William Paul Abbett

RADIATIVE HYDRODYNAMIC MODELS OF THE OPTICAL AND ULTRAVIOLET EMISSION FROM SOLAR FLARES

We report on radiative hydrodynamic simulations of moderate and strong solar flares. The flares were simulated by calculating the atmospheric response to a beam of nonthermal electrons injected at the apex of a one-dimensional closed coronal loop and include heating from thermal soft X-ray, extreme ultraviolet, and ultraviolet (XEUV) emission. The equations of radiative transfer and statistical equilibrium were treated in non-LTE and solved for numerous transitions of hydrogen, helium, and Ca II, allowing the calculation of detailed line profiles and continuum emission. This work improves on previous simulations by incorporating more realistic nonthermal electron beam models and includes a more rigorous model of thermal XEUV heating. We find that XEUV back-warming contributes less than 10% of the heating, even in strong flares. The simulations show elevated coronal and transition region densities resulting in dramatic increases in line and continuum emission in both the UV and optical regions. The optical continuum reaches a peak increase of several percent, which is consistent with enhancements observed in solar white-light flares. For a moderate flare (~M class), the dynamics are characterized by a long gentle phase of near balance between flare heating and radiative cooling, followed by an explosive phase with beam heating dominating over cooling and characterized by strong hydrodynamic waves. For a strong flare (~X class), the gentle phase is much shorter, and we speculate that for even stronger flares the gentle phase may be essentially nonexistent. During the explosive phase, synthetic profiles for lines formed in the upper chromosphere and transition region show blueshifts corresponding to a plasma velocity of ~120 km s-1, and lines formed in the lower chromosphere show redshifts of ~40 km s-1.

Multiwavelength Observations of Flares on AD Leonis

We report results from a multiwavelength observing campaign conducted during 2000 March on the flare star AD Leo. Simultaneous data were obtained from several ground- and space-based observatories, including observations of eight sizable flares. We discuss the correlation of line and continuum emission in the optical and ultraviolet wavelength regimes, as well as the flare energy budget, and we find that the emission properties are remarkably similar even for flares of very different evolutionary morphology. This suggests a common heating mechanism and atmospheric structure that are independent of the detailed evolution of individual flares. We also discuss the Neupert effect, chromospheric line broadening, and velocity fields observed in several transition region emission lines. The latter show significant downflows during and shortly after the flare impulsive phase. Our observations are broadly consistent with the solar model of chromospheric evaporation and condensation following impulsive heating by a flux of nonthermal electrons. These data place strong constraints on the next generation of radiative hydrodynamic models of stellar flares.

Dynamic Models of Optical Emission in Impulsive Solar Flares

Numerical simulations of the dynamics and radiation in a solar flare loop are presented. The heating processes in the lower atmosphere include nonthermal heating by accelerated electrons and thermal soft X-ray irradiation from the flare-heated transition region and corona. Important transitions of hydrogen, helium, and singly ionized calcium and magnesium are treated in non-LTE. The principal results of the analysis are the following:

THE MAGNETIC CONNECTION BETWEEN THE CONVECTION ZONE AND CORONA IN THE QUIET SUN

To understand the dynamic, magnetic, and energetic connection between the convectively unstable layers below the visible surface of the Sun and the overlying solar corona, we have developed a new three-dimensional magnetohydrodynamic code capable of simultaneously evolving a model convection zone and corona within a single computational volume. As a first application of this numerical model, we present a series of simulations of the quiet Sun in a domain that encompasses both the upper convection zone and low corona. We investigate whether the magnetic field generated by a convective surface dynamo can account for some of the observed properties of the quiet-Sun atmosphere. We find that (1) it is possible to heat a model corona to X-ray-emitting temperatures with the magnetic fields generated from a convective dynamo and an empirically based heating mechanism consistent with the observed relationship between X-ray emission and magnetic flux observed at the visible surface; (2) within the limitations of our numerical models of the quiet Sun, resistive and viscous dissipation alone are insufficient to maintain a hot corona; (3) the quiet-Sun model chromosphere is a dynamic, non-force-free layer that exhibits a temperature reversal in the convective pattern in the relatively low density layers above the photosphere; (4) the majority of the unsigned magnetic flux lies below the model photosphere in the convectively unstable portion of the domain; (5) horizontally directed magnetic structures thread the low atmosphere, often connecting relatively distant concentrations of magnetic flux observed at the surface; and (6) low-resolution photospheric magnetograms can significantly underestimate the amount of unsigned magnetic flux threading the quiet-Sun photosphere.

