Pulsation Modes Research Articles

Detection and Seismic Study of Gravity and Rossby Mode Pulsations in Four Contact Binaries

We report the detection of gravity (g) and Rossby (r) mode pulsations of four short-period eclipsing binaries, KIC 5439790, KIC 7501230, KIC 9350889, and KIC 9453192 based on the 4 yr Kepler high-precision photometry. Light-curve modeling reveals that the four binaries are all contact systems with small mass ratios. We study the short-term variability of the light-curve residuals after the removal of the binary model and attribute them to the g- and r-mode pulsations that stem from the primary stars. By introducing a new criterion, we attempt to identify period-spacing patterns in the Fourier spectra, which refers to the determination of the rotation rates of stellar interior and envelope as well as the asymptotic period spacings of the pulsating stars. It is interesting to find that the rotation rates of the stellar envelopes are all nearly equal to the orbits. The near-core rotations, however, are significantly slower by about 10%. Based on the derived asymptotic period spacings, stellar parameters were constrained from asteroseismology models. The pulsators are revealed to be evolved main-sequence stars with high metallicities.

Meandering periods and asymmetries in light curves of Miras: Observational evidence for low mass-loss rates

Context. Some Miras (long-period variables in late evolutionary stages) have meandering pulsation periods and light-curve asymmetries, the causes of which are still unclear. Aims. We aim to better understand the origin of meandering periods and light-curve asymmetries by investigating a sample of Miras in the solar neighbourhood. We characterised this group of stars and related their variability characteristics to other stellar parameters. Methods. We analysed observations from several databases to obtain light curves with maximum time span and temporal coverage for a sample of 548 Miras. We determined their pulsation-period evolution over a time span of many decades, searched for changes in the periods, and determined the amplitude of the period change. We also analysed the Fourier spectra with respect to possible secondary frequency maxima. The sample was divided into two groups with respect to the presence of light-curve asymmetries (‘bumps’). Infrared colours and indicators of the third dredge-up were collected to study the mass loss and deep mixing properties of the stars of our sample. Results. Our analysis reveals one new star, T Lyn, with a continuously changing period. The group of Miras with meandering period changes is exclusively made up of M-type stars. The Fourier spectra of the meandering-period Miras have no prominent additional peaks, suggesting that additional pulsation modes are not the cause of the meandering periods. We confirm that light-curve bumps are more common among S and C Miras and show, for the first time, that Miras with such bumps have lower mass-loss rates than those with regular, symmetric light curves. Also, Miras with meandering period changes have relatively little mass loss. Conclusions. We conclude that Miras with strongly changing periods (including meandering periods) or asymmetries in their light curves have relatively low dust mass-loss rates. Meandering period changes and light-curve asymmetries could be connected to He-shell flashes and third dredge-up episodes.

Frequency Analysis of High Amplitude δ Scuti Star V593 Lyr by American Association of Variable Stars Observers International Database

The new results of light variability and frequency analysis of a high amplitude δ Scuti star (HADS) V593 Lyr were reported. δ Scuti-type variable stars are fascinating short-period stars with luminosity classes from III to V and spectral types from A0 to F6. Their location on the Hertzsprung-Russell (H-R) diagram is in the classical cepheid instability strip. The photometric data in the V filter and clear filter of V593 Lyr were collected from the American Association of Variable Stars Observers (AAVSO) international database. Discrete Fourier transformation and pre-whitening methods were used in the Period04 package to examine time-series light curve data. During 15 observational nights, we obtained 28 times of new light maxima magnitude variability and significant pulsation frequencies for the star. The study found that the fundamental frequency of V593 Lyr is 9.7894180 ± 0.0000002 d−1, corresponding to the main pulsation period of about 0.1021511 d and detected its second to fifth harmonics with a signal-to-noise ratio (S/N) of more than four. A study of the pulsation frequencies and period change of HADS stars can estimate their pulsation modes and evolution. Moreover, HADS stars are suitable targets for understanding asteroseismology, which is the subject that applies a star's pulsations to investigate its internal structure, and the high amplitude stars provide reference points for calculating cosmic distances in the Universe.

