Diamagnetic pumping near the base of a stellar convection zone

The property of inhomogeneous turbulence in conducting fluids to expel large‐scale magnetic fields in the direction of decreasing turbulence intensity is shown as important for the magnetic field dynamics near the base of a stellar convection zone. The downward diamagnetic pumping confines a fossil internal magnetic field in the radiative core so that the field geometry is appropriate for formation of the solar tachocline. For the stars of solar age, the diamagnetic confinement is efficient only if the ratio of turbulent magnetic diffusivity η_T of the convection zone to the (microscopic or turbulent) diffusivity η_in of the radiative interior is η_T/η_in ≥ 10⁵. Confinement in younger stars requires larger η_T/η_in. The observation of persistent magnetic structures on young solar‐type stars can thus provide evidence for the nonexistence of tachoclines in stellar interiors and on the level of turbulence in radiative cores. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Basal heating in the atmospheres of cool stars

Summary This paper reviews observational evidence concerning the existence of so-calledbasal heating that occurs in the outer atmospheres of all stars with convective envelopes. Effects of basal heating depend primarily on the effective temperature, with little sensitivity to surface gravity or elemental abundances. Basal heating occurs predominantly in the chromosphere, possibly in the (lower) transition region, but not at an observable level in coronae (except perhaps in early F-type and in M-type dwarf stars). Basal fluxes are observed in the slowest rotators where it shows no significant modulation. The basal flux level is observed directly on the Sun only over regions void of intrinsically strong photospheric fields. There is substantial quantitative observational and theoretical evidence that the basal emission from stellar outer atmospheres is caused by the dissipation of acoustic waves generated by turbulent convection. The magnetic canopy turns out to be of little consequence, but effects of intrinsically weak fields on the basal mechanism cannot be entirely ruled out. Solar observations constrain the spatio-temporal character of the basal atmosphere and the acoustic flux levels as a function of height, resulting in a model in which intermittent wave dissipation causes emission characteristic of both cool and warm atmospheric areas, in which — at least in the solar case — a time-averaged chromospheric temperature rise may not even exist.     

On the maximal value of the turbulent α ‐parameter in accretion discs

In this short paper we show that making turbulence two‐rather than three‐dimensional may increase the effective turbulent viscosity by about 40 %. Dimensionless hydrodynamical viscosity parameters up to α_max = 0.25 M_t² may be obtained in this approach, which are in better agreement with the observational data on non‐stationary accretion than the values obtained in numerical simulations. However, the α ‐parameter values known from observations are still several times higher (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Late stages of solar type protostars

A consistent hydrodynamical and radiative transfer calculation in spherical symmetry for a 1M protostar is presented. The calculation starts with Larson's initial conditions and continues until almost all the material has fallen onto a hydrostatic core with a large outer convection zone. The innermost percent of the mass is partially degenerate. Due to the numerical technique used, the radius of the hydrostatic core is determined with a high degree of accuracy.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Seismic Diagnostics on Stellar Convection Treatment from Oscillation Amplitudes of p-modes

The excitation rate P of solar p-modes is computed with a model of stochastic excitation which involves constraints on the averaged properties of the solar turbulence. These constraints are obtained from a 3D simulation. Resulting values for P are found 4.5 times larger than when the calculation assumes properties of turbulent convection which are derived from an 1D solar model based on Gough (1977)'s formulation of the mixing-length theory (GMLT). This difference is mainly due to the assumed values for the mean anisotropy of the velocity field in each case.Calculations based on 3D constraints bring the P maximum closer to the observational one.We also compute P for several models of intermediate mass stars (1 M 2 M).Differences in the values of P _max between models computed with the classical mixing-length theory and GMLT models are found large enough for main sequence stars to suggest that measurements of P in this mass range will be able to discriminate between different models of turbulent convection.     

