Axisymmetric smoothed particle hydrodynamics with self-gravity

The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a Sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ablative implosion of a small capsule). New material concerning the standard SPH formalism is given. That includes the numerical handling of those mass points which move close to the singularity axis, more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self-gravity in the simulations. The algorithm developed to compute gravity does not rely in any sort of grid, leading to a numerical scheme totally compatible with the Lagrangian nature of the SPH equations.     

Artificial viscosity in simulation of shock waves by smoothed particle hydrodynamics

This paper reconsiders artificial viscosity in smoothed particle hydrodynamics in order to prevent interparticle penetration, unwanted heating, and unphysical solutions. The coefficients in the Monaghan’s standard artificial viscosity are considered as a time variable, and we propose a restriction on them such that we avoid the undesired effects in the subsonic regions. We use the shock formation in adiabatic and isothermal cases to study the ability of this modified artificial viscosity recipe. Our computer experiments show that the proposal appears to work and the accuracy of this restriction is acceptable.     

Double-mode stellar pulsation

The current observational and theoretical status of the double-mode variables is reviewed. Focusing mostly on the RR Lyrae stars, we address the question of the observational evidence ofmodal stability. The problem of stationarity is a crucial issue in the modelling of these stars.We mention past efforts in hydrodynamical and analytical modelling together with a detailed discussion of some very recent results. It is suggested that stochastic forcing due to turbulent convection may play a crucial role in exciting some marginally stable modes in the limiting pulsation. The latest hydrodynamical results first demonstrate that purelyradiative models are able to showpermanent double-mode behavior in the relevant period regime of RRd stars. The reason for the previous lack of double-mode behavior is attributed to the large dissipation,i.e. artificial viscosity, generally used in the codes to ensure numerical stability and to obtain amplitudes comparable to the observed ones.We think that better models should include some physical dissipation, most probably turbulent convection, and a more accurate numerical treatment of the radiative hydrodynamics.     

On the effect of turbulent anisotropy on pulsation stability of stars

Within the framework of a non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order(radial order n_r 5) p modes.The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most high-order(n r 5) p modes of all low-temperature stars become unstable. Fortunately,within a wide range of the anisotropic parameter c_3, stellar pulsation stability is not sensitive to the specific value of c_3. Therefore it is safe to say that calibration errors of the convective parameter c_3 do not cause any uncertainty in the calculation of stellar pulsation stability.     

恒星的非径向脉动和模式证认

介绍了恒星非径向脉动的一般特性和可观测特征．着重评述早型恒星非径向脉动研究的最新进展以及非径向脉动模式证认的各种方法．     

The rapidly oscillating Ap star HD 99563 and its distorted dipole pulsation mode

We undertook a time-series photometric multisite campaign for the rapidly oscillating Ap (roAp) star HD 99563 and also acquired mean light observations over four seasons. The pulsations of the star, which show flatter light maxima than minima, can be described with a frequency quintuplet centred on 1557.653 μHz and some first harmonics of it. The amplitude of the pulsation is modulated with the rotation period of the star that we determine with 2.91179 ± 0.00007 d from the analysis of the stellar pulsation spectrum and of the mean light data. We break up the distorted oscillation mode into its pure spherical harmonic components and find it is dominated by the ℓ= 1 pulsation, and also has a notable ℓ= 3 contribution, with weak ℓ= 0 and 2 components. The geometrical configuration of the star allows us to see both pulsation poles for about the same amount of time; HD 99563 is only the fourth roAp star for which both pulsation poles are seen and only the third where the distortion of the pulsation modes has been modelled. We point out that HD 99563 is very similar to the well-studied roAp star HR 3831. Finally, we note that the visual companion of HD 99563 is located in the δ Scuti instability strip and may thus show pulsation. We show that if the companion was physical, the roAp star would be a 2.03-M_⊙, object, seen at a rotational inclination of 44°, which then predicts a magnetic obliquity     .     

Patterns of aperiodic pulsation

Techniques for deriving amplitude equations for stellar pulsation are outlined. For the simplest such equations with multiple instabilities, the derivation of a map for the patterns of pulsation phases is described. This map gives the time between two successive maxima of pulsation in terms of the time between the previous pair, under suitable conditions. The phase differences can be regular, chaotic or hyperchaotic.     

