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Hard X-Ray Polarization– a Diagnostic of Electron Acceleration Processes in Solar Flares Gordon Emslie Department of Physics, UAH, Huntsville, AL Polarization in Solar Flares • Impact polarization on neutrals (e.g. Hα) • Fluorescence • Continuum polarization (hard X-rays) Accelerated Electrons in Flares • Revealed by bremsstrahlung signature • Cross-section for bremsstrahlung ~ 10-5 × cross-section for energy loss (principally Coulomb losses on ambient electrons) • ⇒Electron (flux, energy) ~ 105 × hard X-ray (flux, energy) • Electron energy can be 1032 – 1033 ergs in large events Number & Current problems • Rate of e- acceleration ≈ 105 × rate of photon production ≈ 1037 s-1 in large flare – But: number of electrons in flare volume ≈ 1037 ⇒ source would be emptied in ~ 1 s! – Need for recycling and current closure . . . Number & Current problems • Rate of e- acceleration ≈ 105 × rate of photon production ≈ 1037 s-1 in large flare – But: number of electrons in flare volume ≈ 1037 ⇒ source would be emptied in ~ 1 s! – Need for recycling and current closure • Associated Current ≈ 1037 e- s-1 ≈ 1018 A – Ampère law ⇒ B = µoI/2πr ~ 108 G – Faraday law ⇒ V = L dI/dt ~ (µol) I/τ ~ 1019 V “Resolution” of Current Problem? • Current density j ~ 104 A m-2 • Maximum radius of current channel from (Ampère) ∇× B ~ B/r = µo j ⇒ r = B/ µo j ~ 10 m (Faraday) V= µo L(πr2j)/τ ⇒ r ~ 1 m (!) • ⇒ Number of channels ~ 1012 (1014) • ⇒ Aspect ratio of loop ~ 106-7 • Complicated current closure pattern Electron Energization Methods • Large-Scale Direct Electric Field: – Sub-Dreicer – Super-Dreicer • Stochastic • Thermal Direct Electric Field Acceleration m dv/dt = e E - ν mv (cf. m dv/dt = m g - ν mv) • skydiver: “collision frequency” ν ~ v, drag force ~ v2 ⇒ stable terminal velocity vt = g/ν • current in wire: ν ~ v ⇒ vd = eE/mν ⇒ j = ne vd = (ne2/mν) E, i.e. j = σ E (Ohm’s Law) • But, electrons in a dilute plasma: ν ~ 1/v3 for v > vt ⇒ “terminal velocity” concept not valid ⇒ runaway acceleration at sufficiently high speeds vcrit = vt √(ED/E) (ED ~ 10-8 n(cm-3)/T(K) V cm-1) Accelerated Spectrum F(E ) background Maxwellian runaway tail; height ~ dn/dt eεL ε Super-Dreicer Acceleration • Involves large electric fields – E = - (v/c) × B • Driven by external flow field • All electrons in distribution are rapidly accelerated Super-Dreicer Acceleration Geometry y Bx v By Ez Bz v By Bx x Super-Dreicer Acceleration Geometry y Reconnecting B component Bx v By Ez Bz v By Bx x Super-Dreicer Acceleration Geometry Inductive E y Reconnecting B component Bx v By Ez Bz v By Bx x Super-Dreicer Acceleration Geometry Inductive E y Reconnecting B component Bx v By Ez Bz v By Bx In-sheet guiding B x Super-Dreicer Acceleration Geometry Inductive E y Reconnecting B component Bx v By Ez Bz v By Bx In-sheet guiding B Out-of-sheet B component – limits acceleration time x Super-Dreicer Acceleration • Electric field E= (v/c) × B – v=108 cm s-1; B=103 G ⇒ E=103 V cm-1 ~ 106 ED – Acceleration length ~ 1 m; time ~ 10-8 s • Particles remain in acceleration region for very short time and escape along magnetic field component perpendicular to sheet • Rapid reconnection in a very thin (1 m) current sheet – stability? Accelerated Spectrum F(E ) ε Electron Energization Methods • Large-Scale Direct Electric Field: – Sub-Dreicer – Super-Dreicer • Stochastic • Thermal Stochastic Acceleration • Alfvén waves accelerate electrons out of thermal distribution through gyroresonance acceleration • Fast mode waves continue acceleration to high energies through “transit-time” acceleration (Fermi acceleration between moving magnetic mirrors) Accelerated Spectrum F(E ) ε Electron Energization Methods • Large-Scale Direct Electric Field: – Sub-Dreicer – Super-Dreicer • Stochastic • Thermal Thermal Source? • Bulk heating to several × 108 K • Isotropic? . . . . . Thermal Source? • Bulk heating to several × 108 K • Isotropic? • But, region is still connected magnetically to cool (~104 K) chromosphere ⇒ strong thermal gradients present ⇒ anisotropy ⇒ polarization Accelerated Spectrum F(ε ) ε Comparison of Accelerated Spectra F(E) Sub-Dreicer Strongly anisotropic E ε F(E) Comparison of Accelerated Spectra Super-Dreicer Sub-Dreicer F(E) Strongly anisotropic Strongly anisotropic E E ε F(E) Comparison of Accelerated Spectra Super-Dreicer Sub-Dreicer F(E) Strongly anisotropic Strongly anisotropic F(E) Stochastic E E Weakly anisotropic ε E F(E) Comparison of Accelerated Spectra Super-Dreicer Sub-Dreicer F(E) Strongly anisotropic