Constraining the Existence of Axion Clouds in M87* with Closure Trace Analyses

Black holes can amplify incoming bosonic waves via rotational superradiance, inducing bound states of ultralight bosons around them. This phenomenon has the potential to confine the parameter spaces of new bosons. Axions and axion-like particles (ALPs) are candidate beyond-standard-model particles that can form such clouds around supermassive black holes (SMBHs) and impact the polarization signal in a similar fashion to Faraday rotation via axion-photon coupling. Prior efforts have used polarized images from the Event Horizon Telescope (EHT) M87 2017 observations to limit the dimensionless axion-photon coupling to previously unexplored regions. However, with the novel calibration-insensitive quantities, closure traces and conjugate closure trace products, it is possible to constrain the existence of axion clouds while avoiding the dominant sources of systematic uncertainties, e.g., station gains and polarization leakages. We utilize a simple geometric model for the polarization map of M87* to fit the model parameters with both simulated and real data sets and reach a comparable level of constraint in the accuracy with which an axion cloud may be excluded in M87. Future applications of our approach include subsequent M87* and Sgr A* observations by EHT and next-generation EHT (ngEHT) are expected to produce stronger constraints across a wider range of axion and ALP masses. Because it does not require imaging, closure trace analyses may be applied to target AGN for which imaging is marginal, extending the number of SMBHs from which axion limits may be obtained significantly.Comment: 12 pages, 11 figures, 1 table, submitted to Ap

Effective equidistribution for some one parameter unipotent flows

We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\operatorname{SL}_2(\mathbb R)$ in arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and $\operatorname{SL}_2(\mathbb R)\times\operatorname{SL}_2(\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.Comment: 128 page

Quantitative equidistribution and the local statistics of the spectrum of a flat torus

We show that pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate. The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.Comment: 47 page