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Estimating the properties of hard xray solar flares by constraining model parameters 

Jack Ireland Submitted: 20130530 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 Xray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scalesize 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 methoddependent 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 nonBayesian 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 nonBayesian 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 lowenergy 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 lowenergy cutoff, E_c , a crucial parameter in defining the energy content of the flareaccelerated 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 736 keV. Further, the lowenergy cutoff is more likely to be in the range 2535 keV than in any other 10 keV wide energy range. The lowenergy 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 flareaccelerated 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 lowenergy cutoff. The most probable electron power is estimated at 10^{28}.1 erg/s, with a 68% credible interval estimated at 10^{28.129.0} erg/s, and a 95% credible interval estimated at 10^{28.030.2} erg/s. For the 2005 January 19 flare spectrum, the probability density functions for the total number of flareaccelerated electrons and their energy are much more symmetric and narrow: the most probable electron power is estimated at 10^{27.66 ? 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: 20130531 09:15



Automated Detection of Oscillating Regions in the Solar Atmosphere 

Jack Ireland Submitted: 20100706 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 magneticfield 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 userdefined frequency
range. The method is based on Bayesian spectral analysis of
timeseries and image filtering. A Bayesian approach sidesteps the
need for an apriori 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 selfconsistent way. The algorithm also
introduces the notion of quality measures to those regions for
which a positive detection is claimed, allowing simple
postdetection 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: 20100706 10:28



Subject will be restored when possible 

Jack Ireland Submitted: 20080501 08:39
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 beta, betagamma and betagammadelta
active regions increase in the order listed, and that the order is
maintained over all lengthscales. This study
demonstrates that, on average, the Mt. Wilson classification encodes
the notion of activity over all lengthscales in the active region, and not
just those lengthscales at which the strongest flux gradients are found.
Further, it is also shown that the average gradients in the field,
and the average lengthscale at which they occur, also increase in
the same order. Finally, there are significant differences in the
gradient distribution, between flaring and nonflaring active
regions, which are maintained over all lengthscales. 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 lengthscales. All 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.
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: 20080923 21:02



Subject will be restored when possible 

Jack Ireland Submitted: 20080501 08:38
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 beta, betagamma and betagammadelta
active regions increase in the order listed, and that the order is
maintained over all lengthscales. This study
demonstrates that, on average, the Mt. Wilson classification encodes
the notion of activity over all lengthscales in the active region, and not
just those lengthscales at which the strongest flux gradients are found.
Further, it is also shown that the average gradients in the field,
and the average lengthscale at which they occur, also increase in
the same order. Finally, there are significant differences in the
gradient distribution, between flaring and nonflaring active
regions, which are maintained over all lengthscales. 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 lengthscales.
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: 20080923 21:02



Subject will be restored when possible 

Jack Ireland Submitted: 20070911 09:46
Spectralline fitting problems are extremely common in all
remotesensing 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 commonlyused techniques, such as leastsquares
fitting, are highly dependent on the initial parameter values used
and are therefore biassed. In addition, these routines occasionally
fail due to illconditioning. 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 leastsquares algorithm
for test data  a single emission line, a blended line, and very low
signaltonoise 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
signaltonoise 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: SoHOCDS,SoHOSUMER

Publication Status: Published in Solar Physics
Last Modified: 20070912 06:36




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