Radosław Smolec

Period and light‐curve fluctuations of the Kepler Cepheid V1154 Cygni

We present a detailed period analysis of the bright Cepheid-type variable star V1154 Cygni (V1154 Cyg; V = 9.1 mag, P ≈ 4.9 d) based on almost 600 d of continuous observations by the Kepler space telescope. The data reveal significant cycle-to-cycle fluctuations in the pulsation period, indicating that classical Cepheids may not be as accurate astrophysical clocks as commonly believed: regardless of the specific points used to determine the O − C values, the cycle lengths show a scatter of 0.015–0.02 d over 120 cycles covered by the observations. A very slight correlation between the individual Fourier parameters and the O − C values was found, suggesting that the O − C variations might be due to the instability of the light-curve shape. Random-fluctuation tests revealed a linear trend up to a cycle difference 15, but for long term, the period remains around the mean value. We compare the measurements with simulated light curves that were constructed to mimic V1154 Cyg as a perfect pulsator modulated only by the light travel time effect caused by low-mass companions. We show that the observed period jitter in V1154 Cyg represents a serious limitation in the search for binary companions. While the Kepler data are accurate enough to allow the detection of planetary bodies in close orbits around a Cepheid, the astrophysical noise can easily hide the signal of the light-time effect.

Kepler photometry of RRc stars: peculiar double-mode pulsations and period doubling

We present the analysis of four first overtone RR Lyrae stars observed with the Kepler space telescope, based on data obtained over nearly 2.5yr. All four stars are found to be multiperiodic. The strongest secondary mode with frequency f2 has an amplitude of a few mmag, 20 45 times lower than the main radial mode with frequency f1. The two oscillations have a period ratio of P2/P1 = 0.612 0.632 that cannot be reproduced by any two radial modes. Thus, the secondary mode is nonradial. Modes yielding similar period ratios have also recently been discovered in other variables of the RRc and RRd types. These objects form a homogenous group and constitute a new class of multimode RR Lyrae pulsators, analogous to a similar class of multimode classical Cepheids in the Magellanic Clouds. Because a secondary mode with P2/P1 �0.61 is found in almost every RRc and RRd star observed from space, this form of multiperiodicity must be common. In all four Kepler RRc stars studied, we find subharmonics of f2 at �1/2f2 and at �3/2f2. This is a signature of period doubling of the secondary oscillation, and is the first detection of period doubling in RRc stars. The amplitudes and phases of f2 and its subharmonics are variable on a timescale of 10 200d. The dominant radial mode also shows variations on the same timescale, but with much smaller amplitude. In three Kepler RRc stars we detect additional periodicities, with amplitudes below 1mmag, that must correspond to nonradial g-modes. Such modes never before have been observed in RR Lyrae variables.

Variable turbulent convection as the cause of the Blazhko effect – testing the Stothers model

The amplitude and phase modulation observed in a significant fraction of the RR Lyrae variables - the Blazhko effect - represents a longstanding enigma in stellar pulsation theory. No satisfactory explanation for the Blazhko effect has been proposed so far. In this paper we focus on the Stothers idea, in which modulation is caused by changes in the structure of the outer convective zone, caused by a quasi-periodically changing magnetic field. However, up to this date no quantitative estimates were made to investigate whether such a mechanism can be operational and whether it is capable of reproducing the light variation we observe in Blazhko variables. We address the latter problem. We use a simplified model, in which the variation of turbulent convection is introduced into the non-linear hydrodynamic models in an ad hoc way, neglecting interaction with the magnetic field. We study the light-curve variation through the modulation cycle and properties of the resulting frequency spectra. Our results are compared with Kepler observations of RR Lyr. We find that reproducing the light-curve variation, as is observed in RR Lyr, requires a huge modulation of the mixing length, of the order of ±50 per cent, on a relatively short time-scale of less than 40 d. Even then, we are not able to reproduce all the observed relations between modulation components present in the frequency spectrum and the relations between Fourier parameters describing the shape of the instantaneous light curves.

Modelling turbulent fluxes due to thermal convection in rectilinear shearing flow

We revisit a phenomenological description of turbulent thermal convection along the lines proposed originally by Gough (1965) in which eddies grow solely by extracting energy from the unstably stratified mean state and are subsequently destroyed by internal shear instability. This work is part of an ongoing investigation for finding a procedure to calculate the turbulent fluxes of heat and momentum in the presence of a shearing background flow in stars.

Mode selection in pulsating stars

In this review we focus on non-linear phenomena in pulsating stars: mode selection and amplitude limitation. Of many linearly excited modes, only a fraction is detected in pulsating stars. Which of them are excited, and why (the problem of mode selection), and to what amplitude (the problem of amplitude limitation) are intrinsically non-linear and still unsolved problems. Tools for studying these problems are briefly discussed and our understanding of mode selection and amplitude limitation in selected groups of self-excited pulsators is presented. We focus on classical pulsators (Cepheids and RR Lyrae stars) and main-sequence variables (δ Scuti and β Cephei stars). Directions of future studies are briefly discussed.

RR Lyrae stars in NGC 6362

We present the analysis of the top-quality photometry of RR Lyrae stars in the globular cluster NGC 6362, gathered over 11 observing seasons by the CASE project. 16 stars are fundamental mode pulsators (RRab stars) and 16 are first overtone pulsators (RRc stars). In two stars, previously identified as RRab, V3 and V34, we detect additional periodicity identified as radial first overtone mode. Lower than usual period ratios (0.730 and 0.728), dominant pulsation in the radial fundamental mode and presence of a long-period modulation indicate, that these two variables are not classical RRd stars, but are new members of the recently identified class of anomalous RRd variables. In a significant fraction of RRc stars, 63 per cent, we detect additional shorter-period variability in the (0.60, 0.65)

First Detection of Period Doubling in a BL Herculis Type Star: Observations and Theoretical Models

P_1

Order and chaos in hydrodynamic BL Her models

range. This form of double-periodic pulsation must be common in first overtone RR Lyr stars, as space observations indicate. The incidence rate we find in NGC 6362, is the highest in ground-based observations reported so far. We study the properties of these stars in detail; in particular we confirm that in the colour-magnitude diagram, this group is adjacent to the interface between RRab and RRc stars, as first reported in the analysis of M3 observations by Jurcsik et al. The incidence rate of the Blazhko effect is also very high: we observe it in 69 per cent of RRab stars and in 19 per cent of RRc stars. Rare, double-periodic modulation is reported in one RRab and in one RRc star. Finally we discuss V37 - a peculiar variable in which we detect two close high-amplitude periodicities and modulation. Its previous classification as RRc must be treated as tentative.

On Resonant and Non‐Resonant Origin of Double‐Mode Cepheid Pulsation

We report on the discovery of the first BL Herculis star displaying period-doubling behaviour as predicted by the hydrodynamic models of Buchler and Moskalik (ApJ 391:736, 1992). The star, with P 0 = 2. 4 d, is located in the Galactic bulge and was discovered with OGLE-III photometry. We present new nonlinear convective models, which, together with recent evolutionary tracks, put constraints on the stellar parameters. In particular, we estimate the mass and metallicity of the object.

BRITE observations of classical Cepheids

Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are strikingly similar: chaotic bands are born through the series of period doubling bifurcations and merge through interior crises. Within chaotic bands periodic windows are born through the tangent bifurcations, preceded by the intermittent behaviour. This is a universal behaviour of dynamical systems (Feigenbaum 1983). We demonstrate such behaviour in models of pulsating stars.