Solar Axion-Like Particles

• Solar ALPs are hypothetical pseudoscalar particles from extensions of the Standard Model, produced predominantly via the Primakoff effect in the Sun.
• They are generated under extreme solar conditions, yielding an energy spectrum that peaks around 3 keV and involves both photon conversion and magnetic mixing.
• Detection strategies include helioscopes, noble-liquid detectors, and solar X-ray/radio observations, which constrain ALP properties by probing their coupling and mass ranges.

Solar axion-like particles (ALPs) are hypothetical pseudoscalar bosons that arise generically in extensions of the Standard Model and string theory. Unlike the QCD axion, ALPs are not tied to the strong-CP problem and may inhabit a broad range of masses and couplings. The Sun, owing to its high temperature, electron density, and magnetic fields, is a powerful laboratory for their production and detection, primarily via the Primakoff process and photon–ALP mixing. Solar ALP searches probe particle physics, astrophysics, and cosmology, constraining or detecting ALPs through helioscope experiments, X-ray/radio telescopes, and new laboratory concepts.

1. Theoretical Production Mechanisms for Solar ALPs

Primakoff Effect

The dominant solar ALP production mechanism is the Primakoff effect, in which thermal photons in the solar core convert into ALPs in the Coulomb fields of electrons and ions via the ALP–photon coupling,

$$\mathcal{L}_{a\gamma} = -\frac{1}{4}g_{a\gamma} a F_{\mu\nu}\tilde F^{\mu\nu} = g_{a\gamma}a\,\mathbf{E}\cdot\mathbf{B}$$

with $g_{a\gamma}$ in GeV$^{-1}$ (III et al., 2010, Graham et al., 2016, Irastorza et al., 2018).

The resulting solar ALP flux at Earth is parametrized as

$$\frac{d\Phi_a}{dE_a} = 6.02\times10^{10} \left(\frac{g_{a\gamma}}{10^{-10}~\mathrm{GeV}^{-1}}\right)^2 E_a^{2.481} \exp(-E_a/1.205~\mathrm{keV})~\mathrm{cm}^{-2}\mathrm{s}^{-1}\mathrm{keV}^{-1}$$

where $E_a$ is the ALP energy (III et al., 2010, Graham et al., 2016). The spectrum peaks at $E_a\simeq3$ keV.

Additional Solar Production Channels

If an ALP has tree-level couplings to electrons ($g_{ae}$), the so-called ABC flux arises from:

• Axio-recombination and axio-deexcitation (bound-bound transitions)
• Axio-bremsstrahlung ($e+Z\to e+Z+a$)
• Compton-like $e+\gamma\to e+a$ (Graham et al., 2016) These processes dominate below $\sim1$ keV for $g_{ae}\gtrsim10^{-13}$.

Magnetic-field-induced Coherent Production

Macroscale magnetic fields in the solar interior (radiative zone, tachocline, convective envelope) also facilitate photon$\leftrightarrow$ALP conversion via coherent mixing (Guarini et al., 2020). The rate is

$$\Gamma_{a}^{\text{prod}}(r,\omega) = \frac{\Gamma(r,\omega) \Delta^2(r)}{[\Delta\omega(r,\omega)]^2+[\Gamma(r,\omega)/2]^2} \cdot \frac{1}{e^{\omega/T(r)} - 1}$$

where $\Delta = g_{a\gamma}B/2$, and $B$ is the local field (Guarini et al., 2020).

Resonant conversion is possible for $m_a \simeq \omega_p(r)$, enhancing low-energy ALP flux around $m_a=10$–$130$ eV.

Coalescence and Gravitational Trapping

For keV-scale ALPs, photon coalescence ($\gamma\gamma\to a$) dominates the production of non-relativistic, gravitationally trapped ALPs. This gives a local density determined by the solar gravitational potential, with

$$\Gamma_\text{coal}(r) = \frac{g_{a\gamma\gamma}^2 m^3}{64\pi}$$

which matches the axion decay rate in the non-relativistic limit (Beaufort et al., 2023).

2. Propagation and ALP–Photon Conversion in Solar and Terrestrial Magnetic Fields

Solar Magnetic Environments

Solar ALPs may convert to X-rays or radio photons in the structured magnetic fields of the solar atmosphere, characterized by:

• Chromospheric fields $B \sim 10^3$ G (active regions)
• Coronal fields $B \sim 1$ G, declining roughly as $r^{-\alpha}$ with $\alpha=2$–$3$ (Todarello, 27 Jan 2025)

Photonic Conversion Probability

ALPs traversing a magnetic region of length $L$ with transverse field $B$ convert to photons with probability

$$P_{a\to\gamma}(E) = \left(\frac{g_{a\gamma}BL}{2}\right)^2 \mathrm{sinc}^2\left(\frac{\Delta m^2L}{4E}\right)$$

where $\Delta m^2 = m_a^2 - m_\gamma^2$ (III et al., 2010). The resonance condition $m_a = \omega_p$ ($\omega_p=$ plasma frequency) greatly enhances the transition rate (Todarello, 27 Jan 2025).

