J. Robert Buchler

A rapidly convergent iterative solution of the non-LTE line radiation transfer problem

Abstract An iterative scheme has been developed for the solution of the non-LTE line radiation transfer problem. The method uses an approximate operator that is deliberately chosen to be local so that it can be easily extended to multidimensional geometry. The difference between the formal and approximate solutions is used as a driving term for the iterations. In one-dimensional, semiinfinite and free-standing slabs, the technique is found to be very fast, robust, and applicable to a large class of problems.

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.

Evidence for low-dimensional chaos in semiregular variable stars

We present 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. First, multiperiodicity 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 four-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 six-dimensional space.

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 fourth overtone. For the adopted mass-luminosity relation, the resonance center lies near a period of 42 ± 03 as indicated by the observed radial velocity data rather than near 32 as the light curves suggest.

Radiation hydrodynamics in the fluid frame

Abstract The equations of radiation hydrodynamics are derived in the fluid frame description in arbitary geometry or symmetry, inclusive of terms of order ( v / c ). This is the natural frame for the collision terms and no expansion or approximation is necessary. The equations are valid in all regimes, diffusion as well as streaming. The various energy conservation equations are shown to reduce to the well known Eulerian radiation hydrodynamic equations, provided the distinction is made between the local proper fluid-frame time and the lab frame time.

Neutrino processes in dense matter

Expressions for the source and collision terms of the neutrino transport equation relevant to the neutrino transport supernova model are derived in the framework of the theory of neutral currents. In particular we study the capture and emission of neutrini (and anti-neutrini) by free nucleos, the inelastic scattering by free nucleons, the coherent scattering by nuclei, as well as the corresponding muonic processes.We also derive an analytical formula for the neutrino scatteringrate on electrons, valid for large electron degeneracy.

The Cepheid phase lag revisited

We compute the phase lags between the radial velocity curves and the light curves ΔΦ1 = - 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, in which they lie above, and of course for low pulsation amplitudes, in which 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-ΔΦ1 diagram. We discuss the potential application of this observable as a discriminant for pulsation modes and as a test for ultralow-amplitude (ULA) pulsation.

Period–colour and amplitude–colour relations in classical Cepheid variables – II. The Galactic Cepheid models

In this paper, we construct full amplitude non-linear hydrodynamical models of fundamental mode Galactic Cepheids and analyse the resulting theoretical period-colour (PC) and amplitude-colour (AC) relations at maximum, mean and minimum light. These theoretical relations match the general form of the observed relations well. This agreement is, to some extent, independent of the mass-luminosity (ML) relations used, pulsation code, numerical techniques, details of the input physics and methods to convert theoretical quantities, such as bolometric luminosity and temperature, to observational quantities, such as V-band magnitudes or (V - I) colours. We show that the PC and AC properties of fundamental mode Galactic Cepheids with periods such that log (P) > 0.8 can be explained by a simple application of the Stefan-Boltzmann law and the interaction of the photosphere with the hydrogen ionization front (HIF). We discuss the implications of our results for explaining the behaviour of Galactic Cepheid PC and period-luminosity (PL) relations at mean light.

Mode-switching timescales 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 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 timescale 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 timescale, which is typically of the order of 100 periods for Cepheids and RR Lyrae stars. We discuss some of the observational consequences, in particular the paucity of low-amplitude pulsators at the edges of the instability strip.

Scattering functions for neutrino transport

We derive an expression for the scattering functions for electron-neutrino and electronanti-neutrino Compton scattering in a form suitable for a numerical solution of the neutrino transfer equations. An analytical expression is given for the case of large electron degeneracy. The modification due to possible neutral currents is discussed.