Magnetic convection

In this paper the process of magnetic convection is studied. It is shown that outside of a radius of about 2 × 10⁵ km, magnetic fields in the Sun may be buoyant. Outside this limit strong field regions tend to rise at the expense of weak field regions which tend to sink. Magnetic convection may be important in magnetic stars and even in the solar interior. A recent calculation of the angular velocity of the Sun provides a period of rotation for the solar core of from 0.5 to 5 days. This calculation requires that the magnetic field extract angular momentum from the solar interior. Magnetic convection thus seems to be required, if this calculation is correct. Furthermore, magnetic convection may transfer heat and thereby possibly change the internal temperature structure of the Sun from what would be expected solely by radiation transfer.     

Nonradiative activity across the H-R diagram: Which types of stars are solar-like?

Major advances in our understanding of nonradiatively heated outer atmospheric layers (coronae, transition regions, and chromospheres) and other solar-like activity in stars has occurred in the past few years primarily as a result of ultraviolet spectroscopy from IUE, X-ray imaging from the Einstein Observatory, microwave detections by the VLA, and new optical observing techniques. I critically review the observational evidence and comment upon the trends with spectral type, gravity, age, and rotational velocity that are now becoming apparent. I define a solar-like star as one which has a turbulent magnetic field sufficiently strong to control the dynamics and energetics in its outer atmospheric regions. The best indicator of a solar-like star is the direct measurement of a strong, variable magnetic field and such data are now becoming available, but good indirect indicators include photometric variability on a rotational time scale indicating dark starspots and nonthermal microwave emission. X-rays and ultraviolet emission lines produced by plasma hotter than 10⁴ K imply nonradiative heating processes that are likely magnetic in character, except for the hot stars where the heating is likely by shocks in the wind resulting from radiative instabilities. I conclude that dwarf stars of spectral type G-M and rapidly rotating subgiants and giants of spectral type F-K in spectroscopic binary systems are definitely solar-like. Dwarf stars of spectral type A7-F7 are almost certainly solar-like, and T Tauri and other pre-Main-Sequence stars are probably solar-like. Slowly rotating single giants of spectral type F to early K are also probably solar-like, and the helium-strong hottest Bp stars are interesting candidates for being solar-like. The O and B stars exhibit some aspects of activity but probably have weak fields and are not solar-like. Finally, the A dwarfs and the cool giants and supergiants show no evidence of being solar-like.Staff Member, Quantum Physics Division, National Bureau of Standards.     

Asteroseismology: from dream to reality

With the resounding success of helioseismology in determining the interior structure and rotation of the Sun, and in providing unprecedented studies of the interaction of pulsation and magnetic fields in the solar atmosphere, astronomers have been delighted, after decades of disappointing attempts, with the recent discovery of solar-like oscillations in ξ Hya, β Hyi, α Cen A and B, η Boo, ν Ind, ζ Her, δ Eri, HD 20794, HD 160191, and others as this list is growing rapidly. There is now true seismology of some solar-like stars. Asteroseismology also studies stars with a wide variety of interior and surface conditions. For two decades asteroseismic techniques have been applied to many pulsating stars across the HR diagram. This review describes some recent developments for some selected classes of pulsating stars other than the solar-like oscillators.     

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)     

Night‐time science with large solar telescopes: The magnetic Sun through time

Today the Sun has a regular magnetic cycle driven by a dynamo action. But how did this regular cycle develop? How do basic parameters such as rotation rate, age, and differential rotation affect the generation of magnetic fields? Zeeman Doppler imaging (ZDI) is a technique that uses high‐resolution observations in circularly polarised light to map the surface magnetic topology on stars. Utilising the spectropolarimetric capabilities of future large solar telescopes it will be possible to study the evolution and morphology of the magnetic fields on a range of Sun‐like stars from solar twins through to rapidly‐rotating active young Suns and thus study the solar magnetic dynamo through time. In this article I discuss recent results from ZDI of Sun‐like stars and how we can use night‐time observations from future solar telescopes to solve unanswered questions about the origin and evolution of the Sun's magnetic dynamo (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Eddy viscosity and turbulent Schmidt number by kink-type instabilities of toroidal magnetic fields

