Thomas J. Bogdan

Waves in the Magnetized Solar Atmosphere. I. Basic Processes and Internetwork Oscillations

We have modeled numerically the propagation of waves through magnetic structures in a stratified atmosphere. We first simulate the propagation of waves through a number of simple, exemplary field geometries in order to obtain a better insight into the effect of differing field structures on the wave speeds, amplitudes, polarizations, direction of propagation, etc., with a view to understanding the wide variety of wavelike and oscillatory processes observed in the solar atmosphere. As a particular example, we then apply the method to oscillations in the chromospheric network and internetwork. We find that in regions where the field is significantly inclined to the vertical, refraction by the rapidly increasing phase speed of the fast modes results in total internal reflection of the waves at a surface whose altitude is highly variable. We conjecture a relationship between this phenomenon and the observed spatiotemporal intermittancy of the oscillations. By contrast, in regions where the field is close to vertical, the waves continue to propagate upward, channeled along the field lines but otherwise largely unaffected by the field.

Coupled quasi-linear wave damping and stochastic acceleration of pickup ions in the solar wind

Coupled spatially homogeneous quasilinear kinetic equations are derived which describe the evolution of the energetic ion omnidirectional distribution function and the intensities of magnetohydrodynamic waves propagating parallel and antiparallel to the ambient magnetic field. The energetic ions are assumed to be nearly isotropic and possess speeds much greater than the Alfven speed. For application to pickup ions the equations may also include an energetic ion injection rate and wave excitation or damping caused by isotropization of the newborn ions. The wave kinetic equations may be integrated to yield explicit expressions for the wave intensities, which may be substituted into the ion kinetic equations to yield a single self-consistent energy diffusion equation for the energetic ions. The theory represents the first treatment of stochastic (second-order Fermi) acceleration in which the back reaction of the ions on the turbulence is included self-consistently. Numerical solutions of the kinetic equations are presented for four cases of pickup ions in the solar wind which illustrate the essential features of the evolution: (1) interstellar pickup helium near a heliocentric radial distance of 1 AU; (2) interstellar pickup hydrogen near 10 AU; (3) water group pickup ions downstream of the bow wave of Comet Giacobini-Zinner for parameters observed during the International Cometary Explorer flyby; (4) water group pickup ions downstream of the bow wave of Comet Halley for parameters observed during the Giotto flyby. The helium calculation reveals some modification of the solar wind wave spectrum and energy diffusion of the ions; although adiabatic deceleration is not included, acceleration rates are qualitatively consistent with the observed spectrum at 1 AU (Mobius et al., 1985). The hydrogen calculation shows extreme damping of the solar wind wave spectrum in the cyclotron-resonant frequency range and a reduction in the acceleration rate of most of the ions. It is suggested that this behavior is responsible for an underabundance of hydrogen relative to the minor ions in the anomalous cosmic ray component, which is thought to originate from pickup ions accelerated at the solar wind termination shock. Wave damping is small at comet G-Z, and the calculated energy spectra do not appear to be in quantitative agreement with the observed spectra (Richardson et al., 1987). At Comet Halley, on the other hand, wave damping is substantial and the calculated spectra appear to be in general agreement with the observations (McKenna-Lawlor et al., 1989).

Avalanche models for solar flares (Invited Review)

This paper is a pedagogical introduction to avalanche models of solar flares, including a comprehensive review of recent modeling efforts and directions. This class of flare model is built on a recent paradigm in statistical physics, known as self-organized criticality. The basic idea is that flares are the result of an ‘avalanche’ of small-scale magnetic reconnection events cascading through a highly stressed coronal magnetic structure, driven to a critical state by random photospheric motions of its magnetic footpoints. Such models thus provide a natural and convenient computational framework to examine Parkers hypothesis of coronal heating by nanoflares.

Sunspot Oscillations: a Review (Invited Review)

The current state of our knowledge, and ignorance, of the nature of oscillations in sunspots is surveyed. An effort is made to summarize the robust aspects of both the observational and theoretical components of the subject in a coherent, and common, conceptual framework. Detailed discussions of the various controversial issues are avoided except in instances where new viewpoints are advanced. Instead, extensive references are made to the growing literature on the subject, and generous explanatory remarks are made to guide the reader who wishes to delve more deeply into the underpinnings of the subject matter.

Localized sources of propagating acoustic waves in the solar photosphere

A time series of Doppler measurements of the solar photosphere with moderate spatial resolution is described which covers a portion of the solar disk surrounding a small sunspot group. At temporal frequencies above 5.5 mHz, the Doppler field probes the spatial and temporal distribution of regions that emit acoustic energy. In the frequency range between 5.5 and 7.5 mHz, inclusive, a small fraction of the surface area emits a disproportionate amount of acoustic energy. The regions with excess emission are characterized by a patchy structure at spatial scales of a few arcseconds and by association (but not exact co-location) with regions having substantial magnetic field strength. These observations bear on the conjecture that most of the acoustic energy driving solar p-modes is created in localized regions occupying a small fraction of the solar surface area.

