Á. Sódor

The Konkoly Blazhko Survey: is light-curve modulation a common property of RRab stars?

A systematic survey to establish the true incidence rate of Blazhko modulation among short-period, fundamental-mode, Galactic field RR Lyrae stars has been carried out. The Konkoly Blazhko Survey (KBS) was initiated in 2004. Since then, more than 750 nights of observation have been devoted to this project. A sample of 30 RRab stars was extensively observed, and light-curve modulation was detected in 14 cases. The 47 per cent occurrence rate of the modulation is much larger than any previous estimate. The significant increase of the detected incidence rate is mostly a result of the discovery of small-amplitude modulation. Half of the Blazhko variables in our sample show the modulation with such a small amplitude that they would definitely have been missed in previous surveys. We have found that the modulation can be very unstable in some cases; for example, RY Com showed regular modulation during only one part of the observations, and had a stable light curve with abrupt, small changes in the pulsation amplitude during two observing seasons. This type of light-curve variability is hard to detect in the data from other surveys. The higher frequency of the light-curve modulation of RRab stars makes it even more important to find an explanation for the Blazhko phenomenon. The validity of the [Fe/H](P, ϕ31) relationship using the mean light curves of Blazhko variables is checked in our sample. We found that the formula gives accurate result for small-modulation-amplitude Blazhko stars, and this is also the case for large-modulation-amplitude stars if the light curve has complete phase coverage. However, if the data for large-modulation-amplitude Blazhko stars are not extended enough (e.g. fewer than 500 data points from fewer than 15 nights), the formula may give false result owing to the distorted shape of the mean light curve used.

An extensive photometric study of the Blazhko RR Lyrae star MW Lyr – I. Light-curve solution

We have obtained the most extensive and most accurate photometric data of a Blazhko variable MWLyrae (MWLyr) during the 2006-2007 observing seasons. The data within each 0.05 phase bin of the modulation period (P m = f -1 m ) cover the entire light cycle of the primary pulsation period (P 0 = f -1 0 ), making possible a very rigorous and complete analysis. The modulation period is found to be 16.5462 d, which is about half of that was reported earlier from visual observations. Previously unknown features of the modulation have been detected. Besides the main modulation frequency f m , sidelobe modulation frequencies around the pulsation frequency and its harmonics appear at ±2f m , ±4f m and ±12.5f m separations as well. Residual signals in the pre-whitened light curve larger than the observational noise appear at the minimum-rising branch-maximum phase of the pulsation, which most probably arise from some stochastic/chaotic behaviour of the pulsation/modulation. The Fourier parameters of the mean light curve differ significantly from the averages of the Fourier parameters of the observed light curves in the different phases of the Blazhko cycle. Consequently, the mean light curve of MW Lyr never matches its actual light variation. The Φ 21 , Φ 31 phase differences in different phases of the modulation show unexpected stability during the Blazhko cycle. A new phenomenological description of the light-curve variation is defined that separates the amplitude and phase (period) modulations utilizing the phase coherency of the lower order Fourier phases.

An extensive photometric study of the Blazhko RR Lyrae star MW Lyr – II. Changes in the physical parameters★

The analysis of the multicolour photometric observations of MW Lyr, a large modulation amplitude Blazhko variable, shows for the first time how the mean global physical parameters vary during the Blazhko cycle. About 1-2 per cent changes in the mean radius, luminosity and surface effective temperature are detected. The mean radius and temperature changes are in good accordance with pulsation model results, which show that these parameters do indeed vary within this order of magnitude if the amplitude of the pulsation changes significantly. We interpret the phase modulation of the pulsation to be a consequence of period changes. Its magnitude corresponds exactly what one expects from the detected changes of the mean radius assuming that the pulsation constant remains the same during the modulation. Our results indicate that during the modulation the pulsation remains purely radial, and the underlying mechanism is most probably a periodic perturbation of the stellar luminosity with the modulation period.

