Solar Axions from Nuclear Transitions

Using soft X-ray data from India's Chandrayaan-2 mission, this study sets significantly stronger constraints on axion-nucleon and axion-photon couplings for solar axions produced in $^{57}$Fe nuclear transitions compared to those from $^{83}$Kr, due to a nearly three-order-of-magnitude difference in their respective fluxes despite similar effective couplings.

The Gist

Imagine the Sun not just as a giant ball of fire, but as a bustling, invisible factory. For decades, physicists have suspected this factory is churning out tiny, ghostly particles called axions. These particles are the "missing link" in our understanding of the universe, potentially solving a major puzzle about why the laws of physics behave the way they do, and they might even be the dark matter that holds galaxies together.

This paper is a report card on a new attempt to catch these ghosts using a telescope orbiting the Moon.

The Mystery: The Sun's "Ghost" Factory

The Sun is so hot and dense in its core that atoms get excited. Usually, when an excited atom calms down, it releases a flash of light (a photon). But the theory suggests that sometimes, instead of light, it might release an axion.

The authors focused on two specific "machines" in the solar factory:

1. Iron-57 (57Fe): When these atoms relax, they should release axions with a specific energy of 14.4 keV.
2. Krypton-83 (83Kr): When these relax, they should release axions at 9.4 keV.

Think of these axions as monochromatic (single-color) laser beams of invisible energy shooting out from the Sun.

The Hunt: Catching the Ghosts

Axions are so shy they pass through the Earth and our detectors without a trace. However, the paper proposes a clever trick: The Solar Magnetic Field.

As these axions travel away from the Sun, they pass through the Sun's magnetic field. The theory says that in this magnetic field, the axions can "morph" into X-ray photons (light). If this happens, our telescopes should see a sharp, bright spike in the X-ray spectrum at exactly 14.4 keV and 9.4 keV.

The researchers used data from Chandrayaan-2, an Indian lunar orbiter equipped with an X-ray monitor (XSM). This telescope was watching the "quiet Sun" (a calm period with few solar flares) to get a clean background, looking for those specific spikes.

The Analogy: The Noisy Room vs. The Whisper

Imagine you are trying to hear a specific whisper (the axion signal) in a very noisy room (the Sun's natural X-ray background).

• The Problem: The room is loud. You have to guess what the background noise sounds like to subtract it and hear the whisper.
• The Strategy: The team tried three different ways to "silence" the background noise:
  1. Conservative: Only removing the obvious, loud noises (cosmic rays).
  2. Realistic: Removing the measured background noise.
  3. Optimistic: Assuming the background is as quiet as theoretically possible.

The Results: What They Found

After analyzing the data, they did not find the whisper. There were no spikes at 14.4 keV or 9.4 keV.

However, in science, "not finding it" is still a huge victory. It allows them to set limits (rules) on how strong the axions can be.

• The Iron (57Fe) Result: Because iron is very common in the Sun, the team could set a very strict rule. Their "Realistic" and "Optimistic" guesses for the background noise allowed them to set limits that are stronger than previous experiments (like CAST and CUORE). It's like saying, "We know the whisper isn't louder than a specific volume, and we know that better than anyone else before."
• The Krypton (83Kr) Result: Krypton is much rarer in the Sun (like finding a needle in a haystack compared to iron). Because there are so few Krypton atoms, the signal would be much weaker. Consequently, the limits they set for Krypton are about 1,000 times weaker than for Iron. It's like trying to hear a whisper from a person standing 10 miles away versus one standing 10 feet away.

The "Why" Behind the Numbers

The paper explains a fascinating twist:

• Iron is abundant, so even though the telescope (XSM) is smaller than the giant magnets used in other experiments (like CAST), the sheer number of Iron axions produced in the Sun, combined with the fact that the Sun's magnetic field helps convert them to light very efficiently, made the search competitive.
• Krypton is rare. Even though the physics is similar, the lack of raw material (Krypton atoms) in the Sun means the potential signal is tiny, making it much harder to constrain the rules for Krypton axions.

The Bottom Line

The paper concludes that:

1. No axions were found at these specific energies.
2. This absence allows scientists to say, "If axions exist, they must be even more elusive than we thought," specifically regarding how they interact with atomic nuclei and light.
3. The Iron-57 search provided some of the tightest constraints on axion properties ever made, beating out previous major experiments in certain scenarios.
4. The Krypton-83 search was the first of its kind, setting the first-ever limits for this specific channel, though they are currently less strict due to the rarity of Krypton in the Sun.

In short, the Moon-based telescope listened to the Sun's quiet hum, didn't hear the ghostly axion whisper, and used that silence to draw a tighter fence around where these particles might (or might not) be hiding.

Technical Summary

Technical Summary: Solar Axions from Nuclear Transitions

Problem and Motivation
The search for axions and axion-like particles (ALPs) remains a primary avenue for addressing the strong CP problem in the Standard Model and identifying dark matter candidates. While astrophysical searches have traditionally focused on continuous axion production mechanisms (such as the Primakoff effect, bremsstrahlung, and Compton scattering), this paper investigates a specific, monochromatic production channel: axions emitted via magnetic dipole (M1) nuclear transitions in the solar core. Specifically, the authors target the de-excitation of thermally excited nuclei of $^{57}\text{Fe}$ (14.4 keV transition) and $^{83}\text{Kr}$ (9.4 keV transition). Although these isotopes possess low-lying excited states accessible in the solar plasma, their detection via X-ray telescopes has been limited by previous experimental constraints and the lack of dedicated searches for the $^{83}\text{Kr}$ channel.

