Field Theory for Zero Sound and Ion Acoustic Wave in Astrophysical Matter

TL;DR

This paper develops a field theory model to describe low energy collective modes in high-density astrophysical matter, revealing the existence of zero sound and ion acoustic waves in white dwarf interiors.

Contribution

It introduces a novel effective field theory framework for analyzing low energy modes in dense stellar matter, unifying zero sound and ion acoustic waves.

Findings

Existence of a longitudinal gapless mode in high-density matter.

Identification of the mode as zero sound or ion acoustic wave depending on parameters.

Implications for white dwarf properties and astrophysical phenomena.

Abstract

We set up a field theory model to describe the longitudinal low energy modes in high density matter present in white dwarf stars. At the relevant scales, ions -- the nuclei of oxygen, carbon and helium -- are treated as heavy point-like spin-0 charged particles in an effective field theory approach, while the electron dynamics is described by the Dirac Lagrangian at the one-loop level. We show that there always exists a longitudinal gapless mode in the system irrespective whether the ions are in a plasma, crystal, or quantum liquid state. For certain values of the parameters, the gapless mode can be interpreted as a zero sound mode and, for other values, as an ion acoustic wave; we show that the zero sound and ion acoustic wave are complementary to each other. We discuss possible physical consequences of these modes for properties of white dwarfs.