I. Nagy

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.

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.

Four-colour photometry of EY Dra: A study of an ultra-fast rotating active dM1-2e star

We present more than 1000-day long photometry of EY Draconis in BV (RI)C passbands. The changes in the light curve are caused by the spottedness of the rotating surface. Modelling of the spotted surface shows that there are two large active regions present on the star on the opposite hemispheres. The evolution of the surface patterns suggests a flip-flop phenomenon. Using Fourier analysis, we detect a rotation period of Prot = 0.45875 d, and an activity cycle with P ≈ 350 d, similar to the 11-year long cycle of the Sun. This cycle with its year-long period is the shortest one ever detected on active stars. Two bright flares are also detected and analysed (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamical stability of the Gliese 581 exoplanetary system

Using numerical methods we investigate the dynamical stability of the Gliese 581 exoplanetary system. The system is known to harbour four planets (b-e). The existence of another planet (g) in the liquid water habitable zone of the star is debated after the latest analyses of the radial velocity (RV) measurements. We integrated the 4 and 5-planet model of Vogt et al. (AN 333, 561-575, 2012) with initial circular orbits. To characterize stability, the maximum eccentricity was used that the planets reached over the time of the integrations and the LCI and RLI to identify chaotic motion. Since circular orbits in the RV fits seem to be a too strong restriction and the true orbits might be elliptic, we investigated the stability of the planets as a function of their eccentricity. The integration of the circular 4-planet model shows that it is stable on a longer timescale for even an inclination i = 5{\deg}. A fifth planetary body in the 4-planet model could have a stable orbit between the two super-Earth sized planets c and d, and beyond the orbit of planet d, although another planet would likely only be stable on circular or near-circular orbit in the habitable zone of the star. Gliese 581 g in the 5-planet model would have a dynamically stable orbit, even for a wider range of orbital parameters, but its stability is strongly dependent on the eccentricity of planet d. The low-mass planet e, which quickly became unstable in eccentric models, remains stable in the circular 4-planet model, but the stable region around its initial semi-major axis and eccentricity is rather small. The stability of the inner planets e and c is dependent on the eccentricity of the Neptune-size planet b. The outermost planet d is far away from the adjacent planet c to considerably influence its stability, however, the existence of a planet between the two super-Earth planets c and d constrains its eccentricity.

Stable and habitable systems with two giant planets

We have studied planetary systems which are similar to the Solar System and built up from three inner rocky planets (Venus, Earth, Mars) and two outer gas giants. The stability of the orbits of the inner planets is discussed in the cases of different masses of the gas planets. To demonstrate the results stability maps were made and it was found that Jupiter could be four times and Saturn could be three times more massive while the orbits of the inner planets stay stable. Similar calculations were made by changing the mass of the Sun. In this case the position of the rocky planets and the extension of the liquid water habitable and the UV habitable zones were studied for different masses of the Sun. It was found that the orbits of the planets were stable for values greater than 0.33 M⊙ where M⊙ is the mass of the Sun and at lower masses of the Sun (at about 0.8 M⊙) only Venus, but for higher mass values (at about 1.2 M⊙) Earth and also Mars are located in both habitable zones.

Features of librational motions around L4

Trojan bodies are present in the Solar system in great number, as Trojan asteroids and also as Trojan moons. Thus it is possible that their presence is similar in extrasolar planetary systems too. We investigated features of librational motions around L4 with numerical methods on the mass parameter – eccentricity plane in the elliptic restricted three-body problem. We determined the lifetime of Trojan bodies, until they remained in the librational domain around L4, also illustrated the distribution of the three possible endgames of trojan motion. Finally we determined the frequences and resonances of the librational motion in the stable region.

Stability of the orbit of a third body in binary asteroid systems

In this work we studied the stable regions around four binary asteroids in the main asteroid belt. The studied systems were (107) Camilla, (22) Kallipe, (45) Eugenia and (762) Pulcova. The stability was characterized with three motion indicators: relative Lyapunov indicator, maximum eccentricity, and maximum difference of eccentricities. The survay covered the P type orbits, where satellite moves around both primaries. On the basis of our work it can be decided, in which system the discovery of a third component can be expected.