Limits on the axion-photon coupling from Chandrayaan-2 observations

This paper presents the first constraints on the axion-photon coupling ($g_{a \gamma \gamma}$) using soft X-ray observations of the quiet Sun from India's Chandrayaan-2 mission, establishing an upper limit of approximately $(0.50 - 2.26) \times 10^{-10}$ GeV$^{-1}$ at 95% confidence for axion masses below $5 \times 10^{-4}$ eV.

The Gist

The Big Picture: Hunting for Invisible Ghosts

Imagine the universe is filled with a mysterious, invisible "ghost" particle called an axion. Scientists have been looking for these ghosts for decades because they might explain why the universe has mass (Dark Matter) and solve a puzzle about why the laws of physics seem slightly unbalanced.

The problem? These ghosts are shy. They barely interact with anything. However, physicists have a theory: if an axion flies through a strong magnetic field, it might briefly "transform" into a flash of light (a photon), specifically an X-ray.

The Setup: The Sun as a Ghost Factory

The Sun is a massive factory. Inside its core, it's so hot and dense that it likely produces billions of these axion ghosts every second.

• The Escape: Because they are so shy, the axions escape the Sun's core without getting stuck.
• The Transformation: As they fly out through the Sun's atmosphere, they pass through the Sun's magnetic field. According to our theory, some of them should turn into X-rays.
• The Goal: If we can detect these extra X-rays coming from the Sun, we can prove axions exist and measure how strongly they interact with light.

The Detective: Chandrayaan-2's "Eyes"

Usually, we look for these ghosts using giant magnets on Earth (like the CAST experiment) or by looking at the whole sky. But this paper uses a new detective: the Chandrayaan-2 lunar orbiter.

• The Tool: On board this Indian moon mission is a special camera called the X-ray Monitor (XSM).
• The Advantage: Most space telescopes have a "narrow field of view" (like looking through a straw). They can only see a tiny patch of the Sun at a time. The XSM, however, is like a wide-angle security camera. It sees the entire Sun at once.
• The Timing: The team looked at data from 2019–2020, a time when the Sun was very quiet (the "solar minimum"). This is like trying to hear a whisper in a library; if the Sun is quiet, it's easier to spot the faint "whisper" of axion X-rays.

The Investigation: Separating the Signal from the Noise

The team faced a tricky challenge: Background Noise.
Imagine you are trying to hear a specific bird singing in a forest. But there are wind, other birds, and cars passing by.

• The Noise: The XSM camera picks up X-rays from deep space, charged particles hitting the satellite, and even other bright stars.
• The Method: The scientists used three different "noise-canceling" strategies (like trying three different ways to filter out the wind) to isolate the Sun's true signal.
  1. Conservative: They subtracted only the known deep-space noise.
  2. Realistic: They subtracted the background noise measured when the Sun wasn't in the camera's view.
  3. Optimistic: They assumed they could perfectly model and remove all noise.

The Verdict: No Ghosts Found (Yet)

After analyzing millions of seconds of data, the team looked for that extra "axion X-ray" signal.

• The Result: They found nothing. The X-rays they saw were exactly what you would expect from a normal, quiet Sun. There were no extra ghosts turning into light.
• The Conclusion: Since they didn't find the ghosts, they can now say, "If axions exist, they are even shyer than we thought." They set a new upper limit on how likely axions are to turn into light.

Why This Matters

Even though they didn't find the axion, this is a huge success for science.

1. New Limits: They ruled out a range of possibilities. If axions are stronger than their new limit, we would have seen them. Since we didn't, we know where not to look.
2. The "Whole Sun" Advantage: Because the XSM sees the whole Sun, it avoids the errors that happen when you only look at a tiny slice of it (like the NuSTAR telescope did previously).
3. The Future: The paper suggests that the XSM camera is actually very good at this job; it just needs a bigger "net" (a larger collecting area) to catch the faint signal. It argues that we should build a dedicated "Axion Observatory" in space for the next quiet period of the Sun.

The Analogy Summary

Think of the Sun as a factory churning out invisible axion ghosts.
The XSM camera is a wide-angle security guard watching the factory gates.
The magnetic field is a magic mirror that turns ghosts into flashes of light.
The scientists stood guard, looking for flashes of light that shouldn't be there. They didn't see any.
Result: They didn't catch the ghosts, but they proved that if the ghosts are there, they are very, very good at hiding. This helps future detectives know exactly where to look next.

Technical Summary

1. Problem Statement

Axions and Axion-Like Particles (ALPs) are well-motivated candidates for physics beyond the Standard Model (BSM), potentially solving the Strong CP problem and serving as dark matter. While terrestrial experiments (like CAST, ALPS-II, and IAXO) search for axions, astrophysical objects like the Sun serve as powerful natural laboratories.

• The Mechanism: Axions produced in the solar core via processes like the Primakoff effect can escape the Sun. As they traverse the solar magnetic field, a fraction may convert back into photons (x-rays) via the inverse Primakoff effect.
• The Gap: Previous searches using space-based telescopes (e.g., NuSTAR) have been limited by small fields of view (FOV), observing only a portion of the solar disk. There is a need for constraints derived from instruments capable of observing the entire solar disk simultaneously to reduce systematic uncertainties associated with partial-disk observations.