Absolute Properties of the Oscillating Eclipsing Algol X Trianguli

We report results from the TESS photometric data and new high-resolution spectra of the Algol system X Tri showing short-period pulsations. From the echelle spectra, the radial velocities of the eclipsing pair were measured, and the rotational rate and effective temperature of the primary star were obtained to be v 1sini = 84 ± 6 km s−1 and T eff,1 = 7900 ± 110 K, respectively. The synthetic modeling of these observations implies that X Tri is in synchronous rotation and is physically linked to a visual companion TIC 28391715 at a separation of about 6.″5. The absolute parameters of our target star were accurately and directly determined to be M 1 = 2.137 ± 0.018 M ⊙, M 2 = 1.101 ± 0.010 M ⊙, R 1 = 1.664 ± 0.010 R ⊙, R 2 = 1.972 ± 0.010 R ⊙, L 1 = 9.67 ± 0.55 L ⊙, and L 2 = 2.16 ± 0.09 L ⊙. The phase-binned mean light curve was used to remove the binary effect from the observed TESS data. Multifrequency analysis of the residuals revealed 16 significant frequencies, of which the high-frequency signals between 37 day−1 and 48 day−1 can be considered probable pulsation modes. Their oscillation periods of 0.021−0.027 days and pulsation constants of 0.014−0.018 days are typical values of δ Sct variables. The overall results demonstrate that X Tri is an oEA star system consisting of a δ Sct primary and its lobe-filling companion in the semidetached configuration.

A Study of the Pulsation Properties of 57 Non-Blazhko Ab-type RR Lyrae Stars with Homogeneous Metallicities from the LAMOST–Kepler/K2 Survey

Homogeneous metallicities and continuous high-precision light curves play key roles in studying the pulsation properties of RR Lyrae stars. By cross matching LAMOST DR6 with the Kepler and K2 fields, we have determined seven and 50 non-Blazhko RRab stars, respectively, that have homogeneous metallicities determined from low-resolution spectra of the LAMOST–Kepler/K2 survey. The Fourier decomposition method is applied to the light curves of these stars provided by the Kepler space-based telescope to determine the fundamental pulsation periods and parameters. The calculated amplitude ratios of R 21, R 31 and the phase differences of ϕ 21, ϕ 31 are consistent with the parameters of RRab stars in both globular clusters and the Large Magellanic Cloud. We find a linear relationship between the phase differences ϕ 21 and ϕ 31, which is in good agreement with the results in the literature. As far as the amplitude, we find that the amplitude of primary frequency A 1 and the total amplitude A tot follow either a cubic or linear relationship. For the rise time, we do not find its relevance with the period of the fundamental pulsation mode P1, or A tot and ϕ 21. However, it might follow a linear relationship with R 31. Based on the homogeneous metallicities, we have derived a new calibration formula for the period–ϕ 31–[Fe/H] relation, which agrees well with previous studies.

Investigating Stellar Variability in the Open Cluster Region NGC 381

We study variable stars in the field of the open cluster NGC 381 using photometric data observed over 27 nights and identify a total of 57 variable stars, six of which are member stars. The variable stars are classified based on their periods, amplitudes, light-curve shapes, and locations in the H-R diagram. We found a rich variety of variable stars in the cluster. We identified a total of 10 eclipsing binaries, of which two are of Algol type while eight are of W UMa type (EW). The estimated ages of these EW binaries are greater than 0.6 Gyr, which is in agreement with the formation time constraint of ≥0.6 Gyr on short-period eclipsing binaries. The physical parameters of the two EW-type binaries are estimated using PHOEBE model-fitting software. The pulsating variable stars include one each from the δ Scuti and γ Dor variability classes. We determined the pulsation modes of pulsating variables with the help of the FAMIAS package. We obtained 15 rotational variable stars comprising four dwarf stars identified on the basis of their log(g) versus log(T eff) diagram. These dwarf stars are found to have generally longer periods than the remaining rotational variables.

Tidal perturbations and eclipse mapping in the pulsations in the hierarchical triple system U Gru

