Probing ALP-photon couplings in Neutron Stars: Scalar versus pseudoscalar cases

TL;DR

This paper investigates the static distribution of axion-like particles (ALPs) inside a magnetized neutron star by solving the Klein–Gordon equation in a GR background with a density-dependent, axisymmetric magnetic field. It contrasts pseudoscalar and scalar ALP couplings to electromagnetism, $Q(F_0,G_0)$ with $G_0$ and $F_0$ respectively, and shows how the source term $g_{ m eff}Q(F_0,G_0)$—modulated by chiral-MHD effects such as the Chiral Magnetic Effect—shapes the 2D axion profiles. For pseudoscalar ALPs, the $\mathbf{E}\cdot\mathbf{B}$ source can drive central condensation at high axion densities and outer-crust accumulation at low densities, while scalar ALPs couple via $\mathbf{E}^2-\mathbf{B}^2$, producing angular asymmetries that concentrate axions toward polar regions under certain conditions. The study further argues that condensates in the NS crust could enhance axion–photon conversion in flux tubes, potentially contributing to indirect observational signals through crustal heating and NS cooling patterns, and outlines a path toward more complete self-consistent ALP–Maxwell–gravity treatments.

Abstract

We investigate the distribution of an interacting axion-like massive field within a magnetized Neutron Star. For this we consider the effect of an intense density-dependent axially symmetric stellar magnetic field ${\bf B}(r,θ)$ adding another much weaker, but non-vanishing, electric field. We particularize the latter for the case when a finite chiral charge density is present. The axion field is thus coupled to a generic function $Q(F_0,G_0)$ depending on Lorentz invariants $F_0, G_0$ which can be constructed from these electromagnetic fields. From this, the static axion field equations are solved as function of stellar radial coordinate and angular direction, $a(r,θ)$, using a prescribed linear form for $Q$. In addition, we use a semi-analytical approach to calculate the stellar structure in this hybrid system where pressure components are treated under a perturbative scheme, provided induced deformations with respect to spherical symmetry are tiny. Our results show that the axion couplings to magnetic and electric fields along with its mass, critically determine the axion spatial distribution. Furthermore, we focus on the possibility that the axion field might accumulate in specific outer regions of the star, particularly within the crust, where it could form a condensate. We explore the possible presence of magnetic flux tubes from superconductor phases in this outer layers and qualitatively show they may enhance local conversion into photons. We explore prospects of detectability through indirect methods.

Figures (8)

• Figure 1: (left) Stellar mass and pressure radial profiles for a NS with $M= 1.56 M_{\odot}$ and $R=13.93$ km (right) mass density and magnetic field strength radial profiles. We have used a polytropic EoS with $\Gamma=2.207$,$K=1.5\times 10^2$$\mathrm{dyn} \cdot \mathrm{cm}^{3 \Gamma-2} \cdot \mathrm{~g}^{-\Gamma}$. B field is included under the prescribed form in Eq.\ref{['magneticprofile']}, see text for details.
• Figure 2: (right) Axion field spherically equivalent $a_{\rm sph}(r)$ solutions for different axion masses in the range $m_a\in [ 10^{-11},10^{-8}]$ eV. (left) $\Delta$ values in the inner stellar kilometer. The red line marks the isocontour where $\Delta$ vanishes. Below the red line the axion field is overdamped while above the axion field is underdamped.
• Figure 3: (left) Internal axion field distribution in curved and magnetized stellar space-time with no coupling to electromagnetic fields, i.e. $g_{a,\gamma}=0$ and a mass $m_a = 10^{-10} \, \text{eV}$ presented in an axial cross-section view along the polar diameter. (right) Potential energy $\varepsilon_{\rm axion}$. The NS has a mass $M_{\text{sph}} = 1.56 \, M_\odot$ and a radius $R = 13.93 \, \text{km}$. The total axion mass was taken to be $0.01\%$ of the total NS baryonic mass.
• Figure 4: PS-ALP field distribution for a candidate with mass of $m_a=10^{-10}~\text{eV}$ and $g_{a,\gamma}=1.48\times10^{-14} \,\rm GeV^{-1}$ from the source term $G_0$ in Eq. \ref{['axion2d_withS']}. The upper panel displays the field distribution in a meridional slice of the star, while the lower panel presents its normalized energy density profile with respect to its value at the origin. The left (right) column corresponds to an average axion field density $\rho_{\text{a}} = 10^{12} \,\rm g/\rm cm^3$ ( $\rho_{\text{a}} =10^{-3} \,\rm g/ \rm cm^3$).
• Figure 5: PS-Axion distribution for a magnetized NS ($M_{ns}=1.5 M_\odot$$R=13.93 \rm \, km$) with an axion mass density, $\rho_{a}=2.74 \times10^{-19} \rm g\,\,cm^{-3}$. The axion mass is set to $m_a=10^{-11} \rm \,eV$ with a photon-axion coupling constant of $g_{a,\gamma}=1.48\times10^{-14} \,\rm GeV^{-1}$.