A Generative Model for Quasar Spectra

The Astrophysical Journal, vol. 938, pp. 17

Abstract

Abstract We build a multi-output generative model for quasar spectra and the properties of their black hole engines, based on a Gaussian process latent-variable model. This model treats every quasar as a vector of latent properties such that the spectrum and all physical properties of the quasar are associated with non-linear functions of those latent parameters; the Gaussian process kernel functions define priors on the function space. Our generative model is trained with a justifiable likelihood function that allows us to treat heteroscedastic noise and missing data correctly, which is crucial for all astrophysical applications. It can simultaneously predict unobserved spectral regions and the physical properties of quasars in held-out test data. We apply the model to rest-frame ultraviolet and optical quasar spectra for which precise black hole masses (based on reverberation-mapping measurements) are available. Unlike reverberation-mapping studies that require multi-epoch data, our model predicts black hole masses from single-epoch spectra—even with limited spectral coverage. We demonstrate the capabilities of the model by predicting black hole masses and unobserved spectral regions. We find that we predict black hole masses at close to the best possible accuracy.

Authors 6

1. Anna–Christina Eilers corresponding

   Massachusetts Institute of Technology

   Affiliation as printed

   MIT Kavli Institute for Astrophysics and Space Research, 77 Massachusetts Avenue, Cambridge, MA 02139, USA; eilers@mit.edu

   MIT Kavli Institute for Astrophysics and Space Research, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

2. David W. Hogg

   Max Planck Institute for Astronomy · Flatiron Institute · New York University

   Affiliation as printed

   Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

   Center for Cosmology and Particle Physics, Department of Physics, New York University, 726 Broadway, New York, NY 10003, USA

   Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany

3. Bernhard Schölkopf

   Max Planck Institute for Intelligent Systems

   Affiliation as printed

   Max Planck Institute for Intelligent Systems, Tübingen, Germany

4. Daniel T. Foreman-Mackey

   Flatiron Institute

   Affiliation as printed

   Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA

5. Frederick B. Davies

   Max Planck Institute for Astronomy

   Affiliation as printed

   Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany

6. Jan–Torge Schindler Aachen Leiden Observatory

   Leiden University · Max Planck Institute for Astronomy · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University, Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands

   Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany