# Photon enhancement in a homogeneous axion dark matter background

## Abstract

We study the propagation of photons in a homogeneous axion dark matter background. When the axion decay into two photons is stimulated, the photon field exhibits a parametric instability in a small bandwidth centered on one half of the axion mass. We estimate analytically the enhancement for both coherent and non-coherent axion fields and we find that this effect could be relevant in the context of miniclusters and galactic halos.

## 1 Introduction

*P*and

*CP*in strong interactions [1, 2, 3]. In this theoretical framework, the axion is a pseudo-Goldston boson arising from the spontaneous breaking of the PQ (Peccei–Quinn) symmetry defined at some energy scale \(f_a\). Below the QCD energy scale, the axion acquires its mass \(m_a\) by nonperturbative effects. It is related to PQ symmetry breaking scale by

*a*is the axion field and

*g*its coupling to two photons. \(F_{\mu \nu }\) is the electromagnetic strength tensor \(F_{\mu \nu }=\partial _\mu A_\mu -\partial _\nu A_\nu \), where \(A_\mu \) is the electromagnetic field. \({\tilde{F}}^{\mu \nu }\) is the dual of the electromagnetic strength tensor and is defined as \(\tilde{F}^{\mu \nu }={1\over 2}\epsilon ^{\mu \nu \rho \lambda }F_{\rho \lambda }\).

Axions have not been experimentally observed yet, so their existence is still in suspense, but because of their cosmological role as dark matter candidates, the experimental efforts to search for them in the corresponding parameter space have been intense. In the laboratory, axions are searched for using the coupling to two photons described by Eq. (2). Especially, static magnetic fields have been strongly implemented [13, 14, 15]. Some running experiments, such as haloscopes searches [16], already have access to the parameter space where they are cold dark matter candidates, and several new proposals plan to do so in the near future (ALPS-II [17], IAXO [18], HAYSTAC [19, 20], MADMAX [21, 22], among others).

In this paper we are interested in studying the effects on an incident electromagnetic plane wave traveling within a homogeneous axion dark matter background. We find an small window where the photon field experiences parametric resonance, we estimate the rate of the enhancement in coherent and non-coherent axion background and finally, we apply our results to astrophysical structures. Related topics were discussed recently in References [23, 24, 25], but they do not consider non-coherent axion fields. Studies about the propagation of photons in an axion dark matter background had already been performed a few years ago in order to account for their effects in optical experiments [26, 27], however the instability was not considered.

## 2 Electromagnetic plane wave in a homogeneous axion background

*t*, we can approximate \(|A_R|^2\approx {1\over 4}|A_T(0)|^2e^{\gamma t}\) and \(|\alpha |^2\approx |\alpha (0)|^2\). Condition (18) translates to

## 3 Enhancement in a coherent and non-coherent axion background

## 4 Possible astrophysical relevance

*d*corresponds to the distance traveled by the incident photon within the axion dark matter background, which is actually the maximum time during which the parametric resonance can occur. Using some typical physical parameters, we plot in Fig. 3 the regions in the parameter space where condition (27) is satisfied for both axion miniclusters and galactic halos. More details of these results will be explained in the following.

### 4.1 Axion miniclusters

*R*(

*t*) is the scale factor and \(t_{eq}\sim 2\times 10^{12}\text {s}\) is the cosmological time of matter-radiation equality. \(t_1\) corresponds to the cosmological time when the axion field starts to oscillate and is defined by \(m_a(t_1)t_1\sim 1\). In the most general scenario (see [12]), the axion energy density today can be expressed as

### 4.2 Galactic halos

*c*is the speed of light) and a width \(d_h\sim 1\,\text {kpc}\), condition (27) becomes

As a final remark, It is very important to make clear that in this manuscript we are only considering homogeneous axion backgrounds. Inhomogeneities could change partially or drastically our results.

## Notes

### Acknowledgements

We would like to thank Pierre Sikivie for important discussions and Paola Arias for comments. This work was supported by the Chilean Commission on Research, Science and Technology (CONICYT) under Grant 78180100 (Becas Chile, Postdoctorado).

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