Steven R. Cranmer

UVCS/SOHO Empirical Determinations of Anisotropic Velocity Distributions in the Solar Corona

We present a self-consistent empirical model for several plasma parameters of a polar coronal hole near solar minimum, derived from observations with the Solar and Heliospheric Observatory Ultraviolet Coronagraph Spectrometer. The model describes the radial distribution of density for electrons, H0, and O5 + and the outflow velocity and unresolved most probable velocities for H0 and O5 + during the period between 1996 November and 1997 April. In this Letter, we compare observations of H I Lyα and O VI λλ1032, 1037 emission lines with spatial models of the plasma parameters, and we iterate for optimal consistency between measured and synthesized observable quantities. The unexpectedly large line widths of H0 atoms and O5 + ions at most radii are the result of anisotropic velocity distributions, which are not consistent with purely thermal motions or the expected motions from a combination of thermal and transverse wave velocities. Above 2 R, the observed transverse, most probable speeds for O5 + are significantly larger than the corresponding motions for H0, and the outflow velocities of O5 + are also significantly larger than the corresponding velocities of H0. We discuss the constraints and implications on various theoretical models of coronal heating and acceleration.

An Empirical Model of a Polar Coronal Hole at Solar Minimum

We present a comprehensive and self-consistent empirical model for several plasma parameters in the extended solar corona above a polar coronal hole. The model is derived from observations with the SOHO Ultraviolet Coronagraph Spectrometer (UVCS/SOHO) during the period between 1996 November and 1997 April. We compare observations of H I Lyα and O VI λλ1032, 1037 emission lines with detailed three-dimensional models of the plasma parameters and iterate for optimal consistency between measured and synthesized observable quantities. Empirical constraints are obtained for the radial and latitudinal distribution of density for electrons, H0, and O5+, as well as the outflow velocity and unresolved anisotropic most probable speeds for H0 and O5+. The electron density measured by UVCS/SOHO is consistent with previous solar minimum determinations of the white-light coronal structure; we also perform a statistical analysis of the distribution of polar plumes using a long time series. From the emission lines we find that the unexpectedly large line widths of H0 atoms and O5+ ions at most heights are the result of anisotropic velocity distributions. These distributions are not consistent with purely thermal motions or the expected motions from a combination of thermal and transverse wave velocities. Above 2 R☉, the observed transverse most probable speeds for O5+ are significantly larger than the corresponding motions for H0, and the outflow velocities of O5+ are also significantly larger than the corresponding velocities of H0. Also, the latitudinal dependence of intensity constrains the geometry of the wind velocity vectors, and superradial expansion is more consistent with observations than radial flow. We discuss the constraints and implications on various theoretical models of coronal heating and acceleration.

Spectroscopic Constraints on Models of Ion Cyclotron Resonance Heating in the Polar Solar Corona and High-Speed Solar Wind

Using empirical ion velocity distributions derived from Ultraviolet Coronagraph Spectrometer (UVCS) and Solar Ultraviolet Measurements of Emitted Radiation (SUMER) ultraviolet spectroscopy, we construct theoretical models of the nonequilibrium plasma state of the polar solar corona. The primary energy deposition mechanism we investigate is the dissipation of high-frequency (10-10,000 Hz) ion cyclotron resonant Alfven waves which can heat and accelerate ions differently depending on their charge and mass. We solve the internal energy conservation equations for the ion temperature components parallel and perpendicular to the superradially expanding magnetic field lines and use empirical constraints for the remaining parameters. We find that it is possible to explain many of the kinetic properties of the plasma (such as high perpendicular ion temperatures and strong temperature anisotropies) with relatively small amplitudes for the resonant waves. There is suggestive evidence for steepening of the Alfven wave spectrum between the coronal base and the largest heights observed spectroscopically, and it is important to take Coulomb collisions into account to understand observations at the lowest heights. Because the ion cyclotron wave dissipation is rapid, the extended heating seems to demand a constantly replenished population of waves over several solar radii. This indicates that the waves are generated gradually throughout the wind rather than propagated up from the base of the corona.

