1. Particle acceleration by direct electric field in an active region modelled by a CA model CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux PARTICLE ACCELERATION BY DIRECT ELECTRIC FIELDS IN AN ACTIVE REGION MODELLED BY A CELLULAR AUTOMATON Cyril Dauphin – Nicole Vilmer 1- CA model 2- Acceleration model 3- particle energy distributions 4- X-ray and gamma ray fluxes Anastasios Anastasiadis

2. Introduction CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Frequency distributions of, e.g., flares energy  power law Particle acceleration by direct electric field in an active region modelled by a CA model We use a cellular automaton (CA) model to mimic the energy release process (Vlahos et al, 1995...) Crosby et al, 1993 …  no characteristic scale  Simple rules can model the system Aschwanden et al,2000 Hudson, 1991 CA can reproduce statistical properties of solar flares (i.e. for the all sun)

3. Introduction CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Can we use a CA model to mimic the energy release process in an active region ? Extrapolation of magnetic field shows the complexity of an active region Hughes et al, 2003: solar flare can be reproduced by cascades of reconnecting magnetic loops which evolve in space and time in a SOC state Hughes et al, 2003 Current sheet can have a fractal structure (Yankov, 1996)

4. Introduction CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux photospherephotosphere photospherephotosphere energy time Random foot-points motion => buildup of magnetic discontinuities in the corona Particle acceleration by direct electric field in an active region modelled by a CA model Log(energy) -  E Log(dN/dE)

5. CA model Acceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Is the evolution of magnetic discontinuities based on Self Organized Criticality system ?  assumption (Lu et Hamilton, 1993; Vlahos, 1995; McIntosh et al, 1992 …) Basic rules: -3D cubic grid: B i =B(x,y,z) at each grid point - At each time step B i (t+1)=B i (t)+  B i (t) and prob(  B i )=  B i -5/3 t0t0t0t0 t 1 >t 0 - if (Bi-1/6∑Bj)>Bcr  i ~B i 2 Curvature of B at the point i = dB i iiii We use a CA model based on the SOC concept (Vlahos et al, 1995; Georgoulis et al, 1998)

6. CA model Acceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Magnetic field evolution: to mimic the turbulent motion of the magnetic loops foot points Particle acceleration by direct electric field in an active region modelled by a CA model Espagnet et al,1993 Isliker et al, 1998 - Link to diffusion

7. CA model Acceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model  i (t)~B 2 (t) Energy released time series  i (t)~B 2 (t)  power law distribution:  E ~ -1.6

8. Acceleration model CA model Acceleration model Particle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model We have one model of energy release process in an active region We want to accelerate particle  each magnetic energy release process  RCS (reconnecting current sheet; observed in tokamak (Crocker at al, 2003) and in laboratory ) We have to make the link between the energy release process and the acceleration process. One of the first step in this sense Anastasiadis et al, 2004

9. Acceleration model CA model Acceleration model Particle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model We equate the magnetic energy flux to the particle energy gain per unit time y x a b l z v in Inflow v in E0E0E0E0 B // ∆lp∆lp∆lp∆lp ∆le∆le∆le∆le B┴B┴B┴B┴ B0B0B0B0 with

10. CA model Acceleration model Particle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Electric field Particle energy gain (electron, proton and heavy ions) Acceleration model CA Model OR :X-CA (hybrid simulation) OR: MHD simulation ; extrapolation RCS (direct electric field) We use a simple approach of the acceleration by direct electric field  =random([0,1]) efficiency of the acceleration

11. CA model Acceleration model Particle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Acceleration model We use 3 assumptions for B // B // = 0 (Speiser, 1965) y x a b l z v in Inflow v in E0E0E0E0 B // ∆lp∆lp∆lp∆lp ∆le∆le∆le∆le B┴B┴B┴B┴ B0B0B0B0 Protons gain more energy than electrons

