals that in first-principle nonrelativistic models of hot and dense matter, contributions from higher-than-two-body interactions must be screened at high density to preserve causality.

Figure 1

Squared speed of sound vs density in PNM for the models of (a) APR, (b) LS, and (c) SLy4 at fixed entropy.

Figure 2

The effective mass ratio $m^{*}/m$ and the quantity $Q=1-(3n/2m^{*})d{m}^{*}/dn$ vs density in PNM for the APR, LS, and SLy4 models.

Figure 3

Squared speed of sound in PNM for the APR model with (solid curves) and without (dotted curves) causality enforced with ${\beta }_F=0.9$ for (a) fixed entropy and (b) temperature vs density.

Figure 4

Same as Fig. 3, but with the density-dependent ${\beta }_f$ given by Eq. (51).

Figure 5

Total energy density of PNM for the APR model with (solid curves) and without (dotted curves) causality enforced with ${\beta }_f=0.9$ for (a) fixed entropy and (b) temperature vs density.

Figure 6

Pressure of PNM for the APR model with (solid curves) and without (dotted curves) causality enforced with ${\beta }_f=0.9$ for (a) fixed entropy and (b) temperature vs density.

Figure 7

Chemical potential in PNM for the APR model with (solid curves) and without (dotted curves) causality enforced with ${\beta }_f=0.9$ for fixed (a) entropy and (b) temperature vs density.

Figure 8

Specific heat at constant volume in PNM for the APR model with (solid curves) and without (dotted curves) causality enforced with ${\beta }_f=0.9$ for fixed (a) entropy and (b) temperature vs density.

Figure 9

Specific heat at constant pressure in PNM for the APR model with (solid curves) and without (dotted curves) causality enforced with ${\beta }_f=0.9$ for fixed (a) entropy and (b) temperature vs density.

Figure 10

Adiabatic index in PNM for the APR model with (solid curves) and without (dotted curves) causality enforced with ${\beta }_f=0.9$ for fixed (a) entropy and (b) temperature vs density.

Figure 11

The effective mass ratio $m^{*}/m$ and the quantity $Q=1-(3n/2m^{*})d{m}^{*}/dn$ vs density in PNM for the BPAL33 model.

Figure 12

Squared speed of sound in PNM for the BPAL33 model for fixed (a) entropy and (b) temperature vs density.