The potential of the non-axisymmetric magnetic instability to transport angular momentum and to mix chemicals is probed considering the stability of a nearly uniform toroidal field between conducting cylinders with different rotation rates. The fluid between the cylinders is assumed as incompressible and to be of uniform density. With a linear theory, the neutral-stability maps for   m = 1  are computed. Rigid rotation must be sub-Alfvénic to allow instability, while for differential rotation also an unstable domain with faster rotation exists [azimuthal magnetorotational instability (AMRI)]. The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number of the order of unity.
The effective angular momentum transport by the instability is directed outwards for subrotation. The resulting magnetic-induced eddy viscosity exceeds the microscopic values by factors of 10–100. This is only true for AMRI; in the opposite case of Tayler instability, the viscosity results are very small.
The same instability also quenches concentration gradients of chemicals by dynamic fluctuations. The corresponding diffusion coefficient always remains smaller than the magnetic-generated eddy viscosity. A Schmidt number of the order of 30 is found as the ratio of the effective viscosity and the diffusion coefficient. For not too strong magnetic fields in the radiation zone of young solar-type stars, the magnetic instability transports much more angular momentum than that it mixes chemicals.     

Starspots

Starspots are created by local magnetic fields on the surfaces of stars, just as sunspots. Their fields are strong enough to suppress the overturning convective motion and thus block or redirect the flow of energy from the stellar interior outwards to the surface and consequently appear as locally cool and therefore dark regions against an otherwise bright photosphere (Biermann in Astronomische Nachrichten 264:361, 1938; Z Astrophysik 25:135, 1948). As such, starspots are observable tracers of the yet unknown internal dynamo activity and allow a glimpse into the complex internal stellar magnetic field structure. Starspots also enable the precise measurement of stellar rotation which is among the key ingredients for the expected internal magnetic topology. But whether starspots are just blown-up sunspot analogs, we do not know yet. This article is an attempt to review our current knowledge of starspots. A comparison of a white-light image of the Sun (G2V, 5 Gyr) with a Doppler image of a young solar-like star (EK Draconis; G1.5V, age 100 Myr, rotation 10 × Ω _Sun) and with a mean-field dynamo simulation suggests that starspots can be of significantly different appearance and cannot be explained with a scaling of the solar model, even for a star of same mass and effective temperature. Starspots, their surface location and migration pattern, and their link with the stellar dynamo and its internal energy transport, may have far reaching impact also for our understanding of low-mass stellar evolution and formation. Emphasis is given in this review to their importance as activity tracers in particular in the light of more and more precise exoplanet detections around solar-like, and therefore likely spotted, host stars.     

Protodiscs around hot magnetic rotator stars

We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10⁷ K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.     

Rotational evolution of the Sun

The evolutionary behaviour of rotating solar models with different initial angular-momentum distributions has been investigated through the pre-Main-Sequence and Main-Sequence phases. The angular momentum was removed from the convective evelope of the solar models according to the Kawaler's model of magnetic stellar wind (Kawaler, 1988). The models show that (i) the surface rotational velocities of the solar mass stars are independent of initial angular momentum for ages greater than 10⁸ years and (ii) it is not possible to explain the neutrino problem and the sufficient depletion of lithium in the Sun.     

Protostars and the origin of the angular momentum of the solar system

Protostars in a group exert gravitational tidal torques on an aspherical nebula located in the group. The net torque transfers angular momentum from the orbital motions of the stars to rotation of the nebula. A relation can be derived between the parameters describing the protostars and the final angular momentum of the nebula. While the parameters concerned are uncertain, a conservative choice results in a value for the angular momentum equal to about 1/3 of that of the present solar system. This suggests that if the Sun formed in a group, tidal interactions with other protostars may account for a significant part of the angular momentum of the solar system.     

Latitudinal shear instability in the solar tachocline

In an attempt to explain the observed rotation profile in the solar radiative zone and the tachocline, Spiegel & Zahn proposed a model based on anisotropic turbulent angular momentum transport. Although very successful in reproducing some of the features of the solar tachocline, their model assumes without verification that the origin of the turbulence could be caused by latitudinal shear instability. This paper studies the weakly non-linear evolution of two-dimensional shear instability, in which the interaction between the global rotation profile and the Reynolds stresses can be described self-consistently. Provided that the initial rotation profile is sufficiently close to marginal stability (which is the case of the solar tachocline), the instability is shown to saturate and to relax to a marginally stable state, which differs very little from the observed rotation profile. It is therefore likely that the tachocline is in a state of marginal stability with respect to latitudinal shear instability, and shows that angular momentum transport in the tachocline is unlikely to be caused by shear-induced turbulence.     

