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Recent measurements of solar surface magnetic fields suggest that the spatial distribution of these fields is fractal. In order to understand the physical basis for such geometric complexity, we study here the advection of magnetic flux tubes relatively simple random motions on the surface of a fluid and investigate the spatial statistics of the resulting surface field. While this study does not directly address the question of why solar surface fields have the observed spatial structure, it is designed to build our intuition about how surface flows lead to complex spatial structuring of magnetic fields. As part of our study, we discuss the various methods by which one can describe the spatial distribution of the surface magnetic flux and relate them mathematically; this turns out to be a crucial point of our work since, as we show, a number of previous analyses have misinterpreted the analysis procedures for determining fractal dimensions. Our principal result is the explicit demonstration that simple random flows lead to magnetic flux spatial distributions with a multifractal dimension spectrum. Furthermore, we demonstrate that this magnetic spatial structure is generic, i.e., is characteristic of a very large class of random flows.

We have used available IPC data and a critical compilation of cataloged optical data to measure the 0.16-3.5 keV X-ray emission from 88 K and 169 M stars of luminosity classes IV, V, and VI within 25 pc from the Sun. The IPC detected 54 out of the 88 K stars, 70 out of the 138 M stars with M(v) less than 13.4, and 15 out of the 31 fainter M stars. We have identified a subsample of surveyed stars that is statistically representative of the population of K and M stars in the solar neighborhood. On the basis of this subsample (1) we have shown the occurrence of a drop in the level of X-ray emission for M stars later than approximately M5; (2) we have built unbiased maximum likelihood X-ray luminosity functions for the K, early M, and late M stars; (3) we have confirmed, both for K and M stars, the decrease of X-ray luminosity with increasing stellar age in the range of ages of disk population stars: and (4) we have shown that no obvious correlation is present between X-ray and bolometric luminosities in the entire representative samples of K and M stars, but only within flare stars which also seem to mark a saturation in X-ray luminosity level.

We study the linear stability of an optically thin uniform radiating plasma subject to nonlocal heat transport. We derive the dispersion relation appropriate to this problem, and the marginal wavenumbers for instability. Our analysis indicates that nonlocal heat transport acts to reduce the stabilizing influence of thermal conduction, and that there are critical values for the electron mean free path such that the plasma is always unstable. Our results may be applied to a number of astrophysical plasmas, one such example being the halos of clusters of galaxies.

We rediscuss the nature of magnetic field generation in astrophysical systems. We show that as a result of ineffective three-dimensional turbulent diffusion in the presence of strong azimuthal magnetic fields, the standard dynamo equations are not likely to provide a reasonable description of magnetic dynamos in systems such as late-type stars and galaxies. Instead, we propose a new set of dynamo equations, which take into account the modifications of turbulent diffusion by strong magnetic fields.

A combination of a stellar Galaxy model based on optical data, stellar X-ray luminosity functions derived from the full Einstein base, and a model for X-ray absorption derived from hydrogen column densities are used to estimate the contribution to the diffuse soft X-ray background flux from the main-sequence A, F, G, K, and M stars, and RS CVn stars, at various energies ranging from 0.1 to about 5 keV. Previous discrepancies between earlier estimates of the stellar contribution to the diffuse soft X-ray background are resolved; this stellar contribution to the diffuse soft X-ray background is found to be under 3 percent for photon energies less than energy I and J bands (about 0.8-2 keV), at a threshold sensitivity for point source detection about 10 exp -10 ergs/s sq cm. At low latitudes, stellar contribution estimates are less than 3 percent below 0.3 keV, 7-40 percent in the medium-energy bands, and 27-70 percent in the I and J bands. It is shown that while dM stars are the major contributors to the diffuse stellar flux, other stellar types contribute as much as 40 percent of this flux at the higher energies in the passband studied.

