A consequence of QCD axion dark matter being born after inflation is the emergence of small-scale substructures known as miniclusters. Although miniclusters merge to form minihalos, this intrinsic granularity is expected to remain imprinted on small scales in our galaxy, leading to potentially damaging consequences for the campaign to detect axions directly on Earth. This picture, however, is modified when one takes into account the fact that encounters with stars will tidally strip mass from the miniclusters, creating pc-long tidal streams that act to refill the dark matter distribution. Here we ask whether or not this stripping rescues experimental prospects from the worst-case scenario in which the majority of axions remain bound up in unobservably small miniclusters. We find that the density sampled by terrestrial experiment on mpc scales will be, on average, around 70%-90% of the average local DM density, and at a typical point in the solar neighborhood, we expect most of the dark matter to be comprised of debris from O(10^{2}-10^{3}) overlapping streams. If haloscopes can measure the axion signal with high-enough frequency resolution, then these streams are revealed in the form of an intrinsically spiky line shape, in stark contrast with the standard assumption of a smooth, featureless Maxwellian distribution-a unique prediction that constitutes a way for experiments to distinguish between pre- and postinflationary axion cosmologies.
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