ON THE GENERATION, PROPAGATION, AND REFLECTION OF ALFVEN WAVES FROM THE SOLAR PHOTOSPHERE TO THE DISTANT HELIOSPHERE

We present a comprehensive model of the global properties of Alfven waves in the solar atmosphere and the fast solar wind. Linear non-WKB wave transport equations are solved from the photosphere to a distance past the orbit of the Earth, and for wave periods ranging from 3 s to 3 days. We derive a radially varying power spectrum of kinetic and magnetic energy fluctuations for waves propagating in both directions along a superradially expanding magnetic flux tube. This work differs from previous models in three major ways. (1) In the chromosphere and low corona, the successive merging of flux tubes on granular and supergranular scales is described using a two-dimensional magnetostatic model of a network element. Below a critical flux-tube merging height the waves are modeled as thin-tube kink modes, and we assume that all of the kink-mode wave energy is transformed into volume-filling Alfven waves above the merging height. (2) The frequency power spectrum of horizontal motions is specified only at the photosphere, based on prior analyses of G-band bright point kinematics. Everywhere else in the model the amplitudes of outward and inward propagating waves are computed with no free parameters. We find that the wave amplitudes in the corona agree well with off-limb nonthermal line-width constraints. (3) Nonlinear turbulent damping is applied to the results of the linear model using a phenomenological energy loss term. A single choice for the normalization of the turbulent outer-scale length produces both the right amount of damping at large distances (to agree with in situ measurements) and the right amount of heating in the extended corona (to agree with empirically constrained solar wind acceleration models). In the corona, the modeled heating rate differs by more than an order of magnitude from a rate based on isotropic Kolmogorov turbulence.

HEATING OF THE SOLAR CHROMOSPHERE AND CORONA BY ALFVÉN WAVE TURBULENCE

A three-dimensional magnetohydrodynamic (MHD) model for the propagation and dissipation of Alfv?n waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100?km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfv?n waves using the reduced MHD approximation. The increase of Alfv?n speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheric and chromospheric parts of the flux tube. Part of the wave energy is transmitted through the TR and produces turbulence in the corona. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfv?n wave turbulence, provided that the small-scale footpoint motions have velocities of 1-2?km?s?1 and timescales of 60-200?s. The heating rate per unit volume in the chromosphere is two to three orders of magnitude larger than that in the corona. We construct a series of models with different values of the model parameters, and find that the coronal heating rate increases with coronal field strength and decreases with loop length. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfv?nic turbulence.

Electron and proton heating by solar wind turbulence

[1] Previous formulations of heating and transport associated with strong magnetohydrodynamic (MHD) turbulence are generalized to incorporate separate internal energy equations for electrons and protons. Electron heat conduction is included. Energy is supplied by turbulent heating that affects both electrons and protons and is exchanged between them via collisions. Comparison to available Ulysses data shows that a reasonable accounting for the data is provided when (1) the energy exchange timescale is very long and (2) the deposition of heat due to turbulence is divided, with 60% going to proton heating and 40% into electron heating. Heat conduction, determined here by an empirical fit, plays a major role in describing the electron data.

Alfvénic Turbulence in the Extended Solar Corona: Kinetic Effects and Proton Heating

We present a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. Recent observations have shown that preferential heating and acceleration of positive ions occur in the first few solar radii of the high-speed solar wind. Measurements made by the Ultraviolet Coronagraph Spectrometer aboard SOHO have revived interest in the idea that ions are energized by the dissipation of ion cyclotron resonant waves, but such high-frequency (i.e., small-wavelength) fluctuations have not been observed. A turbulent cascade is one possible way of generating small-scale fluctuations from a preexisting population of low-frequency MHD waves. We model this cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, however, there is insufficient power to heat protons and heavy ions. The dominant oblique fluctuations (with dispersion properties of kinetic Alfven waves) undergo Landau damping, which implies strong parallel electron heating. We discuss the probable nonlinear evolution of the electron velocity distributions into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere), which can possibly heat protons via stochastic interactions.