Planetary waves on the Sun?

Some recent observations of the Sun suggest a class of wave-like motions moving both eastward and westward at a uniform velocity with respect to the mean solar angular velocity. It is suggested that these may be hydromagnetic planetary waves. An estimate of the mean toroidal magnetic field is made, based on a theoretical treatment of such waves already in the literature, and a slight correction to the mean rate of rotation of the Sun is inferred.     

Modelling the time variation of the surface differential rotation in AB Doradus and LQ Hydrae

Sequences of Doppler images of the young, rapidly rotating late-type stars AB Dor and LQ Hya show that their equatorial angular velocity and the amplitude of their surface differential rotation vary versus time. Such variations can be modelled to obtain information on the intensity of the azimuthal magnetic stresses within stellar convection zones. We introduce a simple model in the framework of the mean-field theory and discuss briefly the results of its application to those solar-like stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tidal Angular Momentum in Close Binary Systems in presence of Wind Driven Non-conservative Mass Transfer with Uniform Mass Accretion Rate

A very well-known property of close binary stars is that they usually rotate slowly than a similar type single star. Massive stars in close binary systems are supposed to experience an exchange of mass and angular momentum via mass transfer and tidal interaction, and thus the evolution of binary stars becomes more complex than that of individual stars. In recent times, it has become clear that a large number of massive stars interact with binary companions before they die. The observation also reveals that in close pairs the rotation tends to be synchronized with the orbital motion and the companions are naturally tempted to invoke tidal friction. We here introduce the effect of tidal angular momentum in the model of wind driven non-conservative mass transfer taking mass accretion rate as uniform with respect to time. To model the angular momentum evolution of a low mass main sequence companion star can be a challenging task. So, to make the present study more interesting, we have considered initial masses of the donor and gainer stars at the proximity of bottom-line main sequence stars and they are taken with lower angular momentum. We have produced a graphical profile of the rate of change of tidal angular momentum and the variation of tidal angular momentum with respect to time under the present consideration.     

Magnetic field and differential rotation in the radiative zone of the Sun

The problem of the interaction between magnetic fields and differential rotation in the radiative zone of the Sun is investigated. It is demonstrated that effects of magnetic buoyancy can be neglected in the analysis of this interaction. It is shown that hydromagnetic torsional waves propagating from the solar core cannot be responsible for the 22-year solar cycle. A possible geometry of the magnetic field that conforms with stationary differential rotation is considered. A verifying method for hypotheses on the structure of the magnetic field and torsional oscillations in the radiative zone of the Sun is proposed based on helioseismic data.     

Effect of Gravity Waves on Transport Process in Stellar Radiative Region

The aim of this work is to present a transport process which is likely to have a great importance for the internal constitution of the stars. In order to set the problem, we first give a short presentation of the physical properties of the Sun and stars, described usually under the names of `Standard Solar Model' or `Standard Stellar Models' (SSM). Next we show that an important question about SSM is that they do not explain the age dependance of lithium deficiency of stars of known age: stars of galactic clusters and the Sun. It has been suggested a long time ago to assume the presence of a macrosocpic diffusion process in the radiative zone, below the surface convective zone of solar like stars. It is then possible for the lithium present in the convective zone to be carried to the thermonuclear burning level below the convective zone. The first assumption was that differential rotation generates turbulence and therefore that a turbulent diffusion process takes place. However, this model predicts a lithium abundance which is strongly rotation dependant, contrary to the observations. Furthermore, the diffusion coefficient being large all over the radiative zone, it prevents the possibility of gravitational separation by diffusion and consequently leads to an impossibility of explaining the difference of helium abundance between the surface and the center of the Sun. The consequence is obviously that we need to take into account another physical process. Stars having a mass M < 1.3 M _⊙ have a convective zone which begins close to the stellar surface and extends down to a depth which is an appreciable fraction of stellar radius. In the convective zone, strong stochastic motions take care, at least partially, of heat transfer. These motions do not vanish at the lower boundary and generate internal waves into the radiative zone. These random internal waves are at the origin of a diffusion process which can be considered as responsible of the diffusive transport of lithium down to the lithium burning level. This is certainly not the only physical process responsible of lithium deficiency in main sequence stars, but its properties open the way to a completely consistent analysis of lithium deficiency. The model of generation of gravity waves is based on a model of heat transport in the convective zone by diving plumes. The horizontal component of the turbulent motion at the boundary of the convective zone is supposed to generate the horizontal motion of internal waves. The result is a large horizontal component of the diffusion coefficient, which produces in a short time an horizontal uniform chemical composition. It is known that gravity waves, in the absence of any dissipative process, cannot generate vertical mixing. Therefore, the vertical component of the diffusion coefficient is entirely dependant of radiative damping. It decreases quickly in the radiative zone, but is large enough to be responsible of lithium burning. Due to the radial dependance of velocity amplitude, the diffusion coeficient increases when approaching the stellar center. However, very close to the center, non-linear dissipative and radiative damping of internal waves become large and the diffusion coefficient vanishes at the very center. The development of this abstract can be found in E. Schatzman (1996, J. Fluid Mech. 322, 355). This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-Axisymmetric Magnetic Fields and Flip-Flops on the Sun and Cool Stars

