---
title: "Axion–Photon Conversion in Cluster Magnetic Fields Interactive Lab | Sandbox Physics"
description: "Can an invisible light particle change the X-ray spectrum of a distant galaxy?"
canonical_url: "https://sandboxphysics.com/labs/axion-photon-conversion/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/axion-photon-conversion/"
last_modified: "2026-11-14"
---

# Axion–Photon Conversion in Cluster Magnetic Fields

**Can an invisible light particle change the X-ray spectrum of a distant galaxy?** A magnetic field lets a photon turn into a light axion and back, so part of the light from a distant galaxy can vanish on its way to us. The lost share changes with photon energy and would print small ripples on an X-ray spectrum. Smooth observed spectra therefore cap how strongly axions could couple to light, and stellar cooling sets a separate cap.

Turn magnetic domains, change gas density and axion mass, and watch photons trade places with axions along a cluster sightline.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

This is a simplified model of one sightline, not a fit to any observation. The cluster field is a chain of equal cells. Each cell has one uniform field across the beam, with the same strength and a random or common direction. The gas has one constant electron density. Each cell is solved exactly for photons and one axion-like particle. Photon absorption, the turbulent power spectrum of real fields, radial profiles of density and field, the cosmic background light and detector response are all left out. The dashed reference curve is an ideal formula: the uniform-field two-state result, or the average over random field directions. It is not a reconstruction of the solid simulated curve. The stellar-cooling ruler uses a separate equation for horizontal-branch stars from the Particle Data Group review. The numbered limits are printed values from the cited papers and hold only for their own mass ranges and assumptions. The moving tracers only illustrate the computed fractions.

X-ray photons that survive the cluster, by energy

Solid: this simulated sightline Dashed: ideal mean over random field angles

Vertical axis: fraction of photons that arrive. Both curves come from the model, not from a telescope.

Along the sightline at the chosen energy

$P_{\gamma\gamma}$ $P_{\gamma\to a}$ $\Pi_L$

Dotted lines mark domain boundaries. Polarization grows because only one photon direction mixes in each cell.

Stars give a separate limit

Helium-burning lifetime factor

1. Horizontal-branch star counts $g_{a\gamma}<6.6\times10^{-11}\,\mathrm{GeV^{-1}}$ $m_a\lesssim1000\,\mathrm{eV}$ 95% confidence; PDG 2025 review 89, eq. (89.16); Ayala et al. 2014, arXiv:1406.6053v2, eq. (3)
2. CAST solar helioscope $g_{a\gamma}<5.8\times10^{-11}\,\mathrm{GeV^{-1}}$ $m_a\lesssim0.02\,\mathrm{eV}$ 95% confidence; PDG 2025 review 89, eq. (89.20)
3. Fermi-LAT spectrum of NGC 1275 $g_{a\gamma}<5\times10^{-12}\,\mathrm{GeV^{-1}}$ $5\times10^{-10}\lesssim m_a/\mathrm{eV}\lesssim5\times10^{-9}$ 95% confidence; Ajello et al. 2016, arXiv:1603.06978v1, abstract
4. Chandra spectrum of NGC 1275 $g_{a\gamma}<7.9\times10^{-13}\,\mathrm{GeV^{-1}}$ $m_a\lesssim1\times10^{-12}\,\mathrm{eV}$ 99.7% confidence; Reynolds et al. 2020, arXiv:1907.05475v4, eq. (5), field model B

Grey dashed markers do not apply at the current mass. Limits are copied from the papers, not computed here.

## Follow X-ray photons through a magnetized cluster

**Background** Galaxy clusters hold hot gas threaded by magnetic fields of a few microgauss over hundreds of kiloparsecs. If a light axion-like particle exists and couples to photons, that field can turn part of a passing X-ray beam into particles no telescope sees.

**Why it matters** The missing share depends on photon energy, so it would leave a pattern on a bright spectrum behind the cluster. A spectrum without that pattern limits the coupling.

- **Focus question**: Why does the same coupling give a smooth spectrum in one setting and strong ripples in another?
- **One-sentence intuition**: Mixing is strong only when the coupling term beats the mismatch between the photon and axion dispersion terms. In a chain of randomly oriented cells the photon fraction averages toward $2/3$, but any single sightline keeps energy-dependent ripples around that average.