Tests and Comparisons of Velocity-Inversion Techniques

Recently, several methods that measure the velocity of magnetized plasma from time series of photospheric vector magnetograms have been developed. Velocity fields derived using such techniques can be used both to determine the fluxes of magnetic energy and helicity into the corona, which have important consequences for understanding solar flares, coronal mass ejections, and the solar dynamo, and to drive time-dependent numerical models of coronal magnetic fields. To date, these methods have not been rigorously tested against realistic, simulated data sets, in which the magnetic field evolution and velocities are known. Here we present the results of such tests using several velocity-inversion techniques applied to synthetic magnetogram data sets, generated from anelastic MHD simulations of the upper convection zone with the ANMHD code, in which the velocity field is fully known. Broadly speaking, the MEF, DAVE, FLCT, IM, and ILCT algorithms performed comparably in many categories. While DAVE estimated the magnitude and direction of velocities slightly more accurately than the other methods, MEFs estimates of the fluxes of magnetic energy and helicity were far more accurate than any other methods. Overall, therefore, the MEF algorithm performed best in tests using the ANMHD data set. We note that ANMHD data simulate fully relaxed convection in a high-β plasma, and therefore do not realistically model photospheric evolution.

The Three-dimensional Evolution of Rising, Twisted Magnetic Flux Tubes in a Gravitationally Stratified Model Convection Zone

We present three-dimensional numerical simulations of the rise and fragmentation of twisted, initially horizontal magnetic —ux tubes that evolve into emerging )-loops. The —ux tubes rise buoyantly through an adiabatically strati—ed plasma that represents the solar convection zone. The MHD equations are solved in the anelastic approximation, and the results are compared with studies of —ux-tube fragmenta- tion in two dimensions. We —nd that if the initial amount of —eld line twist is below a critical value, the degree of fragmentation at the apex of a rising )-loop depends on its three-dimensional geometry: the greater the apex curvature of a given )-loop, the lesser the degree of fragmentation of the loop as it approaches the photosphere. Thus, the amount of initial twist necessary for the loop to retain its cohe- sion can be reduced substantially from the two-dimensional limit. The simulations also suggest that, as a fragmented —ux tube emerges through a relatively quiet portion of the solar disk, extended crescent- shaped magnetic features of opposite polarity should form and steadily recede from one another. These features eventually coalesce after the fragmented portion of the )-loop emerges through the photosphere. Subject headings: MHDmethods: numericalSun: interiorSun: magnetic —elds

Radiative Hydrodynamic Models of Optical and Ultraviolet Emission from M Dwarf Flares

We report on radiative hydrodynamic simulations of M dwarf stellar flares and compare the model predictions to observations of several flares. The flares were simulated by calculating the hydrodynamic response of a model M dwarf atmosphere to a beam of nonthermal electrons. Radiative back-warming through numerous soft X-ray, extreme-ultraviolet, and ultraviolet transitions are also included. The equations of radiative transfer and statistical equilibrium are treated in non-LTE for many transitions of hydrogen, helium, and the Ca II ion, allowing the calculation of detailed line profiles and continuum radiation. Two simulations were carried out, with electron beam fluxes corresponding to moderate and strong beam heating. In both cases we find that the dynamics can be naturally divided into two phases: an initial gentle phase in which hydrogen and helium radiate away much of the beam energy and an explosive phase characterized by large hydrodynamic waves. During the initial phase, lower chromospheric material is evaporated into higher regions of the atmosphere, causing many lines and continua to brighten dramatically. The He II 304 line is especially enhanced, becoming the brightest line in the flaring spectrum. The hydrogen Balmer lines also become much brighter and show very broad line widths, in agreement with observations. We compare our predicted Balmer decrements to decrements calculated for several flare observations and find the predictions to be in general agreement with the observations. During the explosive phase both condensation and evaporation waves are produced. The moderate flare simulation predicts a peak evaporation wave of ~130 km s-1 and a condensation wave of ~30 km s-1. The velocity of the condensation wave matches velocities observed in several transition region lines. The optical continuum also greatly intensifies, reaching a peak increase of 130% (at 6000 A) for the strong flare, but does not match observed white-light spectra.

