Motivation

1. Acceleration of Anomalous Cosmic Rays in the Heliosheath by a Non-traditional Stochastic Acceleration Mechanism G. Gloeckler, L. A. Fisk Department of Atmospheric, Oceanic and Space Sciences University of Michigan, Ann Arbor, MI 48109, USA, gglo@umich.edu SHINE 2009 Workshop Old Orchard Inn Wolfville, NS Canada August 6, 2009

2. Motivation Prior to the termination shock crossings by Voyager 1 and 2it was generally believed that ACRs were accelerated at the Termination shock (TS) Since Voyager observations showed no evidence for ACR acceleration at the TS, other mechanisms were proposed Previously we had developed an energy redistribution stochastic acceleration mechanism to explain the commonly observed so-called -5 suprathermal tails in the heliosphere We apply this same mechanism accelerate the ACRs and suggest that they are accelerated primarily near the heliopause This model accounts well for Voyager measurements of the differential intensity spectra of six pickup ion species as well as the radial gradient of 16 MeV/nuc ACR He

3. The Model Core pickup ion distributions and associated suprathermal -5 power law tails, commonly observed in the inner heliosphere, evolve with heliocentric distance, maintaining their shapes with the rollover moving to higher speeds In crossing the TS, the density and pressure the of each component, the solar wind, the pickup ions and the -5 power law tails increase according to Rankine-Hugoniot relations • The dominant pressure resides in the pickup protons upstream of the TS and remains in the heated pickup protons downstream • The pressure in the tails is about 10 to 20% that of the core (pickup ions) In the absence of significant adiabatic deceleration the rollovers of the -5 power law tails move to ever higher speeds (or energies) as the spectra evolve with time in propagating deeper into the heliosheath Near the heliopause, where the radial solar wind speed is much lower and the diffusion coefficient may be smaller than near the TS, the rollover reaches that of the ACRs, and additional pressure is transferred from the core to the tails which now are the ACRs Near the TS one observes the superposition of the local -5 power law tails, with rollovers at modest energies (few to ~10 MeV) and the modulated ACRs that originate primarily near the heliospause

4. Evolution of H+ Velocity Distributions from 5 AU to 90 AU upstream and downstream of the TS

5. The Model Core pickup ion distributions and associated suprathermal -5 power law tails, commonly observed in the inner heliosphere, evolve with heliocentric distance maintaining their shapes with the rollover moving to higher speeds In crossing the TS, the density and pressure the of each component, the solar wind, the pickup ions and the -5 power law tails increase according to Rankine-Hugoniot relations • The dominant pressure resides in the pickup protons upstream of the TS and remains in the heated pickup protons downstream • The pressure in the tails is about 10 to 20% that of the core (pickup ions) In the absence of significant adiabatic deceleration the rollovers of the -5 power law tails move to ever higher speeds (or energies) as the spectra evolve with time in propagating deeper into the heliosheath Near the heliopause, where the radial solar wind speed is much lower and the diffusion coefficient may be smaller than near the TS, the rollover reaches that of the ACRs, and additional pressure is transferred from the core to the tails which now are the ACRs Near the TS one observes the superposition of the local -5 power law tails, with rollovers at modest energies (few to ~10 MeV) and the modulated ACRs that originate primarily near the heliospause

6. The Result

7. Model Details Spherically symmetric model –solarwind flow is subsonic; pickup ion pressure dominates; no adiabatic deceleration –spatial diffusion coefficient for tail and ACR particles is k = koAaE(a+1)/2, where ko and a are constants, A is the mass/charge and E the energy in MeV/nuc Basic steady state equation for distribution function f Fisk and Gloeckler, ApJ.686, 1466, 2008 where u is is the radial component of the solar wind speed, v the particle speed and r the heliocentric radial distance Solution , where and is the mean square speed of the compressional turbulence in the heliosheath Solution expressed in terms of the differential intensity, j , where

8. Acceleration Region of ACRs is near the Heliopause Assume for simplicity that the radial solar wind speed ur in the heliosheath varies with radial distance r as where l is characteristic distance at which ur declines to zero at the heliopause (hp) The maximum value for ttransis , where is the characteristic scale length for diffusive escape uts= 135 km/s rts= 90 AU rhp = 140 AU l= 8 AU The transit time as a function r in figure above shows that the particles spend most of their time near the heliopause Because the acceleration time of ~ 10 MeV/nuc O is ~1 yr (Mewaldt et al., ApJ. 466, L43, 1996), the transit time to where the maximum ACR energies are reached is also ~1 yr and thus the prime acceleration region is within a few AU of the heliopause

