Effects of Lighter-than-QCD Axions on Neutron Star Tidal Deformability

TL;DR

This work addresses how lighter-than-QCD axions, sourced by finite-density effects inside neutron stars, backreact on NS structure in a fully dynamical 1+1 GR framework. By solving the coupled Einstein–axion–nucleon system with a realistic EOS and tracking both internal and exterior axion profiles, the authors demonstrate that NS mass, radius, and the tidal deformability $\Lambda$ can change by order unity, breaking the approximate $\Lambda$–$C$ universality and offering a potential observational probe for LQCD axions with future gravitational-wave data. The study provides a concrete numerical pipeline (explicit time evolution, 4th-order RK on a $10^4$ radial grid, sponge boundaries, and artificial viscosity) to explore nonlinear axion–NS dynamics, including domain-wall-like behavior and an extended axion atmosphere. The results imply that GW observations of NS mergers could constrain a previously viable region of axion parameter space, independent of the nuclear EOS, and motivate extensions to rotation and multiple EOS models for robust constraints.

Abstract

Finite density corrections to the lighter-than-QCD axion can invert the effective axion potential, sourcing a non-trivial axion field inside dense objects. We perform the first numerical study of the complete dynamics of the lighter-than-QCD axion in a neutron star in 1+1 general relativity, extending the region of analysis to low-mass axions with kilometer-scale Compton wavelengths. We calculate gravitational effects of the axion field on the neutron star and show that for a broad range of axion masses and decay constants, neutron star properties, such as the mass, radius, and compactness, are affected at the order-1 level. This result indicates that approximate universal tidal deformability-compactness relation for neutron stars is non-trivially broken and can serve as a probe of lighter-than-QCD axions, independent of the unknown nuclear equation of state. We comment on the potential for axion studies with future gravitational-wave observations of neutron stars and applications of this work to other new physics signatures.

Figures (14)

• Figure 1: Parameter space of the LQCD axion which highlights the untested region of parameter space (shaded magenta) that is accessible through measurements of NS structure. The QCD axion line, where $m_a = m_a^{\rm QCD} = \beta m_{\pi} f_{\pi}/(2f_a)$ is shown in solid blue. The gray, shaded regions show various constraints from cosmological, astrophysical, and laboratory measurements piinskywhite-dwarf-2024Zhang_2021Hook_Huang_2018Baryakhtar_2021witte2025Schulthess_2022Blum_2014gue2025searchqcdcoupledaxionZhang_2023Karanth_2023Roussy_2021Abel_2017Zhang_2023_2Alda_2025banerjee2025oscillatingnuclearchargeradiiLucente_2022Caloni_2022stott2020ultralightbosonicfieldmassnal_2021Hoof_2025Raffelt_2024iwamotoBuschmann_2022Springmann_2025.
• Figure 2: Contours for the effective axion potential $V_{\rm eff}^{\rm LQCD}(a)$ plotted for $\epsilon = 10^{-3}$. For this value of $\epsilon$, the critical nucleon number density is $n_N^{\rm crit} = 5.2 \times 10^{-6}~\mathrm{GeV}^3$. Negative values of the effective potential correspond to the suppression of the nucleon mass, and at zero nucleon number density, $V_{\rm eff}^{\rm LQCD}$ is strictly positive.
• Figure 3: The EOS $p(\rho)$ (LEFT), the nucleon energy density as a function of nucleon number density $\rho(n_N)$ (CENTER), and the speed of sound $c_s^2 = dp / d\rho$ (RIGHT) for the SLy4 EOS. Observe that the EOS remains causal (i.e. $c_s^2 < 1$) for the range of densities considered in this work.
• Figure 4: Normalized Fourier coefficients for the external oscillations of five representative axion fields at $r = 20~\mathrm{km}$, simulated with an initial state central baryon density $n_N^c = 5.0 \times 10^{-3}~\mathrm{GeV}^3$ (TOP). Peak frequencies for the seven axion parameter sets $(\epsilon, f_a)$ with initial central baryon density $n_N^c = 5.0 \times 10^{-3}~\mathrm{GeV}^3$ and resolvable frequencies given the simulation time step and run-time (BOTTOM). Ratio of the peak frequencies from the top panel to the axion mass, as a function of the latter. Observe that clearly the external oscillations occur at a frequency dictated by the vacuum axion mass, $\omega_a \simeq m_a = \sqrt{\epsilon} m_a^{\rm (QCD)}$.
• Figure 5: Normalized Fourier coefficients for the central oscillations of nucleon energy density $\rho_N$, simulated with four initial state central baryon densities $n_N^c \in \left\{ 2.5, 3.0, 4.5, 7.4 \right\}n_N^{\rm sat}$ with axion parameters $\epsilon = 0.1$ and $f_a = 10^{16}~\mathrm{GeV}$