On multifractality and synchronization of nonlinear stellar pulsators

Simple models of nonlinear stellar pulsation, whose temporal behavior may reproduce some of the observed features of different classes of variable stars, have been studied. The temporal behavior of dynamical variables of these models exhibits a cascade of period doubling chaos, depending on the specific values of the various control parameters. A multifractal detrended fluctuation analysis (MFDFA) method is further used to identify the scaling behavior of such synthetic time series. The MFDFA of the considered time series, for various models of nonlinear stellar pulsation, shows that the observed multifractal nature is due to long-range correlations. The pulsating star with increased nonadiabaticity and the star with increased convective luminosity, as represented by the simulated data, is shown to possess a strange attractor with noninteger correlation dimension that lies between 2–3. Also the problem of synchronization in coupled nonlinear pulsation models has been investigated using permutation entropy—a complexity measure of the system. The computed order parameter, Γ, representing the correlation of computed permutation entropy for different segments of the simulated time series of displacement of two nonidentical oscillators, has been further used to find the critical coupling parameter for general synchronization of the oscillators.     

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.     

Dynamo action in the presence of an imposed magnetic field

Dynamo action within the cores of Ap stars may offer intriguing possibilities for understanding the persistent magnetic fields observed on the surfaces of these stars. Deep within the cores of Ap stars, the coupling of convection with rotation likely yields magnetic dynamo action, generating strong magnetic fields. However, the surface fields of the magnetic Ap stars are generally thought to be of primordial origin. Recent numerical models suggest that a primordial field in the radiative envelope may possess a highly twisted toroidal shape. We have used detailed 3-D simulations to study the interaction of such a twisted magnetic field in the radiative envelope with the core-dynamo operating in the interior of a 2 solar mass A-type star. The resulting dynamo action is much more vigorous than in the absence of such a fossil field, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as the growth of large-scale magnetic structure that results from imposing a fossil magnetic field. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Maunder convection mode on the Sun and long solar activity minima

A model of velocity field oscillations in the solar convective zone is suggested. The system of convective equations is investigated for a thin rotating spherical envelope when the rotation velocity is depended on the coordinates. It is shown that two different structures of convective cells (longitudinal, or latitudinal) can exist in the envelope depending on gradients values of the rotation velocity and Prandtl number. It is supposed that two different regimes of convection (stationary and autofluctuating) are possible in the envelope when the angular velocity gradients are determined by the convection itself. In the case of autofluctuating regime the alternation of longitudinal and latitudinal structure of convection is realized. If one assumes that on the Sun there exists an autooscillating convection regime, then the periods of the existence of latitudinal convection structure may be associated with long periods of activity minima since according to Cowling's theorem, the action of the axisymmetric magnetic field generation mechanism is impossible under conditions of axisymmetric velocity structures.     

Effect of partial mixing of matter on the hydrodynamic angular momentum transport processes in massive main-sequence stars

We consider the evolution of a rotating star with a mass of 16M _⊙ and an angular momentum of 3.25 × 10⁵² g cm² s^?1, along with the hydrodynamic transport of angular momentum and chemical elements in its interiors. When the partial mixing of matter of the turbulent radiative envelope and the convective core is taken into account, the efficiency of the angular momentum transport by meridional circulation in the stellar interiors and the duration of the hydrogen burning phase increase. Depending on the Schmidt number in the turbulent radiative stellar envelope, the ratio of the equatorial rotational velocity to the circular one increases with time in the process of stellar evolution and can become typical of early-type Be stars during an additional evolution time of the star on the main sequence. Partial mixing of matter is a necessary condition under which the hydrodynamic transport processes can increase the angular momentum of the outer stellar layer to an extent that the equatorial rotational velocity begins to increase during the second half of the evolutionary phase of the star on the main sequence, as shown by observations of the brightest stars in open star clusters with ages of 10–25 Myr. When the turbulent Schmidt number is 0.4, the equatorial rotational velocity of the star increases during the second half of the hydrogen burning phase in the convective core from 330 to 450 km s^?1.     

