arXiv subjects

Z. Kollath

Publications and source records attributed to Z. Kollath.

11 recordsLinked to original sources

arXiv2018

The Delta Scuti star 38 Eri from the ground and from space

We present and discuss the pulsational characteristics of the Delta Scuti star 38 Eri from photometric data obtained at two widely spaced epochs, partly from the ground (1998) and partly from space (MOST, 2011). We found 18 frequencies resolving the discrepancy among the previously published frequencies. Some of the frequencies appeared with different relative amplitudes at two epochs, however, we carried out investigation for amplitude variability for only the MOST data. Amplitude variability was found for one of three frequencies that satisfy the necessary frequency criteria for linear-combination or resonant-mode coupling. Checking the criteria of beating and resonant-mode coupling we excluded them as possible reason for amplitude variability. The two recently developed methods of rotational-splitting and sequence-search were applied to find regular spacings based only on frequencies. Doublets or incomplete multiplets with l=1, 2 and 3 were found in the rotational splitting search. In the sequence search method we identified four sequences. The averaged spacing, probably a combination of the large separation and the rotational frequency, is 1.724+/-0.092 d-1. Using the spacing and the scaling relation $\barρ= [0.0394, 0.0554]$ gcm$^{-3}$ was derived. The shift of the sequences proved to be the integer multiple of the rotational splitting spacing. Using the precise MOST frequencies and multi-colour photometry in a hybrid way, we identified four modes with l=1, two modes with l=2, two modes with l=3, and two modes as l=0 radial modes.

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arXiv2004

Automated Nonlinear Stellar Pulsation Calculations: Applications to RR Lyrae stars. The Slope of the Fundamental Blue Edge and the First RRd Model Survey

We describe a methodology that allows us to follow the pulsational behavior of an RR Lyrae model consistently and automatically along its evolutionary track throughout the whole instability strip. It is based on the powerful amplitude equation formalism, and resorts to a judicious combination of numerical hydrodynamical simulations, the analytical signal time-series analysis, and amplitude equations. A large-scale survey of the nonlinear pulsations in RR Lyr instability strip is then presented, and the mode selection mechanism is delineated throughout the relevant regions of parameter space. We obtain and examine two regions with hysteresis, where the pulsational state depends on the direction of the evolutionary tracks, namely a region with either fundamental (RRab) or first overtone (RRc) pulsations and a region with either fundamental (RRab) or double-mode (RRd) pulsations. The regions where stable double-mode (DM, or RRd) pulsations occur are very narrow and hard to find in astrophysical parameter (L, M, T_eff, X, Z) space with hydrodynamic simulations, but our systematic and efficient methodology allows us to investigate them with unprecedented detail. It is shown that by simultaneously considering the effects of mode selection and of horizontal branch evolution we can naturally solve one of the extant puzzles involving the topologies of the theoretical and observed instability strips, namely the slope of the fundamental blue edge. The importance of the interplay between mode selection and stellar evolutionary effects is also demonstrated for the properties of double-mode RR Lyr. Finally, the Petersen diagram of double-mode RR Lyr models is discussed for the first time.

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arXiv2001

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.

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arXiv2001

Cepheid Mass-Luminosity Relations from the Magellanic Clouds

The OGLE data base is used in conjunction with Kurucz atmosphere models to generate sets of period, effective temperature and luminosity for fundamental and overtone Magellanic Cloud Cepheids. The Florida pulsation code (with linear turbulent convection) is then used to compute masses for these stars, assuming an average composition of ($X$=0.716, $Z$=0.010) for the LMC and of ($X$=0.726, $Z$=0.004) for the SMC. The average $M$--$L$ relation for the fundamental Cepheids matches closely that for the first overtone Cepheids for each Magellanic Cloud. Neither the SMC nor the LMC average $\Log M$--$\Log L$ relations are straight, but have a noticeable curvature. In view of the uncertainties in distance and reddening we have adopted three different choices for these quantities. The results based on the 'long' distance scale to the clouds give a better agreement between theory and and observations than the 'short' one. All the current evolutionary tracks predict systematically larger masses for given luminosities than our observationally derived ones, especially at the high end. Moreover, our study confirms that the evolutionary tracks of the low mass stars in SMC are not in agreement with the observations as they do not extend sufficiently blueward and do not penetrate deep enough into the instability strip, or not at all. The inference of masses directly from the observational database yields a novel and strong constraint on evolutionary calculations.

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arXiv1998

Nonlinear Beat Cepheid Models

The numerical hydrodynamic modelling of beat Cepheid behavior has been a longstanding quest in which purely radiative models have failed miserably. We find that beat pulsations occur naturally when turbulent convection is accounted for in our hydrodynamics codes. The development of a relaxation code and of a Floquet stability analysis greatly facilitates the search for and 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. Here a discriminant D arises whose sign decides whether single mode or double mode pulsations can occur in a model, and this D depends only on the values of the nonlinear coupling coefficients between the fundamental and the first overtone modes. For radiative models D is always found to be negative, but with sufficiently strong turbulent convection its sign reverses.

