TRANSITION FROM GALACTIC TO EXTRAGALACTIC COSMIC RAYS V. Berezinsky INFN, Laboratori Nazionali del Gran Sasso, Italy
OBSERVED CR SPECTRUM 10 4 � Flux (m 2 sr s GeV) -1 � 10 2 � � 10 -1 10 -4 10 -7 Knee � 10 -10 (1 particle per m 2 -year) 10 -13 10 -16 10 -19 2 nd knee 10 -22 Ankle � � 10 -25 (1 particle per km 2 -year) 10 -28 10 9 10 11 10 13 10 15 10 17 10 19 10 21 Energy (eV)
I. TOWARDS THE END OF GALACTIC CR
SUPERNOVA-REMNANT PARADIGM: “Standard Model” for galactic cosmic rays • sources: supernova remnant • acceleration: SNR shock acceleration • chemical composition: rigidity-dependent injection • propagation: diffusive propagation in magnetic fields
DIFFUSIVE SHOCK-ACCELERATION: • spectrum: At fixed SNR age the spectrum of escaped particles is close to δ -function. but time-averaged spectrum is ∝ E − 2 or flatter at highest energies (Ptuskin, Zirakashvili 2006). • E max : Acceleration to the highest energies occurs at the beginning of Sedov phase. Non-linear amplification of turbulent magnetic field in the shock precursor due to streaming instability of CR produces magnetic field with strength δB ∼ B ∼ 10 − 4 G (Bell and Lucek). � W 51 � 2 / 5 B E max = 4 × 10 15 Z eV 10 − 4 G n g / cm 3 E max = 4 × 10 15 B − 4 eV , E max = 1 × 10 17 B − 4 eV Fe p
SM : GALACTIC SPECTRA AND KNEES Berezhko and V¨ olk 2007
MASS COMPOSITION VS ENERGY Compilation of H¨ orandel 2005 Mean logarithmic mass <ln A>� 4� F� e� ✧� CASA-MI� direct� :� JACEE� A� ⊕� RUNJOB� Chacaltaya� ⊕� ✣� EAS-TOP + MACRO� ⊕�⊕� 3.� 5� ✧� ✧� ⊕� ⊕� ✣� ✧� ✧� ⊗� ✕� EAS-TOP (e/m� )� ✕� ⊕�⊕� ✧� ∅� HEGRA (CRT)� ⊗�⊗� M� g� ✣� ⊕� 3� ∇� SPASE/AMANDA� ❄� ✧� ✕� ⊗� ⊕� ∇� ✣� ⊕� ⊗� ⊗� ✧� ⊕�⊕� ∇� ❄� N� 2.� 5� ✣� ✕� ✕� ❄� ❄� ⊕�⊕�⊕�⊕�⊕� ∅� ✧� ⊗�⊗�⊗� ∅� ∅� ✣� ✣� B� e� ✣� ∇� ✕� ∅� ∇� ∇� ∇� 2� ✧� ⊗�⊗�⊗� ✕� ∅� ❄� ❄� ❄� ❄� ⊗� 1.� 5� ∅� ⊗�⊗ ⊗ � H� e� ✧� ✧� ✧� ⊗�⊗� ✧� 1� ❄� KASCADE (nn)� KASCADE (h/m� )� ⊗� KASCADE (e/m) QGSJET� 0.� 5� ⊕� KASCADE (e/m) SIBYLL� 0� H� 4� 5� 6� 7� 8� 10� 10� 10� 10� 10� Energy � E� [GeV]� 0�
CONCLUSION NEEDED FOR ANALYSIS OF TRANSITION In “standard model” the end of Galactic cosmic rays starts at iron knee ∼ 1 × 10 17 eV E knee = ZE knee Fe p Spectrum of Fe-nuclei at E > E knee is steep and it inevitably intersects some- Fe where the more flat extragalactic spectrum .
II. FROM UHECR TOWARDS THE KNEE
MEASURED FLUXES OF UHECR
PROPAGATION OF UHECR THROUGH CMB
INTERACTIONS -7 Protons 10 p + γ CMB → p + e + + e − a) -8 10 p + γ CMB → N + pions -1 Nuclei 1/E dE/dt, yr -9 10 Z + γ CMB → Z + e + + e − 2 A + γ CMB → ( A − 1) + N -10 red-shift 10 A + γ CMB → A ′ + N + pions 1 + e - e -11 10 Photons + e - e pion-prod. γ + γ bcgr → e + + e − -12 10 17 18 19 20 21 22 10 10 10 10 10 10 E, eV
PROPAGATION SIGNATURES Propagation of protons in intergalactic space leaves the imprints on the spectrum most notably in the form: GZK cutoff and pair-production dip These signatures might depend on the distribution of sources and way of propagation.
