Jack Ireland

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.

Joint observations of propagating oscillations with SOHO/CDS and TRACE

Joint Observing Program (JOP) 83 Solar and Heliospheric Observatory/Coronal Diagnostic Spectrometer (SOHO/CDS) and Transition Region and Coronal Explorer (TRACE) data is analysed for evidence of propagating intensity oscillations along loop structures in the solar corona. A propagating intensity oscillation with a minimum estimated speed of 50-195 km s 1 is observed within a TRACE 171 A coronal loop using a running dierence method. Co-spatial and co- temporal CDS and TRACE observations of this loop are analysed using a wavelet analysis method. The TRACE data shows a propagating oscillation with a period of300 s. This period is also observed with CDS suggesting propagating oscillations at chromospheric, transition region and coronal temperatures in the He i ,O v and Mgix lines.

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.

SunPy - Python for Solar Physics

SunPy is a data analysis toolkit which provides the necessary software for analyzing solar and heliospheric datasets in Python. SunPy aims to provide a free and open-source alternative to the current standard, an IDL- based solar data analysis environment known as SolarSoft (SSW). We present the latest release of SunPy, version 0.3. Though still in active development, SunPy already provides important functionality for solar data analysis. SunPy provides data structures for representing the most common solar data types: images, lightcurves, and spectra. To enable the acquisition of scientific data, SunPy provides integration with the Virtual Solar Observatory (VSO), a single source for accessing most solar data sets, and integration with the Heliophysics Event Knowledgebase (HEK), a database of transient solar events such as solar flares or coronal mass ejections. SunPy utilizes many packages from the greater scientific Python community, including NumPy and SciPy for core data types and analysis routines, PyFITS for opening image files, in FITS format, from major solar missions (e.g., SDO/AIA, SOHO/EIT, SOHO/LASCO, and STEREO) into WCS-aware map objects, and pandas for advanced time-series analysis tools for data from missions such as GOES, SDO/EVE, and Proba2/LYRA, as well as support for radio spectra (e.g., e-Callisto). Future releases will build upon and integrate with current work in the Astropy project and the rest of the scientific python community, to bring greater functionality to SunPy users.

Observation of oscillations in coronal loops

High cadence TRACE data (JOP 83) in the 171 A bandpass are used to report on several examples of outward propagating oscillations in the footpoints of large diffuse coronal loop structures close to active regions. The disturbances travel outward with a propagation speed between 70 and 160 km s−1. The variations in intensity are of the order of 2%–4%, compared to the background brightness and these get weaker as the disturbance propagates along the structure. From a wavelet analysis at different positions along the structures, periods in the 200–400 seconds range are found. It is suggested that these oscillations are slow magneto-acoustic waves propagating along the loop, carrying an estimated energy flux of 4×102 ergs cm−2 s−1.

Coronal Fourier Power Spectra: Implications for Coronal Seismology and Coronal Heating

The dynamics of regions of the solar corona are investigated using Atmospheric Imaging Assembly 171 A and 193 A data. The coronal emission from the quiet Sun, coronal loop footprints, coronal moss, and from above a sunspot is studied. It is shown that the mean Fourier power spectra in these regions can be described by a power law at lower frequencies that tails to a flat spectrum at higher frequencies, plus a Gaussian-shaped contribution that varies depending on the region studied. This Fourier spectral shape is in contrast to the commonly held assumption that coronal time series are well described by the sum of a long timescale background trend plus Gaussian-distributed noise, with some specific locations also showing an oscillatory signal. The implications of the observed spectral shape on the fields of coronal seismology and the automated detection of oscillations in the corona are discussed. The power-law contribution to the shape of the Fourier power spectrum is interpreted as being due to the summation of a distribution of exponentially decaying emission events along the line of sight. This is consistent with the idea that the solar atmosphere is heated everywhere by small energy deposition events.

Radiative and magnetic properties of solar active regions - I. Global magnetic field and EUV line intensities

