arXiv subjects

J. Robert Buchler

Publications and source records attributed to J. Robert Buchler.

At least 19 recordsLinked to original sources

arXiv2011

On the Blazhko Effect in RR Lyrae Stars

The Blazhko effect is a long term, generally irregular modulation of the light curves that occurs in a sizeable number of RR Lyrae stars. The physical origin of the effect has been a puzzle ever since its discovery over a hundred years ago. We build here upon the recent observational and theoretical work of Szabo et al. on RRab stars who found with hydrodynamical simulations that the fundamental pulsation mode can get destabilized by a 9:2 resonant interaction with the 9th overtone. Alternating pulsation cycles arise, although these remain periodic, i.e. not modulated as in the observations. Here we use the amplitude equation formalism to study this nonlinear, resonant interaction between the two modes. We show that not only does the fundamental pulsation mode break up into a period two cycle through the nonlinear, resonant interaction with the overtone, but that the amplitudes are modulated, and that in a broad range of parameters the modulations are irregular as in the observations. This irregular behavior is in fact chaotic and arises from a strange attractor in the dynamics.

astro-ph.SR↗

arXiv2009

Modulations in Multi-Periodic Blue Variables in the LMC

As shown by Mennickent, et al(2003), a subset of the blue variable stars in the Large Magellanic Cloud exhibit brightness variability of small amplitude in the period range 2.4 to 16 days as well as larger amplitude variability with periods of 140 to 600 days, with a remarkably tight relation between the long and the short periods. Our re-examination of these objects has led to the discovery of additional variability. The Fourier spectra of 11 of their 30 objects have 3 or 4 peaks above the noise level and a linear relation of the form f_a = 2(f_b - f_L) among three of the frequencies. An explanation of this relation requires an interplay between the binary motion and that of a third object. The two frequency relations together with the Fourier amplitude ratios pose a challenging modeling problem.

astro-ph.SR↗

arXiv2009

The State of Cepheid Pulsation Theory

We review the current state of Cepheid modeling and discuss its dominant deficiency, namely the use of time dependent mixing length. Notwithstanding, Cepheid modeling has achieved some excellent successes, and we mention some of the most recent ones. Discrepancies between observations and modeling appear not so much in the gross properties of single mode Cepheids, but rather when more subtle nonlinear effects are important, such as in double mode or even triple mode pulsations. Finally we discuss what we consider the most important challenges for the next decade. These are, first, realistic multi dimensional modeling of convection in a pulsating environment, and second, the nonlinear modeling of the nonradial pulsations that have been observed, and, relatedly, of the Blazhko like phenomenon that has recently been observed in Cepheids.

astro-ph.SR↗

arXiv2009

Ultra-low Amplitude Variables in the LMC -- Classical Cepheids, Pop. II Cepheids, RV Tau Stars and Binary Variables

A search for variable stars with ultra-low amplitudes (ULA), in the millimag range, has been made in the combined MACHO and OGLE data bases in the broad vicinity of the Cepheid instability strip in the HR diagram. A total of 25 singly periodic and 4 multiply periodic ULA objects has been uncovered. Our analysis does not allow us to distinguish between pulsational and ellipsoidal (binary) variability, nor between LMC and foreground objects. However, the objects are strongly clustered and appear to be associated with the pulsational instability strips of LMC Pop. I and II variables. When combined with the ULA variables of Buchler et al (2005) a total of 20 objects fall close to the classical Cepheid instability strip. However, they appear to fall on parallel period-magnitude relations that are shifted to slightly higher magnitude which would confer them a different evolutionary status. Low amplitude RV Tauri and Pop. II Cepheids have been uncovered that do not appear in the MACHO or OGLE catalogs. Interestingly, a set of binaries seem to lie on a PM relation that is essentially parallel to that of the RV Tauri/Pop. II Cepheids.

astro-ph.SR↗

arXiv2008

Beat Cepheids as Probes of Stellar and Galactic Metallicity: The New AGS Abundances

It is well known that the mere location of a Beat Cepheid model in a Period Ratio \vs Period diagram (Petersen diagram) puts constraints on its metallicity Z. But these bounds are sensitive to the mixture of elements that are lumped into the parameter $Z$. In this short paper we update the previous results that were based on the Grevesse-Noels solar mixture to the recent, revised Asplund, Grevesse & Sauval (2005) (AGS) solar mixture. We also examine the effect of the envelope depth on the accuracy of the computed pulsation periods. We find that for low period Cepheids with high Z the customary approximation of envelope pulsation breaks down. It is necessary to compute stellar models that extend to the center and to include burning and composition inhomogeneities in the modeling. Fortunately, however, most Beat Cepheids that have been observed so far seem to avoid that regime.

astro-ph↗

arXiv2007

The Cepheid Phase Lag Revisited

We compute the phase lags between the radial velocity curves and the light curves $ΔΦ_1= ϕ^{V_r}_1 - ϕ^{mag}_1$ for classical Cepheid model sequences both in the linear and the nonlinear regimes. The nonlinear phase lags generally fall below the linear ones except for high period models where they lie above, and of course for low pulsation amplitudes where the two merge. The calculated phase lags show good agreement with the available observational data of normal amplitude Galactic Cepheids. The metallicity has but a moderate effect on the phase lag, while the mass-luminosity relation and the parameters of the turbulent convective model (time-dependent mixing length) mainly influence the modal selection and the period, which is then reflected in the period -- $ΔΦ_1$ diagram. We discuss the potential application of this observable as a discriminant for pulsation modes and as a test for ultra-low amplitudes (ULA) pulsation.

astro-ph↗

arXiv2007

Beat Cepheids as Probes of Stellar and Galactic Metallicity

The mere location of a Beat Cepheid model in a Period Ratio vs. Period diagram (Petersen diagram) puts very tight constraints on its metallicity Z. The Beat Cepheid Peterson diagrams are revisited with linear nonadiabatic turbulent convective models, and their accuracy as a probe for stellar metallicity is evaluated. They are shown to be largely independent of the helium content Y, and they are also only weakly dependent on the mass-luminosity relation that is used in their construction. However, they are found to show sensitivity to the relative abundances of the elements that are lumped into the metallicity parameter Z. Rotation is estimated to have but a small effect on the 'pulsation metallicities'. A composite Petersen diagram is presented that allows one to read off upper and lower limits on the metallicity Z from the measured period P0 and period ratio P1/P0.

astro-ph↗

arXiv2006

Detection of Beat Cepheids in M33 and Their Use as a Probe of the M33 Metallicity Distribution

Our analysis of the Deep CFHT M33 variability survey database has uncovered 5 Beat Cepheids (BCs) that are pulsating in the fundamental and first overtone modes. With {\it only} the help of stellar pulsation theory and of mass--luminosity (M-L) relations, derived from evolutionary tracks, we can accurately determine the metallicities Z of these stars. The [O/H] metallicity gradient of -0.16 dex/kpc that is inferred from the M33 galacto-centric distances of these Cepheids and from their 'pulsation' metallicities is in excellent agreement with the standard spectroscopic metallicity gradients that are determined from H II regions, early B supergiant stars and planetary nebulae. Beat Cepheids can thus provide an additional, independent probe of galactic metallicity distributions.

astro-ph↗

arXiv2005

Ultra-Low Amplitude Cepheids in the Large Magellanic Cloud

The MACHO variables of LMC Field 77 that lie in the vicinity of the Cepheid instability strip are reexamined. Among the 144 variables that we identify as Cepheids we find 14 that have Fourier amplitudes <0.05 mag in the MACHO red band, of which 7 have an amplitude <0.006 mag : we dub the latter group of stars ultra-low amplitude (ULA) Cepheids. The variability of these objects is verified by a comparison of the MACHO red with the MACHO blue lightcurves and with those of the corresponding OGLE LMC stars. The occurrence of ULA Cepheids is in agreement with theory. We have also discovered 2 low amplitude variables whose periods are about a factor of 5--6 smaller than those of F Cepheids of equal apparent magnitude. We suggest that these objects are Cepheids undergoing pulsations in a surface mode and that they belong to a novel class of Strange Cepheids (or Surface Mode Cepheids) whose existence was predicted by Buchler et al. (1997).

