Quasars are bright and unobscured active galactic nuclei (AGN) thought to be powered by the accretion of matter around supermassive black holes at the centers of galaxies. The temporal variability of a quasar's brightness contains valuable information about its physical properties. The UV/optical variability is thought to be a stochastic process, often represented as a damped random walk described by a stochastic differential equation (SDE). Upcoming wide-field telescopes such as the Rubin Observatory Legacy Survey of Space and Time (LSST) are expected to observe tens of millions of AGN in multiple filters over a ten year period, so there is a need for efficient and automated modeling techniques that can handle the large volume of data. Latent SDEs are machine learning models well suited for modeling quasar variability, as they can explicitly capture the underlying stochastic dynamics. In this work, we adapt latent SDEs to jointly reconstruct multivariate quasar light curves and infer their physical properties such as the black hole mass, inclination angle, and temperature slope. Our model is trained on realistic simulations of LSST ten year quasar light curves, and we demonstrate its ability to reconstruct quasar light curves even in the presence of long seasonal gaps and irregular sampling across different bands, outperforming a multioutput Gaussian process regression baseline. Our method has the potential to provide a deeper understanding of the physical properties of quasars and is applicable to a wide range of other multivariate time series with missing data and irregular sampling.
Latent Stochastic Differential Equations for Modeling Quasar Variability and Inferring Black Hole Properties
Abstract
Copyright and License
© 2024. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Acknowledgement
This research was made possible by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program. Matthew Graham acknowledges support from National Science Foundation (NSF) AST-2108402. V. Ashley Villar acknowledges support from NSF under grant AST-2108676. The data used in this publication were collected through the MENDEL high performance computing (HPC) cluster at the American Museum of Natural History. This HPC cluster was developed with National Science Foundation (NSF) Campus Cyberinfrastructure support through Award #1925590. The authors would like to thank Favio Neira for assistance with rubin_sim. We also thank Xuechen Li and David Duvenaud for their thoughtful comments on our work.
Software References
Matplotlib (Hunter 2007), Numpy (Harris et al. 2020), scipy (Virtanen et al. 2020), Astropy (Astropy Collaboration et al. 2018), astroML (Vanderplas et al. 2012), corner.py (Foreman-Mackey 2016), BoTorch (Balandat et al. 2019), torchsde (Li et al. 2020), PyTorch (Paszke et al. 2019)
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Additional details
- ISSN
- 1538-4357
- National Science Foundation
- AST-2108402
- National Science Foundation
- AST-2108676