Hard X-Ray Imaging of Solar Flares

by Michele Piana, A. Gordon Emslie, Anna Maria Massone, Brian R. Dennis

Overview

The idea for this text emerged over several years as the authors participated in research projects related to analysis of data from NASA's RHESSI Small Explorer mission. The data produced over the operational lifetime of this mission inspired many investigations related to a specific science question: the when, where, and how of electron acceleration during solar flares in the stressed magnetic environment of the active Sun.

A vital key to unlocking this science problem is the ability to produce high-quality images of hard X-rays produced by bremsstrahlung radiation from electrons accelerated during a solar flare. The only practical way to do this within the technological and budgetary limitations of the RHESSI era was to opt for indirect modalities in which imaging information is encoded as a set of two-dimensional spatial Fourier components.

Radio astronomers had employed Fourier imaging for many years. However, differently than for radio astronomy, X-ray images produced by RHESSI had to be constructed from a very limited number of sparsely distributed and very noisy Fourier components. Further, Fourier imaging is hardly intuitive, and extensive validation of the methods was necessary to ensure that they produced images with sufficient accuracy and fidelity for scientific applications.

This book summarizes the results of this development of imaging techniques specifically designed for this form of data. It covers a set of published works that span over two decades, during which various imaging methods were introduced, validated, and applied to observations. Also considering that a new Fourier-based telescope, STIX, is now entering its nominal phase on-board the ESA Solar Orbiter, it became more and more apparent to the authors that it would be a good idea to put together a compendium of these imaging methods and their applications. Hence the book you are now reading.

Product Details

ISBN-13:	9783030872793
Publisher:	Springer International Publishing
Publication date:	12/22/2021
Edition description:	1st ed. 2022
Pages:	164
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Michele Piana is full professor of Numerical Analysis at the Dipartimento di Matematica of the Università di Genova, research associate at CNR - SPIN Genova and Principal Investigator of the Methods for Image and Data Analysis (MIDA) Group. He was Visiting Scholar at the Department of Mathematical Sciences at the University of Delaware, researcher at the Istituto Nazionale di Fisica della Materia (INFM), Associate Professor of Computer Science at the Dipartimento di Informatica of the Università di Verona. He spent visiting periods at the Brain Research Unit, Low Temperature Laboratory, Helsinki University of Technology; Department of Physics and Astronomy, University of Glasgow; NASA Goddard Space Flight Center; and Institute for Data Science, Fachhochschule Nordwestschweiz. He has authored and co-authored more than 100 papers in refereed journals on solar physics, medical imaging, computational neuroscience, and applied mathematics. He has been a member of the Data Analysis Team of the NASA RHESSI mission and is currently co-Investigator for STIX on the Solar Orbiter and HXI on ASO-S. He has been Unit Coordinator for the FLARECAST project in Horizon 2020 and Coordinator of the HESPE project in FP7. He has been Deputy Rector for International Affairs and Deputy Rector for Research and Technological Transfer at the Università di Genova. He is currently Scientific Director of the Life Science Computational Laboratory, jointly established by the Università di Genova and the Ospedale Policlinico San Martino IRCCS Genova.

Brian Dennis has been actively involved in designing, building, and operating X-ray and gamma-ray spectrometers and imaging spectrometers during his over 50-year career as an astrophysicist at NASA’s Goddard Space Flight Center. These include spectrometers on the 5th and 8th Orbiting Solar Observatories in the 1960s and ‘70s and on the Solar Maximum Mission in the 1980’s, and the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) from 2002 to 2018. He is the RHESSI Mission Scientist and lead coinvestigator at Goddard, and has participated in this mission from the development of the original concept in the 1990s through to the final archiving of the data that is currently in progress. He is also an unfunded co-investigator for STIX on the Solar Orbiter. He is the author or co-author of over 200 refereed papers on these instruments and on the scientific analysis of observations made with them.

Gordon Emslie is a Professor of Physics & Astronomy at Western Kentucky University, having previously held a variety of positions at The University of Alabama in Huntsville and Oklahoma State University. With over 200 refereed articles published, his research focuses on mechanisms for energy release and transport in solar eruptive events, with particular emphasis on developing models that are driven by the observed properties of the high-energy radiation produced during the energy release. He was a co-Investigator on the NASA RHESSI mission.