astro-ph↗

arXiv2004

Evidence for Low-Dimensional Chaos in Semiregular Variable Stars

An analysis of the photometric observations of the light curves of the five large amplitude, irregularly pulsating stars R UMi, RS Cyg, V CVn, UX Dra and SX Her is presented. First, multi-periodicity is eliminated for these pulsations, i.e. they are not caused by the excitation of a small number of pulsation modes with constant amplitudes. Next, on the basis of energetics we also eliminate stochasticity as a cause, leaving low dimensional chaos as the only alternative. We then use a global flow reconstruction technique in an attempt to extract quantitative information from the light curves, and to uncover common physical features in this class of irregular variable stars that straddle the RV Tau to the Mira variables. Evidence is presented that the pulsational behavior of R UMi, RS Cyg, V CVn and UX Dra takes place in a 4-dimensional dynamical phase space, suggesting that two vibrational modes are involved in the pulsation. A linear stability analysis of the fixed points of the maps further indicates the existence of a two-mode resonance, similar to the one we had uncovered earlier in R Sct: The irregular pulsations are the result of a continual energy exchange between two strongly nonadiabatic modes, a lower frequency pulsation mode and an overtone that are in a close 2:1 resonance. The evidence is particularly convincing for R UMi, RS Cyg and V CVn, but much weaker for UX Dra. In contrast, the pulsations of SX Her appear to be more complex and may require a 6D space.

astro-ph↗

arXiv2004

Magellanic Cloud Cepheids: Pulsational and Evolutionary Modelling vs. Observations

The pulsational properties of the Cepheid models along the evolutionary tracks from the Padova group (Girardi et al.), as calculated with our turbulent convective pulsation code, are in good agreement with the resonance constraints imposed by the observational OGLE-2 data of the Small and Large Magellanic Clouds. Our study suggests that the P_4/P_1=1/2 resonance for the overtone Cepheids occurs for periods clustering around 4.2 d, in disagreement with the suggestion of Antonello & Poretti based on the observations of light curves, but in agreement with Kienzle et al. and Feuchtinger et al. For the fundamental Cepheids the lowest order Fourier decomposition coefficients from the light curves, \viz R_21 and phi_21 can be used to locate the resonance region, but not so for the first overtone Cepheids. Here, the radial velocity curves can be used to locate the overtone resonance region, or in their absence, one needs to resort to numerical hydrodynamic modelling.

astro-ph↗

arXiv2003

Nonlinear Properties of the Semiregular Variable Stars

We demonstrate how, with a purely empirical analysis of the irregular lightcurve data, one can extract a great deal of information about the stellar pulsation mechanism. An application to R Sct thus shows that the irregular lightcurve is the result of the nonlinear interaction of two highly nonadiabatic pulsation modes, namely a linearly unstable, low frequency mode, and the second mode that, although linearly stable, gets entrained through a 2:1 resonance. In the parlance of nonlinear dynamics the pulsation is the result of a 4 dimensional chaotic dynamics.

astro-ph↗

arXiv2002

Mode Switching Time Scales in the Classical Variable Stars

Near the edges of the instability strip the rate of stellar evolution is larger than the growth-rate of the pulsation amplitude, and the same holds whenever the star is engaged in pulsational mode switching. Stellar evolution therefore controls both the onset of pulsation at the edges of the instability strip and of mode switching inside it. Two types of switchings (bifurcations) occur. In a soft bifurcation the switching time scale is the inverse harmonic mean of the pulsational modal growth-rate and of the stellar evolution rate. In a hard bifurcation the switching times can be substantially longer than the thermal time scale which is typically of the order of a hundred periods for Cepheids and RR Lyrae. We discuss some of the observational consequences, in particular the paucity of low amplitude pulsators at the edges of the instability strip.

