Peter Ulmschneider

Chromospheric and coronal heating mechanisms II

We review the mechanisms which are thought to provide steady heating of chromospheres and coronae. It appears now fairly well established that nonmagnetic chromospheric regions of latetype stars are heated by shock dissipation of acoustic waves which are generated in the stellar surface convection zones. In the case of late-type giants there is additional heating by shocks from pulsational waves. For slowly rotating stars, which have weak or no magnetic fields, these two are the dominant chromospheric heating mechanisms.Except for F-stars, the chromospheric heating of rapidly rotating late-type stars is dominated by magnetic heating either through MHD wave dissipation (AC mechanisms) or through magnetic field dissipation (DC mechanisms). The MHD wave and magnetic field energy comes from fluid motions in the stellar convection zones. Waves are also generated by reconnective events at chromospheric and coronal heights. The high-frequency part of the motion spectrum leads to AC heating, the low frequency part to DC heating. The coronae are almost exclusively heated by magnetic mechanisms. It is not possible to say at the moment whether AC or DC mechanisms are dominant, although presently the DC mechanisms (e.g., nanoflares) appear to be the more important. Only a more detailed study of the formation of and the dissipation in small-scale structures can answer this question.The X-ray emission in early-type stars shows the presence of coronal structures which are very different from those in late-type stars. This emission apparently arises in the hot post-shock regions of gas blobs which are accelerated in the stellar wind by the intense radiation field of these stars.

On sound generation by turbulent convection: A new look at old results

We have revisited the problem of generation of acoustic waves by turbulent convection in an isothermal atmosphere. The theory of sound generated aerodynamically has been originally developed by Lighthill and later modified by Stein to include the effects of stratification. Lighthill and Steins results have been extensively used to estimate the amount of acoustic wave energy generated in the solar and stellar convective zones. We have recently recognized that Steins treatment of turbulence requires some corrections and that these corrections lead to significant changes in the obtained results. In this paper, we present the correct status of computing the acoustic wave energy fluxes by incorporating a physically meaningful description of the spatial and temporal spectrum of the turbulent convection. We show the dependence of the obtained wave fluxes on the nature of the turbulence and discuss the efficiency of acoustic wave generation in the solar convection zone.

Two-Component Theoretical Chromosphere Models for K Dwarfs of Different Magnetic Activity: Exploring the Ca II Emission-Stellar Rotation Relationship

We compute two-component theoretical chromosphere models for K2 V stars with diUerent levels of magnetic activity. The two components are a nonmagnetic component heated by acoustic waves and a magnetic component heated by longitudinal tube waves. The —lling factor for the magnetic component is determined from an observational relationship between the measured magnetic area coverage and the stellar rotation period. We consider stellar rotation periods between 10 and 40 days. We investigate two diUerent geometrical distributions of magnetic —ux tubes: uniformly distributed tubes, and tubes arranged as a chromospheric network embedded in the nonmagnetic region. The chromosphere models are constructed by performing state-of-the-art calculations for the generation of acoustic and magnetic energy in stellar convection zones, the propagation and dissipation of this energy at the diUerent atmo- spheric heights, and the formation of speci—c chromospheric emission lines that are then compared to the observational data. In all these steps, the two-component structure of stellar photospheres and chromospheres is fully taken into account. We —nd that heating and chromospheric emission is signi—- cantly increased in the magnetic component and is strongest in —ux tubes that spread the least with height, expected to occur on rapidly rotating stars with high magnetic —lling factors. For stars with very slow rotation, we are able to reproduce the basal —ux limit of chromospheric emission previously identi- —ed with nonmagnetic regions. Most importantly, however, we —nd that the relationship between the Ca II H)K emission and the stellar rotation rate deduced from our models is consistent with the relationship given by observations. Subject headings: line: formationMHDstars: activitystars: chromospheres ¨ stars: late-typestars: rotation

DOES THE SUN HAVE A FULL-TIME CHROMOSPHERE?

The successful modeling of the dynamics of H2v bright points in the nonmagnetic chromosphere by Carlsson & Stein gave as a by-product a part-time chromosphere lacking the persistent outward temperature increase of time-average empirical models, which is needed to explain observations of UV emission lines and continua. We discuss the failure of the dynamical model to account for most of the observed chromospheric emission, arguing that their model uses only about 1% of the acoustic energy supplied to the medium. Chromospheric heating requires an additional source of energy in the form of acoustic waves of short period (P < 2 minutes), which form shocks and produce the persistent outward temperature increase that can account for the UV emission lines and continua.

