[Paper Review] Transport properties and neutrino emissivity of dense neutron-star matter with localized protons

D. A. Baiko, P. Haensel|arXiv (Cornell University)|Jun 18, 1999

Quantum, superfluid, helium dynamics4 references5 citations

TL;DR

This paper investigates the impact of proton localization in dense neutron-star matter on transport properties and neutrino emission. Using a variational method to solve kinetic equations, it shows that localized protons suppress standard transport coefficients and modify neutrino emissivity, replacing the T⁻² dependence with a T⁶ dependence in pair bremsstrahlung, significantly altering neutron star cooling at low temperatures.

ABSTRACT

As pointed out by Kutschera and W{ó}jcik, very low concentration of protons combined with a specific density dependence of effective neutron-proton interaction could lead to a localization of ``proton impurities'' in neutron medium at densities exceeding four times normal nuclear matter density. We study consequences of the localization of protons for transport processes in dense neutron star cores, assuming random distribution of proton impurities. Kinetic equations, relevant for the transport of charge, heat and momentum, are solved using variational method. Localization of protons removes a T^{-2} factor from the transport coefficients, which leads, at lower temperatures, to a strong decrease of thermal conductivity, electrical conductivity and shear viscosity of neutron star matter, as compared to the standard case, where protons form a Fermi liquid. Due to the localization of protons a number of conventional neutrino emission processes (including modified URCA process) become inoperative in neutron star cores. On the other hand, the energy loss rate from neutrino-antineutrino pair bremsstrahlung due to electron and neutron scattering off (localized) protons, will have a specific T^6 dependence, which could modify the cooling of the neutron star core, as compared to the standard case. Possible astrophysical implications of the localization of protons for neutron star evolution and dynamics are discussed.

Motivation & Objective

• To study the transport properties of dense neutron-star matter when protons are localized due to low concentration and specific interaction density dependence.
• To assess how proton localization alters electrical conductivity, thermal conductivity, and shear viscosity in neutron-star cores.
• To evaluate the impact of localization on neutrino emissivity, particularly for modified URCA and bremsstrahlung processes.
• To explore the astrophysical implications for neutron star cooling and evolution.

Proposed method

• Solving kinetic equations for charge, heat, and momentum transport using a variational method under the assumption of randomly distributed, localized proton impurities.
• Modeling the effective interaction between neutrons and protons to account for localization at densities above four times nuclear saturation density.
• Applying the variational approach to derive transport coefficients in the localized proton regime, removing the standard T⁻² temperature dependence.
• Calculating neutrino emissivity from electron and neutron scattering off localized protons, focusing on neutrino-antineutrino pair bremsstrahlung.
• Comparing results with the standard Fermi liquid model where protons form a continuous Fermi sea.
• Using the derived emissivity to assess cooling rates and their temperature dependence in neutron-star cores.

Experimental results

Research questions

• RQ1 How does proton localization affect the electrical and thermal conductivity of dense neutron-star matter?
• RQ2 What is the temperature dependence of neutrino emissivity from scattering off localized protons compared to the standard T⁻² dependence?
• RQ3 Which conventional neutrino emission processes become inoperative due to proton localization?
• RQ4 How does the modified emissivity influence the cooling evolution of neutron stars at low temperatures?
• RQ5 What are the implications of localized protons for the dynamics and thermal evolution of neutron-star cores?

Key findings

• Proton localization removes the T⁻² temperature dependence from transport coefficients, leading to a strong suppression of electrical conductivity, thermal conductivity, and shear viscosity at low temperatures.
• The modified URCA process and other standard neutrino emission mechanisms become inoperative due to the absence of a continuous proton Fermi surface.
• Neutrino emissivity from electron and neutron scattering off localized protons follows a T⁶ dependence, contrasting with the standard T⁻² dependence.
• This T⁶ dependence could significantly alter the cooling rate of neutron stars at low temperatures, especially in the post-superfluid phase.
• The results suggest that neutron star cooling may be slower than predicted by standard models in the presence of localized protons.
• The study implies that localized protons could lead to observable deviations in neutron star thermal evolution and cooling curves.