Classical Instability Strip Research Articles

Variability and stellar pulsation incidence in Am and Fm stars using TESS and Gaia data

Aims. We aim to study chemically peculiar Am and Fm stars, distinguished by their unique abundance patterns, which are crucial for studying mixing processes in intermediate-mass stars. These stars provide a window into the atomic diffusion in their stellar envelopes, the evolution-dependent changes in mixing, and the resulting effects on pulsation mechanisms. Methods. This study examines the pulsation characteristics of the Am and Fm star group. Our analysis encompasses 1276 stars (available as catalogues on GitHub), utilising data from TESS and Gaia and focussing on stars from the Renson catalogue. Results. In our sample, 51% of stars (649) display no variability, and are thus categorised as constant stars. Among those that remain, 25% (318 stars) are pulsating Am, Fm, and ρ Puppis stars, including 20% (261 stars) that are exclusively Am and Fm stars. Additionally, 17% of stars (210) show variability indicative of binarity and/or rotational modulation and 7% (93 stars) are eclipsing binaries. Of the pulsating stars, 10% (32 stars) are γ Doradus type, 54% (172 stars) δ Scuti type, and 36% (114 stars) are hybrids, underlining a diverse pulsational behaviour of Am and Fm stars. Conclusions. Our findings indicate that pulsating stars predominantly occupy positions near the red edge of the classical instability strip, allowing us to ascertain the incidence of pulsations in this stellar population.

A New Catalog of 100,000 Variable TESS A-F Stars Reveals a Correlation between δ Scuti Pulsator Fraction and Stellar Rotation

δ Scuti variables are found at the intersection of the classical instability strip and the main sequence on the Hertzsprung–Russell diagram. With space-based photometry providing millions of light curves of A-F type stars, we can now probe the occurrence rate of δ Scuti pulsations in detail. Using the 30 minutes cadence light curves from NASA's Transiting Exoplanet Survey Satellite's first 26 sectors, we identify variability in 103,810 stars within 5–24 cycles per day down to a magnitude of T = 11.25. We fit the period–luminosity relation of the fundamental radial mode for δ Scuti stars in the Gaia G band, allowing us to distinguish classical pulsators from contaminants for a subset of 39,367 stars. Out of this subset, over 15,918 are found on or above the expected period–luminosity relation. We derive an empirical red edge to the classical instability strip using Gaia photometry. The center where the pulsator fraction peaks at 50%–70%, combined with the red edge, agrees well with previous work in the Kepler field. While many variable sources are found below the period–luminosity relation, over 85% of sources inside of the classical instability strip derived in this work are consistent with being δ Scuti stars. The remaining 15% of variables within the instability strip are likely hybrid or γ Doradus pulsators. Finally, we discover strong evidence for a correlation between pulsator fraction and spectral line broadening from the Radial Velocity Spectrometer on board the Gaia spacecraft, confirming that rotation has a role in driving pulsations in δ Scuti stars.

Statistical analysis of asteroseismic indices and stellar parameters of TESS-observed δ Scuti stars

