R. T. James McAteer

Propagation of an Earth-directed coronal mass ejection in three dimensions

Solar coronal mass ejections (CMEs) are the most significant drivers of adverse space weather on Earth, but the physics governing their propagation through the heliosphere is not well understood. Although stereoscopic imaging of CMEs with NASAs Solar Terrestrial Relations Observatory (STEREO) has provided some insight into their three-dimensional (3D) propagation, the mechanisms governing their evolution remain unclear because of difficulties in reconstructing their true 3D structure. In this paper, we use a new elliptical tie-pointing technique to reconstruct a full CME front in 3D, enabling us to quantify its deflected trajectory from high latitudes along the ecliptic, and measure its increasing angular width and propagation from 2 to 46 (∼0.2 AU). Beyond 7 , we show that its motion is determined by an aerodynamic drag in the solar wind and, using our reconstruction as input for a 3D magnetohydrodynamic simulation, we determine an accurate arrival time at the Lagrangian L1 point near Earth.

STATISTICS OF ACTIVE REGION COMPLEXITY: A LARGE-SCALE FRACTAL DIMENSION SURVEY

A quantification of the magnetic complexity of active regions using a fractal dimension measure is presented. This fully automated approach uses full-disk MDI magnetograms of active regions from a large data set (2742 days of the SOHO mission, 9342 active region images) to compare the calculated fractal dimension of each region to both its Mount Wilson classification and flare rate. Each Mount Wilson class exhibits a similar fractal dimension frequency distribution, possibly suggesting a self-similar nature of all active regions. Solar flare productivity exhibits an increase in both the frequency and GOES X-ray magnitude of flares from regions with higher fractal dimension. Specifically, a lower threshold fractal dimension of 1.2 and 1.25 exists as a necessary, but not sufficient, requirement for an active region to produce M- and X-class flares, respectively, within 24 hr of the observation.

Wavelet phase coherence analysis: Application to a quiet-sun magnetic element

A new application of wavelet analysis is presented that utilizes the inherent phase information residing within the complex Morlet transform. The technique is applied to a weak solar magnetic network region, and the temporal variation of phase difference between TRACE 1700 A and SOHO/SUMER C II 1037 A intensities is shown. We present, for the first time in an astrophysical setting, the application of wavelet phase coherence, including a comparison between two methods of testing real wavelet phase coherence against that of noise. The example highlights the advantage of wavelet analysis over more classical techniques, such as Fourier analysis, and the effectiveness of the former to identify wave packets of similar frequencies but with differing phase relations is emphasized. Using cotemporal, ground-based Advanced Stokes Polarimeter measurements, changes in the observed phase differences are shown to result from alterations in the magnetic topology.

Observational Evidence for Mode Coupling in the Chromospheric Network

Oscillations in network bright points (NBPs) are studied at a variety of chromospheric heights. In particular, the three-dimensional variation of NBP oscillations is studied using image segmentation and cross-correlation analysis between images taken in light of Ca II K3, Hα core, Mg I b2, and Mg I b1 - 0.4 A. Wavelet analysis is used to isolate wave packets in time and to search for height-dependent time delays that result from upward- or downward-directed traveling waves. In each NBP studied, we find evidence for kink-mode waves (1.3, 1.9 mHz), traveling up through the chromosphere and coupling with sausage-mode waves (2.6, 3.8 mHz). This provides a means for depositing energy in the upper chromosphere. We also find evidence for other upward- and downward-propagating waves in the 1.3-4.6 mHz range. Some oscillations do not correspond to traveling waves, and we attribute these to waves generated in neighboring regions.

The Bursty Nature of Solar Flare X-Ray Emission

The complex and highly varying temporal nature of emission from an X4.8 flare is studied across seven X-ray energy bands. A wavelet transform modulus maxima method is used to obtain the multifractal spectra of the temporal variation of the X-ray emission. As expected from the Neupert effect, the time series of the emission at low energies (3-6, 6-12 keV; thermal) is smooth. The peak Holder exponent, around 1.2, for this low-energy emission is indicative of a signal with a high degree of memory and suggestive of a smooth chromospheric evaporation process. The more bursty emission at higher energies (100-300, 300-800 keV; nonthermal) is described by a multifractal spectrum that peaks at a smaller Holder exponent (less than 0.5 for the largest singularities), indicative of a signal with a low degree of memory. This describes an antipersistent walk and indicates an impulsive, incoherent driving source. We suggest that this may arise from bursty reconnection, with each reconnection event producing a different and uncorrelated nonthermal particle source. The existence of a power-law scaling of wavelet coefficients across timescales is in agreement with the creation of a fractal current sheet diffusion region.

Turbulence, complexity, and solar flares

The issue of predicting solar flares is one of the most fundamental in physics, addressing issues of plasma physics, high-energy physics, and modelling of complex systems. It also poses societal consequences, with our ever-increasing need for accurate space weather forecasts. Solar flares arise naturally as a competition between an input (flux emergence and rearrangement) in the photosphere and an output (electrical current build up and resistive dissipation) in the corona. Although initially localised, this redistribution affects neighbouring regions and an avalanche occurs resulting in large scale eruptions of plasma, particles, and magnetic field. As flares are powered from the stressed field rooted in the photosphere, a study of the photospheric magnetic complexity can be used to both predict activity and understand the physics of the magnetic field. The magnetic energy spectrum and multifractal spectrum are highlighted as two possible approaches to this.

