This work presents the study of multiphase relations of classical Cepheids in the Magellanic Clouds for short periods (log P < 1) and long periods (log P > 1). From the analysis, it has been found that the multiphase relations obtained using the models as well as observations are highly dynamic with pulsational phase. The multiphase relations for short and long periods are found to display contrasting behaviour for both LMC and SMC. It has been observed that the multiphase relations obtained using the models agree better with the observations in the PC plane in most phases in comparison to the PL plane. Multiphase relations obtained using the models display a clear distinction among different convection sets in most phases. Comparison of models and observations in the multiphase plane is one way to test the models with the observations and to constrain the theory of stellar pulsation.

RR Lyrae (RR Lyr) stars are a well-known and useful distance indicator for old stellar populations such as globular clusters and dwarf galaxies. Fundamental-mode RR Lyr (RRab) stars are commonly used to measure distances, and the accuracy of the determined distance is strongly constrained by metallicity. Here, we investigate the metallicity dependence in the period–luminosity (PL) relation of double-mode RR Lyr (RRd) stars. We find and establish a linear relation between metallicity and period or period ratio for RRd stars. This relation can predict the metallicity as accurately as the low-resolution spectra. Based on this relation, we establish a metallicity-independent PL relation for RRd stars. Combining the distance of the Large Magellanic Cloud and Gaia parallaxes, we calibrate the zero point of the derived PL relation to an error of 0.022 mag. Using RRd stars, we measure the distances of globular clusters and dwarf galaxies with an accuracy of 2-3% and 1-2%, respectively. In the future, RRd stars could anchor galaxy distances to an accuracy of 1.0% and become an independent distance ladder in the Local Group.

The instability strip (IS) of classical Cepheids has been extensively studied theoretically. Comparison of the theoretical IS edges with those obtained empirically, using the most recent Cepheids catalogs available, can provide us with insights into the physical processes that determine the position of the IS boundaries. We investigate the empirical positions of the IS of the classical Cepheids in the Large Magellanic Cloud (LMC) using data of classical fundamental-mode and first-overtone LMC Cepheids from the OGLE-IV variable star catalog, together with a recent high-resolution reddening map from the literature. We studied their position on the Hertzsprung-Russell diagram and determined the IS borders by tracing the edges of the color distribution along the strip. We obtain the blue and red edges of the IS in V- and I-photometric bands, in addition to Teff and log L⊙. The results obtained show a break located at the Cepheids’ period of about 3 days, which was not reported before. This phenomenon is most likely explained by the depopulation of second and third crossing classical Cepheids in the faint part of the IS, since blue loops of evolutionary tracks in this mass range do not extend blueward enough to cross the IS at the LMC metallicity. Furthermore, our empirical borders show good agreement with theoretical ones published in the literature. This proves that our empirical IS is a useful tool to put constraints on theoretical models.

Red supergiants (RSGs) are the brightest stars in the near-infrared. The existence of their period-luminosity relation (PLR) will be very helpful in determining cosmological distances. This review discusses the development in identification of RSGs, calculation of their light variation period, determination of the PLR, and the uncertainties associated. It is found that the PLR of RSGs exhibits the smallest scatter in the near-infrared, in particular within the P – MK relation. The PLRs in the LMC, SMC, M31, and M33 show no obvious dependence on the galactic metallicity, which follows approximately the relation as MK ≈ −3.1 log P – 1.9.

Long-period variables are bright, evolved red giant stars showing periodic photometric changes due to stellar pulsation. They follow one or more period-luminosity and period-age relations, which make them highly promising distance indicators and tracers of young and intermediate-age stellar populations. Such a potential is especially interesting in view of the massive amount of data delivered by modern large-scale variability surveys. Crucially, these applications require a clear theoretical understanding of pulsation physics in connection with stellar evolution. Here, I describe an ongoing effort from our collaboration dedicated to the modelling of stellar pulsation in evolved stars, and how this work is impacting our capability of investigating long-period variables and exploiting them for other astrophysical studies. Furthermore, I present our ongoing work aimed at assessing the potential of semi-regular variables, an often neglected sub-type of long-period variables, to be distance indicators complementary to their better-known, more evolved counterparts, the Mira variables.

In the last five years, the number of periodic variable stars has increased by two million. We used the ZTF DR2 data to find and build a catalog that includes 780,000 periodic variable stars. These periodic variable stars were classified into 11 types, which greatly complemented the variable stars in Galactic disk. Based on the latest ZTF DR16 data, we found 2 million variable candidates. We trained a machine learner to classify variable stars, and the learner had a prediction accuracy of 94%. Using millions of variable stars, we carried out studies to optimize the period–luminosity relations and the Galactic structure and the extinction law. With the future China Space Station Telescope, millions of variable stars in the Local Group will be discovered. They help to study the structure of our Local Group and also to cross-check the distance ladders based on different variable stars.

The OH/IR stars evolving on the Asymptotic Giant Branch are large-amplitude variable stars with periods in the range of ~400 to 2500 days, significantly longer than those of the related Mira variables. We use preliminary results from a monitoring program of the 1612-MHz OH maser variations of a sample of > 70 OH/IR stars to study a possible extension of Mira Period-Luminosity Relations to longer periods. The period distribution of the sample is split around P ~ 1100 days. Using WISE W3 absolute magnitudes as proxies for the luminosity and the best available distances, we found no convincing relation between periods and absolute magnitudes. A cause could be rapid evolution of the ‘extreme OH/IR stars’ (the group with P >1100 days) close to the tip of the AGB, where no increase of luminosity is expected on the short time-scales involved.