Statistical methods for assisting computational models for the event horizon telescope

The Event Horizon Telescope conducts very long baseline interferometry to observe black holes at the horizon scale, using the rotation of the Earth to change the orientation of its baselines relative to the source being imaged. However, Sgr A∗ varies on timescales comparable to the duration of an observation, posing a challenge to conventional interferometric methods. Understanding the variability of Sgr A∗ is thus necessary for image reconstruction and parameter estimation. In this work, I describe the methods used to statistically characterize this variability and interpret its effects on numerical models. First, I construct a statistical model of black hole accretion disks generated from anisotropic, inhomogeneous Gaussian random fields and demonstrate its use in the calibration for the image reconstruction pipeline. These models are a component of the synthetic data used in this pipeline and are run with temporal characteristics matching that of Sgr A∗ on the 2017 EHT observation campaign. I describe these temporal characteristics through statistical modeling of Sgr A∗ light curves taken from the 2017 EHT observations, along with historical data of Sgr A∗ going back to 2005. This modeling was done using damped random walks and Matérn processes, two examples of Gaussian processes. I expand on the expected behavior of these processes using structure functions and modulation indexes and provide a mathematical description of these metrics measured on a finite window using Gaussian processes. I then apply the observations of the variability of Sgr A∗ to computational models of the accretion flow. I look at the various observational constraints applied to general relativistic magnetohydrodynamic simulations, with a focus on the effects of the modulation index on constraining the model parameter space. I note that the models have a tendency to be more variable than Sgr A∗ observations and briefly mention some potential causes of this difference in variability between the models and the data. The effects of simulation resolution on this variability excess is unclear. As a step towards increasing the effective resolution, I look at applications of neural networks in applying corrections to fluxes in relativistic magnetohydrodynamic simulations. I show that neural networks have the capability of capturing the behavior of fluxes at a higher effective resolution near shocks in the Orszag-Tang vortex, with the potential to generalize to other problems.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Lee, Daeyoung

Contributors dc:contributor

• Gammie, Charles F
• Holder, Gilbert P
• Kahn, Yonatan F
• Neubauer, Mark S

• Black Holes
• Accretion Disks
• Magnetohydrodynamics, Grmhd
• Gaussian Processes
• Gaussian Random Fields
• Statistical Modeling
• Variability
• Neural Networks
• Convolutional Neural Networks

Statement dc:rights

• Copyright 2024 Daeyoung Lee

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/127147

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127147