Decay Phase of Proton and Electron SEP Events

E.I. Daibog1, K. Kecskeméty2, Yu.I. Logachev1

1 Skobeltsyn Inst. of Nuclear Physics, Moscow State Univ., Russia

2 KFKI RMKI, Budapest, Hungary

Why decays?

the features and conditions in a source of SEPs at the Sun become unessential during decay phase and effects and peculiarities of particle acceleration and losses in interplanetary space become more important.

- rising phase and maximum – origin and propagation mechanism

- decay phase - propagation mechanism and interplanetary medium conditions

Decay phase

Observed flux profile: a mixture of temporal and spatial variations

Functional form of the particle flux decline: power-law – predominantly diffusive propagation exponential – adiabatic deceleration and convection

Statistical investigation (Daibog et al. 2003):

~ 700 events of 1-5 MeV proton fluxes (3 solar cycles, at 1 AU) IMP 8 (CPME)

~90% of SEP decays are exponential power-law mostly at high energiesExponential decays longer than 24 hrs. >4 MeV flux > 1-2 p/cm2ssrBackground: instrumental + remnants of preceding events

Exponential form : J exp(-t/)

dN/dt ~ N. Neglecting diffusion

Lupton and Stone, 1971. Model with absorbing boundary andBurlaga, 1967. Spherically-symmetric diffusion. The volume

limited by a boundary outside of which particles fly away freely. = R2

abs/π2κOwens,1979. Convection = 9/4V2 (2 + α )2 Contrary κ and E dependence

Ng and Gleeson, 1976. ׀׀=0(1+r3). Gradual transition to free particle escape. Nearly exponential solution .

Forman, 1970; Jokipii, 1971. Convection and adiabatic deceleration dominate over gradients, scattering, and drift

τ = 3r / 2V (2 + α ),

α = T+2mc2/(T+mc2) ≈ 2 at nonrelativistic energies.

Lee, 2000. adiabatic deceleration

Right qualitative dependence on all parameters

However

diffusion takes place in any case. No scattering → no either convection and adiabatic deceleration!

Electrons (ten keV – MeV) vs protons (MeV – ten MeV)

What can be expected?

The shapes of proton and electron decays in the event should be the same if particles are subjected to the same mechanisms of propagation and losses.

e and p rigidities differ so strong (0.1 – 250 MV) that far distant parts of IMF inhomogeneouty spectra play a role in their scattering. Similar decays → similar spectra

Statistics

IMP-8. 330 simultaneous decays of е (0.22 - 0.5 - 0.8 МeV) and р (4.6 -15 - 25 МeV). 67- both exponential. 211– p exponential, e power-shaped.

Helios 1,2. е 0.3 - 0.8 MeV, p 4 – 13 - 27 MeV.31 exponential decays (16 - e = p ; 15 - e > p).

SOHO COSTEP EPHIN. 88 decays: p (4.3 - 7.8 - 25 MeV, e (0.25 - 0.7 - 3 MeV). ACE EPAM DE. Low energy electrons (0.038 - 0.053 - 0.103 - 0.175 - 0.312 MeV). 52 е and р shapes coincide , 30 different shapes, 6?

Correlation between e and p ?

IMP 8

p 4.6-15 MeV, e 0.5-0.8 MeV

SOHO COSTEP EPHIN

Major events. Peak flux of 4.3-8 MeV protons

>10 p/cm2 s sr MeV

Mutual angular position of the particle origin and the observer

Eastern position of the flare relative to the observer’s ftp.

Magnetic field lines move toward the observer – prolonged rising and decay phases.

Western position. Field lines move away from the observer –accelerated rising and decay phases.

Change of the regime at the longitude about 50-60 degs.

Protons H1, H2 4-13 MeV, IMP-8 4.6-15 MeV Hel =30 hrs, IMP = 12 hrs

Electrons Hel =30 hrs, IMP = 20 hrs

Conclusions. At late phase of decay1. In half of clear-shaped events the shapes of electron and proton decays

(exponential or power-law) are similar.

2. Most of electron decays with e = (1 ± 0.25) p concerns the cases with р

< e. As a rule the rate of  electron decay is similar or slower than proton

one.3. The rate of e and p decay is practically independent from the power and

prehistory of event.

4. Indications are obtained of existence of e dependence on angular and radial location of the origin similar to proton ones.

5. All these show that in a considerable part of events electrons and protons are subjected to the same processes (convection and adiabatic deceleration?)

More statistics of clean events needed!