Context. Unambiguous examples of the influence of tides on self-excited, free stellar pulsations have recently been observationally detected in space-based photometric data. Aims. We aim to investigate U Gru and contextualise it within the growing class of tidally influenced pulsators. An initial analysis of U Gru revealed frequencies spaced by the orbital frequency that are difficult to explain by currently proposed tidal mechanisms. Methods. We reinvestigate the TESS photometry for U Gru alongside new UVES spectroscopy. We analyse the UVES spectroscopy with least-squares deconvolution and spectral disentangling techniques, and perform an atmospheric analysis. We remove the binary signature from the light curve using an effective model in order to investigate the pulsation signal in the residuals. We track the amplitudes and phases of the residual pulsations as a function of the orbital period to reveal their tidal influence. Results. We establish that U Gru is likely a hierarchical triple system. We identify a single p-mode oscillation that exhibits amplitude and phase variation over the binary orbit. We propose a toy model to demonstrate that the series of frequencies separated by the orbital frequency can be reproduced by eclipse mapping. We find no evidence of modulation to the other independent oscillation modes. Conclusions. We demonstrate that U Gru hosts at least one tidally perturbed pulsation. Additionally, we argue that eclipse mapping of the dominant, tidally perturbed mode can produce the series of frequencies separated by the observed orbital frequency. Our simulations show that the effects of eclipse mapping are mode dependent, and are not expected to produce an observable signature for all pulsation modes in an eclipsing binary.

Precise Empirical Determination of Metallicity Dependence of Near-infrared Period–Luminosity Relations for RR Lyrae Variables

RR Lyrae variables are excellent Population II distance indicators thanks to their well-defined period–luminosity relations (PLRs) at infrared wavelengths. We present results of near-infrared (NIR) monitoring of Galactic globular clusters to empirically quantify the metallicity dependence of NIR PLRs for RR Lyrae variables. Our sample includes homogeneous, accurate, and precise photometric data for 964 RR Lyrae variables in 11 globular clusters covering a large metallicity range (Δ[Fe/H] ∼ 2 dex). We derive JHK s -band period–luminosity–metallicity (PLZ) and period–Wesenheit–metallicity (PWZ) relations anchored using 346 Milky Way field RR Lyrae stars with Gaia parallaxes, and simultaneously solved for independent distances to globular clusters. We find a significant metallicity dependence of ∼0.2 mag dex−1 in the JHK s -band PLZ and PWZ relations for RR Lyrae stars independent of the adopted metallicity scale. The metallicity coefficients and the zero-points of the empirical PLZ and PWZ relations are in excellent agreement with the predictions from the horizontal branch evolution and pulsation models. Furthermore, RR Lyrae–based distances to our sample of globular clusters are also statistically consistent with other independent measurements in the literature. Our recommended empirical JHK s -band PLZ relations for RR Lyrae stars with periods of fundamental mode pulsation (P f) are: MJ=−0.44(±0.03)−1.83(±0.02)log(Pf)+0.20(±0.02)[Fe/H](σ=0.05mag)MH=−0.74(±0.02)−2.29(±0.02)log(Pf)+0.19(±0.01)[Fe/H](σ=0.05mag)MKs=−0.80(±0.02)−2.37(±0.02)log(Pf)+0.18(±0.01)[Fe/H](σ=0.05mag).

Asteroseismology of the Pulsating Extremely Low-mass White Dwarf SDSS J111215.82 + 111745.0: A Model with p-mode Pulsations Consistent with the Observations

SDSS J111215.82+111745.0 is the second pulsating extremely low-mass white dwarf discovered. Two short-period pulsations, 107.56 and 134.275 s, were detected on this star, which would be the first observed pressure mode (p-mode) pulsations observed on a white dwarf. While the two potential p-modes have yet to be confirmed, they make SDSS J111215.82+111745.0 an interesting object. In this work, we analyzed the whole set of seven periods observed on SDSS J111215.82+111745.0. We adopt three independent period-spacing tests to reveal a roughly 93.4 s mean period spacing of ℓ = 1 g-modes, which gives added credence to the ℓ = 1 identifications. Then we perform asteroseismic modeling for this star, in which the H chemical profile is taken as a variable. The stellar parameters M = 0.1650 ± 0.0137 M ☉ and T eff = 9750 ± 560 K are determined from the best-fit model, and the H/He chemical profiles are also defined. The two suspected p-modes are also well represented in the best-fit model, and both the stellar parameters and the pulsation frequencies are in good agreement with the values derived from spectroscopy.

