We advocate for the idea that there is a fundamentally new mechanism for axion production on Earth, as recently suggested in Fischer et al. (2018) and Liang & Zhitnitsky (2018). We specifically focus on production of axions within Earth, with low velocities such that they will be trapped in the gravitational field. Our computations are based on the so-called Axion Quark Nugget (AQN) dark matter model, which was originally invented to explain the similarity of the dark and visible cosmological matter densities. This occurs in the model irrespective of the axion mass $m_mathrm{a}$ or initial misalignment angle $theta_0$. Annihilation of antimatter AQNs with visible matter inevitably produce axions when AQNs hit Earth. The emission rate of axions with velocities below escape velocity is very tiny compared to the overall emission, however these axions will be accumulated over the 4.5 billion year life time of the Earth, which greatly enhances the discovery potential. We perform numerical simulations with a realistically modeled incoming AQN velocity and mass distribution, and explore how AQNs interact as they travel through the interior of the Earth. We use this to estimate the axion flux on the surface of the Earth, the velocity-spectral features of trapped axions, the typical annihilation pattern of AQN, and the density profile of the axion halo around the Earth. Knowledge of these properties is necessary to make predictions for the observability of trapped axions using CAST, ADMX, MADMAX, CULTASK, ORPHEUS, ARIADNE, CASPEr, ABRACADABRA, QUAX, DM Radio.
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