Nonlinear Beat Cepheid and RR Lyrae Models

The numerical hydrodynamic modelling of beat Cepheid behavior has been a long standing quest in which purely radiative models had failed consistently. We find that beat pulsations occur naturally when {\it turbulent convection} is accounted for in our hydrodynamics code. The development of a relaxation code and of a Floquet stability analysis greatly facilitates the search for and the analysis of beat Cepheid models. The conditions for the occurrence of beat behavior can be understood easily and at a fundamental level with the help of amplitude equations.Comment: 8 pages, 5 figures, Astronomy and Astrophysics, submitte

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 long-standing 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 (2006) 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 days. Even then, we are not able to reproduce neither all the observed relations between modulation components present in the frequency spectrum, nor the relations between Fourier parameters describing the shape of the instantaneous light curves.Comment: 17 pages, 13 figures, accepted for publication in MNRAS; for associated animation, see http://homepage.univie.ac.at/radek.smolec/publications/KASC11a

Double-Mode Stellar Pulsations

The status of the hydrodynamical modelling of nonlinear multi-mode stellar pulsations is discussed. The hydrodynamical modelling of steady double-mode (DM) pulsations has been a long-standing quest that is finally being concluded. Recent progress has been made thanks to the introduction of turbulent convection in the numerical hydrodynamical codes which provide detailed results for individual models. An overview of the modal selection problem in the HR diagram can be obtained in the form of bifurcation diagrams with the help of simple nonresonant amplitude equations that capture the DM phenomenon.Comment: 34 pages, to appear as a chapter in Nonlinear Stellar Pulsation in the Astrophysics and Space Science Library (ASSL), Editors: M. Takeuti & D. Sasselov (prints double column with pstops '2:[email protected](22.0cm,-2cm)[email protected](22.0cm,11.0cm)' in.ps out.ps

V440 Per: the longest period overtone Cepheid

V440 Per is a Population I Cepheid with the period of 7.57 day and low amplitude, almost sinusoidal light and radial velocity curves. With no reliable data on the 1st harmonic, its pulsation mode identification remained controversial. We obtained a radial velocity curve of V440 Per with our new high precision and high throughput Poznan Spectroscopic Telescope. Our data reach the accuracy of 130 m/s per individual measurement and yield a secure detection of the 1st harmonic with the amplitude of A_2= 140+/- 15 m/s. The velocity Fourier phase \phi_21 of V440 Per is inconsistent at the 7.25 \sigma level with those of the fundamental mode Cepheids, implying that the star must be an overtone Cepheid, as originally proposed by Kienzle et al.(1999). Thus, V440 Per becomes the longest period Cepheid with the securely established overtone pulsations. We show, that the convective nonlinear pulsation hydrocode can reproduce the Fourier parameters of V440 Per very well. Requirement to match the observed properties of V440 Per constrains free parameters of the dynamical convection model used in the pulsation calculations, in particular the radiative losses parameter.Comment: Submitted to MNRA

YREC: The Yale Rotating Stellar Evolution Code

The stellar evolution code YREC is outlined with emphasis on its applications to helio- and asteroseismology. The procedure for calculating calibrated solar and stellar models is described. Other features of the code such as a non-local treatment of convective core overshoot, and the implementation of a parametrized description of turbulence in stellar models, are considered in some detail. The code has been extensively used for other astrophysical applications, some of which are briefly mentioned at the end of the paper.Comment: 10 pages, 2 figures, ApSS accepte