A systematic survey of the diffuse soft X-ray background as seen directly with the Einstein Observatory is presented. With the aid of 1633 selected 1 x 1 deg fields of view obtained by the IPC to provide about 5-percent sky coverage, with some bias toward the Galactic plane, the background in the 0.16-3.5 keV spectral region was spatially resolved on this angular scale. Maps of the background are characterized and produced at different energies within the Einstein passband. It is confirmed that the Galactic ridge is not present at energies below 0.33 keV and it is demonstrated that the appearance of the ridge above this energy is not due to hard Galactic sources with a flux above 10 exp -13 ergs/sq cm/s. A southern Galactic region is identified, with l between 80 and 180 deg and b less than -5 deg, where the mean background intensity has the lowest value and is homogeneous within better than 9 percent. The implications of these results for the Galactic structure and for the nature of the extragalactic X-ray background are discussed.

Magnetized astrophysical plasmas reveal a great deal of structure when spatially resolved. One possible explanation for this structuring is based on the existence of filamenting instabilities driven by radiation. In this paper, previous linear calculations are extended by considering the weakly nonlinear (finite-amplitude) development of such filamenting instabilities in magnetized unstratified plasmas. It is shown that under most conditions these instabilities (in particular, the Jouse model) are unstable at finite amplitude; in particular, in the temperature and plasma-beta domains characteristic of, for example, much of the solar transition region, these modes - which can be linearly stable under these conditions - become unstable to finite-amplitude perturbations. The relevance of this to the problem of heating the solar low transition region by current dissipation is discussed.

Coronal X-ray emission of the Pleiades stars is investigated, and maximum likelihood, integral X-ray luminosity functions are computed for Pleiades members in selected color-index ranges. A detailed search is conducted for long-term variability in the X-ray emission of those stars observed more than once. An overall comparison of the survey results with those of previous surveys confirms the ubiquity of X-ray emission in the Pleiades cluster stars and its higher rate of emission with respect to older stars. It is found that the X-ray emission from dA and early dF stars cannot be proven to be dissimilar to that of Hyades and field stars of the same spectral type. The Pleiades cluster members show a real rise of the X-ray luminosity from dA stars to early dF stars. X-ray emission for the young, solarlike Pleiades stars is about two orders of magnitude more intense than for the nearby solarlike stars.

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.

Magnetohydrodynamic (MHD) wave energy fluxes for late-type stars are calculated, using previously obtained formulae for the source functions for the generation of MHD waves in a stratified, but otherwise uniform, turbulent atmosphere; the magnetic fields in the wave generation region are assumed to be homogeneous. In contradiction to previous results, it is shown that in this uniform magnetic field case there is no significant increase in the efficiency of MHD wave generation, at least within the theory's limits of applicability. The major results are that the MHD energy fluxes calculated for late-type stars are less than those obtained for compressible modes in the magnetic field-free case, and that these MHD energy fluxes do not vary enough for a given spectral type to explain the observed range of UV and X-ray fluxes from such stars. It is therefore concluded that MHD waves in stellar atmospheres with homogeneous magnetic fields in the wave generation region cannot explain the observed stellar coronal emissions; if such MHD waves are responsible for a significant component of stellar coronal heating, then nonuniform fields within the generation region must be appealed to.

The temporal evolution of disturbances in a spherically symmetric polytropic wind from a central object is studied. Such disturbances may be due to localized momentum addition/subtraction, as, for example, by MHD waves, heating/cooling mechanisms in the outflow, or localized deviations from spherical symmetric expansion. The evolution of an initial perturbed state to a continuous or discontinuous final equilibrium state, as predicted by previous analytic calculations for stationary flows, is followed. It is shown that some of the predicted discontinuous equilibrium states are not physically accessible, while the attainment of the remaining equilibrium states depends on both the temporal and the spatial parameters characterizing the perturbation. The results are derived for solar conditions, but in fact can be applied to outflows in other astrophysical systems. In particular, applications to the solar wind and flows in astrophysical jets are discussed.

A new class of X-ray-luminous 'yellow' stellar objects which contributes significantly to the stellar log N-log S distribution, but which cannot be reconciled with normal G and K main-sequence stars. This identification results from a new analysis of the stellar content of three samples of X-ray-selected X-ray sources observed with the Einstein Observatory, namely the 'Medium Sensitivity Survey', the 'High Sensitivity Survey', and the 'Hyades Region Survey'. In this paper, both X-ray and optical properties of the stellar samples in these surveys are reported. The actual stellar content of the surveys is compared with predictions based on current knowledge of stellar X-ray luminosity functions and the stellar composition and spatial distribution in the Galaxy. It is shown that a plausible identification for the excess population of 'yellow' stars is with the active, RS CVn-like binaries.