Inhibition of Wind-Compressed Disk Formation by Nonradial Line Forces in Rotating Hot-Star Winds

We investigate the effects of nonradial line forces on the formation of a wind-compressed disk (WCD) around a rapidly rotating B star. Such nonradial forces can arise both from asymmetries in the line resonances in the rotating wind and from rotational distortion of the stellar surface. They characteristically include a latitudinal force component directed away from the equator and an azimuthal force component acting against the sense of rotation. Here we present results from radiation-hydrodynamical simulations showing that these nonradial forces can lead to an effective suppression of the equatorward flow needed to form a WCD as well as a modest (~20%) spin-down of the wind rotation. Furthermore, contrary to previous expectations that the wind mass flux should be enhanced by the reduced effective gravity near the equator, we show here that gravity darkening effects can actually lead to a reduced mass loss, and thus lower density, in the wind from the equatorial region. Overall, the results here thus imply a flow configuration that is markedly different from that derived in previous models of winds from rotating early-type stars. In particular, a major conclusion is that equatorial wind compression effects should be effectively suppressed in any radiatively driven stellar wind for which, as in the usual CAK formalism, the driving includes a significant component from optically thick lines. This presents a serious challenge to the WCD paradigm as an explanation for disk formation around Be and other rapidly rotating hot stars thought to have CAK-type, line-driven winds.

Ion Cyclotron Wave Dissipation in the Solar Corona: The Summed Effect of More than 2000 Ion Species

In this paper the dissipation of ion cyclotron resonant waves in the extended solar corona is Alfvec n examined in detail. For the —rst time, the wave damping arising from more than 2000 low-abundance ion species is taken into account. Useful approximations for the computation of coronal ionization equi- libria for elements heavier than nickel are presented. Also, the Sobolev approximation from the theory of hot-star winds is applied to the resonant wave dissipation in the solar wind, and the surprisingly eUective damping ability of ii minor ˇˇ ions is explained in simple terms. High-frequency (10¨10,000 Hz) waves pro- pagating up from the base of the corona are damped signi—cantly when they resonate with ions having charge-to-mass ratios of about 0.1, and negligible wave power would then be available to resonate with higher charge-to-mass ratio ions at larger heights. This result con—rms preliminary suggestions from earlier work that the waves that heat and accelerate the high-speed solar wind must be generated throughout the extended corona. The competition and eventual equilibrium between wave damping and wave replenishment may explain observed diUerences in coronal O VI and Mg X emission line widths. Subject headings: plasmasradiative transfersolar windSun: coronaturbulencewaves

Sudden Radiative Braking in Colliding Hot-Star Winds

Hot, massive stars have strong stellar winds, and in hot-star binaries these winds can undergo violent collision. Because such winds are thought to be radiatively driven, radiative forces may also play an important role in moderating the wind collision. However, previous studies have been limited to considering how such forces may inhibit the initial acceleration of the companion stellar wind. In this paper we analyze the role of an even stronger radiative braking effect, whereby the primary wind is rather suddenly decelerated by the radiative momentum flux it encounters as it approaches a bright companion. We further show that the braking location and velocity law along the line of centers between the stars can be approximated analytically using a simple one-dimensional analysis. The results of this analysis agree well with a detailed two-dimensional hydrodynamical simulation of the wind collision in the WR + O binary V444 Cygni and demonstrate that radiative braking can significantly alter the bow-shock geometry and reduce the strength of the wind collision. We then apply the derived analytic theory to a set of 14 hot-star binary systems, and conclude that radiative braking is likely to be of widespread importance for wind-wind collisions in WR + O binaries with close to medium separation, D 100 R?. It may also be important in other types of hot-star binaries that exhibit a large imbalance between the component wind strengths.