The Shortest Modulation Period Blazhko RR Lyrae Star: SS Cancri

Extended BV(RI)C CCD observations of SS Cnc, a short-period RRab star, are presented. Nearly 1400 data points in each band have been obtained, spanning over 79 days during the spring of 2005. The star exhibits light-curve modulation, the so-called Blazhko effect, with small amplitude (B maximum brightness varies by 0.1 mag) and with the shortest modulation period (5.309 days) ever observed. In the Fourier spectrum of the V light curve, the pulsation frequency components are detected up to the 24th harmonic order, and modulation sidelobe frequencies with significantly asymmetric amplitudes are seen up to the 15th and 9th orders for the lower and higher frequency components, respectively. A detailed comparison of the modulation behavior of SS Cnc and RR Gem, two recently discovered small-amplitude, short-modulation-period Blazhko stars, is presented. The modulation frequency (fm) appears in the Fourier spectrum of both stars with similar amplitude. We also demonstrate that the modulation frequencies have basically different properties from those of the pulsation and modulation sidelobe frequencies, indicating that the physics behind these frequency components is not the same. The discovery of small amplitude modulations of RRab stars cautions that the large photometric surveys (MACHO and OGLE) may seriously underestimate the number of modulated RR Lyrae stars.

The multiperiodic Blazhko modulation of CZ Lacertae

A thorough analysis of the multicolour CCD observations of the RRab-type variable, CZ Lacertae, is presented. The observations were carried out in two consecutive observing seasons in 2004 and 2005 within the framework of the Konkoly Blazhko Survey of bright, northern, short-period RRab variables. The O − C variation of CZ Lac indicated that a significant period decrease took place just around the time of the CCD observations. Our data gave a unique opportunity to study the related changes in the pulsation and modulation properties of a Blazhko star in detail. Two different period components (≈ 14.6 and ≈ 18.6 d) of the Blazhko modulation were identified. Both modulation components had similar strength. The periods and amplitudes of the modulations changed significantly from the first season to the next, while the mean pulsation amplitude decreased slightly. The modulation frequencies were in a 5:4 resonance ratio in the first observing season, and then the frequencies shifted in opposite directions, and their ratio was close to the 4:3 resonance in the next season. The interaction of the two modulations caused beating with a period of 74 d in the first season, which resembled the 4-yr-long cycle of the ≈ 40-d modulation of RR Lyr. The mean values of the global physical parameters and their changes with the Blazhko phase of both modulation components were determined by the inverse photometric method.

An extensive photometric study of the Blazhko RR Lyrae star DM Cyg

DM Cyg, a fundamental mode RRab star, was observed in the 2007 and 2008 seasons in the framework of the Konkoly Blazhko Survey. Very small amplitude light-curve modulation was detected with 10.57 d modulation period. The maximum brightness and phase variations do not exceed 0.07 mag and 7 min, respectively. In spite of the very small amplitude of the modulation, beside the frequency triplets characterizing the Fourier spectrum of the light curve, two quintuplet components were also identified. The accuracy and the good phase coverage of our observations made it possible to analyse the light curves at different phases of the modulation separately. Utilizing the inverse photometric Baade-Wesselink method, we could detect very small systematic changes in the global mean physical parameters of DM Cyg during its Blazhko cycle. The detected changes are similar to what we have already found for a large modulation amplitude Blazhko variable, MW Lyrae. The amplitudes of the detected changes in the physical parameters of DM Cyg are only about 10 per cent of those that have been found in MW Lyr. This is in accordance with its small modulation amplitude being about one-tenth of the modulation amplitude of MW Lyr. The pulsation period of DM Cyg has been increasing by a rate of β = 0.091 d Myr ―1 during the hundred-year time base of the observations. Konkoly archive photographic observations indicate that when the pulsation period of the variable was shorter by Δp puls = 5 x 10 ―6 d the modulation period was longer by Δp mod = 0.066 d than today.

