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

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.

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

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

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

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

Interferometry – RMC Comparison InterferometryRMC’s Spatial periodwavelength / baselineGrid pitch / separation uv pointsN(N-1)/2 (antennas) VLA  351 N (RMCs) RHESSI  9 SynthesisEarth rotation (24 h)S/c rotation (4 s) Visibility-based imaging is required for imaging high energy solar electrons In both cases, basic observables are visibilities (u,v,f)

Diagnostics require spectroscopy Inhomogeneous source structure  imaging spectroscopy

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

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?)

GRIPS Gamma-Ray Imaging Polarimeter for Solar flares P.I. Bob Lin, UCB Multi-pitch rotating modulator Spectrometer/polarimeter with 0.5mm spatial resolution Energy range~20 keV to >~10 MeV Angular resolution12.5 to 162 arcsec First balloon flight: spring m boom length Detector provides time, energy, location and a polarization signature of each photon

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

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

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

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

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

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

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

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)

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

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

Incoherent Microwave Burst Spectra Free-free Gyrosynchrotron (Thermal and nonthermal) 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) Observational confirmation

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

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

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

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.