What is the Origin of the Frequently Observed v -5 Suprathermal Charged-Particle Spectrum? J. R. Jokipii University of Arizona Presented at SHINE, Zermatt, Utah, June 24, 2008

The Original Paper in 2000 pointed out an interesting observational fact This observation generated much interest.

From Gloeckler and Fisk, 2006 The main question is: what produces these particles nearly everywhere? Note: 10 times the wind speed = 250 keV in the fast wind

The spectrum is clearly commonly seen, however, it is not quite ubiquitous! Nonethless, it is an important observation and needs explanation.

A Unique Feature of a v -5 distribution The energy density associated with the spectrum diverges both as V goes to 0 and as it goes to infinity. This is the only distinguishing feature of the spectrum of which I am aware. This may provide feedback.

The acceleration of a charged particle is given by:

Following Fermi, he transport of cosmic rays is described statistically. The turbulent electromagnetic field is described statistically.

The Parker Equation can be used Where the drift velocity due to the large scale curvature and gradient of the average magnetic field is: ) Diffusion ) Convection w. plasma ) Grad & Curvature Drift ) Energy change ) Source

Acceleration Mechanisms dB/dt electric field (Swann,1933) –Applied to electron acceleration in sunspots Stochastic acceleration (Fermi,1949; Alfven,1950) –Relies on randomly moving scattering centers –Also resonant scattering –Generally very slow –Can explain the 3He/4He enhancement in SEP events Diffusive shock acceleration –Universal power laws are naturally produced –Successful and widely applied. Observational support Parallel Electric Fields –Not easy to set up. Not very developed Reconnection: we have heard from Jim Drake

Consider first diffusive shock acceleration. This is Simply the result of Parker’s equation applied to a shock

Diffusive shock acceleration for a shock ratio r produces a power law p - ° with exponent Since the Rankine-Hugoniot jump conditions give the ratio r in terms of the mach number M as we require that the shock have a mach number of M=√(5) or to produce a ° = 5 spectrum. While this is a reasonable value of M, there is nothing that we know which would make this occur in preference to any other value. Hence a ° = 5 spectrum requires special tuning or possibly some other physics.

The effect of 2nd-order Fermi or statistical acceleration on the distribution function f may be written as momentum diffusion: For Alfven waves the momentum diffusion coefficient D pp ¼ (v a 2 /w 2 ) p 2 /  sc. This may simply be added to the Parker equation. This acceleration is usually unimportant. V a 2 /w2 ¼.1 for superthermals in the solar wind.

Here, typically, D pp = 1/2 /  t = (V a 2 /w 2 )(3p 2 /  scatt ). The solution is not a power law except in very special cases! If  leak,  scatt are constant and w c, we do get a power law: f(p) = Ap - . Where:  depends critically on parameters which vary considerably. A “feature” of stat. Acc.

Fisk’s Transport Equation: a problem. Fisk proposed yesterday: And pointed out that it is non-diffusive It can be shown that this equation does not conserve particles: define Then dn/dt is not zero in general. I feel that this is a serious problem. Fisk does not.

Constraints on Statistical Acceleration Since the spectrum is always f / v -5. Gloeckler and Fisk (2006) suggested a stochastic mechanism for this. The acceleration must balance cooling in the expanding solar wind in which case and we must have This must be true if this is to explain the observed spectra with stochastic acceleration. This requires  sc to be less than r/v w

Question: Is a theory “robust” or is fine-tuning required? Robust: the desired outcome occurs over a wide parameter range. Both turbulence and shocks occur nearly everywhere. Shocks generally produce power-law spectra. Fine-tuning: the desired outcome occurs over a very limited parameter range. Although shocks produce power laws, the -5 index requires fine- tuning. Stochastic acceleration requires fine-tuning both to produce a power law and to produce the correct index. Fine-tuning generally requires some feedback mechanism to maintain the fine-tuning.

The important issue is: What produces the fine tuning? Fisk and Gloeckler have published several papers discussing one approach. These have not yet received wide acceptance. I, personally, do not fully understand their papers and regard this issue as still unsettled.

How fast can pickup-ion scattering be? Gloeckler, et al, 1995 discussed large anisotropies. Concluded mfp = 2 AU. This was at high latitude (75 deg). This implies a scattering time 2 AU/w = 2 days for 20 keV protons ~ expansion time at 3 AU (= 2 days in fast wind). Is this a problem?

Summary and Conclusions The nearly ubiquitous v - 5 observed superthermal particle spectrum is important and needs explanation. The standard mechanisms do not produce this robustly. Fine tuning or feedback is necessary. Published models have not yet received wide acceptance.