1. Solar Flare Energy Partition into Energetic Particle Acceleration
Eileen Chollet
Lunar and Planetary Laboratory
Advisor: Joe Giacalone
SHINE Conference
7/30/2006
LASCO C3 coronagraph on SOHO spacecraft
circle=sun, coronagraph blocks out star
Dates: April 2-6, 2001
What occurs: some activity on sun (more about this in a minute)
~ hours to days later, particles hit detector (snow)

2. Solar Energetic Particles: An Introduction
LASCO C3 coronagraph on SOHO spacecraft
circle=sun, coronagraph blocks out star
Dates: April 2-6, 2001
What occurs: some activity on sun (more about this in a minute)
~ hours to days later, particles hit detector (snow)

3. Solar Energetic Particles: An Introduction
LASCO C3 coronagraph on SOHO spacecraft
circle=sun, coronagraph blocks out star
Dates: April 2-6, 2001
What occurs: some activity on sun (more about this in a minute)
~ hours to days later, particles hit detector (snow)

4. Energy Partitioning in Flares
A flare takes ~ 1032 ergs of magnetic energy and converts it into:
X-ray producing electrons
Gamma-ray producing ions
Heating plasma
Mass motion (CME)
Interplanetary particles
X5 flare observed by Trace, 171 Å, 9/8/2005

5. Energy Partitioning in Flares?
How much goes into each component?
Previous work: Emslie et al. 2004, two events.
Still not very well determined, more study needed.

6. Goal: Estimate how much of the original flare energy goes into interplanetary particle acceleration.
What is required to estimate this using 1 AU data?
1) How many times does each particle cross 1 AU on average?
2) What is the distribution function of 1 AU crossings?
3) How much energy is lost during travel from the sun to 1 AU because of adiabatic cooling?

7. Energetic Particle Transport Equation
∂𝑓 ∂𝑡 = ∂ ∂ 𝑥 𝑖  K 𝑖𝑗 ∂𝑓 ∂ 𝑥 𝑗 − 𝑣  ⋅ ∇𝑓   1 3 ∇⋅ 𝑣  ∂𝑓 ∂𝑣 𝑄
Diffusion
Advection
Sources and sinks
Energy change
Assumes abundant scattering.

8. Energetic Particle Transport Effects
In the diffusive limit (abundant scattering) the particle transport equation implies:
𝐸 𝐸 𝑖 =  𝑟 𝑅 𝑖  −4 3
The particles lose energy as they travel outwards from the sun!

9. Simulation: Parameters
Simple particle motion, assume adiabatic over short timescales
Parker spiral magnetic field, radial solar wind
We're not solving the transport equation!
We are calculating the particle trajectories and comparing it with the simple analytic result shown previously.

10. Simulation: Parameters
Mono-energetic, impulsive release of particles at the sun.
Scattering off magnetic irregularities: accepts mean free path as input.
Only considering iron nuclei, can compare with ACE and Wind data.
Non-relativistic: only valid for particle energies up to ~ 50 MeV.
5 mean free paths, 30 energy steps (logarithmically spaced), 10,000 particles each.

11. Simulation: Results I
Average number of 1 AU crossings as a function of energy
Average number of 1 AU crossings increases with energy
Note log-log plot: Dependence is very strong!
Much weaker dependence on mean free path.
Long mean free path gives more crossings at low energy, selection effect?
At high energy, long mean free path gives fewer crossings, as expected.

12. Simulation: Results II
Number of particles vs Number of 1 AU crossings
More particles cross a small number of times, few cross many times
As mean free path increases, becomes steeper (fewer particles that cross many times).
This is one energy. At lower energies, relative results the same, but curves become steeper. At lowest energies, essentially all particles only cross once.

13. Simulation: Results III
Number of particles vs Number of 1 AU crossings
More particles cross a small number of times, few cross many times
As mean free path increases, becomes steeper (fewer particles that cross many times).
This is one energy. At lower energies, relative results the same, but curves become steeper. At lowest energies, essentially all particles only cross once.

14. Simulation: Results IV

15. Conclusions
1 AU crossings increase with particle energies, weak dependence on mean free path
At low energies, essentially all particles cross only once. As energy increases, get an approximately exponential distribution of 1 AU crossings.
At long mean free paths and higher energies, particles retain more of their original energy.
For typical solar system mean free paths (< 1 AU) the diffusive approximation is fairly good.
These results can now be incorporated into a larger study considering the other parts of solar flares.