The paper presents a detailed study of thermal instabilities in cooling flows associated with galaxies and clusters of galaxies. In the case of purely radiation-driven accretion onto a central object such as the cD galaxy M87, it is found that the gas is largely subject to overstability, rather than to monotonic instability. If thermal conductivity is taken into account, the flow is stabilized on scales of several kiloparsecs, even if the conductivity is appreciably reduced (e.g., about 1 percent) with respect to the Spitzer value. In no case are the globular perturbations (i.e., perturbations with comparable radial and azimuthal dimensions) found to be monotonically unstable. The paper presents numerical solutions of the local dispersion relation for the cooling flow in M87 and discusses the possible consequences of the results for a correct understanding of cooling flows.

The generation of MHD waves by turbulent motions in a stratified medium with an embedded uniform magnetic field, a topic which is relevant to the study of the solar atmosphere, is considered. Both compressible and incompressible MHD waves are treated in a one-dimensional approach; however, the direction of the background magnetic field is permitted to vary in an arbitrary direction. Theoretical expressions for MHD energy fluxes are obtained as a function of wave frequency and multipole coefficients. It is shown that monopole, dipole, and quadrupole emissions are responsible for the generation of the compressible components of the fast and slow modes. However, the incompressible components and the Alfven modes can be generated by the dipole emission only. Specific results obtained for special magnetic field geometries are discussed for the fast and slow modes.

A computational code for solving two-dimensional, time-dependent MHD equations by the method of characteristics is presented. Its capabilities are demonstrated by solving two very different problems for which analytical solutions exist: linearized, standing MHD wave motions in a magnetized cylindrical plasma, and nonlinear self-similar expansion of a magnetized plasma ball. The nonlinear development of standing MHD wave solutions in a cylindrical plasma is also studied. The method can be naturally embedded in the computational architecture of massively parallel processors.

Approximate analytic solutions are sought for the dispersion relation for the MHD stability of magnetized medium in current-driven filamentation modes such as those observed in the solar atmosphere. The magnetic field is assumed to have a self-consistent sheared equilibrium structure. The analysis is carried out in the small wavenumber regime, where shear length is similar to the mode wavelength. Instability is found to depend on the ratio between the thermal and magnetic diffusivities, i.e., the Prandtl number, which identifies the unstable transverse wavenumbers. The instability conditions are expressed in an algebraic equation amenable to numerical solution. Results are provided from use of the model to determine the maximum growth rate and typical scale lengths of instabilities in a precoronal atmosphere and the lower transition region.

Attention is given to a number of methods for inverting remote sensing data obtained in a variety of astronomical applications. Applications include image restoration, inversion of helioseismological data to obtain the internal rotation rate of stars such as the sun, fitting of spectra (especially thermal line spectra) to grating or other dispersed observed spectra, differential emission measure analysis, and reconstruction of images derived from interferometric observations. The results consider the tradeoff between resolution and variance and the stability properties for each method and propose an inversion stragegy using the available techniques.

The thermal structure of the medium inside thin, vertical magnetic flux tubes embedded in a given external atmosphere is investigated, assuming cylindrical symmetry and a depth-independent plasma beta. The variation with tube radius of the temperature on the tube axis is computed and the temperature on the tube wall is estimated. The temperature variation across the flux tube is found to be due to the depth variation of the intensity and to the density stratification of the atmosphere. Since the temperature difference between the axis and the wall is small in thin flux tubes (of the order of 10 percent), the horizontal temperature gradient may often be neglected and the temperature in a tube of given radius may be described by a single function of depth. Thus, a more detailed numerical treatment of the radiative transfer within thin flux tubes can be substantially simplified by neglecting horizontal temperature differences within the flux tube proper.

Observations of nonthermal line broadening seen in solar flares by the Solar Maximum Mission satellite are discussed in light of recent results on the generation of magnetic field stochasticity. It is shown that a consistent model for the data can be constructed by assuming that the observations signal the destruction of an ambient magnetohydrodynamic equilibrium.

