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Coronal Fourier power spectra: implications for coronal seismology and coronal heating  

Jack Ireland   Submitted: 2014-10-08 18:28

The dynamics of regions of the solar corona are investigated using Atmospheric Imaging Assembly (AIA) 171Å and 193Å 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 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 time-scale background trend plus Gaussian-distributed noise, with some specific locations also showing an oscillatory signal. The implications of this discovery to the field of coronal seismology and the automated detections of oscillations 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.

Authors: Jack Ireland, R. T. James McAteer, Andrew R. Inglis
Projects: SDO-AIA

Publication Status: Accepted by ApJ
Last Modified: 2014-10-10 10:26
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Estimating the properties of hard x-ray solar flares by constraining model parameters  

Jack Ireland   Submitted: 2013-05-30 13:56

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, E_c , 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 E_c 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, with a 68% credible interval estimated at 1028.1-29.0 erg/s, and a 95% credible interval estimated at 1028.0-30.2 erg/s. 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 (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.

Authors: J. Ireland, A. K. Tolbert, R. A. Schwartz, G. D. Holman, and B. R. Dennis
Projects: RHESSI

Publication Status: In Press
Last Modified: 2013-05-31 09:15
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Automated Detection of Oscillating Regions in the Solar Atmosphere  

Jack Ireland   Submitted: 2010-07-06 08:10

Recently observed oscillations in the solar atmosphere have been interpreted and modeled as magnetohydrodynamic wave modes. This has allowed the estimation of parameters that are otherwise hard to derive, such as the coronal magnetic-field strength. This work crucially relies on the initial detection of the oscillations, which is commonly done manually. The volume of Solar Dynamics Observatory (SDO) data will make manual detection inefficient for detecting all of the oscillating regions. An algorithm is presented which automates the detection of areas of the solar atmosphere that support spatially extended oscillations. The algorithm identifies areas in the solar atmosphere whose oscillation content is described by a single, dominant oscillation within a user-defined frequency range. The method is based on Bayesian spectral analysis of time-series and image filtering. A Bayesian approach sidesteps the need for an a-priori noise estimate to calculate rejection criteria for the observed signal, and it also provides estimates of oscillation frequency, amplitude and noise, and the error in all these quantities, in a self-consistent way. The algorithm also introduces the notion of quality measures to those regions for which a positive detection is claimed, allowing simple post-detection discrimination by the user. The algorithm is demonstrated on two Transition Region and Coronal Explorer (TRACE) datasets, and comments regarding its suitability for oscillation detection in SDO are made.

Authors: J. Ireland, M. S. Marsh, T. A. Kucera, C. A. Young
Projects: TRACE

Publication Status: Accepted
Last Modified: 2010-07-06 10:28
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Subject will be restored when possible  

Jack Ireland   Submitted: 2008-05-01 08:39

Two different multi-resolution 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 beta, beta-gamma and beta-gamma-delta active regions increase in the order listed, and that the order is maintained over all length-scales. 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 the reported results are independent of the multi-resolution transform used. The implications for the Mt. Wilson classification of active regions in relation to the multi-resolution gradient content and flaring activity are discussed.

Authors: J. Ireland , C.A. Young , R.T.J. McAteer , C. Whelan , R.J. Hewett , P.T. Gallagher
Projects: None

Publication Status: Accepted by Solar Physics
Last Modified: 2008-09-23 21:02
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Subject will be restored when possible  

Jack Ireland   Submitted: 2008-05-01 08:38

Two different multi-resolution 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 beta, beta-gamma and beta-gamma-delta active regions increase in the order listed, and that the order is maintained over all length-scales. 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.

Authors: J. Ireland , C.A. Young , R.T.J. McAteer , C. Whelan , R.J. Hewett , P.T. Gallagher
Projects: None

Publication Status: Accepted by Solar Physics
Last Modified: 2008-09-23 21:02
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Subject will be restored when possible  

Jack Ireland   Submitted: 2007-09-11 09:46

Spectral-line fitting problems are extremely common in all remote-sensing disciplines, solar physics included. Spectra in solar physics are frequently parameterized using a model for the background and the emission lines, and various computational techniques are used to find values to the parameters given the data. However, the most commonly-used techniques, such as least-squares fitting, are highly dependent on the initial parameter values used and are therefore biassed. In addition, these routines occasionally fail due to ill-conditioning. Simulated annealing and Bayesian posterior distribution analysis offer different approaches to finding parameter values through a directed, but random, search of the parameter space. The algorithms proposed here easily incorporate any other available information about the emission spectrum, which is shown to improve the fit. Example algorithms are given and their performance is compared to a least-squares algorithm for test data - a single emission line, a blended line, and very low signal-to-noise ratio data. It is found that the algorithms proposed here perform at least as well or better than standard fitting practices, particularly in the case of very low signal-to-noise ratio data. A hybrid simulated annealing and Bayesian posterior algorithm is used to analyze a Mg X line contaminated by an O IV triplet, as observed by the Coronal Diagnostic Spectrometer (CDS) onboard SOHO. The benefits of these algorithms are also discussed.

Authors: Jack Ireland
Projects: SoHO-CDS,SoHO-SUMER

Publication Status: Published in Solar Physics
Last Modified: 2007-09-12 06:36
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Precision limits to emission line profile measuring experiments  

Jack Ireland   Submitted: 2005-02-23 13:39

Spectra, such as astrophysical spectra, can provide detailed diagnostics on the state of their emitting volume. Emission line diagnostics are found by assuming a model for the spectral emission line and then fitting the model to the data. It is shown for Poisson noisy emission line data, via the application of Cramer-Rao lower bounds, that there are limits to the precision that line fitting can achieve. The limits depend on the spectral line model and the noise properties of the data. A Cramer-Rao lower bound treatment introduces a framework in which questions of line fitting in particular, and spectrometers in general, may be posed. Some example applications are given and their implication for the design of spectrometric observations are discussed.

Authors: J. Ireland
Projects: None

Publication Status: 2005, ApJ, 620, 1132
Last Modified: 2005-02-23 13:39
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Abstracts by Author
Coronal Fourier power spectra: implications for coronal seismology and coronal heating
Estimating the properties of hard x-ray solar flares by constraining model parameters
Automated Detection of Oscillating Regions in the Solar Atmosphere
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible
Precision limits to emission line profile measuring experiments

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