Is the Turner Window Open? Seeking Closure with Resonant Absorption of Galactic Axions in NaI Dark Matter Detectors

This paper proposes that existing ultra-clean underground NaI dark matter detectors can search for galactic axions produced by carbon-burning stars via resonant absorption of 440 keV axions, potentially probing axion-nucleon couplings in a parameter space that remains viable despite existing astrophysical constraints.

The Gist

The Big Idea: A New "Ghost" Hunt in Old Detectors

Imagine you have a very sensitive security camera in your basement, designed to catch a specific type of thief (Dark Matter particles called WIMPs) that only show up when they bump into things very gently. You've been watching this camera for years, hoping to see a blip.

Now, a group of physicists says: "Hey, while you're staring at that camera, you might be missing a completely different kind of ghost that is much easier to catch!"

They are talking about Axions. These are hypothetical particles that are a leading candidate for Dark Matter. The paper suggests that our existing underground detectors (made of a crystal called Sodium Iodide, or NaI) can actually hunt for these axions right now, without building anything new.

The Source: The Galactic "Axion Oven"

Where do these axions come from? The paper points to massive stars in our galaxy that are currently burning carbon.

• The Analogy: Think of these stars as giant, cosmic ovens. Inside, they are cooking up a specific ingredient: Sodium-23 (the same element found in table salt).
• The Process: These stars are so hot (about a billion degrees) that the Sodium atoms get "excited." They jump up to a higher energy state and then immediately fall back down.
• The Emission: Usually, when an atom falls back down, it releases a flash of light (a photon). But in this paper's scenario, the star is so hot and the physics are just right that instead of light, the Sodium atom releases a Sodium Axion.
• The Result: These stars are essentially "axion factories," spewing out a steady stream of these particles toward Earth.

The Trap: The "Resonant Absorption"

This is the cleverest part of the paper. How do we catch these invisible axions?

• The Analogy: Imagine you have a radio tuned to a specific station (let's say 101.5 FM). If a radio wave hits your antenna at exactly that frequency, your radio "resonates" and picks up the signal loud and clear. If the wave is even slightly off-frequency, your radio ignores it.
• The Setup: The axions coming from the stars have a very specific "frequency" (energy) of 440 keV.
• The Detector: The NaI detectors on Earth are made of Sodium. Because they are made of the same material that created the axions, they are perfectly tuned to that 440 keV frequency.
• The Catch: When a star axion hits a Sodium atom in the detector, the atom "resonates." It absorbs the axion and immediately spits out a flash of light (a gamma ray) at that exact 440 keV energy.

In short: The detector acts as both the trap and the alarm. The axion enters, the Sodium atom gets excited, and it screams "I caught one!" by flashing a light.

Why This is a "Golden Opportunity"

The authors argue that this is a "target of opportunity" for three main reasons:

1. We Already Have the Tools: There are already massive, ultra-clean NaI detectors underground (like DAMA/LIBRA, COSINE, and SABRE) built to hunt for WIMPs. They are sitting there, waiting.
2. The Signal is Clear: The axion signal would appear as a sharp, distinct spike at 440 keV. It's like hearing a single, pure musical note in a noisy room. It's very hard for background noise to fake this specific note.
3. The "Turner Window": There is a specific range of axion properties (mass and interaction strength) that scientists call the "Turner Window." Current rules from other experiments (like supernova observations) say axions could exist here, but no one has proven it yet. This experiment could finally close that window or open a new door.

The "Catch" (Why we haven't done this yet)

You might ask, "If this is so great, why hasn't everyone done it?"

• The Blind Spot: These detectors are usually set to look for very low-energy signals (tiny bumps from WIMPs). The axion signal is at 440 keV, which is much higher energy. It's like having a microphone set to hear a whisper, but the axion is a shout. The microphone might be turned down too low to hear it.
• The Fix: The paper suggests that many of these detectors can actually be switched to "low gain" mode to listen for the shout, or run two modes at once.