Ultraviolet light curves of V535 Arae

Observations of V535 Ara obtained with IUE define the light curve of this long-period W UMa binary in the ultraviolet and let us estimate its gravity darkening. This star was chosen as a contact binary near the high-T _eff limit for convection. The ultraviolet colours and spectral type correspond to (B–V)₀=0.24, or A8V, and imply the star should have very little residual convection in its envelope. The gravity darkening thus ought to be large, as in a radiative star, unless it is modified by circulation in the common envelope, or unless all stars this warm are convective. The light-curve analysis is complicated by a long-term wave that depresses the orbital phases before and after secondary eclipse. We have obtained four solutions to a combination of optical and ultraviolet light curves, two for high, radiative gravity darkening and two for low, convective gravity darkening. For each value of the gravity-darkening exponent, we let the larger, more massive binary component either (a) have a dark spot in its back side or (b) have an excessively hot side facing its companion. The light curves were fitted equally well in all four cases; however, in all but the one with low-gravity darkening and a hot inner face there was a rather large global temperature difference between the two stars. The primary component of this system appears to be significantly undermassive for its spectral type, more so than the primary in AW UMa, but this probably results simply from systematic errors in a radial-velocity solution by Schöffel. It is suggested that the W UMa binaries are found only at spectral types later than about A8 because their outer envelopes must be convective to transfer luminosity.     

On the interaction between differential rotation and magnetic fields in the Sun

We have performed 3-D numerical simulations of compressible convection under the influence of rotation and magnetic fields in spherical shells. They aim at understanding the subtle coupling between convection, rotation and magnetic fields in the solar convection zone. We show that as the magnetic Reynolds number is increased in the simulations, the magnetic energy saturates via nonlinear dynamo action, to a value smaller but comparable to the kinetic energy contained in the shell, leading to increasingly strong Maxwell stresses that tend to weaken the differential rotation driven by the convection. These simulations also indicate that the mean toroidal and poloidal magnetic fields are small compared to their fluctuating counterparts, most of the magnetic energy being contained in the non-axisymmetric fields. The intermittent nature of the magnetic fields generated by such a turbulent convective dynamo confirms that in the Sun the large-scale ordered dynamo responsible for the 22-year cycle of activity can hardly be located in the solar convective envelope.     

Discrete cellular scales of solar convection

The theoretical power spectrum of velocity fields and flux fluctuations at the solar photosphere is calculated using a quasi-nonlinear framework of superposition of unstable convective eigenmodes excited in the solar convection zone. It is demonstrated that this power spectrum exhibits at least three distinct peaks corresponding to granulation, mesogranulation and supergranulation. The vertical velocity and the brightness fluctuation at the solar surface are found to be correlated. The theoretical framework can be adopted for application to other types of stars in order to predict the dominant length scales in the power spectrum of convection in these stars.     

A Note on the Mixing Length Theory and Massive Star Evolution

1 INTRODUCTIONThe mixing length theory (MLT) for stellar convection originally developed by Vitense(1953, 1958) has been the most popularly used local convection theory in the studies of stellarstructure and evolution. The theory was later modified and revised by many investigators,who suggested some different expressions. In fact, MLT is not a real hydrodynamic theory,rather, it is a simple "ballistic" theory which traces the motion of imaginary convective elements. In reality j stell…     

Seismic study of stellar convective regions: the base of the convective envelope in low-mass stars