Strongly anisotropic F(E) Stochastic E E F(E) Weakly anisotropic Thermal Weakly anisotropic ε E E Bremsstrahlung Cross-Section • Q = Z2 Qep + Z Qee • Qee normally negligible • For fixed direction of emergent photon, and integrated over directions of outgoing electron, Qep = Qep (ε,E,θ,φ, //,⊥) ε = energy of photon E = energy of incoming electron (θ,φ) = direction of incoming electron (//,⊥) = polarization of photon (relative to collision plane) Cross-Section (Gluckstern & Hull 1953) Effect of Magnetic Field •Electrons spiral around magnetic field lines •Must average over θ and φ •Result is that bremsstrahlung cross-section really depends on –ε and E –direction (θ’,φ’) of guiding magnetic field –polarization relative to plane containing B and line to observer Effect of Magnetic Field •Electrons spiral around magnetic field lines •Must average over θ and φ •Result is that bremsstrahlung cross-section really depends on B –ε and E –direction (θ’,φ’) of guiding magnetic field –polarization relative to plane containing B and line to observer Earth Effect of Magnetic Field •Electrons spiral around magnetic field lines •Must average over θ and φ •Result is that bremsstrahlung cross-section really depends on B –ε and E –direction (θ’,φ’) of guiding magnetic field –polarization relative to plane containing B and line to observer –For vertical field, this is radial direction on the solar disk Earth Dilution of Polarization • Maximum bremsstrahlung occurs at same location of maximum collisional scattering • This reduces the observed polarization, unless we can image the highly polarized segment of the source separately • Need to consider (energy-dependent) targetaveraged angular distribution of electrons Non-Thermal Source Schematic Predictions for Solar Flare Polarization Predictions for Solar Flare Polarization Single point within a loop Predictions for Solar Flare Polarization Single point within a loop Langer and Petrosian (1977) Predictions for Solar Flare Polarization Single point within a loop radial Langer and Petrosian (1977) Predictions for Solar Flare Polarization Single point within a loop transverse radial Langer and Petrosian (1977) Predictions for Solar Flare Polarization Single point within a loop transverse radial Langer and Petrosian (1977) Bai and Ramaty (1978) Predictions for Solar Flare Polarization Single point within a loop Source-integrated transverse radial Langer and Petrosian (1977) Bai and Ramaty (1978) Leach and Petrosian (1983) Spectral Index Spectral Index Angular width of beam Spectral Index Angular width of beam Magnetic field convergence Thermal Source Polarization Geometry Thermal Source Polarization Geometry Polarizatio n Complications • Photospheric albedo backscatter – Downward photons can multiple Compton scatter back toward observer – Can reduce or induce polarization • Actual measurement includes – Earth backscatter – Instrumental polarization Backscatter Polarization – Polarized Primary Backscatter Polarization – Unpolarized Primary Complications • Photospheric albedo backscatter – Downward photons can multiple Compton scatter back toward observer – Can reduce or induce polarization • Actual measurement includes – Earth backscatter – Instrumental polarization RHESSI as a Polarimeter (20 – 100 keV) A small (3 cm diam by 3.5 cm high) cylinder of Be serves as scattering element. The Ge detectors measure the distribution of the scattered radiation. The rotation of the spacecraft rotation provides an effective method for fine sampling of the scatter distribution. An Initial Approach to RHESSI Analysis Three pairs of detectors with similar background : detectors 8/9, detectors 3/5 and detectors 4/6. The data from detectors 3-6 can be used as background estimate for the polarimeter mode detectors 8/9. An Initial Approach to RHESSI Analysis Three pairs of detectors with similar background : detectors 8/9, detectors 3/5 and detectors 4/6. The data from detectors 3-6 can be used as background estimate for the polarimeter mode detectors 8/9. Can also use detector-detector scatterings Available Data • X4.8 flare of July 23, 2002 Coronal source C Footpoints North (N) Middle (M) South (S) Available Data • X4.8 flare of July 23, 2002 Available Data • X4.8 flare of July 23, 2002 • Series of great flares of October & November, 2003 Conclusions • A definitive measurement of polarization of hard X-ray solar flare bremsstrahlung would be a powerful constraint on models • RHESSI, while not designed as a polarimeter, does have some capability in this area • Data exists for several large flares