Axion--photon interactions can lead to an enhancement of the electromagnetic field by parametric resonance in the presence of a cold axion background, for modes with a frequency close to half the axion mass. In this paper, we study the role of the axion momentum dispersion as well as the effects of a background gravitational potential, which can detune the resonance due to gravitational redshift. We show, by analytical as well as numerical calculations, that the resonance leads to an exponential growth of the photon field only if (a) the axion momentum spread is smaller than the inverse resonance length, and (b) the gravitational detuning distance is longer than the resonance length. For realistic parameter values, both effects strongly suppress the resonance and prevent the exponential growth of the photon field. In particular, the redshift due to the gravitational potential of our galaxy prevents the resonance from developing for photons in the observable frequency range, even assuming that all the dark matter consists of a perfectly cold axion condensate. For axion clumps with masses below $\sim 10^{-13}\, M_\odot$, the momentum spread condition is more restrictive, whereas, for more massive clumps, the redshift condition dominates.

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如何抑制指数增长——关于轴子背景中光子的参数共振

对于频率接近轴子质量一半的模式，轴子 - 光子相互作用可以在存在冷轴子背景的情况下通过参数共振导致电磁场增强。在本文中，我们研究了轴子动量色散的作用以及背景引力势的影响，这可以使由于引力红移引起的共振失谐。我们通过分析和数值计算表明，仅当 (a) 轴子动量扩展小于反共振长度，并且 (b) 引力失谐距离更长时，共振才会导致光子场的指数增长比共振长度。对于实际的参数值，这两种效应都会强烈抑制共振并阻止光子场的指数增长。特别是，即使假设所有暗物质都由完全冷的轴子凝聚体组成，我们银河系的引力势导致的红移阻止了可观测频率范围内光子的共振。对于质量低于 $\sim 10^{-13}\, M_\odot$ 的轴子团块，动量扩散条件更具限制性，而对于质量更大的团块，红移条件占主导地位。