For vacuum helioscopes in the low-mass, coherent regime ($m_a^2L/4E \ll 1$), $P_{a\to\gamma} \sim (g_{a\gamma}BL/2)^2$.

Multi-ALP Oscillation and Depletion Effects

In theories with multiple light ALPs, the photonic ALP produced in the Sun can oscillate into hidden states during propagation to Earth, suppressing the detected flux by the EM-state survival probability (Chadha-Day, 2021): $\bar{P}_\mathrm{surv}\to1-\tfrac{1}{2}\sin^2(2\theta)\quad(\text{two-state, %%%%28%%%%})$ This may weaken helioscope bounds by up to orders of magnitude for many hidden states.

3. Experimental Searches and Detection Techniques

Helioscopes

Axion helioscopes are the primary experimental tool for solar ALP searches at $m_a\lesssim1$ eV, exploiting conversion in laboratory magnets:

• CAST: $B=9$ T, $L=9.3$ m, $g_{a\gamma}<8.8 \times 10^{-11}$ GeV$^{-1}$ (95% CL, $m_a<0.02$ eV) (Graham et al., 2016, Irastorza et al., 2018).
• IAXO (proposed): $\sim$20–25 m, $\sim$2.5 T, $g_{a\gamma}\lesssim4\times10^{-12}$ GeV$^{-1}$ (projected, $m_a\lesssim0.01$ eV) (Irastorza et al., 2018).

Buffer gas phases permit tuning $m_\gamma$ for $m_a>0.02$ eV, scanning the range up to $\sim1$ eV.

Liquid-Scintillator and Noble-Liquid Detectors

Solar ALPs may be detected via the inverse Primakoff effect in detectors such as XENONnT and TEXONO: $$R_{\text{atom}} \approx 1.83 \times 10^{-36}~\text{s}^{-1}\left(\frac{10^{10}~\text{GeV}}{1/g_{a\gamma}}\right)^4$$ For Xe detectors ($\sim$10 ton, background $10^{-7}$ cts/day/keV/kg), the expected event rate is sub-unity per ton per year for $g_{a\gamma}=10^{-10}$ GeV$^{-1}$ (III et al., 2010, Wu et al., 2022). Projected sensitivities from XENONnT data rule out $g_{a\gamma}>4\times10^{-11}$ GeV$^{-1}$ at $m_a=1$ eV, $g_{a\gamma}>1\times10^{-10}$ GeV$^{-1}$ at $m_a=10$ keV (Wu et al., 2022).

Solar Radio and X-ray Constraints

• Solar Atmosphere X-ray Conversion: NuSTAR and other solar X-ray telescopes set bounds of $g_{a\gamma} \lesssim 6\times10^{-12}$ GeV$^{-1}$ for $m_a\lesssim10^{-2}$ eV (Todarello, 27 Jan 2025).
• Radio Conversion: Next-generation radio interferometry (e.g. SKA-1) could probe $g_{a\gamma} \sim 10^{-14}$ GeV$^{-1}$ for $\mu$eV-mass dark-matter ALPs converting in solar coronal fields (Todarello, 27 Jan 2025).

Alternative Concepts

• Dish Antennas and Dielectric Haloscopes: Non-resonant broadband techniques proposed for solar ALP searches could, with sufficiently high $B\cdot A$, reach $g_{a\gamma}\sim10^{-12}$–$10^{-13}$ GeV$^{-1}$ (Irastorza et al., 2018).
• Photon–Axion Splitting: Strongly inhomogeneous fields enable processes linear in $g_{a\gamma}$, potentially reaching $g_{a\gamma}\sim10^{-14}$ GeV$^{-1}$, though these ideas remain in conceptual development (III et al., 2010).

4. Constraints and Parameter Exclusion

Current and Planned Experimental Bounds

Experiment / Method	Mass Range ($m_a$)	Bound on $g_{a\gamma}$ (GeV$^{-1}$)	Notes
CAST (vacuum)	$<0.02$ eV	$<8.8\times10^{-11}$	95% CL
CAST (buffer gas)	$0.02-1.2$ eV	$2.3$–$3.3\times10^{-10}$	$^4$He/$^3$He phases
IAXO (projected)	$<0.01$ eV	$\lesssim4\times10^{-12}$	Next-gen, 3-year run
NuSTAR (solar X-ray)	$<10^{-2}$ eV	$<6\times10^{-12}$	Solar atmospheric X-rays
XENONnT (solar ALP IP)	1 eV–10 keV	$4\times10^{-11}$–$10^{-10}$	IP, lab bounds (Wu et al., 2022)
Solar luminosity bound	—	$<4\times10^{-11}$	$m_a\sim100$ eV; energy loss

For keV-mass ALPs, the NuSTAR-derived bounds ($$g_{a\gamma\gamma}\lesssim \text{few} \times 10^{-12}$$ GeV$^{-1}$ over $m\sim3$–40 keV) represent a one order-of-magnitude improvement over previous solar-basin limits and are independent of the local dark matter density (Beaufort et al., 2023).