Local Helioseismology of Sunspots: Current Status and Perspectives

Mechanisms of the formation and stability of sunspots are among the longest-standing and intriguing puzzles of solar physics and astrophysics. Sunspots are controlled by subsurface dynamics, hidden from direct observations. Recently, substantial progress in our understanding of the physics of the turbulent magnetized plasma in strong-field regions has been made by using numerical simulations and local helioseismology. Both the simulations and helioseismic measurements are extremely challenging, but it is becoming clear that the key to understanding the enigma of sunspots is a synergy between models and observations. Recent observations and radiative MHD numerical models have provided a convincing explanation for the Evershed flows in sunspot penumbrae. Also, they lead to the understanding of sunspots as self-organized magnetic structures in the turbulent plasma of the upper convection zone, which are maintained by a large-scale dynamics. Local helioseismic diagnostics of sunspots still have many uncertainties, some of which are discussed in this review. However, there have been significant achievements in resolving these uncertainties, verifying the basic results by new high-resolution observations, testing the helioseismic techniques by numerical simulations, and comparing results obtained by different methods. For instance, a recent analysis of helioseismology data from the Hinode space mission has successfully resolved several uncertainties and concerns (such as the inclined-field and phase-speed filtering effects) that might affect the inferences of the subsurface wave-speed structure of sunspots and the flow pattern. It is becoming clear that for the understanding of the phenomenon of sunspots it is important to further improve the helioseismology methods and investigate the whole life cycle of active regions, from magnetic flux emergence to dissipation. The Solar Dynamics Observatory mission has started to provide data for such investigations.     

Shocks and shells in hot star winds

Radiation-driven winds of hot, massive stars showvariability in UV and optical line profiles on time scales of hours to days.Shock heating of wind material is indicated by the observed X-ray emission. We present time-dependent hydrodynamical models of these winds, where flowstructures originate from a strong instability of the radiative driving. Recent calculations (Owocki 1992) of the unstable growth of perturbations were restricted by the assumptions of 1-D spherical symmetry and isothermality of the wind. We drop the latter assumption and include the energy transfer in the wind. This leads to a severe numerical shortcoming, whereby all radiative cooling zones collapse and the shocks become isothermal again. We propose a method to hinder this collapse. Calculations for dense supergiant winds then show: (1) The wind consists of a sequence of narrow and dense shells, which are enclosed by strong reverse shocks (with temperatures of 10⁶ to 10⁷ K) on their starward facing side. (2) Collisions of shells are frequent up to 6 to 7 stellar radii. (3) Radiative cooling is efficient only up to 4 to 6R _*. Beyond these radii, cooling zones behind shocks become broad and alter the wind structure drastically: all reverse shocks disappear, leaving regions ofpreviously heated gas.     

Analysis of the IR and sub-MM emission of four post-AGB stars

The goal of this work is to derive the physical properties of dust envelopes around post-AGB stars by means of radiative transfer calculations. The model spectral energy distributions (SEDs) have been compared with observational data of the post-AGB stars IRAS 10215-5916, 16342-3814, 17150-3224, and 19500-1709 in the wavelength range from 0.4 to 1300µm. The match between our model SEDs and the observational data is very satisfactory. As a result, we have obtained estimates of the inner and outer radii, the density, the temperature, and the mass of the envelopes of the four objects.     

Meridional circulation and turbulence in surface layers of the stars

The meridional circulation is considered in the surface layers of the stars where the optical depth τ?1. It is shown that the radial component of circulation velocity reaches its maximum value at τ≈1 and decreases at τ→0. The tangential velocity reverses its sign at τ≈1 — i.e., the meridional flows are closed in stellar atmospheres. The tangential velocities can be of the order of 10⁶–10⁷ cm s^?1 in atmospheres of O-B-A stars. Such hydrodynamical motions can result in the generation of turbulence in the surface layers. Characteristic turbulent velocities are of the order of 10⁵–10⁶ cm s^?1 in early-type stars. The small-scale turbulent motions generate the acoustic waves and the flux of such waves may be the source of energy to heat coronae in O and B stars.     

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.     

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.     

Semi-regular and alternating pulsations in hydrodynamical models for low-mass giants

On the basis of hydrodynamical simulations the semi-regular and alternating pulsations of the W Vir and RV Tau stars are studied including non-steady radiative transfer effects in gray sphericalsymmetric atmospheres. It is shown that the transition from regular to semi-regular oscillations occurs at periodsP13–15 days due to pulsation energy imbalance provoqued by strong radiating shocks. The differences between the periods and amplitudes of W Vir and RV Tau variables are explained as a result of this imbalance. It is suggested that the semi-regular alternating pulsations of the RV Tau stars appear following a period-doubling phenomenon, which can be also understood in terms of the pulsation energy variations between odd and even fundamental cycles. The pulsational characteristics of the period-doubled models are in general accordance with those observed in the RV Tau stars. On the basis of numberical results, a theoretical estimation of the upper limit for the luminosity of the RV Tau stars is derived asL10³ L .     