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arXiv1998

Turbulent Convective Cepheid Models: Linear Properties

A one-dimensional turbulent convection model in the form of a time-dependent diffusion equation for the turbulent energy is incorporated into our numerical pulsation code. The effect of turbulent convection on the structural rearrangement of the static equilibrium star is taken into account, and the linear eigenvalues (periods and growth-rates) for the complete turbulent convective nonadiabatic pulsations of the equilibrium models are calculated. The linearized code allows us to perform efficiently a systematic survey of the stability of Cepheid models for a wide range of astrophysical parameters (L, M, Teff) and the turbulent convective parameters. A sensitivity analysis of the properties of several sequences of Galactic Cepheids is performed with the goal of using observational constraints, such as the shape and location of the fundamental and first overtone instability strips, to calibrate the turbulent convective input parameters. The locations of the red and blue edges of the fundamental and first overtone instability strips and the overall strip widths are largely determined by the parameters that determine the mixing length, and strengths of the eddy viscosity and of the convective flux. The remaining parameters can be used for fine-tuning agreement with observations.

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arXiv1997

The Nature of Strange Modes in Classical Variable Stars

Strange modes have been found in the radial spectrum of many luminous stars, most recently in Cepheids and RR Lyrae. We show that there is nothing strange about these modes -- they must exist even in the adiabatic limit. With a change of variables and without approximation the adiabatic linear pulsation equation is reduced to a Schroedinger equation in which the radial coordinate is the local sound-traversal time. In this formulation, the narrow hydrogen partial ionization region is seen to act as a potential barrier, separating the star into two regions. Resonances between the two regions result in the strange modes, for which the ratio of interior to exterior amplitude is at a minimum. The relative location of the barrier changes with the stellar parameters, and this gives rise to avoided level-crossings along a sequence of models. 2 The appearance of strange modes and the associated level crossings are exhibited with an analytic toy-model with the potential barrier approximated by a delta function. This toy-model is readily extensible to nonadiabatic modes. Hydrodynamical calculations find that pure strange mode limit-cycles have extremely small photospheric velocities and luminosity variations in the milli-magnitude range. They are therefore expected to be difficult to observe.

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arXiv1997

A ~ 14 Days Star with Two Phase-Locked Modes of Pulsation in the Eros Database

Using CCD photometry obtained by the EROS collaboration in 1991-1993, we have discovered an LMC variable star with a light curve that is oscillating with a mean period of $\sim 14$ days and an amplitude of $\sim$ 0.3 mag. The oscillations appear with irregular amplitude variations. The Fourier spectrum shows that the pulsation of this star is phase locked between two modes of frequencies $f_0$ and 1.5$\times f_0$. Moreover, this object has strong $H α$ and $H β$ emission lines and neutral lines of Helium that suggest a spectral type between late O and early B. In a preliminary analysis, we derive a luminosity of $ L=3.4-3.8L_\odot$ and an effective temperature in the range $\log(T_{eff}) =3.85-4.2$.

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arXiv1997

Modelling the Phase-Locked Pulsations of a P=14d EROS Star

The Fourier spectral analysis of this object suggests a nonlinear pulsation of period approximately 14d with a 3:2 frequency lock between two vibrational modes. We discuss an extensive search that we have performed in the L, M, Teff space for models of period 14 - 16 days that exhibit this particular resonance. We find models satisfying the resonance constraints both in the Cepheid and in the post AGB regimes. The nonlinear pulsations of several candidates are presented. The nature of the star remains a mystery as none of the models satisfies all the observational constraints.

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arXiv1997

Nonlinear Analysis of the Lightcurve of the Variable Star R Scuti

It is first shown that the observational light curve data of R Scuti, a star of the RV Tau type, is not multi-periodic, and that it cannot have been generated by a linear stochastic (AR) process. By default, the signal must be a manifestation of deterministic chaos. We use a novel nonlinear time-series analysis, the global flow reconstruction technique, to probe the properties of the irregular pulsation cycles. We show in particular that the chaotic dynamics of this star's complicated lightcurve is captured by a simple 4D polynomial map or flow (4 first order ODEs). Importantly also, the method allows us to quantify an irregular signal which has the potential benefit for extracting novel stellar constraints from an irregular light-curve. Finally, from the low dimensionality 4 of the flow we can infer a simple physical picture of the pulsations, and arguments are presented that the pulsations of R Sct are the result of the nonlinear interaction of two vibrational normal modes of the star.

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arXiv1997

Analysis of the Irregular Pulsations of AC Her

The AAVSO lightcurve data of the irregularly pulsating star AC Herculis of the RV Tau class are analysed. The lightcurve is shown to be incompatible with a periodic, or even multiperiodic pulsation, even if allowance is made for evolution. Instead the best explanation is that the irregularly alternating cycles are a manifestation of low dimensional chaos. The lightcurve is found to be generated by a 3 or 4 dimensional dynamics -- 3 or 4 first order ODEs. The (Lyapunov) fractal dimension of the underlying dynamic attractor is computed to be d_L ~ 2.2, smaller than the value of d_L ~ 3.1 found for R Sct.

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