Context. Over the last few years, δ Scuti stars have been at the center of the attention of the asteroseismology community thanks to the derivation of seismic indices connected to stellar parameters. The statistical analysis of the wealth of data offered by a large space survey such as the Transiting Exoplanet Survey Satellite (TESS), the identification of new δ Scuti stars, and the correlation between asteroseismic indices and stellar parameters in the resulting sample are therefore of utmost interest. Aims. The goal of our study is to analyze the statistical properties of stellar parameters and characterize the asteroseismic indices of δ Scuti stars observed in TESS cycle 4. Methods. We used TESS 2 min cadence photometric data and the corresponding Fourier transform to identify δ Scuti stars. The asteroseismic indices for these stars were determined using an empirical relation and a 2D autocorrelation method. Results. We discovered 765 δ Scuti stars from the data obtained by the TESS mission, from Sectors 40–55, corresponding to cycle 4 and observed with a 2 min cadence. Of these stars, 179 δ Scuti stars have low-resolution spectral parameters from LAMOST. We first analyzed the relation between pulsation and stellar parameters from TESS observations and the distribution of δ Scuti stars with two different stellar parameters, TESS Input Catalog (TIC) and Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST), within the classical instability strip. Most of the stars lie within the instability strip and follow the period-luminosity relation of δ Scuti stars. Additionally, the majority of the stars exhibit pulsation properties consistent with those expected for δ Scuti stars, including periods falling within the typical range, amplitudes at the millimagnitude level, and fundamental parameters such as spectral type, effective temperature, log g, and luminosity that match the characteristics of δ Scuti stars. This confirms the reliability of the δ Scuti stars we have identified. We subsequently obtained the large frequency separation (∆ν), vmax, and ν(Amax) for 179 δ Scuti stars with LAMOST parameters by using an empirical relation and a 2D autocorrelation method, and obtained the relations between these asteroseismic indices. These stars will provide significant support for a deeper study of the internal structure and evolution of stars.

Testing ultralow amplitude Cepheid candidates in the Galactic disk by TESS and Gaia

Ultralow amplitude (ULA) and strange mode Cepheids are thought to be pulsating variable stars that are near to or are at the edges of the classical instability strip. Until now, a few dozen such variable star candidates have been found both in the Large Magellanic Cloud and the Milky Way. For the present work, we studied six ULA Cepheid candidates in the Milky Way, identified by using CoRoT and 2MASS data. In order to identify their positions in the period–luminosity and color–magnitude diagrams, we used the Gaia DR3 parallax and brightness data of each star to calculate their reddening-free absolute magnitudes and distances. Furthermore, we calculated the Fourier parameters (e.g., period and amplitude) of the light variations based on CoRoT and TESS measurements, and established the long-term phase shifts for four out of six stars. Based on the results, we conclude that none of the six ULA Cepheid candidates are pulsating variable stars, but rather rotation-induced variable stars (rotational spotted and α2 Canum Venaticorum variables) that are either bluer or fainter than Cepheids would be.

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.

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.

RR Lyrae Stars and Anomalous Cepheids as Population Tracers in Local Group Galaxies

We discuss the use and importance of pulsating variable stars as population tracers in Local Group galaxies. Among bright variable crossing the classical instability strip, we mostly focus on RR Lyrae stars and Anomalous Cepheids. We discuss their pulsational properties and how it is possible to use them to constrain the evolution and star formation history of the host galaxy. We discuss RR Lyrae stars as tracers of the old population, and how they can be used to trace the accretion history of large galaxies such as the Milky Way and M31, and also the early chemical evolution. Moreover, we show that the frequency of Anomalous Cepheids follows different relations, and therefore trace the intermediate-age star formation. Finally, we discuss the different methods to derive distances and the impact of the Gaia mission.

Analysis of TESS Field Eclipsing Binary Star V948 Her: A Pulsating or Non-pulsating Star?

Pulsating stars occupy a significant place in the H-R diagram and it was thought that all stars inside the classical instability strip should pulsate. However, recent studies showed that there are many non-pulsating stars located inside the classical instability strip. The existence of these non-pulsating stars is still a mystery. To deeply understand the properties of these non-pulsating and pulsating stars, one needs precise fundamental stellar parameters (e.g. mass). For this purpose, the eclipsing binaries are unique systems. Hence, in this study, we present the TESS data analysis of one candidate pulsating eclipsing binary system, V948 Her. TESS data were used for the binary modeling with the literature radial velocity measurements, and the precise fundamental parameters of the system were obtained. The system’s age was derived as 1 ± 0.24 Gyr. The positions of the binary components in the H-R diagram were examined and the primary component was found inside the δ Scuti instability strip. However, in the frequency analysis of TESS data, we found no significant pulsation frequencies. Only the harmonics of the orbital periods were obtained in the analysis. Therefore, the system was classified as a non-pulsator. V948 Her is an important object to understand the nature of non-pulsating stars inside the δ Scuti instability strip.

