1. Multi-Zone Modeling of Spatially Non-uniform Cosmic Ray Sources Armen Atoyan Concordia University, Montreal FAA60 Barcelona, 7 November 2012

2. Multi-zone modeling of nonthermal radiation of Cas A in collaboration with F. Aharonian, R. Tuffs and H. Voelk. (Paper-I: A&A 354, p.915; Paper-II A&A 355, p.211; 2000) Basic motivation of the study (done in 1998-1999): VHE fluxes to expect from Cas A known as a prominent source of synchrotron radiation (by that time not detected yet in  -rays). Main results : for Cas-A : prediction of  -ray fluxes that could be expected, and what it would mean for the origin (leptonic vs hadronic ) General: Multi-zone model for CR sources that allows (a) modification of CR energy spectra on timescales  t < t loss. (b) relaxing constrains on IC  -ray fluxes from synchrotron X-rays (e.g. for Tycho).

3. (Stage et al. 2006) Chandra X-rays 0.5-6 keV Chandra -4-6 keV (Uchiyama & Aharonian, 2008) Cas A radio map Likely acceleration sites: bow shocks, bright radio ring & knots in the shell, (flux variability on ~yrs scale detected from knots in radio, and recently also in X-rays)

4. Single-zone approach: cannot explain synchrotron (X-rays vs synchrotron self-absorption), problems with breamsstahlung Spectra for B=100  G, 350  G & 700  G (Paper I)

5. Multi-zone modeling: simplest case - two zones. Basic assumptions: (a) the source consists of compact regions with high B field (zone 1), and much larger region with lower B field (zone 2). (b) particles are accelerated (mostly) in compact zone 1, but can escape into zone 2 (by diffusion and/or convection with plasma) Equations derived for the two zone-model:  Possibility for steepening of the energy spectra in zone 1 by diffusive propagation, D(E) ~ E  ; hard spectra in zone 2.

6. Energy distributions of electrons in zone 1 and zone 2 (a)Spectral energy density (b)Total energy distributions Spectral modifications by diffusion: possible only if the energy densities in zone 1 and zone 2 are different (!)

7. Radiation spectra Two-zone model: B 1 = 0.4 mG, B 2 =1.5 mG E cut = 35 TeV Secular decline of radio (assuming B-field in zone 1 declines on timescales ~ 130 yr)

8. Model predictions for  -rays ICompton (target - CMB and FIR) Bremsstrahlung (n gas ~ 10-15 pcc) + pp (hadronic) (W p ~ 2 10 49 ergs) TeV was later on detected (HEGRA, MAGIC, VERITAS) The spectrum is much harder than expected for leptonic origin. Protons accelerated to ~200 TeV explain the data. Data: HEGRA 2001, VERITAS 2010

9. Tycho SNR: type Ia Radio (NRAO)X-rays (Chundra)

10. Two-zone model for Tycho (Atoyan & Dermer, 2012) Difference: acceleration mostly in the rim, lower B field, fast escape into zone II (no spectral modifications) Model parameters: B 1 = 100  G, B 2 =34  G E cut = 40 TeV d = 2.8 kpc

11. Gamma-rays: Leptonic vs Hadronic Models Leptonic: bremsstrahlung (dashed) + Compton (solid); (contribution from zone 1 only ~10%) Conclusion: neither leptonic nor hadronic origins can be excluded at this time. Detection of a cutoff at low energies could help confirm pp. W p ~ 2 10 49 ergs E e ~ 4.6 10 48 ergs E p ~ 3 10 49 (n o = 0.6 pcc)

12. Conclusions Single-zone model can miss most of the electrons which may accumulate in radio-dim regions with low B field. Multi-zone modeling of sources is need for robust predictions.