astro-ph↗

arXiv2001

Du chaos dans la musique des etoiles

La plupart des etoiles variables qui pulsent avec grande amplitude, telles les cepheides, ont un comportement tres regulier et periodique. Mais juste a cote d'elles dans le diagramme Hertzsprung-Russell, se trouve un groupe d'etoiles variables dotees de courbes de lumiere tres irregulieres. A l'aide d'une technique de reconstruction de flot appliquee aux donnees d'observation astronomiques de plusieurs de ces etoiles, on montre que la dynamique sous-jacente est chaotique et de faible dimension, ce qui peut surprendre a cause de la violence de ces pulsations. En plus a l'aide d'une linearisation du flot on deduit que le mecanisme physique de la pulsation consiste en l'interaction entre deux modes vibratoires (vraisemblablement radiaux), l'un lineairement instable, de frequence f_0, et l'autre stable, mais de frequence \~2f_0 (soit un scenario a la Shilnikoff generalise).

nlin.CD↗

arXiv2001

Chaos in the Music of the Spheres

The light curves (time series of the radiated energy) of most large amplitude, pulsating stars such as the well known Cepheid stars are regular. However, a smaller group of variable stars that are located next to them in the Hertzsprung- Russell diagram undergoes irregular light variations and exhibits irregular radial velocities as well. The mechanism behind this irregular behavior was a long standing mystery. A flow reconstruction technique based on the observed lightcurves of six separate stars shows that their underlying dynamics is chaotic and low dimensional (d=4). Furthermore, we present evidence that the physical mechanism behind the behavior is the nonlinear interaction of just two pulsation eigenmodes. In a generalized Shil'nikov scenario, the pulsation energy alternates continuously, but irregularly between a lower frequency mode that is linearly unstable and thus growing, and a stable overtone that gets entrained through a low order resonance (2:1), but that wants to decay. The flow reconstruction from the stellar light curve thus yields interesting physical insight into the pulsation mechanism.

astro-ph↗

arXiv2001

Strange Cepheids and RR Lyrae

Strange modes can occur in radiative classical Cepheids and RR Lyrae models. These are vibrational modes that are trapped near the surface as a result of a 'potential barrier' caused by the sharp hydrogen partial ionization region. Typically the modal number of the strange mode falls between the 7th and 12th overtone, depending on the astrophysical parameters of the equilibrium stellar models (L, M, \Teff, X, Z). Interestingly these modes can be linearly unstable outside the usual instability strip, in which case they should be observable as new kinds of variable stars, 'strange Cepheids' or 'strange RR Lyrae' stars. The present paper reexamines the linear stability properties of the strange modes by taking into account the effects of an isothermal atmosphere, and of turbulent convection. It is found that the linear vibrational instability of the strange modes is resistant to both of these effects. Nonlinear hydrodynamic calculations indicate that the pulsation amplitude of these modes is likely to saturate at the millimagnitude level. These modes should therefore be detectable albeit not without effort.

astro-ph↗

arXiv2000

Hydrodynamical Survey of First Overtone Cepheids

A hydrodynamical survey of the pulsational properties of first overtone Galactic Cepheids is presented. The goal of this study is to reproduce their observed light- and radial velocity curves. The comparison between the models and the observations is made in a quantitative manner on the level of the Fourier coefficients. Purely radiative models fail to reproduce the observed features, but convective models give good agreement. It is found that the sharp features in the Fourier coefficients are indeed caused by the P1/P4 = 2 resonance, despite the very large damping of the 4th overtone. For the adopted mass-luminosity relation the resonance center lies near a period of 4.2d +/- 0.2 as indicated by the observed radial velocity data, rather than near 3.2d as the light-curves suggest.

astro-ph↗

arXiv2000

RR Lyrae - Theory vs Observation

The luminosities, effective temperatures and metallicities that are derived empirically by Kovacs and Jurcsik from the light curves of a large number of globular cluster and field RRab and RRc stars are compared to theoretical RR Lyrae models. The strong luminosity dependence of the empirical blue and red edges (Log L vs Log Teff diagram) is in disagreement with that of both radiative and convective models. A reexamination of the theoretical uncertainties in the modelling leads us to conclude that the disagreement is irreconcilable.

astro-ph↗