High-amplitude Δ Scuti Stars Research Articles

Exploring the unexpected: Disharmonized harmonic pulsation modes in high-amplitude δ Scuti stars

Harmonics are a ubiquitous feature across various pulsating stars. They are traditionally viewed as mere replicas of the independent primary pulsation modes and have thus been excluded from asteroseismological models. Recent research, however, has uncovered a significant discrepancy: in high-amplitude δ Scuti (HADS) stars, harmonics exhibit uncorrelated variations in amplitude and frequency relative to their independent primary pulsation modes. The nature of these disharmonized harmonics is a question of critical importance. In our study we analysed five triple-mode HADS stars observed by the Transiting Exoplanet Survey Satellite (TESS) and discovered some pervasive patterns of disharmonized harmonics in both the fundamental (f0) and first overtone (f1) pulsation modes. Intriguingly, through an in-depth frequency interaction analysis of V1393 Cen, we identified 2f1 as an independent pulsation mode, distinct from f1, and identified it as the progenitor of the frequency variations observed in 3f1, 4f1, 5f1, and 6f1. Similar behaviour can be found in DO CMi and GSC 06047-00749, in which 2f1 and 3f1 are the independent pulsation modes, respectively. Notably, we found an interesting pattern when decomposing the harmonics that might suggest a generation process of harmonics. These findings serve as a new window on the research of harmonics, which remains a hidden corner of contemporary asteroseismology.

TESS Observations of Seven Newly Identified High-amplitude δ Scuti Stars

We report seven newly identified high-amplitude δ Scuti (HADS) stars. Among them, two stars (TIC 30977864 and TIC 387379145) exhibit pure radial pulsation without the excitation of non-radial modes. TIC 30977864 is classified as a double-mode HADS star, while the other four stars potentially show triple-mode HADS behavior. TIC 112682462 and TIC 255603395 closely resemble RR Lyrae stars based on their light curves, position in the period–luminosity diagram, and the period ratio diagram. However, without spectral observations, it is challenging to ascertain whether these two stars are HADS or RR Lyrae stars. TIC 281695001 exhibits a fundamental frequency amplitude smaller than that of the first overtone, suggesting the presence of intriguing phenomena that necessitate further analysis. We analyzed the relationship between metallicity and period using data provided by Netzel & Smolec. The metallicities of the 176 stars display a broad distribution ranging from −2.0 dex to 0.5 dex, with periods spanning 0.05 to 0.20 days. This random distribution of metallicities may contribute to the dispersion observed in the P1/P0 ratio. To derive more accurate conclusions, future spectroscopic observations of a larger sample of HADS stars are crucial. These observations will provide precise rotational velocities and more accurate determinations of metallicities.

Pulsation Analysis of High-Amplitude δ Scuti Stars with TESS

In this work, the pulsation analysis is performed on 83 high-amplitude δ Scuti stars (HADS), which have been observed by the Transiting Exoplanet Survey Satellite. The results show that 49 of these HADS show single-mode pulsation, 27 of them show radial double-modes pulsation (in which 22 of them pulsate with the fundamental and first overtone modes and five of them pulsate with the first and second overtone modes), and seven of them show radial triple-modes pulsation (three of which are newly confirmed triple-mode HADS). The histogram of the fundamental periods and the ratios between the fundamental and first overtone periods show bimodal structures, which might be caused by the stellar evolution in this specific phase. Most of the radial triple-mode HADS have a fundamental amplitude of 41–54 mmag, and 50% of them have similar amplitudes of the fundamental and first overtone pulsation modes. All these hints require further confirmation not only in observations with more HADS samples, but also in theoretical models with suitable treatments of stellar evolution and pulsation.

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.

