SHINE 2008 June, 2008 Utah, USA Visit our Websites: Relativistic Solar Protons on 2006 December 13 David Ruffolo, 1 John W. Bieber, 2 John Clem, 2 Paul Evenson, 2 Roger Pyle, 2 Alejandro Sáiz, 1 & Maneenate Wechakama 3 1 Mahidol Univ., Bangkok 2 Univ. Delaware 3 Kasetsart Univ., Bangkok 1

The “maverick” GLE of December 13, 2006: It occurred near solar minimum, but it was a large event, exceeding 100% increase at Oulu

A blow-up of the peak region reveals some strange features: Mawson initially recorded the fastest rise, but then decreased while Apatity continued rising We believe this may be caused small shifts in the angular distribution axis of symmetry, coupled with a highly anisotropic pitch angle distribution

Spaceship Earth Asymptotic Viewing Directions at Start of Event Circles show station geographical locations Open squares show asymptotic direction for a median rigidity solar particle Lines show range (10- to 90- percentile rigidity) of viewing directions for each station Circled dot and circled X denote nominalSunward and anti-Sunward Parker directions, respectively

MAPPING RADIATION INTENSITY IN POLAR REGIONS: METHOD First, the asymptotic viewing directions of the neutron monitor array are determined, and the cosmic ray pitch angle distribution (here modeled as a constant plus exponential function of pitch angle cosine) is computed in GSE coordinates by least-square fitting To form the map, a preliminary computation is done at each grid point to determine if a 1 GV proton is “allowed.” If it is, then that location is considered to have a geomagnetic cutoff below the atmospheric cutoff, and the grid point is included in the map. The asymptotic viewing direction at the center of the grid point is then computed in GSE coordinates for a median rigidity particle, permitting the “pitch angle” for the location to be determined. From the model pitch angle distribution, the predicted intensity for that grid point is computed and plotted by color code.

Event Modeling Step 1: Individual station data were fitted to an angular distribution of the form f(μ) = c 0 + c 1 exp(b μ), with μ cosine of pitch angle, and c 0, c 1, and b free parameters. The symmetry axis from which pitch angles are measured was also a free parameter.

Event Modeling Step 2: The first 3 Legendre coefficients, f 0, f 1, f 2, of the derived distribution were computed from f(μ). They are shown at left as “Density”, “Weighted Anisotropy”, and “2 nd Legendre.” Longitude and latitude of the derived symmetry axis are also shown, as is the ordinary anisotropy, f 1 /f 0.

t: time, f: cosmic ray phase space density, μ: cosine of pitch angle, v: particle speed, z: distance parallel to mean field, L: magnetic focusing length, defined by L -1 = (-1/B) dB/dz, Ф(μ): Fokker- Planck coefficient for pitch angle scattering, q: source term The Boltzmann equation for cosmic ray transport is solved numerically to yield predictions for the cosmic ray density and anisotropy vs time. Fitting anisotropy as well as density is crucial for separating effects of interplanetary diffusion from extended acceleration or release at the Sun. Scattering strength is usually quantified by the parallel mean free path λ ║ or diffusion coefficient K ║ which are related to Ф(μ) by:

Event Modeling: Standard Parker Field Step 3: The Legendre coefficients as functions of time are fitted to numerical solutions of the Boltzmann equation. Free parameters are the scattering mean free path and profile of particle injection at the Sun, represented by a piecewise-linear function. A standard Parker IMF does not yield a satisfactory fit: The optimal mean free path of 0.23 AU provides a good fit to density, but not to weighted anisotropy or 2 nd Legendre. Based on our experience modeling the Bastille event, we suspect a downstream magnetic mirror may be affecting transport in this event.

Magnetic Mirrors in the Solar Wind GLE particles are sometimes injected into a normal Parker background field, as in (a) – e.g., Easter GLE But frequently they are injected into a background that is highly disturbed as a result of earlier events from the same active region. In (b), particles mirror from a magnetic bottleneck downstream of Earth. We believe this configuration existed in the Bastille Day 2000 event [Bieber et al., Astrophys. J., 567, 622 (2002)]. Sometimes particles are injected into a closed magnetic loop, as in (c). We believe this configuration explains the highly unusual October 22, 1989 event. Figure is from Ruffolo et al., Astrophys. J., 639, 1186 (2006). 12

Event Modeling: Downstream Magnetic Bottleneck (Preliminary) A bottleneck fit works much better. Here, the optimal mean free path is much larger, 1.08 AU, and the optimal bottleneck location is at 1.52 AU.

A Downstream Magnetic Mirror Is Supported by a “Fearless Forecast” of the IMF Configuration A “Fearless Forecast” (left) suggests Earth was connected to a downstream compression region at ~1.5 AU at event onset This is reminiscent of the Bastille event, in which transport was affected by a downstream magnetic bottleneck [Bieber et al., Astrophys. J., 567, , 2002] Fearless forecast from 14

SUMMARY Neutron monitors measure solar cosmic rays with energy >400 MeV. Modeling data from a suitable array of stations permits determination of: – Injection onset to ~1 minute precision – Injection time profile – Interplanetary scattering mean free path – Scattering “q” parameter Two events were presented as examples – Start time of relativistic proton injection (0640 ST ± 2 min. on 2005 Jan 20, 0240 ST ± 2 min. on 2006 Dec 13, for ST= solar time) can be compared with observations of electromagnetic radiation from flare and CME. Mirroring from large-scale interplanetary structures (e.g., loops, bottlenecks) is an important factor in modeling GLE transport (“Kings Do Not Travel Alone” – A. Belov) 15