1. E.G.Berezhko, L.T. Ksenofontov Yu.G.Shafer Institute of Cosmophysical Research and Aeronomy Yakutsk, Russia Energy spectra of electrons and positrons, produced in supernova remnants (SNRs) Do we need except SNRs some extra, “positron rich” CR sources in order to explain the observed energy spectra of electrons and positrons?

2. Standard picture for secondary CR generation Galactic halo Galactic disk CR source Primary CR Gas atom Secondary CR Secondary Primary Energy

3. Positron/electron ratio Energy 10 GeV 100 GeV Pamela Fermi Evidence for positron rich sources? p + p → π + + … → μ + + … → e + + …

4. Production of primary and secondary (Li, Be, B, e +, p, …) CRs in SNRs Injection of primaries from thermal pool SN shock Reacceleration of primary and secondary CRs Primary CR Secondary CR Acceleration of secondaries, created in nuclear collisions of accelerating primary CRs with gas atoms Berezhko, Ksenofontov, Ptuskin, Völk, Zirakashvili (2003) Effect is proportional to the volume sweep up by SN shock Efficient in the case of diluted ISM Effect is proportional to the number of collisions Efficient in the dense ISM Energy spectrum of secondary CRs produced in SNR is harder then produced in ISM s/p ratio flattens with energy CR

5. Computational details ε 2 I, MeV cm -2 sr -1 s -1 ε, MeV 10 10 2 10 3 10 4 10 1 0.1 e¯e¯ e+e+ Moskalenko & Strong (1998) ε inj = 300 MeV N inj = (4π/c) I( ε > ε inj ) B 0 = B ISM = 5 μGupstream (unamplified) magnetic field K ep = 10 -4 for t << 10 4 yr K ep = 10 -2 for t >~ 10 4 yr electron to proton ratio E SN = 10 51 erg M ej = 1.4 M Sun supernova explosion parameters effective energy of injected CR electrons and positrons number density of injected particles

6. Nonlinear kinetic (time-dependent) theory of CR acceleration in SNRs Gas dynamic equations CR transport equation Suprathermal particle injection Gas heating due to wave dissipation Time-dependent (amplified) magnetic field Applied to any individual SNR theory gives at any evolutionary phase t>0 : nuclear N p (p,r), N He (p,r), …, electron N e (p,r) and positron N e +(p,r) momentum and spatial distributions Kang & Jones 2006, Ptuskin & Zirakashvili 2008

7. Energy spectra of electrons and positrons, produced in SNRs J(ε) ~ τ loss J SNR (ε) ~ ε -1 J SNR (ε) At ε > 10 GeV positron spectrum is dominated by component created in p-p collisions (ppSNR) (roughly consistent with previous estimate (Blasi 2009)) ρ = 1.4 N H m p ISM density

8. Energy spectra of electrons and positrons, produced in SNRs At lower ISM density reaccelerated positron component (reSNR) becomes more relevant

9. Conclusions Energy spectrum of positrons, produced in SNRs, are expected to be flatter at 10 – 100 GeV compared with electron spectrum due to acceleration of background CRs and secondary particles, created in p-p collisions Electron and positron spectra expected from SNRs are qualitatively consistent with the experiment. Remark Since electron/positron spectra are very sensitive to the actual distribution of SNRs in solar vicinity (e.g. Pohl & Esposito 1998), which is not well known, it is hardly possible to make reliable prediction of their spectra