Radial pulsations, moment of inertia and tidal deformability of dark energy stars

We construct dark energy stars with Chaplygin-type equation of state (EoS) in the presence of anisotropic pressure within the framework of Einstein gravity. From the classification established by Iyer et al. (Class Quantum Grav 2:219, 1985), we discuss the possible existence of isotropic dark energy stars as compact objects. However, there is the possibility of constructing ultra-compact stars for sufficiently large anisotropies. We investigate the stellar stability against radial oscillations, and we also determine the moment of inertia and tidal deformability of these stars. We find that the usual static criterion for radial stability dM/drho _c >0 still holds for dark energy stars since the squared frequency of the fundamental pulsation mode vanishes at the critical central density corresponding to the maximum-mass configuration. The dependence of the tidal Love number on the anisotropy parameter alpha is also examined. We show that the surface gravitational redshift, moment of inertia and dimensionless tidal deformability undergo significant changes due to anisotropic pressure, primarily in the high-mass region. Furthermore, in light of the detection of gravitational waves GW190814, we explore the possibility of describing the secondary component of such event as a stable dark energy star in the presence of anisotropy.

Experimental investigation of the pulsing flow field around four types of spiked-blunt body at Mach 2.2

In this paper, unsteady flow pulsation over four types of spiked-blunt body model and related pulsation suppression methods are investigated through wind tunnel experiments. Direct-connect wind tunnel is used to provide supersonic incoming flow of Ma 2.2 and a classic pointed spike and three types of aerodome spike are tested at zero/non-zero angle of attack. High-speed schlieren and dynamic pressure sensors are used to capture the dynamic evolution of unsteady flow field around the spikes. Then the measurement results with high spatial-temporal resolution are processed with three statistical methods. Results indicate that the aerodome spike can effectively suppress the flow pulsation both at zero/non-zero angle of attack. The suppression effect of standard/double aerodome and inverse aerodome can reach 60.9% and 47.3%, respectively. By using the aerodome, the pulsation mode can be transformed into a special state between oscillation mode and pulsation mode, named ‘suppressed pulsation mode’. In the suppressed pulsation mode, the original large-scale motion of shock wave system is decomposed into a stable foreshock and a slightly unsteady aftershock with small-scale periodic movement. The statistical results further reveal that the unsteady motion of afterbody shock is closely related to the stability of the recirculation zone and the key to suppress the flow pulsation is to create a stable recirculation zone ahead the blunt body.

Photometric variability of high amplitude δ Scuti stars using AAVSO international database: V2455 Cyg and GP And

This research aims to study photometric variability and Fourier analysis of high amplitude δ Scuti stars (HADS), which are interesting short-period variable stars with spectral types between A2V and F0V. They are located in the area of the classical cepheid instability strip, which crosses the main-sequence (MS) on the Hertzsprung-Russell (H-R) diagram. The CCD photometric V-magnitude data of the selected HADS stars were acquired based on the AAVSO international database (American Association of Variable Stars Observers), which is the most comprehensive digital variable star database. Two interesting targets V2455 Cyg and GP And were selected for the study. The discrete Fourier transformation was used to analyze time-series light curves. The pulsating properties of the selected HADS stars were analyzed using the Period04 astronomical program. We obtained each star’s times of new light maxima, magnitude changes, and pulsation frequencies. The main frequency of V2245 Cyg was determined to be 10.614995 ± 0.000002 d−1 and the main frequency of GP And is 12.709253 ± 0.000001 d−1. V2245 Cyg and GP And are high amplitude δ Scuti stars. The study of the pulsation frequencies and period change of HADS stars can estimate their pulsation modes and their evolution. Moreover, HADS stars are very important as standard candles that can be used to measure galactic distances.

GD 99: Re-investigation of an old ZZ Ceti companion

Context. Thanks to photometric space missions, we have access to more and more information on the properties of white dwarf stars, especially pulsating ones. In the case of pulsators, we have the opportunity to get an insight into their otherwise hidden interiors by the means of asteroseismology. In addition to space-based observations, we also take advantage of the opportunity to study the pulsations of white dwarf stars from the ground, either as observations that are complementary to space-based measurements or individual observing runs on selected targets across long timescales. Aims. We aim to investigate long-term, single-site observations of the bright, yet scarcely studied ZZ Ceti star, GD 99. Our main goals are to determine as many eigenmodes for asteroseismology as possible and then to carry out a seismic analysis of this target. Methods. We performed a Fourier analysis of the light curves obtained in different epochs. After finding the normal modes of the pulsation, we ran the 2018 version of the White Dwarf Evolution Code to build model grids for the period fits. We compared the seismic distance of the best-fit model with the geometric value provided by Gaia measurements. Results. We find that GD 99 is rich in pulsation modes in the ∼200 − 1100 s period range, as we detected seven new periods. Together with the literature data, we were able to use 11 modes for the asteroseismic fits. We accepted an asteroseismic model solution with Teff = 13 500 K and M* = 0.80 M⊙ as a best fit; however, this suggests a hotter and more massive star than we might have expected based on the spectroscopic values. We also estimated the rotational rate of the star to be 13.17 h, based on TESS observations.