Large-amplitude variables in Gaia Data Release 2

Context. Photometric variability is an essential feature that sheds light on the intrinsic properties of celestial variable sources, the more so when photometry is available in various bands. In this respect, the all-sky Gaia mission is particularly attractive as it collects, among other quantities, epoch photometry measured quasi-simultaneously in three optical bands for sources ranging from a few magnitudes to fainter than magnitude 20. Aims. The second data release (DR2) of the mission provides mean G, GBP, and GRP photometry for ∼1.4 billion sources, but light curves and variability properties are available for only ∼0.5 million of them. Here, we provide a census of large-amplitude variables (LAVs) with amplitudes larger than ∼0.2 mag in the G band for objects with mean brightnesses between 5.5 and 19 mag. Methods. To achieve this, we rely on variability amplitude proxies in G, GBP, and GRP computed from the uncertainties on the magnitudes published in DR2. We then apply successive filters to identify two subsets containing sources with reliable mean GBP and GRP (for studies using colours) and sources having compatible amplitude proxies in G, GBP, and GRP (for multi-band variability studies). Results. The full catalogue gathers 23 315 874 LAV candidates, and the two subsets with increased levels of purity contain, respectively, 1 148 861 and 618 966 sources. A multi-band variability analysis of the catalogue shows that different types of variable stars can be categorized according to their colours and blue-to-red amplitude ratios as determined from the G, GBP, and GRP amplitude proxies. More specifically, four groups are globally identified. They include: long-period variables in a first group with amplitudes more than twice larger in the blue than in the red; hot compact variables in a second group with amplitudes smaller in the blue than in the red; classical instability strip pulsators in a third group with amplitudes larger in the blue than in the red by 50% to 80%; and other non-pulsating variables in a fourth group, mainly achromatic, but 10% of them still having 20% to 50% larger amplitudes in the blue than in the red. Conclusions. The catalogue constitutes the first census of Gaia LAV candidates extracted from the public DR2 archive. The overview presented here illustrates the added value of the mission for multi-band variability studies, even at this stage when epoch photometry is not yet available for all sources.

The first view of δ Scuti and γ Doradus stars with the TESS mission

ABSTRACT We present the first asteroseismic results for δ Scuti and γ Doradus stars observed in Sectors 1 and 2 of the TESS mission. We utilize the 2-min cadence TESS data for a sample of 117 stars to classify their behaviour regarding variability and place them in the Hertzsprung–Russell diagram using Gaia DR2 data. Included within our sample are the eponymous members of two pulsator classes, γ Doradus and SX Phoenicis. Our sample of pulsating intermediate-mass stars observed by TESS also allows us to confront theoretical models of pulsation driving in the classical instability strip for the first time and show that mixing processes in the outer envelope play an important role. We derive an empirical estimate of 74 per cent for the relative amplitude suppression factor as a result of the redder TESS passband compared to the Kepler mission using a pulsating eclipsing binary system. Furthermore, our sample contains many high-frequency pulsators, allowing us to probe the frequency variability of hot young δ Scuti stars, which were lacking in the Kepler mission data set, and identify promising targets for future asteroseismic modelling. The TESS data also allow us to refine the stellar parameters of SX Phoenicis, which is believed to be a blue straggler.

Ground-based observation of ZZ Ceti stars and the discovery of four new variables

ABSTRACT We perform ground-based photometric observations of 22 DA white dwarf stars, 10 already known ZZ Cetis and 12 candidates with atmospheric parameters inside the classical instability strip. We report on the discovery of four new variable DA white dwarf stars. Two objects are near the middle of the instability strip, SDSS J082804.63+094956.6 and SDSS J094929.09+101918.8, and two red edge pulsators, GD 195 and L495−82. In addition, we classified four objects as possible variables, since evidence of variability was detected in the light curve, but the signal-to-noise ratio was not sufficient to establish a definite detection. Follow-up observations were performed for 10 known ZZ Ceti stars to verify period stability and search for new periodicities. For each confirmed variable, we perform a detailed asteroseismological fit and compare the structural parameters obtained from the best-fitting models with those obtained from spectroscopy and photometry from Gaia. Finally we present a study of the asteroseismological properties of a sample of 91 ZZ Ceti stars.

