Antoine Calvez TeV Particle Astrophysics 2010 Galactic Sources, Magnetic Fields and the Energy-Dependent composition of UHECRs. 1
Antoine Calvez TeV Particle Astrophysics 2010 Outline 2
Antoine Calvez TeV Particle Astrophysics 2010 Outline • The cosmic ray spectrum 2
Antoine Calvez TeV Particle Astrophysics 2010 Outline • The cosmic ray spectrum • The Pierre Auger Observatory (PAO) and its energy-dependent chemical composition 2
Antoine Calvez TeV Particle Astrophysics 2010 Outline • The cosmic ray spectrum • The Pierre Auger Observatory (PAO) and its energy-dependent chemical composition • The role of galactic sources 2
Antoine Calvez TeV Particle Astrophysics 2010 Outline • The cosmic ray spectrum • The Pierre Auger Observatory (PAO) and its energy-dependent chemical composition • The role of galactic sources • diffusion, anisotropy, spectral features 2
Antoine Calvez TeV Particle Astrophysics 2010 Outline • The cosmic ray spectrum • The Pierre Auger Observatory (PAO) and its energy-dependent chemical composition • The role of galactic sources • diffusion, anisotropy, spectral features [AC, Kusenko, Nagataki] 2
Antoine Calvez TeV Particle Astrophysics 2010 • E < 1 GeV solar modulation make studies of the primary cosmic ray spectrum very complex • 1 GeV < E < 10 5 GeV galactic origin (SNR) UHECR • 10 5 GeV < E < 10 9 GeV galactic origin (supernova explosion into stellar wind) • E > 10 9 GeV Ultra High Energy Cosmic Rays (UHECRs) 3
Antoine Calvez TeV Particle Astrophysics 2010 Above the Ankle UHECRs above the ”ankle” ( E > 10 9 GeV ) are believed to be of extragalactic origin for two reasons: 4
Antoine Calvez TeV Particle Astrophysics 2010 Above the Ankle UHECRs above the ”ankle” ( E > 10 9 GeV ) are believed to be of extragalactic origin for two reasons: • lack of plausible galactic sources 4
Antoine Calvez TeV Particle Astrophysics 2010 Above the Ankle UHECRs above the ”ankle” ( E > 10 9 GeV ) are believed to be of extragalactic origin for two reasons: • lack of plausible galactic sources • lack of galactocentric anisotropy, inconsistent with retaining protons in Galactic micro-Gauss fields. 4
Antoine Calvez TeV Particle Astrophysics 2010 Above the Ankle UHECRs above the ”ankle” ( E > 10 9 GeV ) are believed to be of extragalactic origin for two reasons: • lack of plausible galactic sources • lack of galactocentric anisotropy, inconsistent with retaining protons in Galactic micro-Gauss fields. Both of these reasons can be challenged 4
Antoine Calvez TeV Particle Astrophysics 2010 Above the Ankle UHECRs above the ”ankle” ( E > 10 9 GeV ) are believed to be of extragalactic origin for two reasons: • lack of plausible galactic sources • lack of galactocentric anisotropy, inconsistent with retaining protons in Galactic micro-Gauss fields. Both of these reasons can be challenged Both of these reasons should be challenged in view of a recent PAO discovery 4
Antoine Calvez TeV Particle Astrophysics 2010 Pierre Auger energy-dependent chemical composition [Auger PRL 104 (2010) 091101] 5
Antoine Calvez TeV Particle Astrophysics 2010 Pierre Auger energy-dependent chemical composition [Auger PRL 104 (2010) 091101] The composition gets heavier with energy 5
Antoine Calvez TeV Particle Astrophysics 2010 Pierre Auger energy-dependent chemical composition [Auger PRL 104 (2010) 091101] The composition gets heavier with energy What could cause this effect? 5
Antoine Calvez TeV Particle Astrophysics 2010 Not Observed by HiRes [Auger PRL 104 (2010) 091101, HiRes ApJ 622 (2005) 910, HiRes arXiv:0910.4184] 6
Antoine Calvez TeV Particle Astrophysics 2010 Interpreting the PAO Results There exist two possible solutions to this puzzle: 7
Antoine Calvez TeV Particle Astrophysics 2010 Interpreting the PAO Results There exist two possible solutions to this puzzle: • The segregation occurs at the source with a heavy element favored acceleration mechanism. This is unlikely because of photodissociation 7
Antoine Calvez TeV Particle Astrophysics 2010 Interpreting the PAO Results There exist two possible solutions to this puzzle: • The segregation occurs at the source with a heavy element favored acceleration mechanism. This is unlikely because of photodissociation • The acceleration mechanism affects all the particles the same way and the segregation occurs during the transport of the nuclei. 7
