A Probabilistic Approach to Fitting Period-Luminosity Relations and Validating Gaia Parallaxes

TL;DR

This paper introduces a probabilistic method to accurately fit period-luminosity-metallicity relations for pulsating stars and validate Gaia parallaxes, enhancing distance measurements in astronomy.

Contribution

It presents a novel probabilistic approach that jointly constrains PLZ relations and Gaia parallax uncertainties, improving the use of Gaia data for stellar distance calibration.

Findings

Consistent PLZ relations with previous studies.

Distances with 6% precision using Gaia data.

No significant offset found in Gaia parallaxes for RR Lyrae stars.

Abstract

Pulsating stars, such as Cepheids, Miras, and RR Lyrae stars, are important distance indicators and calibrators of the "cosmic distance ladder", and yet their period-luminosity-metallicity (PLZ) relations are still constrained using simple statistical methods that cannot take full advantage of available data. To enable optimal usage of data provided by the Gaia mission, we present a probabilistic approach that simultaneously constrains parameters of PLZ relations and uncertainties in Gaia parallax measurements. We demonstrate this approach by constraining PLZ relations of type $ab$ RR Lyrae stars in near-infrared W1 and W2 bands, using Tycho-Gaia Astrometric Solution (TGAS) parallax measurements for a sample of $\approx100$ type $ab$ RR Lyrae stars located within 2.5 kpc of the Sun. The fitted PLZ relations are consistent with previous studies, and in combination with other data, deliver distances precise to 6% (once various sources of uncertainty are taken into account). To a precision of 0.05 mas ($1\sigma$), we do not find a statistically significant offset in TGAS parallaxes for this sample of distant RR Lyrae stars (median parallax of 0.8 mas and distance of 1.4 kpc). With only minor modifications, our probabilistic approach can be used to constrain PLZ relations of other pulsating stars, and we intend to apply it to Cepheid and Mira stars in the near future.