A Coupled Model for the Emergence of Active Region Magnetic Flux into the Solar Corona

We present a set of numerical simulations that model the emergence of active region magnetic flux into an initially field-free model corona. We simulate the buoyant rise of twisted magnetic flux tubes initially positioned near the base of a stable stratified model convection zone and use the results of these calculations to drive a three-dimensional magnetohydrodynamic model corona. The simulations show that time-dependent subsurface flows are an important component of the dynamic evolution and subsequent morphology of an emerging magnetic structure. During the initial stages of the flux emergence process, the overlying magnetic field differs significantly from a force-free state. However, as the runs progress and boundary flows adjust, most of the coronal field—with the exception of those structures located relatively close to the model photosphere—relaxes to a more force-free configuration. Potential field extrapolations do not adequately represent the magnetic structure when emerging active region fields are twisted. In the dynamic models, if arched flux ropes emerge with nonzero helicity, the overlying field readily forms sigmoid-shaped structures. However, the chirality of the sigmoid and other details of its structure depend on the observers vantage point and the location within a given loop of emitting plasma. Thus, sigmoids may be an unreliable signature of the sign and magnitude of magnetic twist.

SIMULATION OF FLUX EMERGENCE FROM THE CONVECTION ZONE TO THE CORONA

Here, we present numerical simulations of magnetic flux buoyantly rising from a granular convection zone into the low corona. We study the complex interaction of the magnetic field with the turbulent plasma. The model includes the radiative loss terms, non-ideal equations of state, and empirical corona heating. We find that the convection plays a crucial role in shaping the morphology and evolution of the emerging structure. The emergence of magnetic fields can disrupt the convection pattern as the field strength increases, and form an ephemeral region-like structure, while weak magnetic flux emerges and quickly becomes concentrated in the intergranular lanes, i.e., downflow regions. As the flux rises, a coherent shear pattern in the low corona is observed in the simulation. In the photosphere, both magnetic shearing and velocity shearing occur at a very sharp polarity inversion line. In a case of U-loop magnetic field structure, the field above the surface is highly sheared while below it is relaxed.

THE EFFECTS OF ROTATION ON THE EVOLUTION OF RISING OMEGA LOOPS IN A STRATIFIED MODEL CONVECTION ZONE

We present three-dimensional MHD simulations of buoyant magnetic flux tubes that rise through a stratified model convection zone in the presence of solar rotation. The equations of MHD are solved in the anelastic approximation, and the results are used to determine the effects of solar rotation on the dynamic evolution of an Ω-loop. We find that the Coriolis force significantly suppresses the degree of fragmentation at the apex of the loop during its ascent toward the photosphere. If the initial axial field strength of the tube is reduced, then, in the absence of forces due to convective motions, the degree of apex fragmentation is also reduced. Our simulations confirm the results of thin flux-tube calculations that show the leading polarity of an emerging active region positioned closer to the equator than the trailing polarity and the trailing leg of the loop oriented more vertically than the leading leg. We show that the Coriolis force slows the rise of the tube and induces a retrograde flow in both the magnetized and unmagnetized plasma of an emerging active region. Observationally, we predict that this flow will appear to originate at the leading polarity and will terminate at the trailing polarity.