Simultaneous inference of periods and period-luminosity relations for Mira variable stars

Abstract

The Period--Luminosity relation (PLR) of Mira variable stars is an important tool to determine astronomical distances. The common approach of estimating the PLR is a two-step procedure that first estimates the Mira periods and then runs a linear regression of magnitude on log period. When the light curves are sparse and noisy, the accuracy of period estimation decreases and can suffer from aliasing effects. Some methods improve accuracy by incorporating complex model structures at the expense of significant computational costs. Another drawback of existing methods is that they only provide point estimation without proper estimation of uncertainty. To overcome these challenges, we develop a hierarchical Bayesian model that simultaneously models the quasi-periodic variations for a collection of Mira light curves while estimating their common PLR. By borrowing strengths through the PLR, our method automatically reduces the aliasing effect, improves the accuracy of period estimation, and is capable of characterizing the estimation uncertainty. We develop a scalable stochastic variational inference algorithm for computation that can effectively deal with the multimodal posterior of period. The effectiveness of the proposed method is demonstrated through simulations, and an application to observations of Miras in the Local Group galaxy M33. Without using ad-hoc period correction tricks, our method achieves a distance estimate of M33 that is consistent with published work. Our method also shows superior robustness to downsampling of the light curves.

References in corpus (15)

• Variational Inference: A Review for Statisticians
• Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms
• Periodograms for Multiband Astronomical Time Series
• Frequentist Consistency of Variational Bayes
• The First DIRECT Distance Determination to a Detached Eclipsing Binary in M33
• RR Lyrae Variables in M33. I. Evidence For a Field Halo Population
• A Near-Infrared Period-Luminosity Relation for Miras in NGC 4258, an Anchor for a New Distance Ladder
• DIRECT Distances to Nearby Galaxies Using Detached Eclipsing Binaries and Cepheids. VI. Variables in the Central Part of M33
• Large Magellanic Cloud Near-Infrared Synoptic Survey. V. Period-Luminosity Relations of Miras
• Near-infrared Mira Period-Luminosity Relations in M33
• The UK Infrared Telescope M33 monitoring project. IV. Variable red giant stars across the galactic disc
• Period estimation for sparsely-sampled quasi-periodic light curves applied to Miras
• Estimating a Common Period for a Set of Irregularly Sampled Functions with Applications to Periodic Variable Star Data