Observational approach to star formation

The observational approach to the early stages of stellar evolution has been applied to some problems relating to the formation and dissipation of stellar associations, the origin of OB field stars, and low-mass star formation in OB associations. The OB field stars ejected from parent associations are older on the average than the OB stars in the associations. The average duration of active OB-star formation in associations is evaluated. It is suggested that, under the conditions in OB associations, low-mass stars may be formed from dense protostellar objects.Translated fromAstrofizika, Vol. 39, No. 3, pp. 393–406, July–September, 1996.     

Radiative accelerations, accumulation of iron and thermohaline convection inside stars

The radiative acceleration on iron inside stars may lead to an accumulation of this element in stellar internal layers. As discussed by several authors, this iron accumulation has many important consequences. It may lead to an extra convective zone, and in some cases it may help triggering stellar pulsations. However, the computations which have been done up to now ignore an important effect: the double-diffusive, or “thermohaline” convection induced by the inverse μ gradient. Detailed computations of all these processes have been introduced in the TGEC stellar evolution code. We show how thermohaline convection modifies the profiles of iron inside stars, with important consequences     

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.     

Turbulent compressible convection with rotation–penetration below a convection zone

We examine the behaviour of penetrative turbulent compressible convection under the influence of rotation by means of three dimensional numerical simulations. We estimate the extent of penetration below a stellar-type rotating convection zone in an f-plane configuration. Several models have been computed with a stable-unstable-stable configuration by varying the rotation rate (Ω), the inclination of the rotation vector and the stability of the lower stable layer. The spatial and temporal average of kinetic energy flux (F_k) is computed for several turnover times after the fluid has thermally relaxed and is used to estimate the amount of penetration below the convectively unstable layer. Our numerical experiments show that with the increase in rotational velocity, the downward penetration decreases. A similar behaviour is observed when the stability of the lower stable layer is increased in a rotating configuration. Furthermore, the relative stability parameter S shows an S ^−1/4 dependence on the penetration distance implying the existence of a thermal adjustment region in the lower stable layer rather than a nearly adiabatic penetration region.     

Statistical method for distance determination of a stellar group

In this paper, we developed statistical method for distance determination of a stellar group. The method depends on the assumption that, the stars scatter around a mean magnitude in a Gaussian distribution. The mean apparent magnitude of the stars is then expressed in terms of the frequency function of the apparent magnitudes, so as to correct for observational incompleteness at the faint end. The problem reduces to the solution of a highly transcendental equation for a given apparent magnitude parameter α. Computational algorithm of the method is illustrated and the numerical solutions of the basic equation are given for some values of α .     

A coupled model of magnetic flux generation and transport in stars

We present a combined model for magnetic field generation and transport in cool stars with outer convection zones. The mean toroidal magnetic field, which is generated by a cyclic thin-layer α Ω dynamo at the bottom of the convection zone is taken to determine the emergence probability of magnetic flux tubes in the photosphere. Following the nonlinear rise of the unstable thin flux tubes, emergence latitudes and tilt angles of bipolar magnetic regions are determined. These quantities are put into a surface flux transport model, which simulates the surface evolution of magnetic flux under the effects of large-scale flows and turbulent diffusion. First results are discussed for the case of the Sun and for more rapidly rotating solar-type stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of turbulent mixing on the g‐mode spectrum of MS stars

Understanding transport processes inside stars is one of the main goals of asteroseismology. Chemical turbulent mixing can affect the internal distribution of μ near the energy generating core, having an effect on the evolutionary tracks similar to that of overshooting. This mixing leads to a smoother chemical composition profile near the edge of the convective core, which is reflected in the behavior of the buoyancy frequency and, therefore, in the frequencies of gravity modes. We describe the effects of convective overshooting and turbulent mixing on the frequencies of gravity modes in B‐type main sequence stars. In particular, the cases of p‐g mixed modes in β Cep stars and high‐order modes in SPBs are considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)