Interaction Between Convection and Pulsation

This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages, 14 figure

Amplitude Saturation in Beta Cephei Models

Although the driving mechanism acting in beta Cephei pulsators is well known (e.g. Dziembowski & Pamyatnykh 1993), problems concerning identification of amplitude limitation mechanism and non-uniform filling of the theoretical instability strip, remain to be solved. In the present analysis, these problems are addressed by non-linear modelling of radial pulsations of these stars. In this approach radial modes are treated as representative for all acoustic oscillations. Several models of different masses and metallicities were converged to limit cycles through Stellingwerf (1974) relaxation technique. Resulting peak-to-peak amplitudes are of order of DeltaV=0.3 mag. Such amplitudes are significantly larger than those observed in beta Cephei pulsators. Assuming that all acoustic modes are similar, we show that collective saturation of the driving mechanism by several acoustic modes can easily lower predicted saturation amplitudes to the observed level. Our calculations predict significant decrease of saturation amplitudes as we go to high mass/high luminosity models. However, this effect is not strong enough to explain scarcity of high mass beta Cephei variables. We also discuss robust double-mode behaviour, encountered in our radiative models. On a single evolutionary track we identify two double-mode domains with two different mechanisms resposible for double-mode behaviour. The non-resonant double-mode domain separates first overtone and fundamental mode pulsation domains. The resonant double-mode domain appears in the middle of the first overtone pulsation domain. Its origin can be traced to the 2omega_1=omega_0+omega_2 parametric resonance, which destabilizes the first overtone limit cycle.Comment: 13 pages, 12 figures, accepted for publication in MNRA

Discovery of period doubling in BL Herculis stars of the OGLE survey. Observations and theoretical models

We report the discovery of a period doubling behaviour in a 2.4d BL Herculis-type variable of the Galactic bulge. Another bulge BL Her-type star (P=2.25d) is a strong period doubling candidate. Both objects have been identified with the OGLE-III photometry. Possibility of period doubling in this type of pulsators has been predicted almost twenty years ago by Buchler & Moskalik. Our finding is the first observational confirmation of their theoretical results. Discovery of the first BL Herculis star showing the period doubling effect motivates a new theoretical investigation with the state-of-the-art convective pulsation codes. We present the results of initial model survey, specifically aimed at studying the observed period-doubled BL Her variable. All of our non-linear models have P=2.4d. The computations confirm that the period doubling effect is caused by the 3:2 resonance between the fundamental mode and the first overtone, as indicated by earlier radiative models of Buchler & Moskalik. Comparison of the computed and the observed light curves allows to constrain the parameters of the star, in particular its metallicity, which appears to be high, Z is approximately 0.01. The recent evolutionary tracks put also constraint on the mass of the star, which is close to M=0.50 solar masses.Comment: 18 pages, 18 figures, accepted for publication in MNRA

Introduction: building the history of language learning and teaching (HoLLT)

The papers presented in this issue are the result of a workshop held at the University of Nottingham in December 2012 as part of an Arts and Humanities Research Council research network Towards a History of Modern Foreign Language Teaching and Learning (2012–14) intended to stimulate historical research into language teaching and learning. This, the first workshop in the programme, focused on exchanging information on the history of language learning and teaching (HoLLT) across the different language traditions, for it had become clear to us that scholars working within their own language disciplines were often relatively unaware of work outside these. We hope that this special issue — with overview articles on the history of English, French, German, and Spanish as second/foreign languages — will help overcome that lack of awareness and facilitate further research collaboration. Charting the history of language teaching and learning will, in turn, make us all better informed in facing challenges and changes to policy and practice now and in the future. It is instructive in the current climate, for example, to realize that grave doubts were held about whether second foreign languages could survive alongside French in British schools in the early twentieth century (McLelland, forthcoming), or to look back at earlier attempts to establish foreign languages in primary schools (Bayley, 1989; Burstall et al., 1974; Hoy, 1977). As we write, language learning in England is undergoing yet more radical change. Language teaching for all children from the age of seven is being made compulsory in primary schools from 2014, while at Key Stage 3 (up to age 16), where a foreign language has not been compulsory since 2002, the most recent programme of study for England has virtually abandoned the recent focus on intercultural competence and now requires learners to ‘read great literature in the original language’,1 a radical change in emphasis compared to the previous half-century, which seems to reflect a very different view of what language learning is for. We seem to be little closer in 2014 than we were at the dawn of the twentieth century to answering with any certainty the questions that lie at the very foundations of language teaching: who should learn a foreign language, why learners learn, what they need to learn, and what we want to teach them — answers that we need before we can consider how we want to teach. The research programme begun under our research network is intended to help us to take ‘the long view’ on such questions