12. CA model Acceleration model Particle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Acceleration model B // >B mag (e -,ions) (Litvinenko, 1996) electrons and ions are magnetized => follow the magnetic field lines B // B0B0B0B0 B┴B┴B┴B┴ Electron trajectory Dauphin & Vilmer y x a b l z v in Inflow v in E0E0E0E0 B // ∆l p ∆le∆le∆le∆le B┴B┴B┴B┴ B0B0B0B0 B // Same energy gain for all particle

13. CA model Acceleration model Particle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Acceleration model B // >B mag (e - ) only the electrons are magnetized We have the particle energy gain for 3 different RCS configurations For each particle (e - or ions) we select a value of  and we select a value of B 2 free from the energy release time series y x a b l z v in Inflow v in E0E0E0E0 B // ∆lp∆lp∆lp∆lp ∆le∆le∆le∆le B┴B┴B┴B┴

14. Particle distribution CA modelAcceleration model Particle distribution ConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model z y x Particle energy time Log(dN/dE) Log(Particle energy) ? Particle trajectory Equivalent to a Levy Walk  powerful events govern the particle trajectory We calculate the particle energy distribution for 10 6 particles from a maxwellian distribution (T=10 6 K) We normalize the electric field in the case B // large to the Dreicer electric field. => free parameter - For the 3 different configuration of RCS - For electrons, protons, and heavy ions

15. Particle distribution CA modelAcceleration model Particle distribution ConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Example for electron E min N max

16. Particle distribution CA modelAcceleration model Particle distribution ConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Example for proton E min N max

17. CA modelAcceleration modelConclusionsIntroductionX-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Example of alpha energy distribution No difference between the two spectra in energy/nucleon for the case B small E min N max Particle distribution gamma-ray flux Particle distribution

18. CA modelAcceleration modelConclusionsIntroductionX-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Energy contained in accelerated particles (for 1 arcsec 3) Energy contained gamma-ray flux Particle distribution B small B middle B large B total

19. X-Ray flux CA modelAcceleration modelParticle distributionConclusionsIntroduction X-ray flux gamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Cases observed: - B small, E min =1000E D - E min =10ED Thick target approach E min N max

20. Gamma Ray flux CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray flux gamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model We compute the gamma ray ratio calculated in the thick target approximation 12 C+p 12 C+  16 O+p 16 O+   4.438 MeV 16 O+p 16 O+   6.129 MeV 20 Ne+p 20 Ne+   1.634 MeV 24 Mg+p 24 Mg+   1.364 MeV 28 Si+p 28 Si+   1.779 MeV

21. Gamma Ray flux CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray flux gamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model C/OSi/OMg/ONe/O Abundance of the ambient plasma corona photosphere

22. Gamma Ray flux CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray flux gamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Observations from Share and Murphy, 1995 Average=1.06Average=1.44

23. Gamma Ray flux CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray flux gamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Observations from Share and Murphy, 1995 Average=1Average=0.5

24. Gamma Ray flux CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray flux gamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model C/OSi/OMg/ONe/O Si/O and Mg/O correspond to the coronal abundance C/O in agreement with the ratio deduced by using a photospheric abundance Problem with Ne/O

25. Conclusions CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model We investigate particle acceleration due to interaction with many RCS. The magnetic energy release distribution is given by a power law - particle energy distributions wander from a power law with the increase of the interaction number and strongly depend on the considered RCS configuration  This implies different X-ray spectra and gamma ray line fluence ratio; in most cases X-ray spectra are too flat compared to observations. This is mainly due to the spectral index of the magnetic energy released distribution which is -1.6.  Observed gamma ray lines fluence ratio can be reproduced except for Neon Spectral index of the particle distribution is function of the considered energy range

26. Conclusions CA modelAcceleration modelParticle distributionConclusionsIntroductionX-ray fluxgamma-ray flux Particle acceleration by direct electric field in an active region modelled by a CA model Energy contained in electron and proton strongly depends on the RCS configuration -> see observations With a volume of 10 2 -10 3 arcsec 3, it is possible to obtain enough energy in electron and proton to reproduce most of the observations => This implies different X-ray spectra and gamma ray line fluence ratio