Dipole Radiation and Kinetic Mixing from Dark Photon Solitons

TL;DR

This paper develops an effective non-relativistic framework for dark photon DM in vector solitons and analyzes two radiative channels: (i) dipole radiation from dimension-6 W_ W^ F_{} tilde F^{} interactions in external EM fields, and (ii) radiation from gauge kinetic mixing with ordinary matter currents. It derives Schrödinger–Poisson soliton solutions with a universal radial profile and explores how plasma effects, including an effective photon mass ω_p, amplify or suppress radiation, especially near resonances ω_p pprox 2m or ω_p pprox m. The study extends to astrophysical signatures, estimating spectral flux densities and highlighting neutron-star magnetospheres as favorable environments where resonant emission could reach observable Jansky levels, while also evaluating tidal-disruption constraints and Galactic collision rates with NSs/WDs in the presence of dark-matter density spikes. The results establish a novel indirect dark-matter detection pathway via radio signals linked to vector solitons and motivate further numerical and observational work to pin down feasibility and rates in realistic Galactic environments.

Abstract

Wave-like dark matter composed of spin-1 particles, known as dark photons, is theorized to form clumps called "vector solitons". These solitons are compact astrophysical objects that exhibit coherent oscillations and a high concentration relative to the local dark matter density. A significant portion of dark matter in galactic halos today may consist of these solitons. This study explores how photons can be produced from these vector solitons by the influence of external electromagnetic fields or charge densities, via a dimension-6 dark photon-photon coupling and a kinetic mixing, respectively. We further explore the astrophysical implications of these phenomena, highlighting a novel avenue for dark matter discovery that our research provides.

Figures (6)

• Figure 1: The "universal" profile for non-relativistic ground state vector solitons obtained by numerically solving Eqs. (\ref{['eq:S1']}) and (\ref{['eq:S2']}) indicated by a solid gray line. Ansatz shown in Eq. (\ref{['eq:sech-ans']}) indicated by a dashed orange line.
• Figure 2: Time averaged emitted power by the soliton configuration in terms of the plasma frequency $\omega_p$ and soliton scale length $R^{0.24}_{\text{sol}}$. The plasma frequency is assumed to be constant in scales comparable to the soliton radius. We vary $\omega R^{0.24}_{\text{sol}}$ between 4 (light blue line) and 10 (dark blue line). Top panel: soliton dipole radiation due to an external magnetic field, Eq. (\ref{['eq:P4']}). Bottom panel: soliton radiation produced by a kinetic mixing between the massive vector boson and electromagnetic current of ordinary matter, Eq. (\ref{['eq:PtKM']}) with $c_1 = 1$.
• Figure 3: Diagram for the magnetic field lines around a rotating neutron star or white dwarf, holding an angular velocity along the $z$-axis and $\hat{\Omega}\cdot\hat{m} = \text{cos}(\theta_m)$.
• Figure 4: Parameter space in cylindrical coordinates for the conversion radius within a magnetosphere via dipole radiation (purple) or kinetic mixing (blue) phenomena. The origin is located at the center of the compact object (gray circle). Left: aligned neutron star with properties $R_{\rm{NS}}=10\;\rm{km}$, $B_0=4.5\times10^{12}$ G, and $P=0.3$ s. Dark photon mass $m = 10^{-6}\,\text{eV}$. Right: aligned white dwarf with properties $B_0=10^{9}$ G, $P=10^{4}$ s and $R_{\rm{WD}}=5380\;\rm{km}$. Dark photon mass $m = 10^{-9}\,\text{eV}$ (dipole radiation) and $m = 1.3\times 10^{-9}\,\text{eV}$ (kinetic mixing). Orange regions indicate the minimum distance that solitons can approach the compact object before beginning to undergo tidal disruptions for certain values of $M_{\rm{sol}}$.
• Figure 5: Dark matter spike density profiles $\rho_{\rm{DM,sp}}(r)$ as a function of distance from the galactic center for different power-laws. The initial power-law index $\gamma$ controls the height of the central density peak.