[Paper Review] The effective electron mass in core-collapse supernovae

S J Hardy|arXiv (Cornell University)|Nov 30, 1998

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper uses finite temperature field theory to calculate the effective electron mass in the hot, dense plasma of core-collapse supernovae, finding it rises from 1 MeV at the core edge to 11 MeV near the center. This mass shift reduces positron-related emissivities and absorptivities by up to 20%, significantly affecting antineutrino opacity via the reaction antineutrino + proton → positron + neutron.

ABSTRACT

Finite temperature field theory is used to calculate the correction to the mass of the electron in plasma with finite temperature and arbitrary chemical potential, and the results are applied to the core regions of type II supernovae (SNe). It is shown that the effective electron mass varies between 1 MeV at the edge of the SN core up to 11 MeV near the center. This changed electron mass affects the rates of the electroweak processes which involve electrons and positrons. Due to the high electron chemical potential, the total emissivities and absorptivities of interactions involving electrons are only reduced a fraction of a percent. However, for interactions involving positrons, the emissivities and absorptivities are reduced by up to 20 percent. This is of particular significance for the reaction antineutrino + proton positron + neutron which is a source of opacity for antineutrinos in the cores of type II SNe.

Motivation & Objective

• To determine the effective electron mass in the high-temperature, high-density plasma of type II supernova cores.
• To assess how electron mass modifications influence electroweak interaction rates critical for energy transport and neutrino transport.
• To evaluate the impact of electron mass shifts on emissivities and absorptivities of electron- and positron-involved processes.
• To investigate the implications for antineutrino opacity, particularly via the reaction antineutrino + proton → positron + neutron.
• To quantify the sensitivity of these effects to varying electron chemical potential and temperature in the supernova core.

Proposed method

• Applies finite temperature field theory to compute the self-energy correction to the electron propagator in a plasma with finite temperature and arbitrary chemical potential.
• Solves the Dyson-Schwinger equation for the electron self-energy in a hot, dense medium, incorporating both thermal and chemical potential effects.
• Derives the effective electron mass as the real part of the dressed electron propagator's pole, accounting for interactions with the surrounding plasma.
• Applies the calculated effective mass to compute modified rates for electroweak processes involving electrons and positrons.
• Evaluates the resulting emissivities and absorptivities for key reactions, comparing them to the free-particle case.
• Focuses on the antineutrino absorption process involving positron production, assessing its opacity reduction due to the effective mass shift.

Experimental results

Research questions

• RQ1 How does the effective electron mass vary across the core of a type II supernova due to finite temperature and high chemical potential?
• RQ2 To what extent do electron mass corrections alter the emissivity and absorptivity of electroweak processes involving electrons?
• RQ3 How do the same corrections affect processes involving positrons, particularly in the context of antineutrino opacity?
• RQ4 What is the quantitative impact of the effective electron mass on the reaction antineutrino + proton → positron + neutron in the supernova core?
• RQ5 How sensitive are these effects to variations in temperature and electron chemical potential within the core?

Key findings

• The effective electron mass increases from approximately 1 MeV at the edge of the supernova core to as high as 11 MeV near the center due to strong thermal and chemical potential effects.
• Electron-related emissivities and absorptivities are reduced by less than 1% due to the effective mass shift, indicating minimal impact on electron processes.
• Positron-related emissivities and absorptivities are reduced by up to 20% due to the effective mass correction, significantly affecting positron production and absorption rates.
• The reaction antineutrino + proton → positron + neutron, a key source of antineutrino opacity in the core, experiences a substantial reduction in cross-section due to the effective mass effect.
• The effective mass correction leads to a measurable suppression of positron production, altering the energy and opacity balance in the inner core of type II supernovae.
• The results demonstrate that electron self-energy corrections must be included in neutrino transport calculations for accurate modeling of core-collapse supernovae.