The absorption of p-modes by sunspots: Variations with degree and order

A spherical harmonic decomposition of the p-modes into inward and outward propagating waves is employed to investigate the absorption of solar p-modes by an isolated sunspot. The absorption coefficient (averaged over frequency and azimuthal order) is found to increase with increasing horizontal wavenumber k over the range 0-0.8/Mm. For larger horizontal wavenumbers, in the range 0.8-1.5/Mm, the absorption coefficient decreases with increasing k. The absorption along each individual p-mode ridge tends to peak at an intermediate value of the spherical harmonic degree in the range 200-400. The highest absorption is found along the p(1) ridge, and the absorption decreases with increasing radial order.

Velocity and Magnetic Field Fluctuations in the Photosphere of a Sunspot

We use a data set of exceptionally high quality to measure oscillations of Doppler velocity, intensity, and the vector magnetic field at photospheric heights in a sunspot. Based on the full Stokes inversion of the line profiles of Fe I 630.15 and 630.25 nm, in the sunspot umbra we find upper limits of 4 G (root mean square [rms]) for the amplitude of 5 minute oscillations in magnetic field strength and 009 (rms) for the corresponding oscillations of the inclination of the magnetic field to the line of sight. Our measured magnitude of the oscillation in magnetic field strength is considerably lower than that found in 1997 by Horn, Staude, & Landgraf. Moreover, we find it likely that our measured magnetic field oscillation is at least partly due to instrumental and inversion cross talk between the velocity and magnetic signals, so that the actual magnetic field strength fluctuations are even weaker than 4 G. In support of this we show, on the basis of the eigenmodes of oscillation in a theoretical model of the sunspot umbra, that magnetic field variations of at most 0.5 G are all that is to be expected. The theoretical model also provides an explanation of the shift of power peaks in Doppler velocity to the 3 minute band in chromospheric umbral oscillations, as a natural consequence of the drastic change in character of the eigenmodes of oscillation between frequencies of about 4.5 and 5.0 mHz due to increased tunneling through the acoustic cutoff-frequency barrier. Using measurements of the phase of velocity oscillations above the acoustic cutoff frequency, we determine the relative velocity response height in the umbra of four different photospheric spectral lines from the phase differences between velocities in these lines, assuming that the oscillations propagate vertically at the local sound speed. In spacetime maps of fluctuations in continuum intensity, Doppler velocity, magnetic field strength, and field inclination, we see distinct features that migrate radially inward from the inner penumbra all the way to the center of the umbra, at speeds of a few tenths of a kilometer per second. These moving features are probably a signature of the convective interchange of magnetic flux tubes in the sunspot, although we failed to find any strong correlation among the features in the different quantities, indicating that these features have not been fully resolved.

Simulation of f- and p-Mode Interactions with a Stratified Magnetic Field Concentration

The interaction of f- and p-modes with a slab of vertical magnetic field of sunspot strength is simulated numerically in two spatial dimensions. Both f-modes and p-modes are partially converted to slow magnetoatmospheric gravity (MAG) waves within the magnetic slab because of the strong gravitational stratification of the plasma along the magnetic lines of force. The slow MAG waves propagate away from the conversion layer guided by the magnetic field lines, and the energy they extract from the incident f- and p-modes results in a reduced amplitude for these modes as they exit from the back side of the slab. In addition, the incident p-modes are partially mixed into f-modes of comparable frequency, and therefore larger spherical harmonic degree, when they exit the magnetic flux concentration. These findings have important implications for the interpretation of observations of p-mode absorption by sunspots, both in terms of the successes and failures of this simple numerical simulation viewed in the sunspot seismology context.

A comment on the relationship between the modal and time-distance formulations of local helioseismology

The relationship between the time-distance and modal-decomposition approaches to solar active region seismology is clarified through the consideration of the oscillations of a plane-parallel, isentropic polytrope. It is demonstrated by direct construction that a wave packet formed through the superposition of neighboring p-modes interferes constructively along a ray bundle that follows the appropriate WKBJ ray path obtained by using the eikonal approximation. Because the actual power envelope of the solar 5 minute oscillations restricts the excited p-modes to rather low radial orders, the ray bundles are diffuse and sample portions of the solar envelope that are some ≈ 10-30 Mm distant from the nominal WKBJ ray path. This behavior is consistent with the fact that the eikonal approximation becomes valid only in the limiting case of large radial orders (n 1). The p-mode wave packets that are isolated by employing the time-distance methods must therefore be described either as a superposition of individual p-modes (a wave packet), or as a sum of ray paths (a ray bundle), depending upon which representation proves to be optimal for the given circumstances.

On the generation of sound by turbulent convection. I - A numerical experiment

Motivated by the problem of the origin of the solar p-modes, we study the generation of acoustic waves by turbulent convection. Our approach uses the results of high-resolution 3D simulations as the experimental basis for our investigation. The numerical experiment describes the evolution of a horizontally periodic layer of vigorously convecting fluid. The sound is measured by a procedure, based on a suitable linearization of the equations of compressible convection that allows the amplitude of the acoustic field to be determined. Through this procedure we identify unambiguously some 400 acoustic modes. The total energy of the acoustic field is found to be a fraction of a percent of the kinetic energy of the convection. The amplitudes of the observed modes depend weakly on (horizontal) wavenumber but strongly on frequency. The line widths of the observed modes typically exceed the natural linewidths of the modes as inferred from linear theory. This broadening appears to be related to the (stochastic) interaction between the modes and the underlying turbulence which causes abrupt, episodic events during which the phase coherence of the modes is lost.