Asteroseismology of hot subdwarf B stars observed with TESS: discovery of two new gravity mode pulsating stars

TIC 033834484 and TIC 309658435 are long-period pulsating subdwarf B stars, which were observed extensively (675 and 621 days, respectively) by the Transiting Exoplanet Survey Satellite (TESS). The high-precision photometric light curve reveals the presence of more than 40 pulsation modes including both stars. All the oscillation frequencies that we found are associated with gravity (g)-mode pulsations, with frequencies spanning from ∼80 µHz (2 500 s) to ∼400 µHz (12 000 s). We utilize the asteroseismic tools including asymptotic period spacings and rotational frequency multiplets in order to identify the pulsational modes. We found dipole (l = 1) mode sequences for both targets and calculate the mean period spacing of dipole modes (ΔPl=1), which allows us to identify the modes. Frequency multiplets provide a rotation period of ∼64 d for TIC 033834484. From follow-up ground-based spectroscopy, we find that TIC 033834484 has an effective temperature of 24 210 K (140), a surface gravity of log g/cms-2 = 5.28 (03) and TIC 309658435 has an effective temperature of 25 910 K (150), a surface gravity of log g/cms-2 = 5.48 (03).

Properties of self-excited pulsations in 3D simulations of AGB stars and red supergiants

Context. The characteristic variability of cool giants and supergiants is attributed to a combination of stellar pulsation and large-scale convective flows. Full 3D radiation-hydrodynamical modelling is an essential tool for understanding the nature of these dynamical processes. The parameter space in our 3D model grid of red giants has expanded in recent years. These models can provide many insights on the nature and properties of the pulsations, including the interplay between convection and pulsations. Aims. We treat 3D dynamical models of asymptotic giant branch (AGB) stars and red supergiants (with current masses 1 M⊙ ≤ M* ≤ 12 M⊙) similar to observational data. We aim to explore the relation between stellar parameters and the properties of the self-excited pulsations. Methods. Output from global ‘star-in-a-box’ models computed with the CO5BOLD radiation-hydrodynamics code were analysed, particularly in regards to the pulsation properties, to find possible correlations with input and emergent stellar parameters. The fast Fourier transform was applied to spherically averaged mass flows to identify possible radial pulsation periods beneath the photosphere of the modelled stars. Stellar parameters were investigated for correlations with the extracted pulsation periods. Results. We find that the pulsation periods varied with the stellar parameters in good agreement with the current expectations. The pulsation periods follow Ritter’s period-mean density relation well and our AGB models agree with period-luminosity relations derived from observations. A mass estimate formula was derived from the 3D models, relating the stellar mass to the fundamental mode pulsation period and the stellar radius. Conclusions. While the non-linearity of the interplay between the self-excited pulsations and the self-consistent convection complicates analyses, the resulting correlations are in good agreement with respect to current theoretical and observational understandings.

Mitigating performance deterioration analysis of VC-PEMFC with dead-ended anode by pulsation fuel supplying mode

Hydrogen starvation and water flooding are two principal factors resulting in performance deterioration of the proton exchange membrane fuel cell stack at the dead-end anode. This paper proposes a novel hydrogen supply mode called the pulsation mode aimed at mitigating the problems of performance deterioration in a 10-cell open-cathode vapor chamber proton exchange membrane fuel cell stack to increase the performance. This method does not require complex equipment and structure, only four controllable solenoid valves are sufficient to generate periodic pulsation inside the anode channels. The experiments were used to validate the effectiveness of the new mode and to compare the effects of different pulsation frequencies on the performance of the stack. A series of parameters such as voltage, power growth rate, and voltage stability index are used to analyze the operating characteristics of the stack. The results show that the periodic pulsations generated by the new mode are potent of increasing the species mass transfer rate within the anode channels, and the species mass transfer rate increases with the increase of pulsation frequency. Meanwhile, selection of a suitable pulsation frequency can effectively improve stack water management and reduce the probability of hydrogen starvation. Finally, the new mode is able to enhance the voltage down valley of the stack under large external load variation. The ohmic resistance of the stack in the new mode has proved to be lower by the current interruption method. Furthermore, it is capable of increasing the net power of the stack by up to 7.71%.

