Pawel Moskalik

Toward a resolution of the bump and beat Cepheid mass discrepancies

The extant beat and bump Cepheid mass discrepancy problems are reexamined with the new opacities of Iglesias and Rogers. Compared to calculations with the Los Alamos opacities, the period ratios P 1 /P 0 and P 2 /P 0 (1) are strongly reduced for any fixed stellar parameters (L, M, T eff , X, Z) and (2) exhibit a novel, large sensitivity to luminosity and to metallicity. For the beat Cepheids the P 1 /P 0 period ratios now yield masses between 4 and 7 M ⊙ , in agreement with the other mass determinations

Metal Abundances, Radial Velocities, and Other Physical Characteristics for the RR Lyrae Stars in The Kepler Field

Spectroscopic iron-to-hydrogen ratios, radial velocities, atmospheric parameters, and new photometric analyses are presented for 41 RR Lyrae stars (and one probable high-amplitude δ Sct star) located in the field-of-view of the Kepler space telescope. Thirty-seven of the RR Lyrae stars are fundamental-mode pulsators (i.e., RRab stars) of which sixteen exhibit the Blazhko effect. Four of the stars are multiperiodic RRc pulsators oscillating primarily in the first-overtone mode. Spectroscopic [Fe/H] values for the 34 stars for which we were able to derive estimates range from –2.54 ± 0.13 (NR Lyr) to –0.05 ± 0.13 dex (V784 Cyg), and for the 19 Kepler-field non-Blazhko stars studied by Nemec et al. the abundances agree will with their photometric [Fe/H] values. Four non-Blazhko RR Lyrae stars that they identified as metal-rich (KIC 6100702, V2470 Cyg, V782 Cyg and V784 Cyg) are confirmed as such, and four additional stars (V839 Cyg, KIC 5520878, KIC 8832417, KIC 3868420) are also shown here to be metal-rich. Five of the non-Blazhko RRab stars are found to be more metal-rich than [Fe/H] ~–0.9 dex while all of the 16 Blazhko stars are more metal-poor than this value. New P-O_(31)^s-[Fe/H] relationships are derived based on ~970 days of quasi-continuous high-precision Q0-Q11 long- and short-cadence Kepler photometry. With the exception of some Blazhko stars, the spectroscopic and photometric [Fe/H] values are in good agreement. Several stars with unique photometric characteristics are identified, including a Blazhko variable with the smallest known amplitude and frequency modulations (V838 Cyg).

A survey of bump Cepheid model pulsations

The periodical nonlinear behavior of a number of sequences of radiative Cepheid models is computed and Fourier analyzed. The Fourier phases and amplitudes exhibit systematic and characteristic variations when plotted as a function of the period ratio P2/P0, but not as a function of the period or the effective temperature. The dominant role played by the 2:1 resonance between the fundamental mode and the second overtone is clearly established. The astrophysical consequences of the observed tightness of the Fourier phase phi(21) versus period relation are thoroughly discussed. It is demonstrated that the dispersion of phi(21) can be used to estimate the width of the instability strip, independently of the Cepheid temperature and luminosity calibrations. Comparison of such an estimation with the traditional determination of that width provides a new test for pulsation and evolution theories. 57 refs.

Pulsational study of BL Herculis models. I - Radial velocities

The linear and nonlinear pulsational behavior of nine sequences of BL Herculis models is studied, and their radial velocity curves are discussed in detail. The pulsations of these stars, in analogy to the classical Cepheids, are strongly affected by internal resonances, most importantly the 2:1 resonance with the second overtone. This latter coupling causes a characteristic systematic progression of the Fourier phases and amplitude ratios as the period ratio P 2 /P 0 is varied

Pulsational study of BL Herculis models. II: Light curves

A survey of the nonlinear pulsational properties of nine sequences of low-luminosity Population II Cepheids has been made. The resulting light curves are discussed and confronted with the observational data. Despite the fact that the 2:1 resonance with the second overtone dominates the dynamical behavior of the models, the Fourier phase Φ 21 , exhibits a monotone, nearly featureless progression as the period ratio P 2 /P 0 is varied. This progression is very different from the one displayed by the radial velocity curves. It is also dramatically different from the Φ 21 progression found in the classical Cepheid models. On the other hand, it is in a qualitative argreement with the observed behavior of the BL Her stars

Periodic stellar pulsations : stability analysis and amplitude equations

The stability properties of nonlinear periodic stellar pulsations are studied within the amplitude equation formalism. Both nonresonant and resonant pulsations are considered. A comparison to a sequence of classical Cepheid models shows that the formalism provides a good qualitative and quantitative description of the behavior of the Floquet coefficients and that it also captures the most important features of the Floquet eigenvectors. It thus helps shed new light on the behaviour (bifurcations) of pulsating stars. In addition, the predictive powers of the analytical approach allow a systematic search for models with specific pulsational properties

The effects of 3:1 resonances in stellar pulsations

The effects of a 3:1 resonance are studied and compared to those of a 2:1 resonance. When the growth rate of the higher frequency mode is negative it is shown that a 3:1 resonance affects the pulsation in a very similar fashion to a 2:1 resonance. In fact, it may be very difficult to discriminate in observational data between these two types of coupling. On the other hand, when the higher frequency mode is linearly unstable a 3:1 resonance, contrary to a 2:1 case, is unable to saturate the instability in the absence of nonresonant coupling terms. Astrophysical applications are discussed. 19 refs.

RR Lyrae Studies with Kepler: showcasing RR Lyr

Four years into the Kepler mission, an updated review on the results for RR Lyrae stars is in order. More than 50 RR Lyrae stars in the Kepler field are observed with Kepler and each one of them can provide us with new insight into this class of pulsating stars. Ground-based spectroscopy of the Kepler targets allows us to narrow down their physical parameters. Previously, we already reported a 50% occurrence rate of modulation in the RRab stars, a large variety of modulation behavior, period doubling in several Blazhko stars, the detection of higher- overtone radial modes, probable non-radial modes and new types of multiple-mode RR Lyrae pulsators, among both the RRab and the RRc stars. In addition, the quasi-continuous photometry obtained over several years with Kepler allows one to observe changes in Blazhko behavior and additional longer cycles. These observations have sparked new theoretical modelling efforts. In this short paper we showcase RR Lyr itself. The star has been observed with Kepler in short cadence, and some remarkable features of its pulsation behavior are unveiled in this long-studied prototype, through the Kepler photometry and additional spectroscopic data.

RESONANCES AND BIFURCATIONS

The nonlinear steady pulsations of two sequences of stellar models are computed. The role of internal resonances in determining the bifurcations (’modal selection’) is exhibited. The need to perform systematic studies of sequences of models is thus stressed. The capability to compute exact periodic attractors (limit cycles) and their Hoquet stability coefficients is essential for the construction of the bifurcation diagrams and for the understanding of the pulsations.

The Importance of 3:1 Resonances in Stellar Pulsations

The 2:1 resonance between the fundamental and the second overtone modes has received a great deal of attention in the context of Cepheids. It was clearly shown that it causes the Hertzsprung bump progression and brings about the very characteristic observed variation of the Fourier phases with period (Buchler & Goupil, 1984, Ap.J., 279 , 394; Klapp, Goupil & Buchler, 1985, Ap.J., 296 , 514; Buchler & Kovacs, 1986, Ap.J., 303 , 749).