Particle spectra at CME-driven shocks and upstream turbulence SHINE 2006 Zermatt, Utah August 3rd Gang Li, G. P. Zank and Qiang Hu Institute of Geophysics and Planetary Physics, University of California, Riverside, CA 92521, USA

Outline spectral breaks in large SEP events. (Q/A) ordering of braking energy. Loss term and “broken power law”. maybe an explanation for the Oct.-Nov. events? Upstream and downstream turbulence at a CME difference between parallel and perp. shock

Spectral breaks in large SEP events

More examples October-November 2003 events Cohen et al. 2005

Wisdoms from literature The reasons for roll over at high energies are: finite acceleration time scale. Lee (1983) adiabatic deceleration. Forman (1981) finite size of shock, particle losses. Ellison and Ramaty (1985) Empirical fit, when the shock propagates out, the turbulence decreases and  increases. Particle spectrum will respond the increase of k from high energy end. Assuming a power law spectrum at early times (initial condition), what is the solution of the transport equation?

Fermi acceleration with a loss term Volk et al. (1981) considered various loss terms: Ionization, Coulomb, nuclear collisions, etc. The standard solution of shock acceleration assumes a x- independent u and . Acceleration time scale 4  /u 2, compare with , requires  to be small. In the upstream region,  is decided by the turbulence, far away from the shock, the solution does not hold. Can put a loss term (note, this is physically different from Volk et al.) to account for the finite size of the turbulent region near the shock.

Softer power law Boundary conditions: A)f ->0 at the upstream boundary. B)f = some non-zero value at down stream boundary. C) f and continuous Consider steady state case. Assume the initial spectrum is a power law (i.e. pre- accelerated). Li et al 2005

Turbulence in the upstream Upstream of a parallel shock, turbulence is in Alfven wave form – driven by streaming protons in front of the shock. But, exact form of the turbulence is not important. Turbulence power decays as x increase. The x-dependence could be different for different energy. The length scale d(k) for I(k) is decided by the turbulence. d(k) can be understood as: If particles which resonate with k reach d(k) in front of the shock, they will not return to shock.

Particle diffusion coefficient 1)  is tied with I(k). From , we can get =3  /v. 2) Two length scales, and d(k). Low energy particle << d(k), particles won’t feel the boundary. High energy particle ~d(k), particle will feel the boundary and the loss term becomes important.

Deciding  (=1/  ) The characteristics of loss time depends on (thus particle energy). Define  =(4   / u 1 2 ), then The change of the spectrum index becomes noticeable when  ~ 1. 1) Low energy, diffusive nature.  =(d/ ) 2 ( /v) = (d/v) (d/ ) 1)High energy, ~ d(k) => streaming nature.  =(d/ v) Approximate form:  ~ [1 - exp(- /d(k)) ] v/d.

Broken power law: an extreme example Consider an extreme example: a step function of . Expect a broken power law.  = 0.1 when T<20 MeV  = 1.0 when T>20 MeV Broken power law

The break of particle spectrum is tied to the shape of upstream turbulence power spectrum. Can use particle spectrum to probe turbulence property! Break energy kmin = (Qi/Mi)(eB/c pmax) Emax,i = (Qi/Mi) 2 Emax,p Resonance wave number, same for all species

Wave power: Early observations by ISEE3 Sanderson et al Resonance condition: Huge increases of turbulence power when approaching the shock (energy comparable to that contained in energetic particle) turbulence spectra is NOT a single power law. reduction of power at low frequencies. (?) conversion from sw to sc frame:

Upstream and downstream turbulence Downstream turbulence is stronger than upstream turbulence. Alfven wave transmission suggests that an increase of wave intensity of ~ McKenzie et al (1969). Consider two shocks occur in Oct. 28 th and Oct. 29 th. Plama data is plotted.  bn = 68 and 14 repectively. (from co- planarity analysis. ) From Skoug et al

Turbulence from observations Magnetic turbulence power for the 10/28/2003 event. upstreamdownstream

Turbulence from observations Magnetic turbulence power for the 10/29/2003 event. upstream downstream

Difference between parallel and perp. shock Perpendicular shockQuasi-perp shock

Bastille Day Event Revisited Bamert, et al, 2004

Future work Need a series of turbulence power plots, together with a series of particle spectra. Van Nes et al. (1984) using observational data of I(k) to construct more realistic  (v) ==> compare the derived particle spectra with observation. identify the time scale for the “loss” process (is steady state a valid approximation?) Need to study the (Q/A) dependence since we have many heavy ion observations. Example: using QLTwith ==> if what will dJ/dE look like?

Backup

Conclusion Particle spectra at CME-driven shocks are strongly related to upstream turbulence. The features of particle spectra at high energies in propagating interplanetary shocks are decided by the “escaping” mechanism, not the acceleration process. The escaping of particles from upstream can be treated as a loss term. This loss term is due to the decrease of the turbulence power in front of the shock (and the finite size of the shock). The steady-state solution of 1 st -order Fermi acceleration at a shock with a loss term, assuming an initial power law spectrum, with a step function for the diffusion coefficient, is a broken power law. The breaks occur at some characteristics energy dicided by the upstream turbulence. Studying the particle spectra provides us another way of deciphering the upstream turbulence I(k). Observations from ACE, WIND and SOHO should provide very good test.

Using heavy ion spectra to probe the form of the turbulence Cohen et al. (2003) 25 Sep April 2001 Assuming a power law turbulence: Fe/O ratio is energy dependent I(k) = k   a range of Q/A provide good check

Simple estimation of  Consider a strong shock, u 1 ~10 6 m/s Take proton, T = 20 MeV => v ~ 6* 10 7 m/s, v/ u 1 = 60 For the spectrum to bent over at T = 20 MeV, requires (d/ ) = 60, if d = 0.01 AU, = 1.66* AU, =>  = 2.5*10 14 m 2 /s. Reasonable values!

First order Fermi acceleration in a nutshell Assume a 1-D case and x- independent u and . At the shock front, both f and the current are continuous. Matching condition at the shock gives a power law spectra.