Neural Posterior Estimation for White Dwarf Spectroscopic Characterization

TL;DR

This paper tackles the bottleneck of inferring white dwarf atmospheric parameters in the era of big spectroscopic data. It introduces neural posterior estimation (NPE) using conditional normalizing flows to learn $p( heta|x)$ directly from simulated spectra, enabling rapid and calibrated posterior evaluations that accommodate complex atmospheric models beyond Gaussian likelihoods. The authors validate calibration with simulation-based tests (SBC, TARP) and demonstrate accurate parameter recovery for DA, DB, and hot DQ white dwarfs, achieving millisecond-scale posterior sampling after a upfront training cost. They further integrate photometric information through an iterative spectrophotometric fitting procedure, achieving strong agreement with SDSS/Tremblay labels and providing a scalable pathway for upcoming surveys (SDSS-V, DESI, 4MOST, LSST) while highlighting avenues for future enhancements (magnetic and metal-polluted WDs).

Abstract

White dwarf spectroscopic characterization is entering a big data era, with the number of spectroscopically characterized white dwarfs expected to grow from $\sim$100,000 to over 300,000 in upcoming years. Traditional methods like least-squares fitting and Markov Chain Monte Carlo have become computationally prohibitive for large-scale analysis, requiring minutes to days per star. Furthermore, these methods impose fundamental limitations on model complexity by requiring explicit likelihood functions, typically restricting them to Gaussian assumptions. We present neural posterior estimation (NPE), a simulation-based inference technique that directly approximates posterior distributions through neural networks trained on simulated spectra. Our approach provides accurate parameter inference in milliseconds per star after upfront training costs, enabling statistical tests of the procedure's reliability. We demonstrate NPE's effectiveness on DA, DB, and carbon-atmosphere white dwarfs, validating its calibration with simulation-based calibration and tests of accuracy with random points. Application to SDSS data shows excellent agreement with previous studies, recovering parameters from previous work within 6.8% for effective temperature and 2.1% for surface gravity, on average. We also apply our technique on WD 1153+012, a hot DQ star with a carbon-oxygen-hydrogen atmosphere, using high-resolution spectroscopy. This methodology combines computational efficiency with the flexibility to model complex atmospheres, making it ideal for upcoming surveys. Our approach also integrates spectroscopic and photometric constraints through an iterative procedure, providing comprehensive characterization of white dwarfs.

Figures (9)

• Figure 1: Examples of unnormalized simulated spectra.
• Figure 2: Parameter recovery test using our neural posterior estimation for 2000 simulated carbon-atmosphere spectra between SNR 20 and 40.
• Figure 3: Fit example on one of our simulated carbon-atmosphere objects. The top panel shows the corner plot, with true parameters indicating in blue and best-fit parameters in red. In the bottom panel, the continuum-normalized simulation is shown, overlaid with the average of the top 100 highest probability samples (red) from the posterior and their standard deviation (orange contour).
• Figure 4: Parameter recovery test using our neural posterior estimation for 5000 simulated SDSS DA spectra between SNR 9 and 50.
• Figure 5: Parameter recovery test using our neural posterior estimation for 5000 simulated SDSS DB spectra between SNR 9 and 50.