Investigating the period-luminosity relations of δ Scuti stars: A pathway to distance and 3D dust map inference

¹ Physics Department, Tsinghua University, Beijng 100084, People’s Republic of China
² Astronomy Department, University of California, Berkeley, CA 94720, USA
³ Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 50B-4206, Berkeley, CA 94720, USA
⁴ Department of Astronomy, University of Science and Technology of China, Hefei 230026, China
⁵ CAS Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China
⁶ Department of Physics and Astronomy, Beijing Normal University, Beijing 100875, China
⁷ Beijing Planetarium, Beijing Academy of Sciences and Technology, Beijing 100044, China
⁸ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China

^⋆ Corresponding authors: joshbloom@berkeley.edu, wangxf@mail.tsinghua.edu.cn

Received: 18 February 2025
Accepted: 28 April 2025

Abstract

Context. While δ Scuti stars – intermediate-mass stars pulsating with periods of < 0.3 d – are the most numerous class of κ-mechanism pulsators in the instability strip, the short periods and small peak-to-peak amplitudes have left them understudied and under-utilized. Recently, large-scale time-domain surveys have significantly increased the number of identified δ Scuti stars, enabling more comprehensive investigations into their properties. Notably, the Tsinghua University–Ma Huateng Telescopes for Survey (TMTS), with its high-cadence observations at 1-minute intervals, has identified thousands of δ Scuti stars, greatly expanding the sample of these short-period pulsating variables.

Aims. This study makes use of multiband photometric time-series data to refine the period–luminosity (P − L) relations of δ Scuti stars and show how observed P − L relations can be used to simultaneously infer dust obscuration and distance. Using spectroscopy, we also study the dependence of the P − L relations on metallicity.

Methods. Using the δ Scuti stars from the TMTS catalogs of Periodic Variable Stars, we cross-matched the dataset with Pan-STARRS1, 2MASS, and WISE to obtain photometric measurements across optical (g, r, i, z, and y), near-infrared (J, H, and K_s), and mid-infrared (W1, W2, and W3) bands, respectively. Parallax data, used as Bayesian priors, were retrieved from Gaia DR3, and line-of-sight dust extinction priors were estimated from a 3D dust map. Using PyMC, we performed a simultaneous determination of the 11-band P − L relations of δ Scuti stars.

Results. The simultaneous determination of multiband P − L relations of δ Scuti stars not only yields precise measurements of these relations, but also greatly improves constraints on the distance moduli and color excesses, as evidenced by the reduced uncertainties in the posterior distributions. Furthermore, our methodology enables an independent estimation of the color excess through the P − L relations, offering a potential complement to existing 3D dust maps. Moreover, by cross-matching with LAMOST DR7, we investigated the influence of metallicity on the P − L relations. Our analysis reveals that incorporating metallicity might reduce the intrinsic scatter at longer wavelengths. However, this result does not achieve 3σ significance, leaving open the possibility that the observed reduction is attributable to statistical fluctuations.

Conclusions. We introduce an innovative approach to studying the P − L relations of δ Scuti stars, facilitating more comprehensive investigations into their utility as distance indicators and their significance in understanding stellar evolution. Our extensible methodology also enables the inference of dust extinction using pulsating stars beyond δ Scuti stars. Although the inclusion of metallicity in the P − L relations appears to reduce intrinsic scatter at longer wavelengths, further analysis is required to fully understand the impact of metal abundances on the properties of δ Scuti stars.