2. Methodology

The authors utilized data from the Solar X-ray Monitor (XSM) onboard the Indian Space Research Organization's (ISRO) Chandrayaan-2 lunar orbiter.

Data Acquisition

• Observation Period: September 2019 to May 2020, corresponding to the 2019–2020 solar minimum (quiet Sun conditions).
• Energy Range: 1–15 keV.
• Background Handling: The analysis focused on the "quiet Sun" spectrum (excluding flares and active regions). The authors employed three distinct background subtraction schemes to assess systematic uncertainties:
  1. Case 1 (Conservative): Subtracted only the Cosmic X-ray Background (CXB) model.
  2. Case 2 (Realistic/Baseline): Subtracted the measured background (when the Sun was out of the FOV) while excluding periods with bright astrophysical sources (e.g., Sco X-1) or high charged particle events.
  3. Case 3 (Optimistic/Target): Empirically modeled the entire observed spectrum as background and subtracted the best-fit model, assuming an ideal background understanding.

Theoretical Framework

• Axion Production: Calculated the solar axion flux ($\phi_a$) using standard solar models. The flux arises from four processes: Primakoff, Compton scattering, and electron-ion/electron-electron bremsstrahlung. The Primakoff process (governed by axion-photon coupling $g_{a\gamma\gamma}$) dominates for light axions.
• Axion-Photon Conversion: The conversion probability ($P_{a\gamma}$) of axions turning into x-rays in the solar atmosphere was calculated by numerically integrating the axion-photon mixing equation in the presence of the solar magnetic field and plasma frequency.
  • The calculation included the plasma frequency ($\omega_p$) and absorption coefficients ($\Gamma$) derived from the CHIANTI atomic database and NIST XCOM cross-sections.
  • The conversion probability was found to be largely independent of axion mass for $m_a \lesssim 10^{-7}$ eV.
• Statistical Analysis: A Bayesian framework (using the MultiNest algorithm) was used to compute the posterior probability density for the axion-photon coupling ($g_{a\gamma\gamma}$) given the observed counts ($N_{obs}$) and expected counts ($N_{exp}$) in energy bins between 3.4 keV and 15 keV.

3. Key Contributions

• First Use of Chandrayaan-2 XSM: This is the first study to utilize Chandrayaan-2 XSM data to constrain axion parameters.
• Full-Disk Observation: Unlike NuSTAR (which has a $12' \times 12'$ FOV), the XSM observes the entire solar disk. This eliminates systematics related to spatial variations in the solar corona and magnetic field that affect partial-disk observations.
• Comprehensive Background Modeling: The paper explicitly quantifies the sensitivity dependence on background modeling by presenting three distinct cases, providing a robust range of limits from conservative to optimistic.
• Independent Constraint: It provides an independent astrophysical constraint on the axion-photon coupling that complements existing helioscope and stellar cooling limits.

4. Results

The analysis yielded 95% confidence level (C.L.) upper limits on the axion-photon coupling ($g_{a\gamma\gamma}$) for axion masses $m_a \lesssim 5 \times 10^{-4}$ eV. The limits are effectively mass-independent in this low-mass regime.

• Case 1 (Conservative): $g_{a\gamma\gamma} \lesssim 2.26 \times 10^{-10} \text{ GeV}^{-1}$
• Case 2 (Realistic/Baseline): $g_{a\gamma\gamma} \lesssim 1.29 \times 10^{-10} \text{ GeV}^{-1}$
• Case 3 (Optimistic): $g_{a\gamma\gamma} \lesssim 0.50 \times 10^{-10} \text{ GeV}^{-1}$

Comparison with Other Experiments:

• The results are competitive with the CERN Axion Solar Telescope (CAST).
• They are currently about an order of magnitude weaker than the recent NuSTAR limit ($7.3 \times 10^{-12} \text{ GeV}^{-1}$).
• Reason for Difference: The primary limitation of the XSM is its small effective collecting area ($A_{eff} \approx 800 \text{ cm}^2$) compared to NuSTAR. However, the full-disk observation offers a unique systematic advantage.

5. Significance and Future Outlook

• Validation of Method: The consistency of limits across the three background treatments (within an order of magnitude) confirms that the constraints are statistically limited rather than dominated by modeling systematics.
• Motivation for Future Missions: The paper argues that a dedicated solar observatory with a significantly larger collecting area and improved spectral resolution, operating during the next solar minimum, could improve these bounds by an order of magnitude.
• Broader Impact: The study demonstrates the viability of using lunar orbiter instruments for solar physics and BSM searches, encouraging the development of future space-based solar x-ray observatories specifically designed for axion detection.

In conclusion, this work establishes a new, independent constraint on axion-photon coupling using full-disk solar observations, bridging the gap between terrestrial helioscopes and other astrophysical probes, and highlighting the potential for future high-sensitivity solar x-ray missions.