1. Time-Dependent Spectra of Cosmic Rays escaped from SNRs Igor Telezhinsky, DESY, Zeuthen, Germany. Vikram Dwarkadas, University of Chicago, Chicago, USA. Martin Pohl, DESY, Zeuthen, and Potsdam University, Potsdam, Germany.

2. Cosmic Rays Problem: no yet a direct evidence for CR nuclei acceleration at SNR shocks. isotropic 99% protons/nuclei 1% electrons SNRs -> 10 15-16 eV S. Lafebre, after S.Swordy 2001

4. (Brogan et al. 2006 ApJ 639, L25) Blue: VLA 90cm -- thermal and non-thermal emission Red: MSX 8 mm -- warm thermal dust emission Green: Bonn 11cm If we look at the Galactic Plane...

5. Leave sites of acceleration CREDIT: NASA/DOE/Fermi LAT Collaboration

6. Transport Equation Test-particle approximation Numerical evolution SNR Account for two shocks Spherically-symmetric geometry CR dilution is taken into account Can trace escaped particles up to a few tens of SNR radii CR escape is intrinsic part of solution allows obtain CR spectral shape at the given time E max of the escaped CR distribution

7. Diffusion ModelsRL DBDBDBDB DBDBDBDB DGDGDGDG 1 20 D1 RL DBDBDBDB DBDBDBDB DGDGDGDG 0.01D G 1.05 1 2 0 l D2

8. Magnetic Field  Magnetic field can be amplified close to the shock region  Assume B FS (t)=(2  0  V FS (t) 3 /c) 0.5 (Caprioli+2009)  Assume B profiles scale as density B(r,t)=B FS  (r,t)/  FS (r,t)

9. Scenarios Cloud Cloud: R MC = 4 pc M = 1000 M s n = 100 cm -3 Cloud Cloud: R MC = 4 pc M = 1000 M s n = 100 cm -3 D=22 pc,  = const Ia,f D=22 pc,  ~ r -2 Ic,f D=12 pc,  = const Ia,n

10. Results: particle spectra, t=400 yrRL DBDBDBDB DBDBDBDB DGDGDGDG RL DBDBDBDB DBDBDBDB DGDGDGDG 0.01D G l

11. Results: particle spectra, t=400 yrRL DBDBDBDB DBDBDBDB DGDGDGDG RL DBDBDBDB DBDBDBDB DGDGDGDG 0.01D G l

12. Results: particle spectra, t=1000 yrRL DBDBDBDB DBDBDBDB DGDGDGDG RL DBDBDBDB DBDBDBDB DGDGDGDG 0.01D G l

13. Results: particle spectra, t=1000 yrRL DBDBDBDB DBDBDBDB DGDGDGDG RL DBDBDBDB DBDBDBDB DGDGDGDG 0.01D G l

14. Results: particle spectra, t=2000 yrRL DBDBDBDB DBDBDBDB DGDGDGDG RL DBDBDBDB DBDBDBDB DGDGDGDG 0.01D G l Escape effective only in region close to shock!

15. Results: radial distributions, E max Ia, D1Ia, D2 Ic, D1Ic, D2

16. Results: radial distributions, E=20 TeV Ia, D1Ia, D2 Ic, D1Ic, D2 Particles are trapped around the shock!

17. Results: E max of the escaped CRs Not Sedov scaling!

18. Results: emission spectra, t=400 yr D1 D2

19. Results: emission spectra, t=1000 yr D1 D2

20. Results: emission spectra, t=2000 yr D1 D2 Illumination effective only when close to the shock!

21. Conclusions We reconstructed the shapes as well as the maximum energies of escaped CR distributions directly from simulations (no Sedov!) We account for dilution of CR energy density ahead of spherical shock In case of Bohm diffusion in upstream region, CRs are trapped around SNR for a long time Illumination of MC is effective only if very nearby!