The Bottom Line

The paper is a proposal to the scientific community: "Don't just look for WIMPs. Turn your existing Sodium detectors toward the sky, tune them to the 440 keV frequency, and see if you can catch the axions being cooked up by massive stars in our galaxy."

If they find it, it solves a massive mystery about the universe. If they don't find it, they can rule out a huge range of possibilities, helping us understand what Dark Matter isn't. Either way, it's a win.

Technical Summary

1. Problem Statement

The dark matter community has invested heavily in ultra-clean underground Sodium Iodide (NaI) detectors (e.g., DAMA/LIBRA, ANAIS, COSINE, SABRE) primarily to search for light Weakly Interacting Massive Particles (WIMPs) based on the annual modulation signal reported by DAMA/LIBRA. However, these detectors possess a unique capability that has been underutilized: the potential to detect galactic axions via resonant absorption.

The paper addresses the "Turner window," a parameter space for axions with masses $m_a \gtrsim 1$ eV and couplings large enough to evade the SN1987A cooling bound but small enough to escape stellar trapping. While constraints exist, significant gaps remain in the coupling parameter space ($g_{aNN}$). The authors propose a new target of opportunity: detecting axions produced by carbon-burning stars in the Milky Way, which synthesize significant quantities of $^{23}$Na.

2. Methodology

A. The Axion Source: Carbon-Burning Stars

• Production Mechanism: Massive stars ($\gtrsim 7.5 M_\odot$) undergoing carbon burning synthesize $^{23}$Na via the reaction $^{12}\text{C} + ^{12}\text{C} \to ^{24}\text{Mg}^* \to ^{23}\text{Na} + p$.
• Conditions: These stars maintain $^{23}$Na at temperatures $T \sim 10^9$ K for periods up to $10^4$ years.
• Emission Process: Under these conditions, $^{23}$Na acts as a "pump." The nucleus undergoes repeated photo-excitation and axio-deexcitation of its first excited state (440 keV), emitting monochromatic axions.
• Flux Modeling: The authors utilize a galactic model (fitting disk/bulge populations with a Salpeter IMF) and stellar evolution codes (MESA) to simulate an ensemble of progenitors. The resulting axion flux at Earth is modeled as a statistical distribution (skewed Gaussian/Lorentzian) dependent on the axion-nucleon coupling.

B. Nuclear Physics and Coupling

• Interaction: The axion-nucleon interaction is described by an effective Lagrangian involving isoscalar ($g_{aNN}^0$) and isovector ($g_{aNN}^3$) couplings.
• Effective Coupling: For $^{23}$Na, the transition is governed by a specific effective coupling:
  $$g_{aNN}^{\text{eff}}(^{23}\text{Na}) \propto (g_{app} - 0.062 g_{ann})$$
  where $g_{app}$ and $g_{ann}$ are the proton and neutron couplings, respectively.
• Resonant Absorption: The detection mechanism relies on the inverse process: a galactic axion is resonantly absorbed by a $^{23}$Na nucleus in the detector, producing a 440 keV de-excitation photon ($\gamma$).
• Cross-Section: The resonant cross-section is calculated using the known radiative width ($\Gamma_\gamma$) of the $^{23}$Na excited state and thermal broadening factors ($\sigma_{TH}$) derived from stellar temperatures.

C. Escape Probability and Opacity

• Reabsorption: A critical calculation involves the probability of axions escaping their source stars. For large couplings, resonant reabsorption on $^{23}$Na within the star becomes the dominant opacity source, creating a "thin" emission layer (axiosphere).
• Other Processes: Compton scattering and the Primakoff process were evaluated but found to be sub-dominant or negligible for the relevant coupling ranges under DFSZ axion models.