The Influence of Magnetic Field on Oscillations in the Solar Chromosphere

Two sequences of solar images obtained by the Transition Region and Coronal Explorer in three UV passbands are studied using wavelet and Fourier analysis and compared to the photospheric magnetic flux measured by the Michelson Doppler Interferometer on the Solar Heliospheric Observatory to study wave behavior in differing magnetic environments. Wavelet periods show deviations from the theoretical cutoff value and are interpreted in terms of inclined fields. The variation of wave speeds indicates that a transition from dominant fast-magnetoacoustic waves to slow modes is observed when moving from network into plages and umbrae. This implies preferential transmission of slow modes into the upper atmosphere, where they may lead to heating or be detected in coronal loops and plumes.

QUANTIFYING THE EVOLVING MAGNETIC STRUCTURE OF ACTIVE REGIONS

The topical and controversial issue of parameterizing the magnetic structure of solar active regions has vital implications in the understanding of how these structures form, evolve, produce solar flares, and decay. This interdisciplinary and ill-constrained problem of quantifying complexity is addressed by using a two-dimensional wavelet transform modulus maxima (WTMM) method to study the multifractal properties of active region photospheric magnetic fields. The WTMM method provides an adaptive space-scale partition of a fractal distribution, from which one can extract the multifractal spectra. The use of a novel segmentation procedure allows us to remove the quiet Sun component and reliably study the evolution of active region multifractal parameters. It is shown that prior to the onset of solar flares, the magnetic field undergoes restructuring as Dirac-like features (with a Holder exponent, h = –1) coalesce to form step functions (where h = 0). The resulting configuration has a higher concentration of gradients along neutral line features. We propose that when sufficient flux is present in an active region for a period of time, it must be structured with a fractal dimension greater than 1.2, and a Holder exponent greater than –0.7, in order to produce M- and X-class flares. This result has immediate applications in the study of the underlying physics of active region evolution and space weather forecasting.

Long-Period Chromospheric Oscillations in Network Bright Points

The spatial variation of chromospheric oscillations in network bright points (NBPs) is studied using high-resolution observations in Ca II K3. Light curves and hence power spectra were created by isolating distinct regions of the NBP via a simple intensity thresholding technique. Using this technique, it was possible to identify peaks in the power spectra with particular spatial positions within the NBPs. In particular, long-period waves with periods of 4-15 minutes (1-4 mHz) were found in the central portions of each NBP, indicating that these waves are certainly not acoustic but possibly due to magnetoacoustic or magnetogravity wave modes. We also show that spatially averaged or low spatial resolution power spectra can lead to an inability to detect such long-period waves.

Propagating Waves and Magnetohydrodynamic Mode Coupling in the Quiet-Sun Network

Mullard Space Science Laboratory ,Dorking, Surrey RH5 6NT, England, UKAbstractHigh-cadence, multiwavelength optical observations,taken during two separate observing runs at the NationalSolar Observatory/Sacramento Peak, are presented here.A total of fifteen network bright points have been stud-ied at differing atmospheric heights, using images takenin narrow wavebands. Wavelet analysis was used to studywavepackets,andidentifytravelingmagnetohydrodynamic(MHD) waves. Wave speeds were estimated through tem-poral cross-correlation of signals, in selected frequencybands of wavelet power, in each wavelength. Seven mode-coupling cases were identified, one in each of seven of theNBPs. MHD mode coupling is a viable mechanism fortransport of energy from the photosphere into the chro-mosphere, where subsequent deposition can contribute toatmospheric heating.Key words: Sun: oscillations – Sun: chromosphere – Sun:photosphere – Sun: magnetic fields1. Background theoryIt has been known for a long time that the Sun exhibits areversal in its temperature profile above the photosphere,which then increases throughout the chromosphere. How-ever, it is not known what mechanism heats this regionof the atmosphere. Any complete theory attempting toaddress this matter must manage to explain a number ofprocesses: (1) the generation of non-radiative energy; (2)the transportation from the source region to that which isto be heated; and (3) the deposition of this energy.One theory to explain the transportation of energyfrom the underlying photosphere into the chromospherehas been proposed by Kalkofen (1997). This states thatnon-dissipative, transverse-mode, magnetohydrodynamic(MHD) waves travel up magnetic flux tubes located atthe supergranular cell boundaries (network bright points– NBPs) into less dense regions. Consequently the wave ve-locity amplitude increases and enters a non-linear regime,enabling efficient transfer of transverse-mode energy tolongitudinal-mode waves at twice the transverse-mode fre-quency. These longitudinal waves may then heat the sur-rounding plasma either through shocks, since they arecompressible (Zhugzhda et al. 1995), or by driving dissi-pative Pedersen currents (Goodman 2000, 2004). As such,the concept of mode coupling may provide an explana-tion for point (2) mentioned above, and lead to suitablesituations to describe point (3).To address the generation of MHD waves in the un-derlying photosphere, Hasan & Kalkofen (1999) modelledthe generation of both transverse- and longitudinal-modeMHD waves in a thin flux tube through external granu-lar buffeting. They found the energy flux of the transversemode to be an order of magnitude greater than that of thelongitudinal mode for typical NBP field strengths. This in-dicates preferential transverse-mode generation from thephotosphere, providing a mechanism which satisfies point(1) above, and leads directly into the requirements formode coupling.2. ObservationsAll the data presented here were obtained with the DunnSolarTelescopeattheNationalSolarObservatory