1 July 14, SHINE WorkshopKeauhou, Hawaii, USA Chanruangrith Channok, 1 David Ruffolo, 1 Mihir Desai, 2 and Glenn Mason 2 1 THAILAND 2 USA Finite-Time Shock Acceleration and Fits to ESP Ion Spectra

2 July 14, SHINE WorkshopKeauhou, Hawaii, USA … and in the spirit End-to-End Modeling of CMEs and SEPs, a few words on Modeling SEP transport to infer injection and transport parameters Interplanetary turbulence and perpendicular transport

November (UT) ACE ULEIS + SIS Oxygen Intensities MeV n S S15W34 Oxygen Intensities for November IP shock (Desai et al. 2003) ESP SEP

(Desai et al. 2004) Fe/O at IP shocks is depleted relative to ambient values Larger decrease at higher energy

Spectra and abundances for Nov IP shock (Desai et al. 2004, ApJ).

6 July 14, SHINE WorkshopKeauhou, Hawaii, USA Possible mechanisms suggested by Ellison & Ramaty (1985) l shock thickness ~ κ/u energy is too low l drift over shock width rollover at ~ 100 MeV/Q l finite time for shock acceleration considered here (see also: Klecker et al. 1981; Lee 1983) Why do ESP spectra roll over at ~ MeV/n? (data - see also: Gosling et al. 1981; van Nes et al. 1985)

7 July 14, SHINE WorkshopKeauhou, Hawaii, USA Finite-Time Shock Acceleration Probability approach (like Bell 1978, Drury 1983) Acceleration rate, r = 1/Δt Escape rate,  Time at present (age of shock), t Simulation parameters: λ = λ 0 (P/ MV) α so vary λ 0 and α (shorter λ 0 is equivalent to longer time duration) Time t fixed by observations, v 0 = 200 km/s in wind frame, shock angles & speeds as observed.

8 July 14, SHINE WorkshopKeauhou, Hawaii, USA We solve the PDE … … discretized as a system of ODEs Initial & inflow conditions correspond to the observed ambient seed spectrum

9 July 14, SHINE WorkshopKeauhou, Hawaii, USA (well above injection energy) λ = const. E c /A ∞ t 2, independent of Q/A λ ∞ P α E c /A ∞ t 2/(α+1) (Q/A) 2α/(α+1) Rollover energy (E c /A)

10 July 14, SHINE WorkshopKeauhou, Hawaii, USA We use the FTSA model to fit 3 ESP events from the sample of Desai et al. (2004):

11 July 14, SHINE WorkshopKeauhou, Hawaii, USA Event #3: λ 0 = 0.24 AU, α = 0.18 λ is consistent with typical IP values FTSA rollover is at lower E, minor accel. of seed population

12 July 14, SHINE WorkshopKeauhou, Hawaii, USA Event #2: λ 0 = AU, α = 0.10 λ is smaller but not inconsistent with IP values FTSA rollover is at lower E, moderate accel. of seed population

13 July 14, SHINE WorkshopKeauhou, Hawaii, USA Event #1: λ 0 = 4.0x10 -3 AU, α = 0.07 λ at shock is much lower than typical IP values … … as expected for proton-amplified waves [Ng et al. 1999] model rollover is sharper than observed, probably due to use of spatially const. λ

14 July 14, SHINE WorkshopKeauhou, Hawaii, USA Fe/O ratios Fe/O lower at shock, due to higher λ for Fe model does not match observed trend for Event 2 expect trend vs. E like seed population above the rollover

15 July 14, SHINE WorkshopKeauhou, Hawaii, USA Conclusions on ESP spectra … 1. Finite-time shock acceleration model power law spectrum at low energy faster dropoff at high energy 2. Expect E c /A ∞ t 2/(α+1) (Q/A) 2α/(α+1) 3. For 3 events, able to simultaneously fit measurements of C, O, and Fe ions 4. Fits to weak events: Infer λ as typical IP values 5. Fit to strong event: Infer much lower λ, consistent with expectations for proton-amplified waves

16 July 14, SHINE WorkshopKeauhou, Hawaii, USA … but wait – there’s more! Key processes of interplanetary transport Scattering Focusing (a.k.a. mirroring) Solar wind effects - Convection - Adiabatic deceleration Note: mean free path is ~ 0.1 to 3 AU Aim to quantitatively explain profiles of intensity & anisotropy vs. time [Jokipii 1966] [Roelof 1969] [DR 1995]

17 July 14, SHINE WorkshopKeauhou, Hawaii, USA Pitch-angle transport equation [DR, ApJ ’95]

18 July 14, SHINE WorkshopKeauhou, Hawaii, USA Fitting SEP data - Simultaneous fit to intensity vs. time anisotropy vs. time - Optimal piecewise linear injection (least squares) - Optimal scattering mean free path, λ [Ruffolo et al. 1998] - Optimal magnetic configuration [Bieber et al. 2002] Simulation of interplanetary transport - Specify magnetic field configuration - Solve PDE - Runs in a few minutes [Nutaro et al. 2001]

19 July 14, SHINE WorkshopKeauhou, Hawaii, USA Magnetic Configurations

20 July 14, SHINE WorkshopKeauhou, Hawaii, USA Results of fitting GLE data (relativistic solar protons) l Bastille Day: July 14, magnetic bottleneck [Bieber et al. 2002] l Easter: April 15, full Spaceship Earth network, 1-minute timing of injection [Bieber et al. 2004] October 22, injection along both legs of a closed interplanetary loop [poster, this meeting] October 28, 2003 … well, we don’t claim to understand everything … [Bieber et al. 2005] January 20, possible effect of self-generated waves: nonlinear transport! [poster, this meeting]