### Core mathematical model

#### Mixing in one magnetic cell

$$
i\frac{d}{dz}\begin{pmatrix}A_\perp\\A_\parallel\\a\end{pmatrix}=-\begin{pmatrix}\Delta_{\rm pl}&0&0\\0&\Delta_{\rm pl}&\Delta_{a\gamma}\\0&\Delta_{a\gamma}&\Delta_a\end{pmatrix}\begin{pmatrix}A_\perp\\A_\parallel\\a\end{pmatrix}
$$

Only the photon polarization parallel to the transverse field mixes. Here $\Delta_{a\gamma}=g_{a\gamma}B_\perp/2$, $\Delta_{\rm pl}=-\omega_{\rm pl}^2/(2E)$ and $\Delta_a=-m_a^2/(2E)$.

#### Two-state conversion in a uniform field

$$
P_{\gamma\to a}=\left(\frac{2\Delta_{a\gamma}}{\Delta_{\rm osc}}\right)^2\sin^2\!\left(\frac{\Delta_{\rm osc}L}{2}\right),\qquad \Delta_{\rm osc}^2=(\Delta_{\rm pl}-\Delta_a)^2+4\Delta_{a\gamma}^2
$$

This is for photons polarized along the field. Unpolarized light converts half as often. The Lab solves each cell exactly and checks this formula in the uniform case.

#### Mean over random field directions

$$
\langle P_{\gamma\to a}\rangle_N=\frac{1}{3}\left[1-\prod_{j=1}^{N}\left(1-\frac{3}{2}P_j\right)\right]
$$

Each $P_j$ is the parallel-polarization probability of cell j. Many cells drive the mean toward one third, the equipartition among two photon states and one axion state.

#### A separate stellar equation

$$
\frac{t_{\rm HB}(g)}{t_{\rm HB}(0)}\approx\frac{80}{80+30\,g_{10}^2},\qquad g_{10}=\frac{g_{a\gamma}}{10^{-10}\,\mathrm{GeV^{-1}}}
$$

Primakoff emission in helium-burning cores competes with nuclear burning. Fewer horizontal-branch stars in globular clusters than this predicts would signal axion cooling. The sightline model is not used here.

### Common difficulties

#### Stronger field is not always more conversion

**Typical misconception** Doubling the field doubles the converted share.

**Better mental model** The probability oscillates with distance. Once a cell holds more than half an oscillation, a stronger field can lower the photon loss at a given energy.

#### The dashed curve is not a fit

**Typical misconception** The dashed reference was reconstructed from the simulated curve.

**Better mental model** It is an independent ideal formula. In the tangled field it is the average over all field directions, so one sightline scatters around it.

### Run the experiment

1. 01

   #### Watch the default sightline

   Leave the tangled cluster running and watch the tracers drift between the two lanes.

   **What to observe:** The photon lane thins and refills cell by cell, and the spectrum below dips unevenly with energy.

2. 02

   #### Turn one domain

   Drag one arrow in the middle of the chain through a half turn.

   **What to observe:** The path profile changes from that cell onward, and the polarization at the telescope rotates.

3. 03

   #### Make the field uniform

   Choose Oscillation in a uniform field and drag the energy cursor.

   **What to observe:** The solid and dashed curves coincide, because the exact transfer reproduces the two-state formula.

4. 04

   #### Compare with stars

   Raise the coupling to the first numbered limit on the stellar ruler.

   **What to observe:** There helium burning is about 14 percent shorter, while the cluster sightline is already close to fully mixed. Under their field assumptions, X-ray spectra reach far weaker couplings than star counts.

Physical conclusion

Axion searches in clusters read the absence of a pattern. Keep the field model, the plasma density and the mass range attached to any limit you quote.

## Related experiments and articles

Searching for axions with cosmic magnetic fields · Reading path

### From two mixing states to a published limit

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How could an invisible particle change a distant spectrum?**](https://sandboxphysics.com/stories/axion-photon-mixing/invisible-particles-and-distant-spectra/)
2. [Article **Photon and axion as two mixing states**](https://sandboxphysics.com/stories/axion-photon-mixing/photon-and-axion-as-two-states/)
3. [Article **Mixing in a cluster magnetic field and plasma**](https://sandboxphysics.com/stories/axion-photon-mixing/mixing-in-cluster-fields-and-plasma/)
4. [Article **Random domains, polarization and stellar cooling**](https://sandboxphysics.com/stories/axion-photon-mixing/random-domains-polarization-and-stars/)
5. [Article **Recompute a cluster sightline from saved inputs**](https://sandboxphysics.com/stories/axion-photon-mixing/recompute-a-cluster-sightline/)
6. [Article **Reading the Chandra NGC 1275 axion limit**](https://sandboxphysics.com/stories/axion-photon-mixing/reading-the-chandra-ngc-1275-limit/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)