KIC 2857323: A Double-mode High-amplitude δ Scuti Star with Amplitude Decline of the First Overtone Mode

We investigate the pulsating behavior of KIC 2857323 using high-precision observations from the Kepler mission. Fourier analysis of 4 yr time-series data reveals five independent frequencies for the light variation. Among them, two strong frequencies f 1 and f 3 with a period ratio of 0.774 identify this star as a double-mode (i.e., the fundamental mode F0 and first overtone mode F1) high-amplitude δ Scuti star (HADS). Seismic modeling using the two radial modes F0 and F1 indicates that KIC 2857323 is a main-sequence star with mass M = 1.78 ± 0.02 M ⊙ and metallicity Z from 0.009 to 0.012. We analyze the phase and amplitude variations of F0 and F1 using the phase modulation method and find that the first overtone mode F1 shows a slow decline in amplitude. We discuss several possible causes for the amplitude variation and speculate that the amplitude decline in this star may be due to pulsation energy loss. We note that KIC 2857323 is the first double-mode HADS to show amplitude decline and warrants further study to ascertain its nature.

A Double-modulation Effect Detected in a Double-mode High-amplitude δ Scuti Star: KIC 10284901

Abstract In this paper, we present an analysis of the pulsating behavior of Kepler target KIC 10284901. The Fourier transform of the high-precision light curve reveals seven independent frequencies for its light variations. Among them, the first two frequencies are main pulsation modes: F0 = 18.994054(1) day−1 and F1 = 24.335804(4) day−1; the ratio F0/F1 = 0.7805 classifies this star as a double-mode high-amplitude δ Scuti (HADS) star; another two frequencies, f m1 = 0.4407 day−1 and f m2 = 0.8125 day−1, are detected directly, and the modulations of f m1 and f m2 to F0 and F1 modes (seen as quintuplet structures centered on these two modes in the frequency spectrum) are also found. This is the first detection of a double-modulation effect in the HADS stars. The features of the frequency pattern and the ratio (f m1/f m2 ≈ 1:2), as well as the cyclic variation of amplitude of the two dominant pulsation modes, which seem to be similar to that in Blazhko RR Lyrae stars, indicate this modulation might be related to the Blazhko effect. A preliminary analysis suggests that KIC 10284901 is in the bottom of the HADS instability strip and situated in the main sequence.

Convection and Overshoot in Models of γ Doradus and δ Scuti Stars

Abstract We investigate the pulsation properties of stellar models that are representative of δ Scuti and γ Doradus variables. We have calculated a grid of stellar models from 1.2 to 2.2 M ⊙, including the effects of both rotation and convective overshoot using MESA, and we investigate the pulsation properties of these models using GYRE. We discuss the observable patterns in the frequency spacing for p modes and the period spacings for g modes. Using the observable patterns in the g mode period spacings, it may be possible to observationally constrain the convective overshoot and rotation of a model. We also calculate the pulsation constant (Q) for all models in our grid and investigate the variation with convective overshoot and rotation. The variation in the Q values of the radial modes can be used to place constraints on the convective overshoot and rotation of stars in this region. As a test case, we apply this method to a sample of 22 High-Amplitude δ Scuti stars (HADS) and provide estimates for the convective overshoot of the sample.

RAPID EVOLUTION OF GSC 03144-595, A NEW TRIPLE-MODE RADIALLY PULSATING HIGH-AMPLITUDE δ SCUTI

ABSTRACT We present the results of a multi-year study of the high-amplitude δ Scuti (HADS) star GSC 03144-595. The star was observed between June and September in 2011 and 2014 for 13 nights and 28 nights, respectively. Based on our results, we argue that GSC 03144-595 is a new triple-mode radially pulsating HADS, only the fifth discovered and only the second that has a fundamental frequency in the traditional δ Scuti regime. While the frequencies and amplitudes of the fundamental and first harmonic were found to be unchanged between 2011 and 2014, we found that the amplitude of the second harmonic increased by 44%, a form of evolution not previously seen. This finding suggests that the second harmonic may be transient, thus explaining the scarcity of triple-mode HADS stars.