The modulation of solar activity closely follows the solar rotation period suggesting the existence of long-lived active regions at preferred longitudes. For instance, two preferred active longitudes in both southern and northern hemispheres are found to be persistent at the century time scale. These regions migrate with differential rotation and periodically alternate their activity levels showing a flip-flop cycle. The pattern and behaviour of active longitudes on the Sun is similar to that on cool, rapidly rotating stars with outer convective envelopes. This suggests that the magnetic dynamo, including non-axisymmetric magnetic fields and flip-flop cycles, is also similar in these stars. This allows us to overview the phenomenon of stellar magnetic activity and to study it in detail on the Sun.     

行星和太阳内部的磁流体力学

许多行星 (如木卫三 ,水星 ,地球 ,木星和土星 )和恒星 (如太阳 )具有内部磁场。对这些磁场的存在和变化的解释对行星科学家和天体物理学家是一个巨大的挑战。本文试图总结行星和恒星的导电流体内部磁流体力学研究的新近发展和困难。一般由热对流驱动的流动通过磁流体力学过程产生并维持在行星和恒星中的磁场。在行星中磁流体力学过程强烈地受到转动 ,磁场和球几何位型的综合影响。其动力学的关键方面涉及科里奥利力和洛伦兹力间的相互作用。在太阳中其流线 ,即处于对流层的薄的剪切流层在太阳的磁流体力学过程中扮演了一个基本的角色 ,并由之产生了 1 1年的太阳黑子周期。本文也给出了一个新的非线性三维太阳发电机模型。     

On the generation of the large-scale and turbulent magnetic fields in solar-type stars

It is thought that the large-scale solar-cycle magnetic field is generated in a thin region at the interface of the radiative core (RC) and solar convection zone (SCZ). We show that the bulk of the SCZ virogoursly generates a small-scale turbulent magnetic field. Rotation, while not essential, increases the generation rate of this field.Thus, fully convective stars should have significant turbulent magnetic fields generated in their lower convection zones. In these stars the absence of a radiative core, i.e., the absence of a region of weak buoyancy, precludes the generation of a large-scale magnetic field, and as a consequence the angular momentum loss is reduced. This is, in our opinion, the explanation for the rapid rotation of the M-dwarfs in the Hyades cluster.Adopting the Utrecht's group terminology, we argue that the residual chromospheric emission should have three distinctive components: the basal emission, the emission due to the large-scale field, and the emission due to the turbulent field, with the last component being particularly strong for low mass stars.In the conventional dynamo equations, the dynamo frequencies and the propagation of the dynamo wave towards the equator are based on the highly questionable assumption of a constant . Furthermore, meridional motions, a necessary consequence of the interaction of rotation with convection, are ignored. In this context we discuss Stenflo's results about the global wave pattern decomposition of the solar magnetic field and conclude that it cannot be interpreted in the framework of the conventional dynamo equations.We discuss solar dynamo theories and argue that the surface layers could be essential for the generation of the poloidal field. If this is the case an -effect would not be needed at the RC-SCZ interface (where the toroidal field is generated). The two central problems facing solar dynamo theories may the transport of the surface poloidal field to the RC-SCZ interface and the uncertainty about the contributions to the global magnetic field by the small-scale magnetic features.Visitor, National Solar Observatory, National Optical Astronomy Observatories.The National Optical Astronomy Observatories are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.