Axion condensates in neutron stars and radial oscillation modes

TL;DR

The paper investigates how light QCD axion condensates inside neutron stars alter their equilibrium structure and radial oscillation spectra. By solving a coupled Tolman-Oppenheimer-Volkoff and Klein-Gordon system with a realistic BSk26 EOS and performing linear perturbations, the authors reveal two families of radial modes: fluid-dominated and axion-dominated, with the latter experiencing damping due to axion emission. A simplified two-field model clarifies the mode hybridization and shows damping timescales of order seconds for kHz-mass axions, with high-frequency modes ($\omega > m_a$) preferentially damped. The findings suggest axion asteroseismology as a novel probe of axion properties in neutron stars and motivate extending the analysis to non-radial modes and gravitational-wave observations. Overall, the work demonstrates that axion condensates can leave observable imprints on NS structure and dynamics, potentially constraining axion mass and couplings through future multimessenger observations.

Abstract

Light QCD axions, introduced to solve the strong CP problem, may form condensates inside neutron stars, giving rise to a novel ground state of dense matter. We investigate how such axion condensates modify the equilibrium structure and radial oscillation spectrum of NSs. Using a realistic NS model with the BSk26 equation of state, and solving the coupled Tolman-Oppenheimer-Volkoff and Klein-Gordon equations together with a linear perturbation analysis, we find two distinct families of quasi-normal modes: weakly damped fluid-dominated oscillations and highly damped axion modes. The coupling between the fluid and the axion field introduces axion-induced damping of radial oscillations, with decay timescales of order seconds for kHz axion masses. Modes with frequencies above the axion mass are strongly damped, while those below remain unaffected. These results suggest that stellar oscillations could provide a novel probe of axion properties, opening prospects for axion asteroseismology in neutron stars.

Figures (5)

• Figure 1: Normalized axion field $a/f_a$ (left) and pressure (right) profiles for different values of $m_a$ (in kHz) for $\epsilon=0.1$. The dash-dotted lines mark the axion profiles outside the NS. The central pressure of the NS is $p_0=100~\mathrm{MeV/fm^3}$ and its gravitational mass is approximately $1.5~M_{\odot}$ (with the latter exhibiting variations up to 2% due to the corresponding variations in the energy content of the axion field profile for each $m_a$.)
• Figure 2: Mass–radius relation for NS models in the presence of an axion condensate, compared to the standard TOV solution for the same EOS (BSk26) without axions. The dashed black line represents the conventional TOV solutions without axions, whereas the solid colored curves illustrate the effect of including a bosonic condensate of axions inside the star, for different choices of the axion mass (3, 6, and 12 kHz) and for $\epsilon = 0.1$.
• Figure 3: QNM spectrum landscape for the simplified model. The plot displays the values of Eq. \ref{['eq:trasceq_deltapprime0']} in the complex plane, for $\lambda^2=0.001, \alpha=10, c_s^2=0.3$ and $x_0=0.6$. The bright yellow regions indicate the locations of the QNMs, with the two distinct families clearly identifiable.
• Figure 4: $\left|\Delta p(R)\right|$ (in arbitrary units) as a function of the real part of the frequency $f$ (in kHz), for $\epsilon=0.1$ and different axion masses $m_a$ (in kHz). The three curves correspond to the solution without an axion field (blue), the solution for which the axion perturbations are omitted (orange), and the full solution (cyan).
• Figure 5: QNM spectrum landscape for $m_a$ set to $3.0~\mathrm{kHz}$. It reveals the two families of modes: fluid-dominated ones with mild damping, and axion-led modes with stronger damping. The simplified model introduced in Sec.\ref{['sec:simple']} and illustrated in Fig. \ref{['fig:toymodelfunction_deltapprime0=0']} showed the same qualitative characteristics of this plot.