Frequencies and mode identifications of theδScuti star EE Camelopardalis

Aims. EE Cam belongs to a group of slightly evolved main-sequence A stars with intermediate rotational velocities. The pulsation frequencies and their mode identification of this star are of interest in order to compare these with those known for the high-amplitude δ Scuti stars (HADS) and the common fast-rotating low-amplitude δ Scuti pulsators. Methods. The variability of the δ Scuti star EE Cam was observed photometrically for more than 300 nights from 2006 to 2010. Results. Forty pulsation frequencies are identified, ranging from 3.4 to 13.3 cd −1 (40 to 154 μHz). The frequency distribution of the residuals suggests the presence of a large number of additional small-amplitude modes in the same frequency range. We compare the observed phase differences and amplitude ratios with those predicted by pulsation models. The dominant mode at 4.93 cd −1 is found to be a radial mode, while the mode at 5.21 cd −1 is identified as a nonradial � = 1 mode. Furthermore, when we compare the frequency range of the detected modes with detailed stellar models of pulsational instability, the radial mode is found to be the fundamental mode. Conclusions. We have studied and presented the pulsation behavior of EE Cam. It demonstrates that a moderately rotating star can exhibit the behavior of the two groups of δ Scuti stars: the identification of the dominant mode as the radial fundamental is similar to that found in the slowly rotating HADS, and the presence of a very large number of low-amplitude nonradial modes resembles the property of the fast rotating low-amplitude δ Scuti stars.

New variable stars on digitized plates of the Moscow collection. Field SA9

The new stage of work on digitizing the astronomical plates of the Sternberg Astronomical Institute’s collection and searching for new variable stars using the digitized photographic plates includes a considerable improvement of the automated search techniques for objects with variable brightnesses. In particular, the technique for taking into account the non-linear response of the photographic light detector has been improved. Applying the improved techniques to 182 digitized images of a 10° × 10° field centered at SA9, obtained from scanning photographic plates taken with the Sternberg Astronomical Institute 40-cm astrograph, has enabled the discover and study of 77 new variable stars (MDV 519–595). These include 3 Cepheids, 2 probable BY Draconis stars, 65 eclipsing binaries, 3RR Lyrae stars, 1 high-amplitude δ Scuti star (HADS), and 3 irregular variables. Special CCD observations have confirmed the presence of brightness variations in 7 of the 77 variables that were initially considered uncertain.

Kepler observations of the high-amplitude δ Scuti star V2367 Cyg

We analyse Kepler observations of the high-amplitude δ Scuti (HADS) star V2367 Cyg (KIC 9408694). The variations are dominated by a mode with frequency f1= 5.6611 d−1. Two other independent modes with f2= 7.1490 d−1 and f3= 7.7756 d−1 have amplitudes an order of magnitude smaller than f1. Nearly all the light variation is due to these three modes and their combination frequencies, but several hundred other frequencies of very low amplitude are also present. The amplitudes of the principal modes may vary slightly with time. The star has twice the projected rotational velocity of any other HADS star, which makes it unusual. We find a correlation between the phases of the combination frequencies and their pulsation frequencies, which is not understood. Since modes of highest amplitude in HADS stars are normally radial modes, we assumed that this would also be true in this star. However, attempts to model the observed frequencies as radial modes without mode interaction were not successful. For a star with such a relatively high rotational velocity, it is important to consider the effect of mode interaction. Indeed, when this was done, we were able to obtain a model in which a good match with f1 and f2 is obtained, with f1 being the fundamental radial mode.

New variable stars on digitized Moscow collection plates. The field of 66 Ophiuchi

In the course of a program to digitize the astronomical plates of the Sternberg Astronomical Institute’s plate stacks, we are developing algorithms for searching for new variable stars and studying them using digitized photographic plates. We have discovered and studied 480 new variable stars in a 10° × 10° field of view centered on 66 Ophiuchi. The digitized plate negatives used are from the 40-cm astrograph, and are 30 × 30 cm in size. These stars include three new Cepheids of the Galaxy’s spherical component, 157 eclipsing binaries, 11 high-amplitude δ Scuti stars (HADSs), 144 RR Lyrae stars, 110 irregular variables (109 LB and one white star), and 55 semi-regular red variables. New important information has been obtained for 43 known variables, which we have classified and derived or improved their light elements; an erroneous identification of the Mira V404 Oph has been corrected. We have also identified more than 50 suspect brightness variables; a program of CCD observations of these suspected variables has been initiated. Our discoveries of new variable stars were performed in a star field with a large number of known variables, detected earlier photographically or using CCD techniques. The discovery of hundreds of new variables in a well-studied region of sky demonstrates that archive photographs possess a large information potential that has remained unrealized.