Chromospheric and coronal heating mechanisms

Mathematical models of the global electron density distribution in the corona were first constructed from solar eclipse images at the end of the last century. Since then, the complexity of these density models has increased steadily, as additional free parameters and new mathematical tools were incorporated. The ultimate goal of this effort has always been to improve the representation of the inhomogeneous coronal structure, wbile maintaining a restricted set of parameters. This review puts the successive steps of this maturation process in a general perspective. A recent model, developed at the Royal Observatory of Belgium for the 1991 and 1994 eclipses, is described to illustrate the modeling tedmiques and some current issues.

On the generation of flux tube waves in stellar convection zones. I - Longitudinal tube waves driven by external turbulence

The source functions and the energy fluxes for wave generation in magnetic flux tubes embedded in an otherwise magnetic field-free, turbulent, and compressible fluid are derived. The calculations presented here assume that the tube interior is not itself turbulent, e.g., that motions within the flux tube are due simply to external excitation. Specific results for the generation of longitudinal tube waves are presented. 39 references.

KINK AND LONGITUDINAL OSCILLATIONS IN THE MAGNETIC NETWORK ON THE SUN: NONLINEAR EFFECTS AND MODE TRANSFORMATION

We examine the propagation of kink and longitudinal waves in the solar magnetic network. Previously, we investigated the excitation of network oscillations in vertical magnetic flux tubes through buffeting by granules and found that footpoint motions of the tubes can generate sufficient wave energy for chromospheric heating. We assumed that the kink and longitudinal waves are decoupled and linear. We overcome these limitations by treating the nonlinear MHD equations for coupled kink and longitudinal waves in a thin flux tube. For the parameters we have chosen, the thin tube approximation is valid up to the layers of formation of the emission features in the H and K lines of Ca II, at a height of about 1 Mm. By solving the nonlinear, time-dependent MHD equations we are able to study the onset of wave coupling, which occurs when the Mach number of the kink waves is of the order of 0.3. We also investigate the transfer of energy from the kink to the longitudinal waves, which is important for the dissipation of the wave energy in shocks. We find that kink waves excited by footpoint motions of a flux tube generate longitudinal modes by mode coupling. For subsonic velocities, the amplitude of a longitudinal wave increases as the square of the amplitude of the transverse wave, and for amplitudes near Mach number unity, the coupling saturates and becomes linear when the energy is nearly evenly divided between the two modes.

On frequency and strength of shock waves in the solar atmosphere

Comparison of computed radiative energy losses of several new empirical chromospheric models with heating by shock wave dissipation gives information on the frequency and strength of shock waves in the solar chromosphere. A mechanical flux of around 2.5 × 106 erg/cm2 sec is found for the base of the chromosphere. The shocks are weak and the wave period is around 10 sec.

Acoustic and magnetic wave heating in stars - I. Theoretical chromospheric models and emerging radiative fluxes

We describe a method to construct theoretical, time-dependent, two-component and wave heated chromosphere models for late-type dwarfs. The models depend only on four basic stellar parameters: effective temperature, gravity, metallicity and filling factor, which determines the coverage of these stars by surface magnetic fields. They consist of non-magnetic regions heated by acoustic waves and vertically oriented magnetic flux tubes heated by longitudinal tube waves with contributions from transverse tube waves. Acoustic, longitudinal and transverse wave energy spectra and fluxes generated in stellar convection zones are computed and used as input parameters for the theoretical models. The waves are allowed to propagate and heat both components by shock dissipation. We compute the time-dependent energy balance between the dissipated wave energy and the most prominent chromospheric radiative losses as function of height in the stellar atmosphere. For the flux tube covered stars, the emerging radiative fluxes in the Ca II and Mg II lines are computed by using a newly developed multi-ray radiative transfer method.

Excitation of transverse magnetic tube waves in stellar convection zones - I. Analytical approach

Analytical treatment of the excitation of transverse magnetic tube waves in stellar convection zones is presented. The waves are produced by the interaction between thin and vertically oriented magnetic flux tubes embedded in stellar convection zones and the external turbulent motions. A general theory describing this interaction is developed and used to compute the wave energy spectra and fluxes for the Sun.