G. Gloeckler and L. A. Fisk, University of Michigan, Ann Arbor, MI, USA AGU Chapman Conference

1. The Universal Nature of Suprathermal Power Law Tails with Spectral Index of –5 on theVelocity Distributions of Solar Wind and Pickup Ions G. Gloeckler and L. A. Fisk, University of Michigan, Ann Arbor, MI, USA AGU Chapman Conference On Universal Heliophysical Processes (IHY) Savannah, Georgia, USA 10 - 14 November 2008

2. Observations ofSuprathermal Tailsduring quiet solar wind flows

3. Simple average of two ~ 1 year long time periods in the fast solar wind from the north and south polar coronal holes • Three-component spectrum • Bulk Solar wind • - Core particle (halo solar • wind and pickup protons) • Suprathermal tail • In the solar wind frame the distribution function of the suprathermal tail has the form • f(v) = fov–5 • up to the speed limit of SWICS

4. Ensemble average of many individual time periods during 1998 with low suprathermal tail fluxes • Three-component spectrum • Bulk Solar wind • - Core particle (halo solar • wind and pickup protons) • Suprathermal tail • In the solar wind frame the distribution function of the suprathermal tail has the form • f(v) = fov–5 • up to the speed limit of SWICS

5. Ensemble average of many individual time periods during 2007 with low solar wind speed Phase space density now extends to ~1.7•109 cm/s (~1.5 MeV) Three-component spectrum Spectrum rolls over at ~ 1.2•109 cm/s (~0.75 MeV) In the solar wind frame the distribution function of the suprathermal tail has the form f(v) = fov–5exp[–(v/vo)1.26] vo = 1.18•109 cm/s

6. Quiet Solar Wind at 1 AU: H, He+, He++, He, C, O, Fe Model spectra of the form dj/dE = joE–1.5exp[–(m/q)a(E/Eo)(1+ a)/2] samea = 0.27 same Eo = 0.72 MeV provide good fits to all tails Contributions of He+ to the tail He spectrum are small No measurable fluxes for heavy nuclei below ~30 keV/nuc

7. Suprathermal power law tails are commonly observed during quiet times The fact that the common spectral shape can occur in the quiet solar wind, far from shocks, suggests that the acceleration mechanism is some form of stochastic acceleration • It cannot, however, be a traditional stochastic acceleration mechanism, which in general has a governing equation that is a diffusion in velocity space • In this traditional stochastic acceleration, many different solutions to the diffusion equation are possible, including power law solutions. But the solutions are dependent on the choice of the diffusion coefficient, which is unlikely to be the same in all the different conditions where the common spectral shape occurs

8. •Considered a different stochastic acceleration mechanism which explains the observations that in the solar wind frame the commonly observed tails have a unique spectral index of –5, and exponentially rollover at e-folding speeds corresponding to e-folding energies Ec of ~0.1 to ~10 MeV •Assuming that the core and tail particles form an isolated system and are subject to compressional turbulence, the equilibrium tail spectral form is derived to be (Fisk and Gloeckler, ApJ Oct 4, 2008) f(v) = fov–5exp[–(m/q)a(v/vc)av ] = fov–5exp[–(R/Rc)av ], or dj/dE = joE–1.5exp[–(m/q)a(E/Ec)g ] where g = (a + 1)/2 and vc, Rc andEc depend onusw (solar wind bulk speed), vs (sound speed) and rgo (proton gyro-radius) computed from measured solar wind parameters and magnetic field •The high-energy e-folding cutoff energy, Ec, remains roughly the same throughout the heliosphere because of competition between stochastic acceleration and adiabatic cooling in the expanding solar wind (Fisk and Gloeckler, ApJ Oct 4, 2008)

9. Observations ofSuprathermal Tailsin individual the Shocks and CIRs

10. Upstream spectrum (blue) - 1992 DOY 285.42 – 290.42 - Three-component spectrum - Anisotropic upstream beams dominate and eclipse the underlying quiet time tail Downstream (red) - 1992 DOY283.83 – 285.38 - Three-component spectrum In the solar wind frame the velocity distribution of the suprathermal tails have the form f(v) = fov–5exp[–(v/vo)g] mpvo2 ≈ 1.7 MeV The shock increases the pressure of each component by the R_H jump determined by the shock Mach number (Ms = 5.2). The high turbulence downstream creates stronger tails by pushing more core particles into the tailthus increasing its pressure Proton Spectra Upstream and Downstream of a CIR Reverse Shock 1 2

11. Suprathermal Tail in the Magnetosheath of Jupiter’s Bow Shock Upstream and downstream velocity distributions are measured above ~300 km/s Upstream Mach number is ~10.5 and corresponding R-H pressure and temperature jumps are ~135 and ~35 respectively The measured tail pressure jump of ~150 is a bit higher and the core temperature jump somewhat lower than R-H resulting from some core particles flowing into the tail See Gloeckler and Fisk, 6th IGPP/AIP, 2007 for details