The stability of current-driven filamentary modes in magnetic flux tubes embedded in a plane-parallel atmosphere in LTE and in hydrostatic equilibrium is discussed. Within the tube, energy transport by radiation only is considered. The dominant contribution to the opacity is due to H- ions and H atoms (in the Paschen continuum). A region in the parameter space of the equilibrium configuration in which the instability is effective is delimited, and the relevance of this process for the formation of structured coronae in late-type stars and accretion disks is discussed.

Results are presented from a survey of RS CVn binaries which were observed with the imaging proportional counter (IPC) on board the Einstein Observatory. Spectral analyses of the IPC pulse height spectra show that the coronae of RS CVn binaries always contain hot gas with temperatures in excess of 10 to the 7th K, similar to active late-type main-sequence stars, and that at least two temperature components are necessary to account for the higher quality IPC spectra (when absorption is unimportant). It is argued that these bimodal temperature distributions found by the IPC are indicative of true distributions of emission measure versus temperature that are continuous (just as is the case of magnetically confined coronal plasma loops observed on the sun). It is further shown that none of the derivable X-ray characteristics of RS CVn binaries depend on rotation period, implying that previous claims of period-activity relationships in RS CVn binaries were unfounded.

A model atmosphere within a thin magnetic flux tube that is embedded in an arbitrarily stratified medium is presently constructed by solving the radiative transfer equation in the two-stream approximation for gray opacity, under the assumption that the magnetic field is sufficiently strong to warrant the neglect of both thermal conduction and convective diffusion; energy inside the flux tube therefore being transported solely by radiation. The structure of the internal atmosphere is determined on the basis of the hydrostatic and radiative equilibrium conditions of the tube embedded in an external atmosphere. The gas temperature along the axis of the tube is computed, and the geometry of the flux tube is determined on the basis of magnetic flux conservation and total pressure equilibrium.

Steady polytropic wind flows are studied by examining their solution topologies. The problem of whether the degeneracy of the continuous and standing shocked solutions in the isothermal case persist in the more general case of a polytropic expanding atmosphere is addressed. The effects of departures from spherical symmetry and nonthermal momentum addition are considered within the context of the new class of magnetospheric models proposed by Low and Tsinganos (1985). The flow near the boundary of a polar coronal hole is considered for the specific case of a magnetosphere in which this boundary asymptotically approaches the equator at large heliocentric distances.

The data obtained with two pointed observations of 1 deg by 1 deg fields of the Pleiades region have been analyzed, and the results are presented. The maximum-likelihood X-ray luminosity functions for the Pleiades G and K stars in the cluster are derived, and it is shown that, for the G stars, the Pleiades X-ray luminosity function is significantly brighter than the corresponding function for Hyades G dwarf stars. This finding indicates a dependence of X-ray luminosity on stellar age, which is confirmed by comparison of the same data with median X-ray luminosities of pre-main sequence and local disk population dwarf G stars. It is suggested that the significantly larger number of bright X-ray sources associated with G stars than with K stars, the lack of detection of M stars, and the relatively rapid rotation of the Pleiades K stars can be explained in terms of the onset of internal differential rotation near the convective envelope-radidative core interface after the spin-up phase during evolution to the main sequence.

The stability of magnetic loops to current-driven filamentation instabilities is investigated. The unperturbed atmosphere is assumed to be composed of an (upper) isothermal optically thin low-density portion and a (lower) higher-density portion which is in radiative equilibrium; in both cases, the atmosphere is in hydrostatic equilibrium, so that gravitational stratification is taken into account. In order to provide specific equilibrium conditions for evaluation of the dispersion relation, conditions appropriate for the surface of a solar-type star are adopted; i.e., a fairly low temperature (T = 5000 K) appropriate for a 'precoronal' state associated, for example, with magnetic flux emerging from photospheric levels under the action of magnetic buoyancy. A linear stability analysis is performed, and numerical results show that physically plausible current densities, which would be generated by typical loop-footpoint motions, are effective in driving MHD instabilities in such a plasma. The instability growth rates are strongly dependent on the assumed current density distribution and on the density scale height.