Candidates for non-pulsating stars located in the Cepheid instability strip in the Large Magellanic Cloud based on Strömgren photometry

ABSTRACT We present candidates for non-pulsating stars lying in the classical Cepheid instability strip based on the Optical Gravitational Lensing Experiment (OGLE) photometric maps combined with Strömgren photometry obtained with the 4.1-m Southern Astrophysical Research (SOAR) telescope, and Gaia Data Release 2 data in four fields in the Large Magellanic Cloud. We selected 19 candidates in total. After analysis of their light curves from OGLE surveys we found that all these stars appear to be photometrically stable at the level of a few mmag. Our results show that non-pulsating stars might constitute to about $21\!-\!30\, {\rm per\, cent}$ of the whole sample of giant stars located in the classical instability strip. Furthermore, we identified potential candidates for classical Cepheids with hot companions based on their Strömgren colours.

Physical Properties of Galactic RV Tauri Stars from Gaia DR2 Data

Abstract We present the first period–luminosity and period–radius relation of Galactic RV Tauri variable stars. We have surveyed the literature for all variable stars belonging to this class and compiled the full set of their photometric and spectroscopic measurements. We crossmatched the final list of stars with the Gaia Data Release 2 database and took the parallaxes, G-band magnitudes, and effective temperatures to calculate the distances, luminosities, and radii using a probabilistic approach. As it turned out, the sample was very contaminated, and thus we restricted our study to those objects for which the RV Tau nature was securely confirmed. We found that several stars are located outside the red edge of the classical instability strip, which implies a wider pulsational region for RV Tau stars. The period–luminosity relation of galactic RV Tauri stars is steeper than that of the shorter-period Type II Cepheids, in agreement with previous results obtained for the Magellanic Clouds and globular clusters. The median masses of RVa and RVb stars were calculated to be 0.45–0.52 M ⊙ and 0.83 M ⊙, respectively.

Discovery of δ Scuti Pulsations in the Young Hybrid Debris Disk Star HD 156623

Abstract The bRing robotic observatory network was built to search for circumplanetary material within the transiting Hill sphere of the exoplanet β Pic b across its bright host star β Pic. During the bRing survey of β Pic, it simultaneously monitored the brightnesses of thousands of bright stars in the southern sky (V ≃ 4–8, δ ≲ −30°). In this work, we announce the discovery of δ Scuti pulsations in the A-type star HD 156623 using bRing data. HD 156623 is notable as it is a well-studied young star with a dusty and gas-rich debris disk, previously detected using ALMA. We present the observational results on the pulsation periods and amplitudes for HD 156623, discuss its evolutionary status, and provide further constraints on its nature and age. We find strong evidence of frequency regularity and grouping. We do not find evidence of frequency, amplitude, or phase modulation for any of the frequencies over the course of the observations. We show that HD 156623 is consistent with other hot and high-frequency pre-main sequence and early zero-age main sequence (ZAMS) δ Scutis as predicted by theoretical models and corresponding evolutionary tracks, although we observe that HD 156623 lies hotter than the theoretical blue edge of the classical instability strip. This, coupled with our characterization and Sco–Cen membership analyses, suggests that the star is most likely an outlying ZAMS member of the ∼16 Myr Upper Centaurus-Lupus subgroup of the Sco–Cen association.