The Pulsation of EE Camelopardalis

EE Cam is a previously little-studied δ Scuti pulsator with amplitudes between those of the HADS (high-amplitude δ Scuti star) group and average low-amplitude pulsators. Since the size of stellar rotation determines both which pulsation modes are selected by the star as well as their amplitudes, this star offers a great opportunity to examine the astrophysical connections. Extensive photometric measurements covering several months were carried out. Fifteen significant pulsation frequencies were extracted. The dominant mode at 4.934 cycles day-1 was identified as a radial mode by examining the phase shifts at different wavelengths. Medium-dispersion spectra yielded a v sin i value of 40 ± 3 km s-1. This shows that EE Cam belongs to the important transition region between HADSs and normal δ Scuti stars.

The Monoperiodic Scuti Star UY Camelopardalis: An Analog to SX Phoenicis and RR Lyrae Variables

We present the results of a 4 year photometric study of the high-amplitude δ Scuti (HADS) star UY Camelopardalis. Analysis of the available data from 1985 to 2003 shows that UY Cam is monoperiodic. Fourier solutions for individual data sets do not reveal period changes in the star. Although forced parabolic fits to the O-C residuals indicate a measurable period change, the distribution of the data points in the O-C diagram and the deviations between fits and observations suggest that the existence of the period change still has not been established. We demonstrate the presence of amplitude variations from cycle to cycle and on longer timescales. The pulsation amplitude seemed to change from 1985 to the 2000s, but it remained constant in 2000–2003. UY Cam is located in the upper portion of the δ Scuti instability region. Its photometric properties and estimated physical parameters reveal that UY Cam is an interesting object in terms of its poor metallicity, long period, high luminosity, low surface gravity, and large radius among the HADS stars. UY Cam could be a younger (0.7 ± 0.1 Gyr) Population I HADS star with low metal abundance (Z = 0.004) evolving on its post–main-sequence shell hydrogen burning evolutionary phase. UY Cam intervenes among the Population I/II HADS and type c RR Lyrae variables. These characteristics suggest the star to be an analog of HADS, SX Phoenicis, and RRc variables.

Fourier decomposition and frequency analysis of the pulsating stars with $\vec{P< }$ 1 d in the OGLE database

The OGLE database is revisited to investigate in more detail the properties of the Fourier parameters. Methodological improvements led us to identify a clear separation among High-Amplitude δ Scuti (HADS), RRc and RRab stars. The bimodal distribution of the R21 parameter in HADS stars is explained as a contamination effect from RRc stars: there is evidence that all stars with d are RRc variables. The previously claimed existence of a subclass of unusual HADS is demonstrated to be a spurious result. Candidate overtone pulsators are found among HADS and RRc variables. The properties of the Fourier parameters are discussed as a function of the physical conditions in the stars involved. Among the field RRab stars we detected different light-curve groups producing distinct "tails" in the Fourier plots for d; evolutionary phases or the combination of different physical conditions (not only metallicity) are suggested to explain this separation, observed also in the cluster RRab stars. The stellar parameters of RRc stars in a given globular cluster show different tendencies than those of RRc stars from different clusters.

