In 2019, combining the observations from telescopes all around the Earth, the Event Horizon Telescope (EHT) collaboration published a photo of a supermassive black hole M87* with extremely high resolution. The shining donut-like structure comes from the radiation of the accretion flow around the black hole. The black hole swallows the light in the central region, creating a big shadow inside the donut. The EHT collaboration updates the same photo with more delicate structures two years later. The sweeping lines, showing the linear polarization orientation (electric vector position angles), transform the donut into a cruller. These first-ever images give the most direct evidence of black holes and reveal the magnetic fields outside M87*.

Besides rich information for astronomy and gravity, what else can we learn from those beautiful images? As particle physicists, we are fascinated by the idea that ultralight particles can accumulate outside the black hole. We realized that if ultralight axion exists and stays outside the black hole, they would make the cruller dance! Using the four days variations of the crullers, we can constrain the coupling between axion and photon to the previously unexplored region.

How to turn supermassive black holes into detectors for ultralight particles? It dates back to a thought experiment by Roger Penrose in 1969. Imagine someone throwing a rock into a fast-spinning black hole, and the stone has a certain chance to escape with a larger velocity than the previous. The additional energy it carries is taken from the rotation of the black hole. Now think about the particle-wave duality in quantum mechanics. We can replace the rock with a wave outside the spinning black hole. It can form a dense cloud by extracting energy and angular momentum from the black bole, called the superradiance mechanism. To make this process sufficiently fast, it requires the Compton wavelength of the boson to be comparable with the horizon size of the black hole. Thus supermassive black holes become natural detectors for ultralight particles!

Among different types of ultralight fields beyond the standard model of particle physics, axion is one of the most well-motivated candidates. Searching for the axion is among the top priorities in particle physics. It naturally appears in many fundamental theories with extra dimensions, like the string theory. Axion is also a perfect cold dark matter candidate. In the ultralight mass window, some small-scale problems of the galaxy can be potentially solved by those fields forming a core in the center.

Once the ultralight axion exists within the right mass window, a dense axion cloud and the center black hole form a bound state similar to the hydrogenic atom and being called the gravitational atom. Besides purely gravitational effects, the existence of axion can rotate the orientation of the linear polarization periodically as well, with a period between 5 to 20 days. The variations of the EVPA behave as a propagating wave along the bright photon ring, which the dance of the crullers has a particular pattern instead of a random walk by a drunken man.

 Figure 1: Illustration of the polarized emission from a Kerr BH surrounded by an axion cloud, using IPOLE. Different colors on the electric vector position angles (EVPA) quivers, which range from red through to purple, represent the time variation of the EVPA in the presence of the axion-photon coupling. White quivers are the EVPAs when the axion field is absent. The intensity scale is normalized so that the brightest pixel is unity.

The EHT's polarimetric measurements provide the spatial distribution of the linear polarization orientations for four days, precisely the information we need to search for axion. Embedding the axion-induced birefringence into the radiative transfer code IPOLE, we simulated a movie of black hole images with oscillating linear polarization orientations at each point of the sky plane. To suppress the turbulent variations of the accretion flow, we introduced a novel analysis strategy where the difference between two sequential are used as observables to constrain the axion-induced EVPA variations. A much larger parameter space can be probed with more detailed data provided in the future, especially the more sequential time observation and better spatial resolutions.

 Figure 2: Our constraints on dimensionless axion-photon coupling c from the EHT polarimetric observations of SMBH M87* are shown. The black hole spin aJ is assumed to be 0.99 or 0.80. The latter case corresponds to a smaller mass window, overlapping with a_J = 0.99 cases in the lower mass region. The gray band at the bottom represents the uncertainty from the five different EVPA reconstruction methods. Previous bounds on axion-photon coupling are shown for comparison.