Antoine Calvez TeV Particle Astrophysics 2010 Interpreting the PAO Results There exist two possible solutions to this puzzle: • The segregation occurs at the source with a heavy element favored acceleration mechanism. This is unlikely because of photodissociation • The acceleration mechanism affects all the particles the same way and the segregation occurs during the transport of the nuclei. This is exactly what you would expect for Galactic sources... 7
Antoine Calvez TeV Particle Astrophysics 2010 Interpreting the PAO Results There exist two possible solutions to this puzzle: • The segregation occurs at the source with a heavy element favored acceleration mechanism. This is unlikely because of photodissociation • The acceleration mechanism affects all the particles the same way and the segregation occurs during the transport of the nuclei. This is exactly what you would expect for Galactic sources... Why? 7
Antoine Calvez TeV Particle Astrophysics 2010 Diffusion l c B B l Two different regimes depending on the energy of the particle 8
Antoine Calvez TeV Particle Astrophysics 2010 Diffusion critical energy E 0 where r L = l c for E > E 0 , we get l c ∼ r L for E < E 0 , we get l c >> r L • mean free path >> l • mean free path ∼ l ) 2 ( • D = l E 3 ≡ D 0 • D = D 0 E 0 9
Antoine Calvez TeV Particle Astrophysics 2010 Diffusion critical energy E 0 where r L = l c for E > E 0 , we get l c ∼ r L for E < E 0 , we get l c >> r L • mean free path >> l • mean free path ∼ l ) 2 ( • D = l E 3 ≡ D 0 • D = D 0 E 0 E 0 depends on the charge of the nuclei 9
Antoine Calvez TeV Particle Astrophysics 2010 Diffusion with Non-Unit Charge For a particle with charge q i = eZ i , we get a critical energy E 0 ,i with r L,i = l c : E • r L,i = Bq i • E 0 ,i = eBl c Z i 10 8 eV ) ( ) ( ) B l c ( • E 0 ,i = Z i × 3 × 10 − 6 G 0 . 3 kpc 10
Antoine Calvez TeV Particle Astrophysics 2010 Diffusion with Non-Unit Charge For a particle with charge q i = eZ i , we get a critical energy E 0 ,i with r L,i = l c : E • r L,i = Bq i • E 0 ,i = eBl c Z i 10 8 eV ) ( ) ( ) B l c ( • E 0 ,i = Z i × 3 × 10 − 6 G 0 . 3 kpc The diffusion coefficient is therefore: ) δ 1 ( E D 0 E ≤ E 0 ,i , E 0 ,i D i ( E ) = ) (2 − δ 2 ) ( E D 0 E > E 0 ,i E 0 ,i 10
Antoine Calvez TeV Particle Astrophysics 2010 Diffusion Equation For a point-like source : ( E ) − γ Q i ( E,⃗ r ) = Q 0 ξ i δ ( ⃗ r ) E 0 ,i We solve the following differential equation: ∂n i ∇ n i ) + ∂ ∫ ∂t − ⃗ ∇ ( D i ⃗ ∑ P ik ( E, E ′ ) n k ( E ′ ) dE ′ ∂E ( b i n i ) = Q i ( E,⃗ r, t ) + k 11
Antoine Calvez TeV Particle Astrophysics 2010 Diffusion Equation For a point-like source : ( E ) − γ Q i ( E,⃗ r ) = Q 0 ξ i δ ( ⃗ r ) E 0 ,i We solve the following differential equation: ∂n i ∇ n i ) + ∂ ∫ ∂t − ⃗ ∇ ( D i ⃗ ∑ P ik ( E, E ′ ) n k ( E ′ ) dE ′ ∂E ( b i n i ) = Q i ( E,⃗ r, t ) + k Below GZK energies, energy losses are negligible thus we only consider diffusion terms. 11
Antoine Calvez TeV Particle Astrophysics 2010 Solution The flux is: ( E ) − γ Q 0 n i ( E, r ) = 4 πrD i ( E ) E 0 ,i with diffusion time t D : × 10 19 eV ) 2 − δ 2 ) 2 ( 26 t D ∼ R 2 ( R ∼ 10 7 yr 10 kpc D i Z i E 12
Antoine Calvez TeV Particle Astrophysics 2010 Consequences 13
Antoine Calvez TeV Particle Astrophysics 2010 Consequences • Diffusion is energy denpendent 13
Antoine Calvez TeV Particle Astrophysics 2010 Consequences • Diffusion is energy denpendent The spectral slope changes at E ∼ E 0 ,i 13
Antoine Calvez TeV Particle Astrophysics 2010 Consequences • Diffusion is energy denpendent The spectral slope changes at E ∼ E 0 ,i • The flux drops dramatically because the particles escape from the galaxy 13
Antoine Calvez TeV Particle Astrophysics 2010 Consequences • Diffusion is energy denpendent The spectral slope changes at E ∼ E 0 ,i • The flux drops dramatically because the particles escape from the galaxy • Diffusion time depends on charge 13
Antoine Calvez TeV Particle Astrophysics 2010 Consequences • Diffusion is energy denpendent The spectral slope changes at E ∼ E 0 ,i • The flux drops dramatically because the particles escape from the galaxy • Diffusion time depends on charge Diffusion times for nuclei are longer than for protons of the same energy 13
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