The possibility of observing solar-type oscillations on other stars is of great relevance to investigating the uncertain aspects of the internal structure of stars. One of these aspects is the convective overshoot that takes place at the borders of the envelopes of stars of mass similar to, or lower than, the Sun. It affects the temperature stratification, mixing, rotation and magnetic-field generation. Asteroseismology can provide an observational test for the studies of the structure of such overshoot regions.
The seismic study of the transition in the Sun, located at the base of the convection zone, has been successful in determining the characteristics of this layer in the Sun. In this work we consider the extension of the analysis to other solar-type stars (of mass between 0.85 and 1.2 M_⊙) in order to establish a method for determining the characteristics of their convective envelopes. In particular, we hope to be able to establish seismologically that a star does indeed possess a convective envelope, to measure the size of the convective region and also to constrain the properties of an overshoot layer at the bottom of the envelope. The limitations in terms of observational uncertainties and stellar characteristics, and the detectability of an overshoot layer, are discussed.     

Analysis of Near Infrared Observations of the Symbiotic Mira RR Tel

JHKL photometry of the symbiotic Mira RR Tel over 25 years shows variable fading in all bands, which can be explained by variable obscuration due to dust. The evolutionary track of the star is presented in a two-colour diagram together with the corresponding mean values for normal Miras with thick and thin dust shells and pulsation periods between 350 and 600 days. The observed colours for RR Tel are significantly shifted from the range shown by normal unreddened Miras. The distance of RR Tel is estimated from its K magnitude and the Mira period luminosity relation after correcting for reddening. The dust envelope is discussed with respect to a simple model involving two blackbodies. There appears to be rather little dust emission even at 3 μm, but considerable extinction.     

The influences of convective overshooting and semiconvection on the chemical evolution of massive stars

In massive stars,convection in the interior is different from that of intermediate and small mass stars. In the main-sequence phase of small mass stars,there is a convective core and a radiative envelope,between which are the radiative intermediate layers with uneven chemical abundances. Semiconvection would occur in the intermediate layers between the convective core and the homogeneous envelope in massive stars. We treat core convective overshooting and semiconvection together as a process. We found that when decreasing overshooting,the semiconvection is more pronounced. In these two processes,we introduce one diffusive parameter D,which is different from other authors who have introduced different parameters for these two zones. The influences of the turbulent diffusion process on chemical evolution and other quantities of the stellar structure are shown in the present paper.     

One zone modeling of irregular variability of stellar convective envelope

One zone modeling of the irregular variability of red super-giants is intended with regard to the nonlinear coupling of finite amplitude pulsation with convection. The nonlocal mixing length is employed for the evaluation of the convective flux, the turbulent pressure and the turbulent power of temperature fluctuations. The radial pulsation and the Boussinesq convection are assumed for simplicity. The one zone is defined as the layer having the entropy maximum and the minimum at the bottom and at the top, respectively. The quasi-adiabatic approximation is consistent with this definition in fixing the zone to the same mass range. The spatial derivatives are evaluated under the assumption of homologous changes with the equilibrium homologous parameters. Then, a set of 6 simultaneous first order nonlinear ordinary differential equations are obtained as the one zone representation of the irregular variability of the convective envelope.     

Numerical simulations of downward convective overshooting in giants

An attempt at understanding downward overshooting in the convective envelopes of post-main-sequence stars has been made on the basis of three-dimensional large-eddy simulations, using artificially modified OPAL opacity and taking into account radiation and ionization in the equation of state. Two types of star, an intermediate-mass star and a massive star, were considered. To avoid a long thermal relaxation time of the intermediate-mass star, we increased the stellar energy flux artificially while trying to maintain a structure close to the one given by a 1D stellar model. A parametric study of the flux factor was performed. For the massive star, no such process was necessary. Numerical results were analysed when the system reached the statistical steady state. It was shown that the penetration distance in pressure scaleheights is of the order of unity. The scaling relations between penetration distance, input flux and vertical velocity fluctuations studied by Singh et al. were checked. The anisotropy of the turbulent convection and the diffusion models of the third-order moments representing the non-local transport were also investigated. These models are dramatically affected by the velocity fields and no universal constant parameters seem to exist. The limitations of the numerical results were also discussed.     

