Galaxy 3D Shape Recovery using Mixture Density Network

Since the turn of the century, astronomers have been exploiting the rich information afforded by combining stellar kinematic maps and imaging in an attempt to recover the intrinsic, three-dimensional (3D) shape of a galaxy. A common intrinsic shape recovery method relies on an expected monotonic relationship between the intrinsic misalignment of the kinematic and morphological axes and the triaxiality parameter. Recent studies have, however, cast doubt about underlying assumptions relating shape and intrinsic kinematic misalignment. In this work, we aim to recover the 3D shape of individual galaxies using their projected stellar kinematic and flux distributions using a supervised machine learning approach with mixture density network (MDN). Using a mock dataset of the EAGLE hydrodynamical cosmological simulation, we train the MDN model for a carefully selected set of common kinematic and photometric parameters. Compared to previous methods, we demonstrate potential improvements achieved with the MDN model to retrieve the 3D galaxy shape along with the uncertainties, especially for prolate and triaxial systems. We make specific recommendations for recovering galaxy intrinsic shapes relevant for current and future integral field spectroscopic galaxy surveys.

Uncertainty Quantification of the Virial Black Hole Mass with Conformal Prediction

Precise measurements of the black hole mass are essential to gain insight on the black hole and host galaxy co-evolution. A direct measure of the black hole mass is often restricted to nearest galaxies and instead, an indirect method using the single-epoch virial black hole mass estimation is used for objects at high redshifts. However, this method is subjected to biases and uncertainties as it is reliant on the scaling relation from a small sample of local active galactic nuclei. In this study, we propose the application of conformalised quantile regression (CQR) to quantify the uncertainties of the black hole predictions in a machine learning setting. We compare CQR with various prediction interval techniques and demonstrated that CQR can provide a more useful prediction interval indicator. In contrast to baseline approaches for prediction interval estimation, we show that the CQR method provides prediction intervals that adjust to the black hole mass and its related properties. That is it yields a tighter constraint on the prediction interval (hence more certain) for a larger black hole mass, and accordingly, bright and broad spectral line width source. Using a combination of neural network model and CQR framework, the recovered virial black hole mass predictions and uncertainties are comparable to those measured from the Sloan Digital Sky Survey. The code is publicly available at https://github.com/yongsukyee/uncertain_blackholemass.