12. Suprathermal Tails Downstream of Shocks • Shocks heat solar wind, core particles (halo solar wind and pickup ions) and tail particles, with the density and pressure of each component increasing as required by Rankine-Hugoniot relationships • Some of the heated core particles flow into the tail in the turbulent downstream regions

13. Proton phase space density versus particle speed upstream and downstream of the Termination Shock. Observed spectra (filled circles) are from the LECP experiment on V1 averaged over the indicated time periods. Model upstream spectra for solar wind and pickup protons are based on extrapolations from 1 and 5 AU Model downstream spectra for solar wind and pickup protons are computed assuming that each population separately obeys R-H density and pressure jumps of 3.3 and 17.5 respectively, corresponding to a Mach number of 3.8 for Spectra above were published (Gloeckler and Fisk, AIPCP858, 153, 2006) before Voyager 2 observed the down stream solar wind

14. Pressure jump of solar wind is ~23 (mach number ~4.3) Assume same pressure jump (23) and a density jump of 3.4 for core (pickup protons) downstream Pt /Pc = 0.24 Solar wind thermal speed, Vth ≈ 14 km/s upstream and ~57 km/s in the heliosheath asd observed by Voyager 2

15. Suprathermal Tails Downstream of Shocks • Shocks heat solar wind, core particles (halo solar wind and pickup ions) and tail particles, with the density and pressure of each component increasing as required by Rankine-Hugoniot relationships • Some of the heated core particles flow into the tail in the turbulent downstream regions

16. Observations ofSuprathermal Tailsaveraged over many Shocks and CIRs

17. Model spectra of the form dj/dE = joE–1.5exp[–(m/q)0.43(E/Eo)0.71] provide good fits to all tails Contributions of He+ and He++ to the tail He spectrum are about the same, thus (He/O)tail ≈ 2• (He/O)sw (C/O)tail ≈ 0.6 (Fe/O)tail ≈ 0.09 Ec for the 2007 CIR is 0.28 MeV/n, lower than the quiet time 2007 value (0.72 MeV/n) C/O approaches ~1 (observed in the 1970s) at high energies due to m/q dependence of roll over e-folding energy, Eo

18. Average of all data during 1998 Model spectra of the form f(v) = fov–5exp[–(v/vo)2] (in the solar wind frame) provide good fits to the tail Ec is only about 25 keV lower than the CIR value of 280 keV/nuc

19. Voyager 1 LECP observations above ~40 keV of supra-thermal tail Solar wind and pickup ion spectra are extra-polations from 5 AU Model tail spectrum of the form f(v) = fov–5exp[–(v/vo)2] (in the solar wind frame) provide good fits to the tail Ec (mvo2/2) is 4.9 MeV

20. Ratios of tail to core pressure †Core (Pickup proton) pressure is based on model calculations

21. Suprathermal TailsandAnomalous Cosmic Raysin the outer Heliosphere and Heliosheath

22. Suprathermal Tails in the Heliosheath and ACRs • The Termination Shock heats solar wind, core particles (halo solar wind and pickup ions) and tail particles, with the density and pressure of each component increasing as required by Rankine-Hugoniot relationships • In the heliosheath the pressure in tail particles, initially heated by the termination shock, is further increase by flow of core particles into the tail • In the heliosheath, unlike in the heliosphere, the roll over speed vcincreases with distance traveled, eventually reaching ACR energies • Tails from regions near the heliopause diffuse inward and are observed as modulated Anomalous Cosmic Rays • Prediction: Near the heliopause the observed ACR spectra should be dj/dE = joE–1.5exp[–(m/q)a(E/Ec)(1+a)/2] withEc ≈ 150 to 200 MeV/nuc

23. The three-component spectra upstream (blue) and downstream (red) consist of: • bulk solar wind • core (pickup H and some halo solar wind) • suprathermal tail Solar wind upstream: extrapolations from Voyager 2 measurements downstream: Voyager 2 measurements in heliosheath Pickup hydrogen upstream: model calculations downstream: STEREO measurements of ENAs In the solar wind frame the velocity distribution of the suprathermal tails have the form f(v) = fov–5exp[–(v/vo)g] mpvo2 = 8 MeV Pt /Pc = 0.24 1 – 2

24. Separate Tails from ACRs Voyager 1 Oxygen velocity distribution in the heliosheath, averaged over 2.8 years, showing the (a) suprathermal power law tail with spectral index -5 gently rolling over at ~ 3•109 cm/sec (~5 MeV/nuc) (b) Modulated ACR Oxygen The sum of (a) and (b) is an excellent fit to the data

25. dj/dE = jAtE – 1.5exp– Aa(E/17)a = 0.87 dj/dE = 2•jAtE – 1.5exp– A(E/160)exp– 38AE

26. Pressures (dyne/cm2) in bulk solar wind, core and tail †Core (Pickup proton) pressure is based on model calculations

27. • A traditional stochastic acceleration mechanism, which takes energy from the turbulence will not work because there is not enough energy in the solar wind to account for the pressure of the ACRs near the heliopause. • In our stochastic mechanism energy from the core (pickup ions) flows into the tail, so there is no energy problem

28. END