Definitive microlensing constraints on the QCD axion minicluster fraction: realistic survey detection efficiencies for extended lenses and a simulation-settled minicluster population

Fairbairn, Marsh and Quevillon (2017) used EROS-2 and Subaru HSC microlensing data to place the first observational bound on the fraction of axion dark matter collapsed into miniclusters, but with approximate survey efficiencies (HSC modeled as a step function) and bracketing models for the minicluster population. They identified what is needed to make these limits definitive: dedicated survey reanalyses with realistic detection efficiencies for spatially extended lenses, and simulation-settled predictions for the minicluster mass function, internal profiles, and surviving bound fraction. As of 2026, the simulation side is substantially advanced but unfinished, while no observing team has performed the extended-lens efficiency reanalysis the source called for; the open core is the combination of both prongs into definitive exclusion or detection limits on the post-inflationary QCD axion via microlensing.

Background

The QCD axion is a hypothetical light particle proposed to solve the strong-CP problem of quantum chromodynamics (the unexplained smallness of the neutron's electric dipole moment) and a leading dark-matter candidate. If the Peccei–Quinn symmetry breaking that generates the axion occurs after inflation, the axion field has order-one density fluctuations at the time it begins to oscillate (set by the QCD phase transition): the decay of the cosmic axion-string and domain-wall network leaves overdensities that gravitationally collapse during radiation domination into dense bound clumps called axion miniclusters, with a characteristic mass $M_0$ set by the dark-matter mass inside the horizon at the onset of oscillations (in the source's spherical-horizon-volume convention, $M_0\approx1.8\times10^{-10}\,M_\odot$ across the favored QCD-axion window $50$–$200\,\mu{\rm eV}$; definitions based on a cubic volume $\sim k_0^{-3}$ give values a factor $4\pi^4/3\approx130$ smaller, i.e. $\sim10^{-12}\,M_\odot$, and $M_0$ is larger for lighter axion-like particles). After matter–radiation equality, hierarchical merging builds these seeds into larger minicluster halos (MCHs); the fraction of axion dark matter bound in miniclusters today is denoted $f_{\rm MC}$ and was, at the time of the source paper, poorly known. Gravitational microlensing — the transient magnification of a background star when a compact dark-matter object crosses the line of sight — can probe such clumps if they are dense enough to act effectively as compact lenses. Fairbairn, Marsh and Quevillon (PRL 119, 021101, 2017), with the detailed calculation in the companion paper Fairbairn, Marsh, Quevillon and Rozier (PRD 97, 083502, 2018), computed the microlensing event rate for spatially extended lenses (Navarro–Frenk–White (NFW) profiles, i.e. $\rho\propto r^{-1}$ inner cusps, truncated at $100\,r_s$, as a bracketing alternative to the steeper $r^{-9/4}$ profile expected from self-similar secondary infall, i.e. matter accreting self-similarly onto an initially compact seed), applied it to the EROS-2 survey (Expérience de Recherche d'Objets Sombres, a dedicated microlensing survey) of the Large Magellanic Cloud and to high-cadence observations of the Andromeda galaxy (M31) with the Subaru Hyper Suprime-Cam (HSC), a wide-field camera on the Subaru telescope, and derived the first bound on the minicluster fraction, $f_{\rm MC}<0.083\,(m_a/100\,\mu{\rm eV})^{0.12}$ in the isolated-minicluster case, where $m_a$ is the axion mass. Later work also draws on the OGLE survey (Optical Gravitational Lensing Experiment), a long-running microlensing survey of the Magellanic Clouds and the Galactic bulge, whose event samples enter axion-clump interpretations. Because extended lenses magnify with smaller amplitude and, as they become more diffuse, the cross-section for magnification above the detection threshold $A\ge1.34$ shrinks — vanishing entirely below a minimum central overdensity — the source finds the expected event number reduced by $\mathcal{O}(10^2)$ for isolated miniclusters relative to point masses, and because finite stellar source sizes suppress the signal for lens masses below about $10^{-9}\,M_\odot$, the detectability depends sensitively on the assumed internal profile, truncation, and detection efficiency of the survey. The authors approximated the HSC detection efficiency as a step function of $\epsilon=0.5$ normalized to reproduce published primordial-black-hole limits, bracketed the population models between dense (miniclusters surviving as tight clumps inside MCHs) and diffuse (mergers dispersing miniclusters) scenarios, and stated that converting their bounds into definitive limits — or a detection — requires (i) dedicated reanalyses by the observing teams using full light-curve injection, cadence, finite-source effects, and magnitude-dependent efficiencies, and (ii) numerical simulations that settle $f_{\rm MC}$, the outcome of hierarchical assembly, and the internal density profiles, including the model dependence of $M_0$.

Problem Statement

Convert the approximate 2017 microlensing bounds on axion miniclusters into definitive observational limits on, or evidence for, the post-inflationary QCD axion, by jointly: (1) settling, through targeted numerical simulations that follow minicluster formation from the post-inflationary axion-string decay, hierarchical assembly into minicluster halos, and tidal/stellar disruption in the Milky Way, the present-day minicluster population — the bound fraction $f_{\rm MC}$, the mass function, the internal density profiles (NFW-like versus steeper self-similar cusps) and truncation — including the dependence of the characteristic mass $M_0$ on the axion-mass–temperature relation, where a settled prediction is one in which the residual method-to-method spread in the string-network initial conditions is either eliminated by convergent results or quantified and propagated into the final constraints; and (2) reanalyzing survey microlensing data (Subaru HSC observations of Andromeda, and EROS-2 observations of the Large Magellanic Cloud) with realistic detection efficiencies determined by full light-curve injection and recovery that account for cadence, finite-source effects, spatially extended lenses drawn from the simulated mass-concentration distribution, and magnitude-dependent detection, thereby deriving statistically defensible limits or detection significance for $f_{\rm MC}(m_a)$ over the QCD-axion mass window accessible to microlensing — that is, over the axion masses for which the settled population predicts miniclusters dense enough to give detectable magnification under the survey efficiencies (the source's favored QCD-axion window is $50$–$200\,\mu{\rm eV}$, with its bound normalized at $m_a=100\,\mu{\rm eV}$, while the later simulations reported below indicate microlensing-relevant densities only for $m_a\sim0.2$–$3$ meV; the accessible range is set by the settled population rather than by the source's favored window). The target is a quantitative upper limit on $f_{\rm MC}(m_a)$ over the accessible window, in the source's convention in which zero observed candidates imply $N_{\rm exp}\le3$ at 95% C.L., obtained with the settled population and the realistic injection-recovery efficiencies, tightening or quantitatively revising the source's approximate bound rather than merely excluding the maximal case $f_{\rm MC}=1$ — the axion accounting for all of the dark matter — which that bound already achieves. The two parts are logically dependent: survey limits are only as good as the population model, and population predictions are only tested by the survey analysis.

References

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