D. Detection Strategy

• Detector: Existing NaI(Tl) detectors (e.g., DAMA/LIBRA, COSINE-100) serve as both the source of the conversion $\gamma$ (via the target nuclei) and the detector.
• Signal: A mono-energetic peak at 440 keV.
• Exposure: The analysis assumes a hypothetical exposure of 500 kg-yr (approx. 2 years of data from a 242 kg detector like DAMA/LIBRA).
• Background Estimation: Background rates at 440 keV are estimated using COSINE-100 data ($\sim 0.37$ counts/kg/d/keV) with an energy resolution ($\Gamma_{FWHM}$) of $\sim 22$ keV.

3. Key Contributions

1. Identification of a New Source: The paper identifies galactic carbon-burning stars as a potent, previously overlooked source of 440 keV axions, distinct from the solar $^{57}$Fe source.
2. Dual Role of NaI: It highlights the unique advantage of NaI detectors: they contain 100% $^{23}$Na (unlike the 2% abundance in natural iron for $^{57}$Fe searches) and act as both the emitter (in the star) and the absorber (in the detector).
3. Re-evaluation of Astrophysical Bounds: The authors re-examine constraints from SN1987A (KII $\gamma$-rays) and SNO (neutron production), showing that previous bounds were overly conservative due to simplified opacity models. Their refined models reveal substantial "gaps" in the exclusion contours.
4. Feasibility Study: They demonstrate that existing or near-future NaI experiments can probe axion-nucleon couplings in the range $|g_{aNN}^{\text{eff}}| \sim 10^{-6}$ to $10^{-2}$, covering the "Turner window" and potentially excluding QCD axions with masses $m_a \gtrsim 10$ eV.

4. Results

• Flux and Event Rates:
  • The median galactic axion flux at Earth is estimated as $\langle \phi \rangle \approx 0.214 \times 10^6 |g_{aNN}^{\text{eff}}/10^{-7}|^2 \text{ cm}^{-2}\text{s}^{-1}$.
  • For a 500 kg-yr exposure, the expected signal events at 440 keV are calculated.
• Exclusion Limits:
  • Assuming a 3$\sigma$ statistical significance over the background, the proposed search can exclude couplings in the range:
    $$8.4 \times 10^{-7} \lesssim |g_{aNN}^{\text{eff}}(^{23}\text{Na})| \lesssim 1.5 \times 10^{-2}$$
  • This range is visualized in the $g_{aNN}^0$ vs. $g_{aNN}^3$ plane (Fig. 2), showing a large excluded region (tan shaded) that overlaps with and extends beyond current astrophysical limits (SNO, SN1987A).
• Impact on Models:
  • The search covers the parameter space for KSVZ axions with masses $10 \text{ eV} \lesssim m_a \lesssim 10^5 \text{ eV}$.
  • It also constrains DFSZ axion models, particularly those with specific $\sin^2 \beta$ values.
• Comparison with SN1987A: The NaI search offers a continuous, statistically robust signal, unlike the single-event nature of SN1987A, providing a more definitive test of the axion hypothesis in this mass/coupling regime.

5. Significance

• Maximizing Existing Infrastructure: The paper provides a compelling argument for utilizing the massive investment in NaI dark matter detectors for a secondary, high-impact physics goal (axion detection) without requiring new hardware.
• Closing the Turner Window: It offers a realistic path to "close" the Turner window, a region where axions could exist without violating current supernova cooling bounds but remain undetected by other means.
• Model Independence: The search relies on a single effective coupling ($g_{aNN}^{\text{eff}}$) governing production, propagation, and detection, making the interpretation of results cleaner than multi-channel astrophysical constraints.
• Immediate Actionability: The authors suggest that some detectors (like COSINE-100) can operate at low gain simultaneously with high gain, allowing for parallel searches for light WIMPs and 440 keV axions, maximizing the scientific return on current experimental runs.

In conclusion, the paper argues that the galactic flux of 440 keV axions from carbon-burning stars represents a "target of opportunity" that existing NaI detectors are uniquely positioned to detect, potentially leading to the discovery of axions or the exclusion of a significant portion of the QCD axion parameter space.