Institute of Astronomy, Radio Astronomy and Plasma Physics Group Eidgenössische Technische Hochschule Zürich Swiss Federal Institute of Technology, Zürich Observational Constraints on Flare Acceleration Working Group 5 Arnold Benz

"Flares are unique in the astrophysical realm for the great diversity of diagnostic data that are available." Miller et al. 1997

MHD perspective: 1. Cusp 2. Two interacting loops 3. Statistical flare But: Particle acceleration is not MHD Reconnection in Earth's magnetotail is collisionless

Acceleration ??? Acceleration ??? Forbes

1. Constraints on Acceleration Radio observations Interplanetary particles X-rays Gamma rays

Radio Observations 1.Diagnostics on high-frequency phenomena 2.Diagnostics of non-thermal velocity distributions 3.Diagnostics on high-frequency waves in plasma 4.Radio emission at 100 GHz and beyond → highly relativistic electrons in > 1000 G magnetic fields

Interplanetary Particles 1.Ion acceleration up to 100 MeV per nucleon 2.Enrichments of Ne, Mg, Si, Fe relative to C, N, O over coronal ratios 3.Enrichment of 3 He relative to 4 He

Hard X-Rays 1.Flare energy release up to erg, largest part into kinetic particle energies. 2.Number of accelerated electrons up to per flare (number problem!) 3.Significant number of electrons at tens of MeV 4.Acceleration in < 0.1 s (SMM, BATSE)

Gamma Rays 1.Ratio electrons/ions varies in different flares 2.Ion accelerated up to 10 GeV per nucleon 3.Footpoints at different locations from X-rays

2. Signatures of Accelerated Electrons Incoherent emissions: - bremsstrahlung (soft and hard X-rays) - synchrotron, gyro-synchrotron, cyclotron emission (dm and cm radio) Coherent emissions ( radio waves via wave-wave coupling ): - bump-on-tail instability of electron beams, Langmuir waves - loss-cone instability of trapped electrons, upper-hybrid waves or electron cyclotron waves (maser) Others?

TeTe γ P. Saint-Hilaire thermal non-thermal RHESSI: much energy in non-thermal, thick target electrons A. Incoherent emissions

Saint-Hilaire & B., 2005 ∫ E kin dt E th

Grigis & B. flux spectral index

P. Grigis

Battaglia et al. 2005

B. Coherent emissions - Electrons have anisotropic velocity distribution (free energy) - High-frequency plasma waves in resonance with energetic electrons - Plasma waves couple to propagating radio waves 1. Bump-on-tail instability vװvװ f(v װ ) vbvb Resonance: v b ≈ ω/k Wave growth: |E 1 | 2 = |E th | 2 e -2γt ω ≈ ω p ~ √n e γ ≈ (v b /Δv) 2 (n b /n e )ω

Coherent emissions by velocity space instabilities vװvװ v T bump on tail loss cone Result: high-frequency waves that easily couple into radio waves Expect good correlation between non-thermal electrons and radio emissions

3. Proposed Mechanism for Acceleration 1. Shock acceleration 2. Parallel electric field 3. Stochastic waves and fields Reviews by Ramaty, 1980 Heyvaerts, 1981 Vlahos et al., 1986 Melrose, 1990 Benz et al., 1994 Miller et al., 1997

1. Shock acceleration - flare shock, CME front (secondary phase) - reconnection jet termination shock (rare, controversial) Proposed Mechanisms 1. Shock acceleration 2. Parallel electric field 3. Stochastic waves

radio-quiet flare GOES class M1.0 6 – 12 keV 12 – 25 keV 25 – 50 keV 50 – 100 keV

Frequent Absence of Radio Emissions 1.17 % of flares > C5.0 have no assoicated coherent radio emission (excl. type I: 22%). 2.Only 33% of the flares have classic type III events at meter waves. 3.Detailed correlations with decimeteric spikes and pulsations exist, but rare. Suggests bulk heating (energization) rather than acceleration. Flares are often well contained. Suggests multiple acceleration sites per flare. Benz et al. 2005

Proposed Mechanisms 1. Shock acceleration 2. Parallel electric field 3. Stochastic waves

Proposed Mechanisms 2. Parallel electric field - reconnection (∂B/∂t) (number and energy problems) - current interruption ( I ≈ const.) (auroral zone)

Proposed Mechanisms 1. Shock acceleration 2. DC electric field 3. Stochastic waves

Proposed Mechanisms 3. Stochastic waves and fields - resonant waves (s= ±1) (heavy ions) - transit time damping (s=0) (electrons) - stochastic parallel electric fields (non-resonant)

Resonant Waves Resonance: ω – sΩ – k ║ v ║ = 0 Wave damping: [ {sΩ/v ┴ } ∂/∂p ┴ + k ║ ∂/∂p ║ ] f(p ║,p ┴ ) < 0 Quasi-linear diffusion: ∂ ∂ ∂ ∂t ∂v ∂v Diffusion coefficient: D = W(k,t) | k=ω k /v = (D ) ω p 2 mnv

Transit Time Damping (s = 0) Stochastic Parallel Electric Fields Second order Fermi acceleration: - Particle gains energy in head-on collisions, but loses in overtaking collision - Overtaking collisions are more frequent - In second order, a particle gains more than it loses. - Consider random, stationary electric fields. - Particles (electrons and ions) move randomly and interact. - Not second order Fermi acceleration: - Particle gains energy in qv║E, but loses in antiparallel interactions - Both interactions are equally frequent - Particle gains energy by stochastic diffusion in energy space. Different processes! → different diffusion constants? → different observational signatures?

Observational Constraints on Flare Particle Acceleration 1.Absence of radio emission in 17% of flares does not support violent acceleration processes, such as single shocks or single DC fields. 2.Consistent with heating processes (bulk energization). 3.RHESSI observations show that flares start with soft non-thermal spectrum. In the beginning it is difficult to distinguish from a thermal spectrum (γ ≈ 8). 4. The spectrum of non-thermal electrons gets harder with flux of non- thermal electrons both in time during one flare, as well as with peak flare flux (Battaglia et al. 2005). 5. The evidence supports stochastic bulk energization to hot thermal distribution and, if driven enough with power-law wings.

Open Questions What acceleration mechanism? How to prove stochastic acceleration? Magnetic (MHD) or parallel electric turbulence? Observable differences? Why power-law energy distribution?