Context. The relationships between the photospheric magnetic flux and either the X-ray or extreme ultraviolet emission from the solar atmosphere have been studied by several authors. Power-law relations have been found between the total magnetic flux and X-ray flux or intensities of the chromospheric, transition region, and coronal emission lines in solar active regions. These relations were then used to infer the mechanism of the coronal heating. Aims. We derive accurate power laws between EUV line intensities and the total magnetic flux in solar active regions and discuss their applications. We examine whether these global power laws are capable of providing the diagnostics of the coronal heating mechanism. Methods. This analysis is based on EUV lines recorded by the Coronal Diagnostic Spectrometer (CDS) on SOHO for 48 solar active regions, as they crossed the central meridian in years 1996–1998. Four spectral lines are used: He I 584.3 A (3 × 10 4 K), O V 629.7 A (2.2 × 10 5 K), Mg IX 368.06 A (9.5 × 10 5 K), and Fe XVI 360.76 A (2.0 × 10 6 K). In particular, the Fe XVI 360.76 A line, seen only in areas of enhanced heating in active regions or bright points, has not been used before for this analysis. Results. Empirical power laws are established between the total active region intensity in the lines listed above and the total magnetic flux. We demonstrate the usefulness of some spatially integrated EUV line intensities, IT, as a proxy for the total magnetic flux, Φ, in active regions. We point out the approximate, empirical nature of the IT − Φ relationships and discuss the interpretation of the global power index. Different power index values for transition region and coronal lines are explained by their different dependence on pressure under the assumption of hydrostatic loop models. However, the global power laws are dominated by the size of the active regions, and we demonstrate for the first time the difficulties in uniquely relating the power index in the global IT − Φ relationship to the power index for individual loops and comment on results obtained by other authors. We caution against using global power laws to infer the coronal heating mechanism without a detailed knowledge of the distributions of the magnetic flux densities and instrumental response as a function of temperature. Despite these uncertainties, we show that the intensities of the transition region lines in individual loops depend on the photospheric magnetic flux density, φ, through Itr ∝ φ δt , δt 1, and under the assumption of hydrostatic loops we can place a constraint on the coronal heating models, obtaining the volumetric heating rate, EH (erg cm −3 s −1 ), EH ∝ φ γ ,w here 0.6

Multiresolution Analysis of Active Region Magnetic Structure and its Correlation with the Mount Wilson Classification and Flaring Activity

Two different multiresolution analyses are used to decompose the structure of active-region magnetic flux into concentrations of different size scales. Lines separating these opposite polarity regions of flux at each size scale are found. These lines are used as a mask on a map of the magnetic field gradient to sample the local gradient between opposite polarity regions of given scale sizes. It is shown that the maximum, average, and standard deviation of the magnetic flux gradient for α,β,βγ, and βγδ active-regions increase in the order listed, and that the order is maintained over all length scales. Since magnetic flux gradient is strongly linked to active-region activity, such as flares, this study demonstrates that, on average, the Mt. Wilson classification encodes the notion of activity over all length scales in the active-region, and not just those length scales at which the strongest flux gradients are found. Further, it is also shown that the average gradients in the field, and the average length-scale at which they occur, also increase in the same order. Finally, there are significant differences in the gradient distribution, between flaring and non-flaring active regions, which are maintained over all length scales. It is also shown that the average gradient content of active-regions that have large flares (GOES class “M” and above) is larger than that for active regions containing flares of all flare sizes; this difference is also maintained at all length scales. All of the reported results are independent of the multiresolution transform used. The implications for the Mt. Wilson classification of active-regions in relation to the multiresolution gradient content and flaring activity are discussed.

Quasi-Periodic Pulsations During the Impulsive and Decay Phases of an X-Class Flare

Quasi-periodic pulsations (QPP) are often observed in X-ray emission from solar flares. To date, it is unclear what their physical origins are. Here, we present a multi-instrument investigation of the nature of QPP during the impulsive and decay phases of the X1.0 flare of 28 October 2013. We focus on the character of the fine structure pulsations evident in the soft X-ray time derivatives and compare this variability with structure across multiple wavelengths including hard X-ray and microwave emission. We find that during the impulsive phase of the flare, high correlations between pulsations in the thermal and non-thermal emissions are seen. A characteristic timescale of ~20s is observed in all channels and a second timescale of ~55s is observed in the non-thermal emissions. Soft X-ray pulsations are seen to persist into the decay phase of this flare, up to 20 minutes after the non-thermal emission has ceased. We find that these decay phase thermal pulsations have very small amplitude and show an increase in characteristic timescale from ~40s up to ~70s. We interpret the bursty nature of the co-existing multi-wavelength QPP during the impulsive phase in terms of episodic particle acceleration and plasma heating. The persistent thermal decay phase QPP are most likely connected with compressive MHD processes in the post-flare loops such as the fast sausage mode or the vertical kink mode.

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23. We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non-Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec , a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40?keV, and a 68% probability that it lies in the range 7-36?keV. Further, the low-energy cutoff is more likely to be in the range 25-35?keV than in any other 10?keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 ? 4?keV with 68% probability. Using the Bayesian/MCMC approach, we also estimate for the first time probability density functions for the total number of flare-accelerated electrons and the energy they carry for each flare studied. For the 2002 July 23 event, these probability density functions are asymmetric with long tails orders of magnitude higher than the most probable value, caused by the poorly constrained value of the low-energy cutoff. The most probable electron power is estimated at 1028.1 erg s?1, with a 68% credible interval estimated at 1028.1-1029.0 erg s?1, and a 95% credible interval estimated at 1028.0-1030.2 erg s?1. For the 2005 January 19 flare spectrum, the probability density functions for the total number of flare-accelerated electrons and their energy are much more symmetric and narrow: the most probable electron power is estimated at 1027.66 ? 0.01 erg s?1 (68% credible intervals). However, in this case the uncertainty due to systematic sources of error is estimated to dominate the uncertainty due to statistical sources of error.