The semi-detached binary system IU Per and its intrinsic oscillation

We present a long-term time-resolved photometry of the short-period eclipsing binary IU Per. It confirms the intrinsic δ Scuti-like pulsation of the system reported by Kim et al.. With the obtained data, an orbital period study and an eclipsing light curve synthesis based on the Wilson-Devinney method were carried out. The photometric so- lution reveals a semi-detached configuration with the less-massive component filling its own Roche-lobe. By subtracting the eclipsing light changes from the data, we obtained the pure pulsating light curve of the mass-accreting primary component. A Fourier anal- ysis reveals four pulsation modes with confidence larger than 99%. A mode identification based on the results of the photometric solution was made. It suggests that the star may be in radial pulsation with a fundamental period of about 0.0628 d. A brief discussion concerning the evolutionary status and the pulsation nature is finally given.     

Bifurcation in hydrodynamic models of stellar pulsation

Phenomena of bifurcation in hydrodynamic stellar models of radial pulsation are reviewed. By changing control parameters of models, we can see qualitatively different pulsation behaviors in hydrodynamic models with transitions due to various types of bifurcation.In weakly dissipative models (classical Cepheids), the bifurcation is induced by modal resonances. Two types of the modal resonances found in models are discussed: The higherharmonic resonances of the second overtone mode in the fundamental mode pulsator and of the fourth overtone mode in the first overtone pulsator are relevant to observations. The subharmonic resonance between the fundamental and first overtone modes is confirmed in classical Cepheid models.In strongly dissipative models (less-massive supergiant stars), the bifurcation of nonlinear pulsation is induced by the hydrodynamics of ionization zones as well as modal resonances. The sequence of the bifurcation sometimes leads to chaotic behaviors in nonlinear pulsation. The transition routes from regular to the chaotic pulsations found in models are discussed with respect to the theory of chaos in simple dynamical systems: The cascade of period-doubling bifurcation is confirmed to cause chaotic pulsation in W Virginis models. For models of higher luminosity, the tangent bifurcation is found to lead intermittent chaos.Finally, hydrodynamic models for chaotic pulsation with small amplitudes observed in the post-AGB stars are briefly discussed.     

Nonlinear,nonradial pulsation in rapidly oscillating Ap stars

The rapidly oscillating Ap stars pulsate in high-overtone, low degreep-modes with their pulsation axes aligned with their oblique magnetic axes. They show non-linearity in their pulsation in three ways:

1. The harmonics of the basic pulsation frequency are detectable.
2. The pulsation phase seems to vary stochastically on a time scale of days to years depending on the star.
3. The form of the nonradial surface distortion is not constant with time.

These three effects are illustrated with HR 3831, the best studied of the roAp stars. HR 3831 pulsates in distorted dipole mode which can be modelled as a linear sum of axisymmetricl = 0, 1, 2, and 3 spherical harmonics aligned with the magnetic axis. This gives rise to a 7-frequency multiplet split by exactly the rotation frequency. The form of the distortion shows small changes on a time-scale of years. HR 3831 shows a 5-frequency rotationally split first harmonic multiplet, a 3-frequency rotationally split second harmonic multiplet, and a single third harmonic frequency has probably been detected at an amplitude of 0.065 mmag. The first harmonic has changed its form significantly over the last 10 years. A technique for decomposing the fundamental frequency septuplet into its component spherical harmonics is used to fit the pulsation phase as a function of rotation phase. This allows a unique O-C to be defined for any length of light curve. The long term behaviour of the O-C diagram cannot be modelled adequately with a combination of periodic (Doppler shift) and quadratic (evolution) terms; there seems to be a significant stochastic component. The direction of the pulsation phase reversal at rotational phase 0.747 is indeterminate; sometimes it is a positive-going reversal, sometimes negative-going. At present it is not known whether this is a numerical artifact, or a physical effect in the star. If it is a physical effect, it means that small non-periodic differences in pulsation amplitude between the bipolar hemispheres have been detected.     

中等质量富金属AGB长周期变星的振动研究

本文采用恒星演化计算与恒星振动计算相结合的方法，对中等质量富金属恒星演化到渐近巨星分支时的振动性质进行了分析研究，从理论上得出这类恒星的振动方式是处于一阶谐频振动，而振动的激发则是在氢电离区和氦的二次电离区由多种机制共同作用造成的，同时提出很长周期的ＡＧＢ长周期变星只能是由中等质量恒星演化到ＡＧＢ阶段形成的。我们的理论计算结果还比较支持在ＡＧＢ顶端存在巨大星风物质损失的观点，且这种星风物质损失很可能与恒星振动有关。     

On the diurnal period variation of midlatitude ULF pulsations

Magnetometer studies of the periods of mid-latitude ULF pulsations have produced conflicting results on the variation of the pulsation periods with both latitude and local time. Since the mid-latitude geomagnetic field is not expected to be significantly distorted by the solar wind, the observed diurnal period variations should be determined by changes in the ambient plasma density. We have applied a physically realistic plasmasphere model to the determination of pulsation eigenperiods over a 24-h interval at L=2.3 (appropriate to Wellington, New Zealand). The resulting model pulsation eigenperiods are largest during the day, with minimum and maximum values at 05.00 and 18.00 L.T. respectively. The model predicts a general increase in the eigenperiods during the replenishment of the protonosphere after a period of geomagnetic activity.     

