Black Hole Theory and Simulations

See my Youtube channel for some movies of my simulations!

In the local universe, including the center of our own galaxy (Sgr A*), most supermassive black holes are surrounded by hot, thick, and dim accretion disks. Many of these black holes, like the one in the giant elliptical galaxy M87, launch relativistic jets powered by the rotational energy of the black hole itself. To understand how plasma behaves in spacetime – how it emits radiation, launches jets, and feeds the black hole – I create analytic models of accretion disks and jets and compare them to supercomputer simulations.

In the hot, weakly coupled plasmas around the black holes M87* and Sgr A* , protons and electrons are not in thermal equilibrium with each other. Most simulations assume thermodynamic equilibrium, so it is impossible to directly predict the radiation emitted from these simulations without making additional assumptions in post-processing. This makes connecting simulations to the near-horizon images observed by the Event Horizon Telescope difficult.

Images of Sgr A* from my simulations (Chael+ 2018) with four different values of black hole spin and electron heating functions, as viewed by the EHT at 230 GHz.

Images of of the M87 jet at different frequencies from one of my magnetically arrested simulations (Chael+ 2019). As the frequency increases, the brightest emission moves down the jet closer and closer to the black hole.

In my research, I use the massively parallel code KORAL which moves beyond standard single-fluid General Relativistic Magnetohydrodynamics (GRMHD) to a three-fluid approximation where electrons, ions, and photons exchange energy self-consistently. This method allows us to directly predict what the Event Horizon Telescope will see at 230 GHz and understand how different models emit across the entire electromagnetic spectrum.

In Chael+ 2018 I tested two physical mechanisms for electron heating in plasmas – turbulence and magnetic reconnection – to investigate how plasma microphysics changes the images and variability of Sgr A* at different frequencies. In Chael+ 2019, I applied the same method to M87’s jet and determined that the observed characteristics are well explained by a Magnetically Arrested Disc model, where extreme magnetic fields on the black hole choke accretion. I extended these simulations in Chael 2024, where I developed a new method for more stably evolving magnetically-dominated jets in GRMHD simulations.

In 2021, I was a coordinator of the paper interpreting the EHT’s first polarimetric images of M87. We found that EHT polarimetric observations also strongly favor a magnetically arrested accretion flow. I later led the EHT’s 2023 analysis of circular polarization, which also supports a magnetically arrested accretion disk in M87.

230 GHz images from my magnetically arrested simulations of M87 using magnetic reconnection (center) with the position of the photon ring and black hole inner shadow indicated. The left image shows a simulated EHT reconstruction of this simulation snapshot, and the right image shows the snapshot in a gamma color scale, where faint features are more visible

In Chael+ 2021, I used my simulation images to examine the role of the ``inner shadow’’ in black hole images. In magnetically arrested simulations, the 230 GHz emission is nearly equatorial and extends to the black hole event horizon. As a result, the lensed image of the horizon itself is visible as a deep brightness depression in these images, but only at very high dynamic range. Measuring the size and shape of the inner shadow with the next-generation EHT will provide additional constraints on the black hole metric from future EHT observations.

The EHT’s 2017 image of M87 in polarized light (left) shows a distinctive right-handed spiral of polarization vectors, which is quantified by the observable $\angle\beta_2 < 0$. ($\beta_2$ is the coefficient of the 2nd azimuthal Fourier mode of the with the polarized image, introduced in Palumbo+ 2020). In Chael+ 2023, I showed that this handedness of the polarization swirl indicates that electromagnetic energy is outflowing from close to the horizon in M87.

In Chael+ 2023, I examined how we can use polarized images from the EHT to infer the direction of electromagnetic energy flow close to the horizon. Looking at analytic models and simulations, I found that the handedness of the polarization spiral around the black hole in M87 encodes the direction of energy flow; the EHT’s polarized image indicates that energy is flowing out from close to the central black hole. The techniques developed in this analysis could be used on future, more sensitive observations to conclusively determine if the jet in M87 is powered by the Blandford-Znajek mechanism and to measure the spin of the black hole.

I actively develop new simulation techniques to more accurately explore the extreme spacetime and plasma environments around black holes In Chael+ 2017, I updated to KORAL to evolve a population of nonthermal electrons in space, time, and energy in parallel with the thermal fluid. This represents the first time that spectral resolution of electron distributions is possible in grid-based accretion simulations. My current work is focused on extending this method to realistic presciptions for electron acceleration and running the first global 3D simulations of black hole accretion including the spectral evolution of electrons. This method will open up new ground in understanding the nonthermal jet emission in M87 and nonthermal infrared and X-ray flares in Sgr A*.

In Chael+ 2024, I developed a new method that better couples the force-free, highly magnetized jet region in simulations with the accretion disk. This technique solves a persistent problem in black hole simulations that usually requires codes to inject artifical mass into the jet; by applying this method to long-duration, 3D simulations of jets and outflows, we will explore jet launching, acceleration, and emission from horizon to large scales.