Methodology
The authors utilize soft X-ray observations of the quiet Sun collected by the Solar X-ray Monitor (XSM) aboard India's Chandrayaan-2 lunar mission during the 2019–2020 solar minimum. The analysis proceeds through the following steps:

1. Flux Calculation: The solar axion flux is calculated based on the thermal population of excited nuclear states in the solar core, governed by the Boltzmann factor. The emission rate depends on the effective axion-nucleon couplings ($g_{aN}^{\text{eff}}$) and the branching ratio of axion emission versus photon emission for M1 transitions. The authors compute the differential fluxes for $^{57}\text{Fe}$ and $^{83}\text{Kr}$ using standard solar models (B23-AGSS09) and updated photospheric abundances.
2. Conversion Probability: The detection mechanism relies on the conversion of these solar axions into X-ray photons via the inverse Primakoff effect as they traverse the solar magnetic field. The authors solve the equations of motion for axion-photon mixing in a magnetized plasma, accounting for the solar magnetic field profile and electron density up to a heliocentric distance of $29 R_{\odot}$. The conversion probability ($P_{a\gamma}$) is evaluated as a function of axion mass ($m_a$), noting that coherence is maintained for $m_a \lesssim 10^{-5}$ eV, leading to a mass-independent conversion plateau in the low-mass regime.
3. Data Analysis: The theoretical signal (monochromatic lines at 14.4 keV and 9.4 keV) is convolved with the XSM energy resolution (FWHM = 175 eV). The authors analyze background-subtracted residual spectra using three distinct subtraction schemes derived from previous work: Case 1 (Conservative), Case 2 (Realistic), and Case 3 (Optimistic). A Gaussian likelihood function is constructed over the 3.4–15 keV energy range to derive 95% confidence level (C.L.) upper limits on the coupling products $|g_{aN}^{\text{eff}} \times g_{a\gamma\gamma}|$ and the axion-photon coupling $g_{a\gamma\gamma}$ (assuming fixed $g_{aN}^{\text{eff}}$).

Key Contributions and Results

• Flux Disparity: The analysis reveals a significant disparity in the expected axion fluxes between the two isotopes. Despite the effective axion-nucleon couplings for $^{57}\text{Fe}$ and $^{83}\text{Kr}$ being numerically similar, the $^{83}\text{Kr}$ flux is suppressed by nearly three orders of magnitude compared to $^{57}\text{Fe}$. This is attributed to the much lower solar abundance of krypton ($\epsilon_{\text{Kr}} \approx 3.12$) relative to iron ($\epsilon_{\text{Fe}} \approx 7.46$).
• Constraints on $^{57}\text{Fe}$ (14.4 keV):
  • For the conservative background subtraction (Case 1), the derived limits on $|g_{aN}^{\text{eff}} \times g_{a\gamma\gamma}|$ and $g_{a\gamma\gamma}$ are slightly more stringent than the CAST experiment results but weaker than the CUORE experiment limits.
  • For the realistic (Case 2) and optimistic (Case 3) scenarios, the constraints surpass both CAST and CUORE limits. The authors attribute this improvement to the resonant conversion enhancement in the solar atmosphere, which compensates for the smaller effective area of the XSM compared to laboratory helioscopes, despite the higher raw event count limits.
  • For $m_a \lesssim 10^{-6}$ eV, the limits are approximately $|g_{aN}^{\text{eff}} \times g_{a\gamma\gamma}| \lesssim 5.0 \times 10^{-17} \text{ GeV}^{-1}$ (Realistic) and $g_{a\gamma\gamma} \lesssim 1.5 \times 10^{-11} \text{ GeV}^{-1}$.
• Constraints on $^{83}\text{Kr}$ (9.4 keV):
  • This work presents the first dedicated search for 9.4 keV solar axions using the $^{83}\text{Kr}$ channel.
  • The derived limits on $|g_{aN}^{\text{eff}} \times g_{a\gamma\gamma}|$ are roughly an order of magnitude weaker than those for $^{57}\text{Fe}$, consistent with the flux suppression.
  • The analysis provides the first constraints on the axion-photon coupling $g_{a\gamma\gamma}$ specifically for the $^{83}\text{Kr}$ transition channel.
• Mass Dependence: The constraints are mass-dependent, remaining flat for $m_a \lesssim 10^{-6}$ eV and weakening monotonically at higher masses due to the loss of coherence in the solar atmosphere (momentum mismatch).

Significance
The paper demonstrates that solar X-ray observations from the Chandrayaan-2 XSM provide a competitive and independent probe of axion models, particularly for the $^{57}\text{Fe}$ channel. The study highlights that astrophysical searches can leverage resonant conversion in the solar atmosphere to achieve sensitivity comparable to or exceeding laboratory experiments, provided the background modeling is sufficiently optimized. Furthermore, the work establishes the first experimental limits for the 9.4 keV $^{83}\text{Kr}$ channel, expanding the parameter space for nuclear-transition-based axion searches. The authors conclude that future observations with next-generation solar X-ray instruments, combined with improved solar magnetic field models, could further sharpen these constraints and probe regions of the axion parameter space currently inaccessible to laboratory experiments.