恒星内部的超声速对流区

依传统的局部混合长理论进行了对流包层模型计算,在黄红巨星和超巨星对流区的顶部出现超声速对流的情况,这与局部对流理论本身是不自恰的．文章详细分析了恒星大气超声速对流的成因,并按照星族Ⅰ恒星的演化轨迹,在赫罗图上给出了出现超声速对流的区域．其结果是。在演化过程中, (1)低质量星基本不出现超声速对流; (2)中等质量星的超声速对流主要出现在3．6相似文献   

Differential rotation and meridional circulation in global models of solar convection

In the outer envelope of the Sun and in other stars, differential rotation and meridional circulation are maintained via the redistribution of momentum and energy by convective motions. In order to properly capture such processes in a numerical model, the correct spherical geometry is essential. In this paper I review recent insights into the maintenance of mean flows in the solar interior obtained from high-resolution simulations of solar convection in rotating spherical shells. The Coriolis force induces a Reynolds stress which transports angular momentum equatorward and also yields latitudinal variations in the convective heat flux. Meridional circulations induced by baroclinicity and rotational shear further redistribute angular momentum and alter the mean stratification. This gives rise to a complex nonlinear interplay between turbulent convection, differential rotation, meridional circulation, and the mean specific entropy profile. I will describe how this drama plays out in our simulations as well as in solar and stellar convection zones. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Note on the Supersonic Convection in Stellar Atmospheres

By using a non-local convection theory, both the local and nonlocal convective envelope models of evolutionary series of stars with masses from 1 to 30 solar masses are calculated. The problem of supersonic convection is reviewed. The results show that the convective velocities in the stellar atmosphere are seriously overestimated by the local mixing-length theory. Convection is strongly supersonic in the atmospheres of yellow giant and super-giants, while the local mixing-length theory is used. However, it becomes subsonic for most stars when convection returns to the normal nonlocal treatment. Convection velocities increase with increase of luminosities of stars. There is still weak supersonic convection in few red and yellow giant and super-giants. It is suspected whether this supersonic convection in stellar atmospheres is true.     

The influence of magnetic field and rotation on the onset of convection in the envelopes of neutron stars

The influence of magnetic field and rotation on the occurrence of convective instabilities in the liquid layer of neutron star envelopes has been investigated. The critical wavelength _c , which denotes the boundary between stable and unstable behaviour of convective disturbances, is calculated for a neutron star model as a function of magnetic field and rotation. It is shown that the strength of the magnetic fields of neutron stars strongly suppresses the onset of convection, whereas the limiting effect of rotation acts only if the magnetic field vanishes.     

Time-series spectroscopy of the rapidly oscillating Ap star HR 3831

We present time-series spectroscopy of the rapidly oscillating Ap (roAp) star HR 3831. This star has a dominant pulsation period of 11.7 min and a rotation period of 2.85 d. We have analysed 1400 intermediate-resolution spectra of the wavelength region 6100–7100 Å obtained over one week, using techniques similar to those we applied to another roAp star, α  Cir.
We confirm that the H α velocity amplitude of HR 3831 is modulated with rotation phase. Such a modulation was predicted by the oblique pulsator model, and rules out the spotted pulsator model. However, further analysis of H α and other lines reveals rotational modulations that cannot easily be explained using the oblique pulsator model. In particular, the phase of the pulsation as measured by the width of the H α line varies with height in the line.
The variation of the H α bisector shows a very similar pattern to that observed in α Cir, which we have previously attributed to a radial node in the stellar atmosphere. However, the striking similarities between the two stars, despite the much shorter period of α Cir (6.8 min), argues against this interpretation unless the structure of the atmosphere is somewhat different between the two stars. Alternatively, the bisector variation is a signature of the degree ℓ of the mode and not the overtone value n .
High-resolution studies of the metal lines in roAp stars are needed to understand fully the form of the pulsation in the atmosphere.