Impact of gaps in the asteroseismic characterization of pulsating stars

Context. It is known that the observed distribution of frequencies in CoRoT and Kepler δ Scuti stars has no parallelism with any theoretical model. Pre-whitening is a widespread technique in the analysis of time series with gaps from pulsating stars located in the classical instability strip, such as δ Scuti stars. However, some studies have pointed out that this technique might introduce biases in the results of the frequency analysis. Aims. This work aims at studying the biases that can result from pre-whitening in asteroseismology. The results will depend on the intrinsic range and distribution of frequencies of the stars. The periodic nature of the gaps in CoRoT observations, only in the range of the pulsational frequency content of the δ Scuti stars, is shown to be crucial to determining their oscillation frequencies, the first step in performing asteroseismology of these objects. Hence, here we focus on the impact of pre-whitening on the asteroseismic characterization of δ Scuti stars. Methods. We select a sample of 15 δ Scuti stars observed by the CoRoT satellite, for which ultra-high-quality photometric data have been obtained by its seismic channel. In order to study the impact on the asteroseismic characterization of δ Scuti stars we perform the pre-whitening procedure on three datasets: gapped data, linearly interpolated data, and data with gaps interpolated using Autoregressive and Moving Average models (ARMA). Results. The different results obtained show that at least in some cases pre-whitening is not an efficient procedure for the deconvolution of the spectral window. Therefore, in order to reduce the effect of the spectral window to a minimum, in addition to performing a pre-whitening of the data, it is necessary to interpolate with an algorithm that is aimed to preserve the original frequency content.

Characterizing the observational properties of δ Sct stars in the era of space photometry from the Kepler mission

The {\delta} Sct stars are a diverse group of intermediate-mass pulsating stars located on and near the main sequence within the classical instability strip in the Hertzsprung-Russell diagram. Many of these stars are hybrid stars pulsating simultaneously with pressure and gravity modes that probe the physics at different depths within a star's interior. Using two large ensembles of {\delta} Sct stars observed by the Kepler Space Telescope, the instrumental biases inherent to Kepler mission data and the statistical properties of these stars are investigated. An important focus of this work is an analysis of the relationships between the pulsational and stellar parameters, and their distribution within the classical instability strip. It is found that a non-negligible fraction of main sequence {\delta} Sct stars exist outside theoretical predictions of the classical instability boundaries, which indicates the necessity of a mass-dependent mixing length parameter to simultaneously explain low- and high-radial order pressure modes in {\delta} Sct stars within the Hertzsprung-Russell diagram. Furthermore, a search for regularities in the amplitude spectra of these stars is also presented, specifically the frequency difference between pressure modes of consecutive radial order. In this work, it is demonstrated that an ensemble-based approach using space photometry from the Kepler mission is not only plausible for {\delta} Sct stars, but that it is a valuable method for identifying the most promising stars for mode identification and asteroseismic modelling. The full scientific potential of studying {\delta} Sct stars is as yet unrealised. The ensembles discussed in this paper represent a high-quality data set for future studies of rotation and angular momentum transport inside A and F stars using asteroseismology.

High-resolution spectroscopy and abundance analysis of δ Scuti stars near the γ Doradus instability strip

$\delta$ Scuti stars are remarkable objects for asteroseismology. In spite of decades of investigations, there are still important questions about these pulsating stars to be answered, such as their positions in $\log$$T_{\rm eff}$ $-$ $\log g$ diagram, or the dependence of the pulsation modes on atmospheric parameters and rotation. Therefore, we performed a detailed spectroscopic study of $41$ $\delta$ Scuti stars. The selected objects are located near the $\gamma$ Doradus instability strip to make a reliable comparison between both types of variables. Spectral classification, stellar atmospheric parameters ($T_{\rm eff}$, $\log g$, $\xi$) and $v \sin i$ values were determined. The spectral types and luminosity classes of stars were found to be A1$-$F5 and III$-$V, respectively. The $T_{\rm eff}$ ranges from $6600$ to $9400$ K, whereas the obtained $\log g$ values are from $3.4$ to $4.3$. The $v \sin i$ values were found between $10$ and $222$ km s$^{-1}$. The derived chemical abundances of $\delta$ Scuti stars were compared to those of the non-pulsating stars and $\gamma$ Doradus variables. It turned out that both $\delta$ Scuti and $\gamma$ Doradus variables have similar abundance patterns, which are slightly different from the non-pulsating stars. These chemical differences can help us to understand why there are non-pulsating stars in classical instability strip. Effects of the obtained parameters on pulsation period and amplitude were examined. It appears that the pulsation period decreases with increasing $T_{\rm eff}$. No significant correlations were found between pulsation period, amplitude and $v \sin i$.