21 July 14, SHINE WorkshopKeauhou, Hawaii, USA Comparison with EM timing All times are “Solar Time” or UT minus 8 min. for EM emissions EMISSIONAPR. 15, 2001OCT. 28, 2003 STARTPEAKENDSTARTPEAKEND Relativistic Protons13:4213:4811:0311:41 Soft X-rays13:1113:4213:4710:52**11:0211:16 H-alpha13:2813:4115:2709:5311:5714:12 Type III radio burst13:3613:38-- CME liftoff*13: :53-58 Type II radio burst13:4013:4710:5411:03 Type IV radio burst13:4414:5710:2515:23 * Linear - quadratic fits ** Sudden onset of intense emission [Bieber et al. 2004][Bieber et al. 2005]

22 July 14, SHINE WorkshopKeauhou, Hawaii, USA “halo” of low SEP density over wide lateral region “core” of SEP with dropouts [DR, Matthaeus, & Chuychai 2003]

23 July 14, SHINE WorkshopKeauhou, Hawaii, USA Thank you for your attention ขอบคุณครับ

24 July 14, SHINE WorkshopKeauhou, Hawaii, USA

25 July 14, SHINE WorkshopKeauhou, Hawaii, USA … and also in the spirit End-to-End Modeling of CMEs and SEPs: See some posters! 87 DR et al. – Turbulence, dropouts, and suppression of the field line random walk 96 Bieber et al. – Record-setting Ground Level Enhancement: January 20, DR et al. – Relativistic Solar Protons on 1989 October 22: Injection along Both Legs of a Loop … and also someone else’s poster … 105 Mulligan et al. – validates our results for July 14, 2000!

26 July 14, SHINE WorkshopKeauhou, Hawaii, USA Early observations [Bryant et al. 1962]

Spectral Properties of Heavy Ions Accelerated by Interplanetary Shocks Near 1 AU M. I. Desai University of Maryland, College Park, MD 20742, USA Co-Authors: G. M. Mason, C. M. S. Cohen, R. A. Mewaldt, M. E. Wiedenbeck, J. E. Mazur, J. R. Dwyer, A. C. Cummings, E. C. Stone, R. A. Leske, R.E. Gold, E. R. Christian, S. M. Krimigis, C.W. Smith, Q. Hu, R. M. Skoug, and T. T. von Rosenvinge

Upstream & IP shock abundances Solar wind & IP shock abundances (Desai et al ApJ 558, 1149).

Upstream and SEP Abundances (Desai et al ApJ 558, 1149). Upstream material comprises ~30% contribution from impulsive flares, and ~70% from large gradual SEPs

Spectral Variability in IP shocks (Desai et al to be submitted to ApJ).

Fe/O Ratio at shock versus Fe/O ratio upstream (Desai et al ApJ vol. 558, 1149)

32 July 14, SHINE WorkshopKeauhou, Hawaii, USA 3. Particle acceleration in space: Shock acceleration

33 July 14, SHINE WorkshopKeauhou, Hawaii, USA Fundamental mechanism of shock acceleration Following collision with a scattering center: lose energy Head-on collision with a scattering center: gain energy Since u 1 > u 2 there is a net gain in energy

34 July 14, SHINE WorkshopKeauhou, Hawaii, USA Poisson distribution for n acceleration events with accel. rate r Distribution of residence time T for particles with escape rate  Overall probability of n acceleration events after time t t is time at present T T = t P(T) r,  constant w/ energy - combinatorial model

35 July 14, SHINE WorkshopKeauhou, Hawaii, USA Using r =0.9 &  = T < t (temporary residents) T = t ( permanent residents)

36 July 14, SHINE WorkshopKeauhou, Hawaii, USA (related to log p)

37 July 14, SHINE WorkshopKeauhou, Hawaii, USA (related to log p)

38 July 14, SHINE WorkshopKeauhou, Hawaii, USA (related to log p)

39 July 14, SHINE WorkshopKeauhou, Hawaii, USA (related to log p)

40 July 14, SHINE WorkshopKeauhou, Hawaii, USA (related to log p)

41 July 14, SHINE WorkshopKeauhou, Hawaii, USA (related to log p)

42 July 14, SHINE WorkshopKeauhou, Hawaii, USA Application to an interplanetary shock: What if  r vary with time? l Physical characteristics of a shock change greatly as it moves out from the Sun l Observations: high energy particles are accelerated only when shock is near the Sun l Near Sun: t acc (=1/r) was low, t /t acc was high, spectrum does not roll over until high energy (rollover mechanism not clear) l Interplanetary space: t acc greatly increased l Effectively decouple SEP, ESP acceleration

43 July 14, SHINE WorkshopKeauhou, Hawaii, USA r,  varying - ODE model Analytic solution:

44 July 14, SHINE WorkshopKeauhou, Hawaii, USA More model parameters... … after Drury (1983)

45 July 14, SHINE WorkshopKeauhou, Hawaii, USA Numerical Results t / t acc =

46 July 14, SHINE WorkshopKeauhou, Hawaii, USA Four Lines of Work: 1. Particle Acceleration 2. Magnetic Turbulence & Effects on Particle Transport 3. Detection/ Data Analysis 4. Earth Effects CME