9. Modulation of ACRs Modulation of ACRs in the heliosheath simple convection-diffusion modulation without adiabatic deceleration –spatial diffusion coefficient for tail and ACR particles is k = koAaE(a+1)/2, where ko and a are constants, A is the mass/charge and E the energy in MeV/nuc Governing equation for the differential intensity j where u is is the radial component of the solar wind speed, kthe spatial diffusion coefficient and r the heliocentric radial distance Solution where , and j = jACR ACR r ACR EACR uts  kor

10. Composite spectrum of Oxygen in the Heliosheath at ~100 AU The fit parameters athe rigidity power law index of the spatial diffusion coefficient Etailthe rollover e-folding energy of the local tail spectra EACRthe rollover e-folding energy of the ACR spectra zrthe ACR modulation parameter ~100 AU

11. Composite spectra of six pickup ion species in the heliosheath at ~ 100 AU • Values of fit parameters for all six species a =0.87 Etail=17 MeV/nuc • EACR=160 MeV/nuc • zr=38 • jkACR/ jktail =2

12. EACR uts  kor Values of spatial diffusion coefficients • Diffusion coefficient in the heliosheath at ~100 AU • • from 16 MeV/nuc ACR He radial gradient of ~ 5%/AU (Stone et al. Nature454, 71, 2008) • ko = uts/[(dj/jdr)•AaE(a+1)/2 = 1.35•107•1.5•1013/(0.05•40.87•16(0.87+1)/2) = 9.1•1019cm2/s • • from modulation parameter zr = 38 • ko = uts I/zr = 1.35•107•14.23•1.5•1013/38 = 7.6 •1019 cm2/s • (corresponding to a ~ 6%/AU radial gradient of 16 MeV/nuc ACR He) • where I = = 14.23, and zr = 38 • Diffusion coefficient in the inner heliosheath near the heliopause • • with du = 100 km/s, ttrans,acc = 1 yr, Eo = 160 MeV/nuc and a = 0.87, • we obtain ko,hp = 1.1 •1019 cm2/s using • Diffusive escape length  of ACRs across the heliopause • • with du = 100 km/s and ttrans,acc = 1 yr • we obtain  = 12 AU using

13. Conclusions 1 Anomalous Cosmic Rays (ACRs) are accelerated out of the core pickup ion populations in the inner heliosheath, primarily within a few AU of the heliopause where the radial outflow of the solar wind goes to zero and the wind turns to flow parallel to the heliopause. 2 The effect – the injection and the acceleration – should be largest where the width of the heliosheath is the narrowest • The ACR differential intensity spectra that the Voyagers will measure near the heliopause should be -1.5 power laws with a rollover at e-folding energy of ~160/A0.93 MeV/nucleon • ACRs propagate inward by simple convection-diffusion, and downstream, close to the TS, the modulated ACR spectra combine with the local -1.5 power law tail spectra to form the spectra of the six pickup ion species observed by Voyager 1 • The principal escape of ACRs outwards across the heliopause is by diffusion with a characteristic escape length of ~12 AU • Assuming a simple rigidity dependence of the spatial diffusion coefficient, k = koAaE(a+1)/2 , we obtain from fits to the six observed spectra values for a = 0.87, ko,hs= 7.6•1019 cm2/s in the inner heliosheath and a smaller ko,hp= 1.1•1019 cm2/s near the heliopause • The ratio of jACR /jtail = 2 indicates that near the heliopause additional particles flow from the pickup ion cores to the ACR tails caused by lowering of the threshold speed vth between the core and tail population (note that vth  k which is lower near the heliopause than elsewhere in the heliosheath) • Additional modulation of Galactic Cosmic Rays takes place in the interaction region the beyond the heliopause. For additional details see Fisk and Gloeckler, Adv. Space Res. 43, 1471, 2009.

14. END

15. Mach number = 3.75 Pressure jump = 17.3 Compression ratio = 3.3 Solar wind thermal speed, Vth = 15 km/s upstream and 42.5 km/s in the heliosheath