Amplitude modulation in δ Sct stars: statistics from an ensemble of Kepler targets

The results of a search for amplitude modulation of pulsation modes in 983 δ Sct stars, which have effective temperatures between 6400 ⩽ Teff ⩽ 10 000 K in the Kepler Input Catalogue and were continuously observed by the Kepler Space Telescope for 4 yr, are presented. A total of 603 δ Sct stars (61.3 per cent) are found to exhibit at least one pulsation mode that varies significantly in amplitude over 4 yr. Furthermore, it is found that amplitude modulation is not restricted to a specific region within the classical instability strip in the HR diagram, therefore its cause is not necessarily dependent on stellar parameters such as Teff or log g . On the other hand, many δ Sct stars show constant pulsation amplitudes demonstrating that the cause of pulsational non-linearity in these stars is not well understood.

The occurrence of binary evolution pulsators in classical instability strip of RR Lyrae and Cepheid variables

Single star evolution does not allow extremely low-mass stars to cross the classical instability strip (IS) during the Hubble time. However, within binary evolution framework low-mass stars can appear inside the IS once the mass transfer (MT) is taken into account. Triggered by a discovery of low-mass 0.26 Msun RR Lyrae-like variable in a binary system, OGLE-BLG-RRLYR-02792, we investigate the occurrence of similar binary components in the IS, which set up a new class of low-mass pulsators. They are referred to as Binary Evolution Pulsators (BEPs) to underline the interaction between components, which is crucial for substantial mass loss prior to the IS entrance. We simulate a population of 500 000 metal-rich binaries and report that 28 143 components of binary systems experience severe MT (loosing up to 90% of mass), followed by at least one IS crossing in luminosity range of RR Lyrae (RRL) or Cepheid variables. A half of these systems enter the IS before the age of 4 Gyr. BEPs display a variety of physical and orbital parameters, with the most important being the BEP mass in range 0.2-0.8 Msun, and the orbital period in range 10-2500 d. Based on the light curve only, BEPs can be misclassified as genuine classical pulsators, and as such they would contaminate genuine RRL and classical Cepheid variables at levels of 0.8% and 5%, respectively. We state that the majority of BEPs will remain undetected and we discuss relevant detection limitations.

Survey of non-linear hydrodynamic models of type-II Cepheids

We present a grid on non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6M_Sun and a range of metallicities ([Fe/H]=-2.0,-1.5,-1.0), and for 0.8M_Sun ([Fe/H]=-1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russel diagram we detect two domains in which period doubled pulsation is possible. The first extends through the BL Her domain and low luminosity W Vir domain (pulsation periods ~2-6.5 d). The second domain extends at higher luminosities (W Vir domain; periods >9.5d). Some models within these domains display period-4 pulsation. We also detect very narrow domains (~10 K wide) in which modulation of pulsation is possible. Another interesting phenomenon we detect is double-mode pulsation in the fundamental mode and in the fourth radial overtone. Fourth overtone is a surface mode, trapped in the outer model layers. Single-mode pulsation in the fourth overtone is also possible on the hot side of the classical instability strip. The origin of the above phenomena is discussed. In particular, the role of resonances in driving different pulsation dynamics as well as in shaping the morphology of the radius variation curves is analysed.