First Quintuplet Frequency Solution of a Blazhko Variable: Light Curve Analysis of RV UMa

RV UMa is one of the RRab stars showing regular large-amplitude light-curve modulation. Extended photoelectric observations of RV UMa obtained at the Konkoly Observatory were published by Kany?, and the data were analysed by Kov?cs. After detecting an error in the reduction procedure of the published Konkoly data, corrected photometric data are presented with additional, previously unpublished measurements. The re-analysis of the combination of the corrected Konkoly data supplemented by Preston & Spinrads observations has led to the discovery that the appropriate mathematical model of the light curve is, in fact, a quintuplet frequency solution, rather than, a triplet. This finding has crucial importance in the interpretation of the Blazhko phenomenon, as a triplet (doublet) is the preferred structure in resonance models, quintuplet in magnetic models. Period changes of both the pulsation and modulation light variations of RV UMa have been detected based on its century-long photometric observations. An overall anticorrelation between the pulsation and modulation period changes can be defined by dPBl /dP 0 = ?8.6 ? 104 gradient, i.e., the modulation period is longer if the pulsation period is shorter. Between 1946 and 1975 the pulsation and modulation periods showed, however, parallel changes, which points to the fact that there is no strict relation between the changes in the periods of the pulsation and modulation.

A new method for determining physical parameters of fundamental mode RR Lyrae stars from multicolour light curves

We present a new method for determining physical parameters of RRab variables ex- clusively from multicolour light curves. Our method is an Inverse Photometric Baade- Wesselink analysis which, using a nonlinear least squares algorithm, searches for the effective temperature (Teff) and pulsational velocity (Vp) curves and other physical parameters that best fit the observed light curves, utilising synthetic colours and bolo- metric corrections from static atmosphere models. The Teff and Vp curves are initially derived from empirical relations then they are varied by the fitting algorithm. The method yields the variations and the absolute values of the radius, the effective tem- perature, the visual brightness, and the luminosity of individual objects. Distance and mass are also determined. The method is tested on 9 RRab stars subjected to Baade- Wesselink analyses earlier by several authors. The physical parameters derived by our method using only the light curve data of these stars are well within their possible ranges defined by direct Baade-Wesselink and other techniques. A new empirical re- lation between the IC magnitude and the pulsational velocity is also presented, which allows to construct the Vp curve of an RRab star purely from photometric observations to an accuracy of about 3.5km/s.

Whole Earth Telescope Observations of the Pulsating Subdwarf B Star PG 0014+067

PG 0014+067 is one of the most promising pulsating subdwarf B stars for seismic analysis, as it has a rich pulsation spectrum. The richness of its pulsations, however, poses a fundamental challenge to understanding the pulsations of these stars, as the mode density is too complex to be explained only with radial and nonradial low-degree (l < 3) p-modes without rotational splittings. One proposed solution, suggested by Brassard et al. in 2001 for the case of PG 0014+067 in particular, assigns some modes with high degree (l = 3). On the other hand, theoretical models of sdB stars suggest that they may retain rapidly rotating cores, and so the high mode density may result from the presence of a few rotationally split triplet (l = 1) and quintuplet (l = 2) modes, along with radial (l = 0) p-modes. To examine alternative theoretical models for these stars, we need better frequency resolution and denser longitude coverage. Therefore, we observed this star with the Whole Earth Telescope for two weeks in 2004 October. In this paper we report the results of Whole Earth Telescope observations of the pulsating subdwarf B star PG 0014+067. We find that the frequencies seen in PG 0014+067 do not appear to fit any theoretical model currently available; however, we find a simple empirical relation that is able to match all of the well-determined frequencies in this star.

The Kepler Cepheid V1154 Cyg revisited: light curve modulation and detection of granulation

We present a detailed analysis of the bright Cepheid-type variable star V1154 Cygni using 4 years of continuous observations by the Kepler space telescope. We detected 28 frequencies using standard Fourier transform method.We identified modulation of the main pulsation frequency and its harmonics with a period of ~159 d. This modulation is also present in the Fourier parameters of the light curve and the O-C diagram. We detected another modulation with a period of about 1160 d. The star also shows significant power in the low-frequency region that we identified as granulation noise. The effective timescale of the granulation agrees with the extrapolated scalings of red giant stars. Non-detection of solar-like oscillations indicates that the pulsation inhibits other oscillations. We obtained new radial velocity observations which are in a perfect agreement with previous years data, suggesting that there is no high mass star companion of V1154 Cygni. Finally, we discuss the possible origin of the detected frequency modulations.