3D Modelling of Heavy Ion SEP Propagation S. Dalla, T. Laitinen, M. Battarbee University of Central Lancashire, Preston, UK M.S. Marsh Met Office, Exeter, UK

Heavy ion SEPs An important probe into m/q-dependent acceleration and transport processes Assumption that heavy ions propagate in 1D is a key foundation of interpretations This talk: propagation of heavy ion SEPs is 3D

Time variation of Fe/O ratio Tylka et al, 2012

O at double average E Mason et al, 2006

Fe/O: O at double average E Mason et al, 2006

Fe/O decay interpretation Mason et al (2006) concluded that Fe/O decay is a result of interplanetary transport, and not a signature of acceleration process 1D modelling with a rigidity dependent mean free path can reproduce the effect (Scholer et al 1978, Cohen et al 2005, Mason et al 2006) Exponent a related to turbulence power spectrum

Energy dependent charge states Möbius et al, 1999

Fe charge states Within a 1D model, measured Q at 1 AU reflect source properties Popecki et al, 2003

<Q> vs E interpretation Increase in <Q> with E as signature of acceleration process (Barghouty & Mewaldt 1999, Ostryakov et al 2000) Energy dependent escape from acceleration region Barghouty & Mewaldt, 1999

3D full orbit propagation code Integrate test particle trajectories in specified magnetic and electric fields (Dalla et al 2005, Marsh et al 2013) Effect of small scale turbulence implemented as ‘ad-hoc scattering’ according to mean free path l

Simulation 1: Fe ions with multiple Q 1.4 million Fe ions Power law spectrum in [10,400] MeV/nuc Unipolar Parker spiral Constant l=1 AU (rigidity independ.) – no scattering across field 6°x6° source at latitude=20°

Fe propagation Q=20 Q=16 Q=12 Q=8 z y rxy x

Guiding centre drifts Sum of Parker spiral gradient & curvature drifts: q =colatitude Complex dependence on r and q Dalla et al, 2013

Fe intensity profile at 1 AU 10-100 MeV/nuc

Fe intensity profiles 10-100 MeV/nuc

Energy distribution of charge states Dalla et al, ApJ, in press, 2016

Conclusions from Simulation 1  

Simulation 2: Fe and O ions

Fe and O intensity profiles Fe and O both at 10-30 MeV/nuc

Fe/O ratio Fe and O both at 10-30 MeV/nuc Dalla et al, A&A, in press, 2016 Fe and O both at 10-30 MeV/nuc

O at double average E compared to Fe Fe at 10-30 MeV/nuc; O at 30-50 MeV/nuc

Fe/O for O at double energy Fe at 10-30 MeV/nuc; O at 30-50 MeV/nuc Behaviour observed experimentally by Mason et al (2006)

Conclusions from Simulation 2 Within a 3D propagation model, drift to a not well-connected observer produces Fe/O decaying in time The effect disappears when the comparison and ratio calculations are done for O at double the average energy of Fe (as observed by Mason et al (2006)) Within our simulation this results from the dependence of drift velocity on mE/q

Shock-like injection region Effect of variation of SEP acceleration efficiency along shock front Latitude dependence of drift velocity Overall 3D propagation will ‘process’ the injection properties

Conclusions Propagation of heavy ions is 3D, due to drift and deceleration effects (Dalla et al 2015) 3D drift-associated propagation qualitatively reproduces two key heavy ion observations: energy dependence of <Q> and time dependence of Fe/O ratio

Fe locations at t=20 hr y Q=20 Q=16 Q=12 Q=8 z rxy x rxy

SPARX SPARX: Solar PArticle Radiation swX (Marsh et al, 2015) SPARX outputs: SEP flux profiles for E>10 MeV and E>60 MeV E20 W20 W60

SEP propagation in Parker spiral l=0.3 AU l=1 AU l =10 AU

SEP Fe propagation Fe at 100 Mev/nuc t=100 hrs Q=20 Q=15 Marsh et al, 2013

1 AU view Map of fluence through 1 AU sphere Marsh et al, ApJ 2013; Dalla et al , JGR 2013

Energy change Inject monoenergetic populations with initial kinetic energy K0=1, 10, 100 MeV and 1 GeV Strong deceleration observed after 4 days Dalla et al, 2015

Time dependence Fast deceleration during the first ~20 hours Deceleration is present also in the scatter-free case Dalla et al, 2015

Dependence on mean free path Dalla et al, A&A, 2016