Sensitivity Scaling

For background-limited solar ALP searches via the inverse Primakoff effect, the signal scales as $g_{a\gamma}^4$ and sensitivity improves slowly: $$g_{a\gamma}^{\text{lim}} \propto \left(\frac{B}{\mathcal{E}}\right)^{1/8}$$ Thus, improving $g_{a\gamma}$ by a factor of 10 requires $10^4$-fold gains in exposure or background rejection (III et al., 2010).

5. Phenomenological, Astrophysical, and Experimental Implications

Astrophysical Impacts

Solar ALP searches yield constraints on new physics with minimal model dependence—Primakoff production and solar core parameters are precisely known. For keV ALPs, the solar-basin constraint is independent of local DM assumptions, unlike halo decay searches (Beaufort et al., 2023).

Large-scale solar B-fields generate new sub-keV and keV ALP flux components, potentially dominating over classical Primakoff at $m_a$ near resonance ($\sim100$ eV) or in the sub-keV regime, motivating future low-threshold detectors (Guarini et al., 2020).

Future Prospects

• IAXO will improve $g_{a\gamma}$ sensitivity by $\sim100\times$ over CAST, with lower thresholds, improved optics, and massive B-field volume (Irastorza et al., 2018).
• DARWIN-class multi-ton noble-liquid detectors can target $g_{a\gamma}\sim10^{-12}$ GeV$^{-1}$ in the 100 eV–1 MeV window (Wu et al., 2022).
• Solar radio and X-ray programs (NuSTAR, Athena, SKA-1 Low) will access $g_{a\gamma}\sim10^{-12}$–$10^{-14}$ GeV$^{-1}$ below eV masses (Todarello, 27 Jan 2025).
• Novel laboratory approaches aiming for $g_{a\gamma}\sim10^{-14}$ GeV$^{-1}$ remain theoretical (III et al., 2010).

6. Experimental Challenges and Conceptual Limits

Helioscopes

Magnet strength and length ($BL$) present significant engineering constraints for future gains. Solar tracking, low backgrounds ($\lesssim10^{-7}$ cts/keV/kg/day), and low-energy thresholds ($\lesssim0.1$ keV) are key for next-generation sensitivity (Graham et al., 2016, Irastorza et al., 2018).

Noble-Liquid and Scintillator Detectors

Scaling laboratory detectors to probe $g_{a\gamma}\sim10^{-11}$ GeV$^{-1}$ requires $\gtrsim100$ ton$\cdot$yr exposure and backgrounds $<10^{-8}$ cts/keV/kg/day, with stringent energy resolution and stability. For $g_{a\gamma}\sim10^{-12}$ GeV$^{-1}$, exposures in the $10^4$–$10^5$ ton$\cdot$yr range would be necessary absent radically improved background suppression (III et al., 2010).

Astrophysical Uncertainties

Magnetic field models dominate the prediction and interpretation of solar-atmosphere conversion signals, especially in the Sun's outer regions. Oscillations among multiple ALP states can suppress or even entirely deplete the photonic ALP component, complicating the mapping between coupling and observed flux unless model alignment is known (Chadha-Day, 2021).

7. Outlook and Open Directions

Solar ALP searches remain a cornerstone of axion phenomenology, setting world-leading bounds in $g_{a\gamma}$–$m_a$ space from sub-eV to tens of keV. Complementary methods—helioscopes, laboratory detectors, solar X-ray/radio telescopes—jointly cover a wide swath of parameter space. For model space with generic axion-like multiplets, oscillation-induced signal suppression must be included in experimental interpretation.

The next decade will be defined by the commissioning of IAXO, deep-exposure XENON/DARWIN-scale detectors, and advanced radio/X-ray solar observation strategies. Future improvements depend critically on advances in magnet technology, ultra-low background reduction, precise atomic/magnetic modeling, and possibly the development of linear-in-coupling detection concepts (III et al., 2010, Irastorza et al., 2018). Successful detection of solar ALPs would have transformative implications for particle physics and astrophysics, while ongoing null results will continue to constrain or eliminate large swaths of viable axion/ALP parameter space.