Inverse Problems in Solar Imaging Spectroscopy - Future Applications

1. Inverse Problems in Solar Imaging Spectroscopy - Future Applications G.J. Hurford Space Sciences Lab University of California, Berkeley Vienna 20 July 2009

2. Outline • Physics-based arguments to show that the algorithms discussed by previous speakers are relevant to field as a whole (as opposed to just a specific mission.) • Illustrate this with 3 future applications of the double inversion techniques.

3. Role of RHESSI Inversion Algorithms • Convert Fourier-based imaging data as a function of energy to spatial maps of physical parameters • Convert incomplete visibility data to maps • At each spatial location, convert spectral data into physical parameters

4. Why does solar hard x-ray imaging use visibilities ? • High energy physics  two diagnostics for accelerated solar electrons • Hard x-rays • Radio • Solar observations require ~ arcsecond resolution • Focusing optics is not feasible in this x-ray regime  Use collimation techniques • Solar range of angular scales + need for sensitivity  Bigrid collimators Basic x-ray imaging observable is visibilities

6. High Resolution Radio Imaging • At radio wavelengths • Diffraction  Antenna diameter needed for ~arcsecond imaging is prohibitively large e.g. 100m diameter antenna has only 140 arcsec resolution at 5 GHz but need ~4 arcsec.  use interferometry

7. Measuring Fourier Components:The Radio Interferometer Analog • Mathematical equivalence between information in a correlated radio signal and a modulated x-ray signal • In both cases, observed amplitude and phase measure a Fourier component of source distribution

8. Interferometry – RMC Comparison • In both cases, basic observables are visibilities (u,v,f) Visibility-based imaging is required for imaging high energy solar electrons

9. Diagnostics require spectroscopy • Inhomogeneous source structure  imaging spectroscopy

10. Summary • FACTORS • Physics of emission processes  hard x-rays and radio observations • Angular Size scales of solar phenomena • Physics of detection processes  visibility-based imaging • Emission processes convolve physical parameters with energy • Spatial non-uniformity of solar phenomena Visibility-based imaging spectroscopy is fundamental to the study of high-energy solar electrons Spatial reconstruction Spectral deconvolution

11. Future Applications (1)BETTER IMAGING + POLARIMETRY • RHESSI imaging was limited by measurements at only 9 spatial frequencies uv plane • No imaging polarimetry • No information on directivity of electrons • (e.g. electron beams?)

12. GRIPSGamma-Ray Imaging Polarimeter for Solar flaresP.I. Bob Lin, UCB First balloon flight: spring 2012 Multi-pitch rotating modulator 8 m boom length Spectrometer/polarimeter with 0.5mm spatial resolution Detector provides time, energy, location and a polarization signature of each photon

13. Two Perspectives on GRIPS Imaging Time sequence of counts beneath each mask location/orientation measures one visibility • Each photon identifies a set of ‘probability stripes’ on Sun from which it could have originated • Observations of many photons  image uv plane 1 3 10 Continuous set of gid pitches measures solid annulus in uv plane Radial profile of PSF 30 100 1000

14. GRIPS • RHESSI algorithms can be applied directly • Much better image quality • Polarization adds new dimension to spectral deconvolution

15. Future Improvements (2)BETTER VANTAGE POINT Direct information on accelerated electrons is lost in propagation effects Observations from close to Sun enable direct comparison to accelerated electrons

16. Solar Orbiter ESA 2017 launch 0.22 au perihelion Magnetic coupling of Sun to heliosphere

17. How do you measure visibilities with a stationary collimator? • Grids are stationary • Top and bottom grids have slightly different pitch • Location and amplitude of Moire pattern  visibility • Grids are moving • Top and bottom grids have identical pitch • Time and amplitude of count rate variations  visibility

18. 2 subcollimators with grids phase shifted by ¼ pitch (plus an integrated flux measurement)  amplitude and phase of Fourier component.

19. Spectrometer/Telescope for Imaging X-rays (STIX) P.I. Arnold Benz, ETHZ Front Grids Telescope Tube Rear Grids CZT Detectors Electronics Box

20. Solar Orbiter / STIX • Algorithms directly applicable • Challenges: • Sparse coverage in UV plane – limited image quality • Robustness of algorithms • (automated analysis of 2000 images/hour x 5+ years)

21. Future Applications (3)MICROWAVE IMAGING SPECTROSCOPY • Surface brightness (=brightness temperature) spectra accelerated electron spectral parameters, ambient density and/or magnetic field

22. FASR Frequency-Agile Solar Radiotelescope Tim Bastian, NRAO 0.05 to 21 GHz 1 arcsecond resolution at 20 GHz Design and development funded by NSF Pathfinder version could be operational by 2012 at Owens Valley, California

23. Incoherent Microwave Burst Spectra Free-free Gyrosynchrotron (Thermal and nonthermal) Observational confirmation Brightness Temperature spectra contain diagnostic information on magnetic fields, plasma & accelerated electron parameters. • Shape depends on mechanism • Position in Tb – Frequency plane depends on physical parameters • (BUT dependence is non linear)

24. Radio imaging • No need to deconvolve detector frequency response. • N antennas  N(N-1)/2 pairs • Cannot exploit earth rotation for burst sources  limited number of observed visibilities uv plane

25. Frequency-synthesis • Angular resolution = antenna separation wavelength • For each antenna pair, each frequency measures a different Fourier component Many more visibilities uv plane  Couples spectral deconvolution to spatial deconvolution

26. Implications for Algorithms • New deconvolution algorithms required • Spectral deconvolution is coupled to spatial deconvolution • Non-linear relation between physical parameters and spectrum

27. Summary • Visibility-based imaging/spectroscopy of hard x-rays and microwaves is the key observational tool for studying accelerated electrons at the Sun. • The success of the next generation of solar microwave and x-ray telescopes is critically dependent on the solution of spatial/spectral inverse problems.