January 22, 2015

Protons (85 %) Nuclei (13%) Electrons/Positrons (2%) Galactic Origin α=2.7

RESONANT INSTABILITY (Skilling 1975) RESONANT INSTABILITY (Skilling 1975) NON RESONANT INSTABILITY (Bell 2004) NON RESONANT INSTABILITY (Bell 2004) Excitation of Alfvén waves with λ ≅ r L  saturation at δB/B ≅ 1  E M < 1 PeV Purely growing waves at wavelengths λ << r L, driven by the CR current j CR  generation of power at larger spatial scales up to λ ≅ r L  larger E M

Current at distance R Balanc e Growth Rate e-folding Maximum Energy Cardillo, Amato & Blasi 2015 Source Spectrum

Escape Spectrum Shock Radius Shock Velocit y CR Current Cardillo, Amato & Blasi 2015

Type I m=0, k=7 Type I m=0, k=7 No sharp cut-off above E M ! No sharp cut-off above E M ! Cardillo, Amato & Blasi 2015 Type II m=2, k=9 Type II m=2, k=9 Ejecta density Medium density Shock radius k=[7,10]

Cardillo, Amato & Blasi 2015 Ejecta Mass ISM density Wind density ST radius Ejecta density ST time Shock radius Shock velocity

ISM WIND Type II SNR provide higher maximum energy Proportional to CR efficiency (ξ CR ) Strong dependence on shock velocity ED phase ED phase Cardillo, Amato & Blasi 2015 Observational problem!

B/C ratio flat steep Cardillo, Amato & Blasi 2015 Diffusion Spallation (Ptuskin 2009) Cross Section (Horandel 2007) Grammage

Diffusion Spallation Assumption s Variables M ej = 1 M  dM/dt= M  /yrs V w = 10 km/s R d = 10 kpc X(E)=k(Rg/ 3GV) -δ δ= p inj n d = 1 cm -3 σ sp = α(E) Α β(E) E SN = Supernova energy R = Explosion rate EMEM EMEM t0t0 t0t0 V0V0 V0V0 ξ CR Escape Cardillo, Amato & Blasi 2015 From TRACER and CREAM

flat steep E M = 1 PeV  Ra= 1/30 yrs ξ CR = 11% (for standard E sn =10 51 erg) E M = 1 PeV  Ra= 1/800 yrs ξ CR = 240% (!!) (for standard E sn =10 51 erg) Cardillo, Amato & Blasi 2015 E M > 1 PeV

E SN = erg R= 1/30 yrs E M = 1 PeV ξ CR = 11% t 0 = 85 yrs v 0 = km/s Cardillo, Amato & Blasi 2015

Cardillo, Amato, Blasi, submitted

k=9 E SN = 2 x erg R= 1/110 yrs E M ≅ 3.7 x eV ξ CR ≅ 20 % t 0 ≅ 60 yrs v 0 ≅ km/s Cardillo, Amato & Blasi 2015 k=9 E SN = erg R= 1/15 yrs E M ≅ 507 TeV ξ CR ≅ 5.2 % t 0 ≅ 85 yrs v 0 ≅ km/s

k=9 E SN = 2 x erg R= 1/110 yrs E M ≅ 3.7 x eV ξ CR ≅ 20 % t 0 ≅ 60 yrs v 0 ≅ km/s Cardillo, Amato & Blasi 2015 k=9 E SN = erg R= 1/15 yrs E M ≅ 507 TeV ξ CR ≅ 5.2 % t 0 ≅ 85 yrs v 0 ≅ km/s Uncertainty on the data? Additional component?

k=7 E SN = erg R= 1/25 yrs E M ≅ 781 TeV ξ CR ≅ 12 % t 0 ≅ 96 yrs v 0 ≅ km/s Cardillo, Amato & Blasi 2015

 NHR instability leads to the release of a steep power-law spectrum in the ejecta dominated phase  no sharp cut-off!  KASCADE Grande and ARGO data can be fitted with reasonable values of SN parameters.  No model that can fit both ARGO and KASCADE-Grande data  need a better data understanding with a consequent theory improvement.  Type II SNRs can accelerate particles up to the knee at very early time  detection problem.  Bell non-resonant instability predicts that very energetic SNRs can reach PeV energies.