Anna Maria Massone is Associate Professor of Numerical Analysis at the Dipartimento di Matematica, Università di Genova and Research Associate at CNR - SPIN Genova. She has been researcher at CNR - SPIN and at the Istituto Nazionale di Fisica della Materia (INFM), and Assistante Diplômée at the Université de Lausanne. She spent visiting periods at the Institut für Data Science, Fachhochschule Nordwestschweiz, Trinity College, University of Dublin, Institut für Kernphysik, Universitaet Mainz, Department of Physics and Astronomy, University of Glasgow, Low Temperature Laboratory, Brain Research Unit, Helsinki University of Technology, Helsinki, NASA Goddard Space Flight Center, Greenbelt (MD), USA, and Leibniz-Institut für Astrophysik Potsdam. She has been Honorary Research Associate at the School of Physics and Astronomy, University of Glasgow. She has been Unit Coordinator for FLARECAST in Horizon Europe and member of the NASA RHESSI Data Analysis Team. She has been leader of three International Teams at the International Space Science Institute Bern. She is currently co-Investigator for STIX in Solar Orbiter and HXI in ASO-S. She has authored or co-authored more than 60 papers in refereed journals concerning solar physics, medical imaging, computer science and applied mathematics.

Table of Contents

1 Hard X-ray Emission in Solar Flares
1.1 A Brief Overview of Solar Flares
1.2 Hard X-Ray Emission from Flares and its Significance
1.2.1 Acceleration of Nonthermal Electrons
1.2.2 Hard X-Ray Production by Accelerated Electrons: The Bremsstrahlung Process1.2.3 Relation of the Mean Source Electron Spectrum to the Accelerated Spectrum
1.3 History of Solar Hard X-Ray Imaging Observations
2 X-Ray Imaging Methods
2.1 Medical Imaging
2.2 Astrophysical X-ray Imaging Techniques
2.2.1 Absorption2.2.2 Scattering
2.2.3 Reflection
2.2.4 Diffraction
3 RHESSI and STIX
3.1 RHESSI Design / Brief History of Concept Development
3.2 The RHESSI imaging concept
3.3 Strengths and Limitations of the RHESSI RMC Imaging Technique3.4 RHESSI Imaging Example
3.5 SSW and the RHESSI GUIs
3.6 STIX Design / Brief History of Concept Development
3.7 The STIX imaging concept
3.8 STIX software
3.9 RHESSI vs. STIX - a comparison of strengths and limitations

4 Image Reconstruction Methods4.1 The Essence of the Image Reconstruction Problem
4.1.1 Count-based versus visibility-based imaging
4.1.2 Point Spread Functions
4.2 The ill-posedness of the image reconstruction problem
4.3 The Regularization Concept
4.4 Numerical Optimization
5 Count-based Imaging Methods
5.1 Back-projection
5.2 CLEAN
5.2.1 Two-step CLEAN Method
5.3 Forward Fit
5.4 Pixon
5.4.1 Maximum Entropy Methods
5.4.2 The Pixon Methodology
5.5 Expectation Maximization6 Visibility-based Imaging Methods
6.1 Visibilities
6.2 Visibility-based Methods
6.3 VIS_FWDFIT
6.4 Bayesian Optimization
6.5 MEM_NJIT and MEM_GE
6.6 uv_smooth
6.7 VIS_CLEAN and Multi-scale CLEAN
6.8 Compressed Sensing - VIS_CS and VIS_WV
6.9 Electron Flux Maps
7 Application to Solar Flares
7.1 Number and Nature of Hard X-Ray Sources in the 2002 February 20 Event
7.2 The Physical Nature of Multiple Hard X-Ray Sources in the 2002 July 23 Event
7.3 Properties of the Electron Acceleration Region7.3.1 Using the VIS_FWDFIT method to estimate the acceleration region length and density
7.3.2 Using the MEM_NJIT method to revisit earlier results
7.4 Empirical Determination of the Electron Energy Loss Rate
7.5 Hard X-Ray Imaging and the Global Energetics of Solar Flares
8 Future Possibilities
8.1 STIX
8.2 NuSTAR
8.3 FOXSI
8.4 Advanced Spaced-based Solar Observatory

8.5 GRIPS
8.6 Hard X-ray Polarimetry
8.7 Conclusion
References
Index