The results of an X-ray survey of bright late A and early F stars on the main B-V sequence between 0.1 and 0.5 are presented. All the stars were observed with the Einstein Observatory for a period of at least 500 seconds. The survey results show significantly larger X-ray luminosities for the sample binaries than for the single stars. It is suggested that the difference is due to the presence of multiple X-ray sources in binaries. It is shown that the X-ray luminosities for single stars increase rapidly with increasing color, and that the relation Lx/Lbol is equal to about 10 to the -7th does not hold for A stars. No correlation was found between X-ray luminosity and projected equatorial rotation velocity. It is argued on the basis of the observations that X-ray emission in the sample stars originated from coronae. The available observational evidence supporting this view is discussed.

X-ray emission from the nearby system Procyon A/B (F5 IV + DF) was detected, using the IPC (Imaging Proportional Counter) on board the Einstein Observatory. Analysis of the X-ray pulse height spectrum suggests that the observed X-ray emission originates in Procyon A rather than in the white dwarf companion Procyon B, since the derived X-ray temperature, log T = 6.2, agrees well with temperatures found for quiescent solar X-ray emission. Modeling Procyon's corona with loops characterized by some apex temperature Tmax and emission length scale L, it is found that Tmax is well constrained, but L, and consequently the filling factor of the X-ray emitting gas, are essentially unconstrained even when EUV emission from the transition region is included in the analysis.

The extent and thermal stratification of the region of convective overshoot underneath the convection zone of the sun are investigated. The phenomenon of convective overshoot in general is discussed, and some of the modal and model approaches to studying it are briefly reviewed. A detailed theoretical description of the motion of plumes in a stably stratified medium is given, leading to a 'derivation' of the plume equations from the hydrodynamic equations. Entrainment is discussed, and it is shown how the plume equations can be used to compute convective overshoot in the sun. The limitations of the plume model are addressed, arguing that a thin boundary layer must exist which separates convective and radiative regions. The results of numerical integrations of the plume equations, as applied to the region of convective overshoot underneath the solar convective zone, are discussed.

The topological stability of MHD equilibria is investigated by exploring the formal analogy, in the ideal MHD limit, between the topology of magnetic lines of force in coordinate space and the topology of integral surfaces of one- and two-dimensional Hamiltonian systems in phase space. It is demonstrated that in an astrophysical setting, symmetric magnetostatic equilibria satisfying the ideal MHD equations are exceptional. The principal result of the study is that previous infinitesimal perturbation theory calculations can be generalized to include finite-amplitude and symmetry-breaking effects. The effect of the ergodicity of perturbed symmetric equilibria on heat dispersal in magnetically dominated plasmas is discussed.

Results are reported from the combined CfA Stellar Survey of selected bright A stars and an Einstein Guest Observer program for Ap and Am stars. In an initial report of results from the CfA Stellar Surveys by Vaiana et al. (1981) it was noted that the spread in observed X-ray luminosities among the few A stars observed was quite large. The reasons for this large spread was studied by Pallavicini et al. (1981). It was found that the X-ray emission from normal stars is related very strongly to bolometric luminosity for early-type stars and to rotation rate for late-type stars. However, an exception to this rule has been the apparently anomalous behavior of A star X-ray emission, for which the large spread in luminosity showed no apparent correlation with either bolometric luminosity or stellar rotation rate. In the present study, it is shown that the level of emission from normal A stars agrees with the correlation observed for O and B stars.

A time-dependent one-dimensional code incorporating energy, momentum and mass conservation equations, and taking the entire solar atmospheric structure into account, is used to investigate the hydrodynamic response of confined magnetic structures to strong heating perturbations. Model calculation results are compared with flare observations which include the light curves of spectral lines formed over a wide range of coronal flare temperatures, as well as determinations of Doppler shifts for the high temperature plasma. It is shown that the numerical simulation predictions are in good overall agreement with the observed flare coronal plasma evolution, correctly reproducing the temporal profile of X-ray spectral lines and their relative intensities. The predicted upflow velocities support the interpretation of the blueshifts as due to evaporation of chromospheric material.

A hydrostatic model for the X-ray halo around the giant elliptical galaxy M87 is presented. It is shown that by taking into account the processes of thermal conduction, and nonthermal heating by relativistic electrons in the radio lobes, a self-consistent hydrostatic model can be constructed. There is no need to invoke radiative accretion or the suppression of thermal conductivity.