O-bearing Molecules in Carbon-rich Proto-Planetary Objects

We use high-precision multiband photometric data of the first-overtone RR Lyrae star U Comae to investigate the predictive capability of full-amplitude, nonlinear, convective hydrodynamical models. The main outcome of this investigation is that theoretical predictions properly account for the luminosity variations along a full pulsation cycle. Moreover, we find that this approach, because of the strong dependence of this observable and of the pulsation period on stellar parameters, supplies tight constraints on stellar mass, effective temperature, and distance modulus. Pulsational estimates of these parameters appear in good agreement with empirical ones. Finally, a well-defined bump just before the luminosity maximum gave the unique opportunity to calibrate the turbulent convection model adopted for handling the coupling between pulsation and convection.     

Nonlinear models of pulsation and mass loss

We briefly discuss the current status of our radiation-hydrodynamical models of pulsation in various stellar objects and of dust-driven mass loss in LPVs. We emphasize the importance of a future combined modelling of pulsation and mass loss in AGB stars which has to be based on reliable physical and numerical methods.     

The route to chaos during a pulsation event

A time series analysis of a pulsation event in solar radio emission provides an evolution from a regular doubly periodic phase to an irregular behaviour. Applying some techniques developed in the theory of nonlinear dynamic systems to this irregular stage suggests that there exists a low-dimensional attractor. Estimates of the maximum Lyapunov exponent give some evidence to deterministic chaos. The sudden transition from a regular to a chaotic structure is identified as a part of the Ruelle-Takens-Newhouse route to chaos which is typical in nonlinear systems. It is checked whether this pulsation event may be interpreted in terms of known pulsation models. Consequences for models, which are suitable to describe such an evolution, are discussed.     

A hydrodynamic pulsation model under subharmonic resonance

We found a hydrodynamic pulsation model of yellow supergiants under subharmonic resonance. It is confirmed that the feature of pulsation by the resonance is long-lived in the model by performing the hydrodynamical simulation for a long time.     

关于太阳耀斑脉动现象机制的译注

近年来,人们在日冕中发现了许多准周期脉动现象,对脉动机制的研究引起了广泛的关注。本文译注了三类典型的脉动理论机制,并初步讨论了它们之间的联系和区别。这些理论机制有助于研究和解释新的观测事件     

Spatial wavelet analysis of line-profile variations

The technique of wavelet analysis is discussed in the context of line-profile variations in rapidly rotating stars undergoing non-radial pulsation. This technique may be used to determine the harmonic degree l of the pulsation using isolated residual spectra; it is able to handle spectra with relatively low signal-to-noise ratio levels, and is well suited to extracting previously unobtainable information from low-quality, patchy data. A demonstration of the technique is presented using data generated from a spectral synthesis code.     

The Stability of the Light Curve of DL Cassiopeiae Between 1959–1997

A variability survey on the shape of the light curve of the classical Cepheid DL Cas has been performed on the basis of Johnson V photometry data covering about 38 years. The input parameters (mean magnitude, pulsation frequency and period, light curve amplitude, harmonics amplitudes, Fourier type structural parameters) for our study were determined through the Fourier decomposition technique applied to each data set. The analysis of the outcoming time series, using different and complementary methods, seems to indicate the constancy of these parameters within the precision limits of the available data, although the hypothesis of the presence of a low level variability cannot be excluded. The only exception is the pulsation period, which displays a possible increasing trend with a rate of 0.109 ± 0.037 s yr⁻¹. This trend may be, at least partly, an effect of the unequal precision of pulsation period estimated values, corresponding to each considered data set. This revised version was published online in July 2006 with corrections to the Cover Date.     

Adiabatic radial pulsations of a composite stellar model

Small adiabatic radial oscillations of composite models have been investigated. The effect of central condensation ρ_c√ρ on the period of pulsation have also been examined. In has been shown that the second moment of mass concentration characterize the periods of pulsation more effectively than central condensation.