Oscillations of highly magnetized non-rotating neutron stars

Highly magnetized neutron stars are promising candidates to explain some of the most peculiar astronomical phenomena, for instance, fast radio bursts, gamma-ray bursts, and superluminous supernovae. Pulsations of these highly magnetized neutron stars are also speculated to produce detectable gravitational waves. In addition, pulsations are important probes of the structure and equation of state of the neutron stars. The major challenge in studying the pulsations of highly magnetized neutron stars is the demanding numerical cost of consistently solving the nonlinear Einstein and Maxwell equations under minimum assumptions. With the recent breakthroughs in numerical solvers, we investigate pulsation modes of non-rotating neutron stars which harbour strong purely toroidal magnetic fields of 1015−17 G through two-dimensional axisymmetric general-relativistic magnetohydrodynamics simulations. We show that stellar oscillations are insensitive to magnetization effects until the magnetic to binding energy ratio goes beyond 10%, where the pulsation mode frequencies are strongly suppressed. We further show that this is the direct consequence of the decrease in stellar compactness when the extreme magnetic fields introduce strong deformations of the neutron stars.

The Behavior of HgMn Stars in the Far UV—Paper 20: HD 14228

Abstract The analysis of three spectra of the Mn Hg Sr star HD 14228 recorded by the SWP camera on board the International Ultraviolet Explorer does not reveal variations of the far-ultraviolet flux over a nine years time interval. The analysis of the TESS lightcurve of HD 14228 confirms a very short period of 0.34 day already reported in the literature. This periodicity, attributed to rotation, could be a mode of radial pulsation too.

Internal rotation and buoyancy travel time of 60 γ Doradus stars from uninterrupted TESS light curves spanning 352 days

Context. Gamma Doradus (hereafter γ Dor) stars are gravity-mode pulsators whose periods carry information about their internal structure. These periods are especially sensitive to the internal rotation and chemical mixing, two processes that are currently not well constrained in the theory of stellar evolution. Aims. We aim to identify the pulsation modes and deduce the internal rotation and buoyancy travel time for 106 γ Dor stars observed by the Transiting Exoplanet Survey Satellite (TESS) mission in its southern continuous viewing zone (hereafter S-CVZ). We rely on 140 previously detected period-spacing patterns, that is, series of (near-)consecutive pulsation mode periods. Methods. We used the asymptotic expression to compute gravity-mode frequencies for ranges of the rotation rate and buoyancy travel time that cover the physical range in γ Dor stars. Those frequencies were fitted to the observed period-spacing patterns by minimising a custom cost function. The effects of rotation were evaluated using the traditional approximation of rotation, using the stellar pulsation code GYRE. Results. We obtained the pulsation mode identification, internal rotation, and buoyancy travel time for 60 TESS γ Dor stars. For the remaining 46 targets, the detected patterns were either too short or contained too many missing modes for unambiguous mode identification, and longer light curves are required. For the successfully analysed stars, we found that period-spacing patterns from 1-yr-long TESS light curves can constrain the internal rotation and buoyancy travel time to a precision of 0.03 d-1 and 400 s, respectively, which is about half as precise as literature results based on 4-yr-long Kepler light curves of γ Dor stars.

Period–Luminosity Relations in the Local Group of Galaxies

AbstractLocal Group galaxies, particularly the Large and Small Magellanic Clouds, have historically played and continue to play a unique role in studies of the period–luminosity (PL), period–luminosity–color (PLC), and period–Wesenheit (PW) relations, not just for pulsating stars. In recent years, significant efforts have been devoted to calibrate the PL, PLC, and PW relationships at different wavelengths, including studies of the influence of metallicity and nonlinearities on the accuracy of measured distances. However, the PL diagram has many more astrophysical applications. It serves as a vital tool for classifying different types of pulsating stars and can even facilitate the discovery of new classes of variable stars. Moreover, it aids in distinguishing among various modes of pulsation, facilitates the identification of pulsating stars that are members of binary systems, and enables studies of the three-dimensional structures of neighboring galaxies. In this contribution, I present the latest results on the PL, PLC, and PW relations obeyed by various types of variable stars in Local Group galaxies – from δ Scuti stars to Mira variabless and from close binary systems to the mysterious long secondary periods exhibited by red giant and supergiant stars.