The Identification of Pulsation Modes of High‐Amplitude δ Scuti Stars in ω Centauri and the Carina Galaxy

ABSTRACTWe analyze photometric observations of high‐amplitude δ Scuti stars (HADS) in the globular cluster ω Cen and the Carina galaxy. The pulsation modes of the HADS are inferred primarily from their positions in V, log P diagrams. For ω Cen we identify nine fundamental pulsators (F), 22 first‐overtone (1, O), one second‐overtone (2, O), and probably two third‐overtone (3, O) stars. The majority of the F pulsators have light amplitudes ΔV≥0.15 mag, but two have ΔV<0.15 mag. Four of the 1, O pulsators have ΔV>0.15 mag, but the majority have smaller amplitudes. We find that the F pulsators tend to have more asymmetric light curves. The Carina variables are all large‐amplitude variables. Fourteen are F pulsators and six are 1, O pulsators. At least one and possibly two 1, O stars appear to have asymmetric light curves unlike those found in ω Cen. The data are very uncertain, so the asymmetry may be an artifact of observational uncertainty.The HADS data along with their P‐L relation are utilized to find the distances to ω Cen and the Carina galaxy and absolute magnitudes of their horizontal branches (HB) or RR Lyrae stars. We find the distances to be d = 6370 pc to ω Cen and d = 124,000 pc to the Carina galaxy. The Mv(RR)‐values for the ω Cen RR Lyrae stars are Mv(RR) = 0.14 (Oost II variables) and Mv(RR) = 0.28 (Oost I stars); Mv(HB) = 0.29 for the Carina galaxy.

The MACHO Project Sample of Galactic Bulge High‐Amplitude δ Scuti Stars: Pulsation Behavior and Stellar Properties

We have detected 90 objects with periods and light-curve structures similar to those of field δ Scuti stars using the Massive Compact Halo Object (MACHO) Project database of Galactic bulge photometry. If we assume similar extinction values for all candidates and absolute magnitudes similar to those of other field high-amplitude δ Scuti stars (HADS), the majority of these objects lie in or near the Galactic bulge. At least two of these objects are likely foreground δ Scuti stars, one of which may be an evolved nonradial pulsator, similar to other evolved, disk-population δ Scuti stars. We have analyzed the light curves of these objects and find that they are similar to the light curves of field δ Scuti stars and the δ Scuti stars found by the Optical Gravitational Lens Experiment (OGLE). However, the amplitude distribution of these sources lies between those of low- and high-amplitude δ Scuti stars, which suggests that they may be an intermediate population. We have found nine double-mode HADS with frequency ratios ranging from 0.75 to 0.79, four probable double- and multiple-mode objects, and another four objects with marginal detections of secondary modes. The low frequencies (5-14 cycles day-1) and the observed period ratios of ~0.77 suggest that the majority of these objects are evolved stars pulsating in fundamental or first overtone radial modes.

The Distance to the Galactic Center

ABSTRACTThe Optical Gravitational Lensing Experiment (OGLE) data on high‐amplitude δ Scuti stars (HADS) and RR Lyrae stars have been analyzed to determine the distance to the Galactic bulge. Individual color excesses and V absorption for each individual variable star have been computed, which lead to accurate 〈V0〉 magnitudes. The period‐luminosity relation of the HADS is utilized to calculate distance moduli. We find that the metal‐strong HADS are concentrated strongly to the bulge. The best distance modulus to the bulge from the HADS data is 14.49 ± 0.06 mag. The dependence of Mv on period for the bulge RR Lyrae stars can be found from the reddening‐free magnitude VV - I. The zero point of the Mv–log P relation is set with the horizontal branches of Oosterhoff type I globular clusters. Mv≅0.44 mag (long‐distance scale) in the log P interval −0.29 to −0.22 as inferred by main‐sequence fitting of the clusters to local subdwarfs and utilizing short‐period HADS in the clusters. The best distance modulus to the bulge from the RR Lyrae (ab) stars is 14.45 mag, which compares favorably with the distance modulus of 14.49 mag found from the HADS. We adopt the mean value 14.47 ± 0.08 mag for the bulge distance modulus. A small additive correction leads to 7.9 ± 0.3 kpc as the best distance to the Galactic center.

The Fourier Decomposition of the Light Curves of High Amplitude δ Set Stars

AbstractA significant improvement of the relationships between observed and physical properties of high amplitude δ Scuti stars (HADS), SX Phe stars, and RRc stars can be obtained by the systematic application of Fourier decomposition to their light curves.