Coupled ion acceleration and Alfven wave excitation at an expanding coronal shock E. Berezhko and S. Taneev Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy Yakutsk, Russia Main question: What is a role of selfexcited Alfven waves in Solar Energetic Particles (SEP) production by CME driven shock? Remark: Solar Energetic Particles = Solar Cosmic Rays (SCRs) SH 0125 11.08.12 17:30-19:30

SEP event characteristics Miroshnichenko & Perez-Peraza, 2008

Diffusive shock acceleration of CRs Krymsky 1977 Bell 1978 log nCR p- Δp log p Cutoff due to finite shock size or due to restricted system age scattering centers  = ( + 2)/( -1) shock compression ratio

Coronal Mass Ejection driven shock w Shock Earth Vp Vs Sun CME Rs Solar wind escaping particles SCRs, g > 0.1 freshly accelerated particles, g < 0.1 Modulation parameter: I flare ε1 > ε2 > ε3 ε3 Berezhko, Krymsky (1987) Intensity of energetic particles, measured by distinct observer ε2 ε1 shock t

SCRs

At which distances from the Sun SCRs are produced? Zank, Rice, Wu (2000): Solar wind (RS > 20RSun),”onion-shell” plane wave approach, assumed efficient Alfven wave excitation leading to Bohm limit diffusion. εmax ~ 100 MeV Rice, Zank, Li (2003): Solar wind (RS > 20RSun),”onion-shell” plane wave approach, upstream Alfven wave intensity according to quasilinear model (Gordon et al.1999) εmax ~ (1- 10) MeV ( too small !) Ng, Reames, Tylka (2003): Solar wind (RS > 10RSun ), focused upstream transport of SCRs with their ad hoc source term, Alfven wave excitation by SCRs in upstream region Lee (2005): Solar wind (RS > 10RSun), plane wave steady state approach, upstream Alfven wave intensity according to quasilinear model (Gordon et al.1999) However according to observations SCR onset usually occur at ~ 0.2 – 1 hr after flare at height of (2-4)RSun above photosphere (Kahler 1994; Krucker, Lin 2000)

Physical factors relevant for acceleration efficiency NCR CR energy spectrum ninj NCR = A ε−γexp(−ε/εmax) ε - γ vinj ~ VS− w speed of injected ions εinj εmax ε CR diffusion coefficient κ(εmax) ≈ 0.1 RS(VS – w – cA) maximal CR energy A ~ RS3ρ(RS)(VS – w)3/(σeff -1) total number of accelerated CRs γ = 0.5 (σeff +2)/(σeff - 1) power law index σeff = σ(1 – cA/VS) effective compression ratio

Solar corona parameters Alfven speed solar wind speed Solar wind number density r/RSun

γ SCR acceleration efficiency within the region r < 1 AU 1500 Vs, km/s 1000 500 1 inefficient 10-3 A, AU efficient 10-6 100 εmax, MeV 10 4 3 γ 2 1 1 10 100

Alfven waves in solar corona Fw = 106 erg/(cm2 s) Alfven wave energy flux at r = RSun P(ν)=dEw /dν~ r -δ ν -λ Alfven wave energy spectrum νP δ ≈ 4.3 λ = 1 at 10-3 < ν < 5×10-2 Hz λ = 3/2 at ν > 5×10-2 Hz Relevant for SCRs r = 1 AU (e.g. Suzuki, Inusuka 2006) (e.g. Tu, Marsh 1995) B = B0(r0/r)2 ν, Hz 10-3 10-2 10-1

Alfven wave excitation by shock accelerated CRs CR anisotropy → wave excitation f = f0 + f1 cosθ p VS θ f1 ~ - df0/dx ~ f0VS/v Bell (1978) Lee(1982) Gordon et al.(1999) x shock front ∂Ew/∂t = Γ Ew + … wave energy Γ ~ f1 wave growth rate ∂f/∂t = ∂(κ∂f/∂x)/∂x + … κ ~ 1/Ew particle diffusion coefficient τacc ~ κ/VS2 acceleration time

Quasilinear model of SCRs acceleration CR transport equations (Krymsky, 1964) source (injection) term diffusion coefficient Alfven wave transport equation growth (damping) rate (Gordon et al., 1999) System of equations is solved numerically within the distance range of efficient shock acceleration RS < R* = (2-5) RSun At r > R* accelerated SCRs are assumed to propagate purely diffusively

Compared with the previous considerations the model includes: SCR acceleration within corona (r < 5 RSun) Selfexcited Alfven waves The influence of Alfven speed on the effective compression ratio, which determines SCR spectrum Consistent determination of SCR maximal energy Compared with our previous study (Berezhko&Taneev 2003) the model incledes selfexcited Alfven waves

Overall energy spectra of SCRs, produced by CME driven shock in solar corona linear approach quasilinear approach Selfexcited Alfven waves reduce the number of SCRs ( due to decrease of effective shock compression ratio) and do not affect SCR maximal energy/

Proton energy spectrum at 1 AU in the event 1977 November 22 VS = 1000 km/s η = 10-3 linear quasilinear

Conclusions Efficient SCR production by CME driven shock takes place within the region r < 2-5 RSun Selfexcited Alfven waves reduce the number of SCRs due to the decrease of effective shock compression Alfven wave generation insignificantly influence SCR maximal energy due to steep energy spectrum of accelerated SCRs Calculated spectra of shock accelerated SCRs in satisfactory way agree with SCR spectra measured in gradual events

Alfven wave spectra near the shock front VS = 1500 km/s

CR diffusion coefficient VS = 1500 km/s κL ≈ κQL linear approach qusilinear approach Bohm limit

Solar Cosmic Ray spectrum at the Earth’s orbit Berezhko, Taneev (2003) VS = 2000 km/s

Solar corona/wind parameters Vs = 1500 km/s Vs = 600 km/s

Overall particle energy spectrum in/near acceleration region injection rate Expected injection rate η ~ 10-3 η > 10-5 → efficient CR production