Axion sourcing in dense stellar matter via $CP$-violating couplings

Compact objects such as neutron stars and white dwarfs can source axionlike particles and QCD axions due to $CP$-violating axion-fermion couplings. The magnitude of the axion field depends on the stellar density and on the strength of the axion-fermion couplings. We show that even $CP$-violating couplings one order of magnitude smaller than existing constraints source extended axion field configurations. For axionlike particles, the axion energy is comparable to the magnetic energy in neutron stars with inferred magnetic fields of the order of ${10}^{13}\mathrm{G}$ and exceeds by more than one order of magnitude the magnetic energy content of white dwarfs with inferred fields of the order of ${10}^4\mathrm{G}$. On the other hand, the energy stored in the QCD axion field is orders of magnitude lower due to the smallness of the predicted $CP$-violating couplings. It is shown that the sourced axion field can polarize the photons emitted from the stellar surface, and stimulate the production of photons with energies in the radio band.

Figure 1

ALP field in NSs versus for different values of $m_a{R}_{\mathrm{NS}}$. Left panel: radial profiles of $(m_a{R}_{\mathrm{NS}}{)}^2|\phi (r)|$ versus normalized radius for $m_a{R}_{\mathrm{NS}}=1$, 2, 5, 10, 100 (see the legend in the central panel for the color labels). The dotted curve represents the $f(r)$ profile of the $M_{\mathrm{NS}}=1.49M_{\odot }$ model, to which the solution converges as $m_a{R}_{\mathrm{NS}}$ increases. Central panel: amplitude of the axion field $a$ in physical units (GeV) versus normalized radius. Right panel: scaling of the central value ${\phi }_0$ with $m_a{R}_{\mathrm{NS}}$.

Figure 2

Energy stored in the ALP field. Left: energy density profiles of the axion field for different values of $m_a{R}_{\mathrm{NS}}$, in units of $e_a^2/R_{\mathrm{NS}}^2$ [see Eq. (13)]. Right: total energy integrated over the star volume inside ($E_{\mathrm{in}}$) and outside ($E_{\mathrm{out}}$) the star. The maximum energy stored in the axion field ($E_{\mathrm{in}}\approx 7\times {10}^{43}\mathrm{erg}$) is reached for $m_a{R}_{\mathrm{NS}}\lesssim 1$. The dashed lines show the scalings $(m_a{R}_{\mathrm{NS}}{)}^{-1}$ and $(m_a{R}_{\mathrm{NS}}{)}^{-2}$ in the limit $m_a{R}_{\mathrm{NS}}\gg 1$.

Figure 3

QCD axion field sourced by NSs and corresponding energy. Left: QCD axion field sourced by NSs for different values of $f_a$. In the legend, $m_a^{\mathrm{out}}$ denotes the QCD axion mass in vacuo. Right: total energy integrated over the star volume versus $f_a$. The gray shaded region corresponds to the $f_a$ interval excluded by stellar black-hole superradiance arguments [42, 49].

Figure 4

Bounds on the product ${\overline{g}}_{aN}{g}_{a\gamma }$ obtained from the condition $\mathrm{\Delta }\theta <1°$. The blue shaded region is excluded since it implies $\mathrm{\Delta }\theta >1°$, which is larger than the sensitivity of polarimeters searching for light polarization from NSs [54, 55].

Figure 5

Timescale for the exponential growth of the number density of photons produced via axion-photon interaction for different values of the dimensionless axion mass $m_a{R}_{\mathrm{NS}}$. The photons are produced with typical momenta $k=\mathcal{O}(m_a)$, which for the axion masses considered in our work leads to the production of photons with energies in the radio band. The axion-photon coupling is fixed to $g_{a\gamma }={10}^{-13}{\mathrm{GeV}}^{-1}$.