GZK CUTOFF GZK cutoff is modified by discreteness in source distribution and by source local overdensity/deficit and by different values of E max . 25 10 2 -1 eV -1 sr -2 s 3 , m 24 10 J(E)E 3 2 HiRes I - HiRes II 1 23 10 6 5 17 18 19 20 21 10 10 10 10 10 E, eV
GZK CUTOFF IN HiRes DATA In the integral spectrum GZK cutoff is numerically characterized by energy E 1 / 2 where the calculated spectrum J ( > E ) becomes half of power-law extrapolation spectrum KE − γ at low energies. As calculations (V.B.&Grigorieva 1988) show E 1 / 2 = 10 19 . 72 eV valid for a wide range of generation indices from 2.1 to 2.8. HiRes obtained: E 1 / 2 = 10 19 . 73 ± 0 . 07 eV 1.2 1 J(>E)/KE −γ 0.8 0.6 0.4 0.2 0 17 17.5 18 18.5 19 19.5 20 20.5 21 log 10 (E) (eV)
PAIR-PRODUCTION DIP IN THE DIFFUSE SPECTRUM VB, Grigorieva 1988; Aloisio, VB, Blasi, Gazizov, Grigorieva (2004 - 2007). DEFINITION OF MODIFICATION FACTOR J p ( E ) η ( E ) = J unm ( E ) p where J unm ( E ) includes only adiabatic energy losses (redshift) and J p ( E ) includes p total energy losses, η tot ( E ) or adiabatic, e + e − energy losses, η ee ( E ) . Since both J unm ( E ) and J p ( E ) include factor E − γ g , η ( E ) depends weakly on γ g . p
DIP IN DIFFUSE SPECTRA 0 10 2 modification factor 1 η ee -1 10 1: γ g =2.7 2: γ g =2.0 -2 10 2 η total 1 17 18 19 20 21 10 10 10 10 10 E, eV The dotted curve shows η ee , when only adiabatic and pair-production energy losses are included. The solid and dashed curves include also the pion-production losses.
DIP IN COMPARISON WITH AKENO-AGASA DATA 0 10 η ee modification factor -1 10 Akeno-AGASA η total -2 10 γ g =2.7 17 18 19 20 21 10 10 10 10 10 E, eV
DIP IN COMPARISON WITH HIRES DATA 0 10 η ee modification factor -1 10 HiRes I - HiRes II η total -2 10 γ g =2.7 17 18 19 20 21 10 10 10 10 10 E, eV
DIP IN COMPARISON WITH YAKUTSK DATA 0 10 η ee modification factor -1 10 Yakutsk η total -2 10 γ g =2.7 17 18 19 20 21 10 10 10 10 10 E, eV
DIP IN COMPARISON WITH AUGER DATA
ENERGY CALIBRATION BY DIP : AGASA-HIRES DISCREPANCY 25 25 10 10 2 -1 -1 eV -1 sr -2 s -1 sr 2 m -2 s 3 , eV 3 , m 24 24 10 10 J(E)E J(E)E Akeno - AGASA Akeno-AGASA HiRes I - HiResII HiRes I - HiRes II 23 23 10 10 17 18 19 20 21 17 18 19 20 21 10 10 10 10 10 10 10 10 10 10 E, eV E, eV AGASA and HiRes spectra calibrated by the dip. The energy shift needed for χ 2 min is λ AGASA = 0 . 9 and λ HiRes = 1 . 2 . Both are allowed by systematic errors.
DIP AND AGASA-YAKUTSK DISCREPANCY 25 25 10 10 -1 -1 -1 sr -1 sr -2 s -2 s 2 m 2 m 3 , eV 3 , eV 24 24 10 10 J(E)E J(E)E Akeno-AGASA Akeno-AGASA Yakutsk Yakutsk 23 23 10 10 17 18 19 20 21 17 18 19 20 21 10 10 10 10 10 10 10 10 10 10 E, eV E, eV AGASA and Yakutsk spectra calibrated by the dip. The energy shift needed for χ 2 min is λ AGASA = 0 . 9 and λ Yakutsk = 0 . 75 . Both are allowed by systematic errors.
AGASA-HIRES-YAKUTSK DISCREPANCY 25 25 10 10 2 2 -1 eV -1 eV -1 sr -1 sr -2 s -2 s 3 , m 3 , m 24 24 10 10 J(E)E J(E)E Akeno - AGASA Akeno - AGASA Yakutsk Yakutsk HiRes I - HiRes II HiRes I - HiRes II 23 23 10 10 17 18 19 20 21 17 18 19 20 21 10 10 10 10 10 10 10 10 10 10 E, eV E, eV AGASA, Hires and Yakutsk spectra calibrated by the dip.
COMPARISON OF AUGER WITH CALIBRATED DATA
COMPARISON OF AUGER WITH CALIBRATED DATA
CONCLUSIONS NEEDED FOR ANALYSIS OF TRANSITION • Very good agreement of the predicted dip energy-shape with the data of all detectors demonstrates that large fraction of particles observed at 1 × 10 18 − 4 × 10 19 eV are extragalactic protons propagating through CMB. • The numerical agreement of HiRes data with GZK cutoff implies that at energy E ≥ 5 × 10 19 eV protons dominate, too.
III. TRANSITION
THREE MODELS OF TRANSITION: DIP, ANKLE, and MIXED-COMPOSITION MODELS • In the dip model, dip automatically includes ankle. • In ankle model, E a ∼ 1 × 10 19 corresponds to equal fluxes J gal = J extr . • In the mixed model, E a ∼ 3 × 10 18 eV is the end of transition. Necessary assumption for ankle and mixed models: AGREEMENT OF DATA WITH PAIR-PRODUCTION DIP IS ACCIDENTAL
THE DIP and ANKLE TRANSITIONS In the dip model transition occurs at E tr < E b = 1 × 10 18 eV, i.e. at second knee. This transition agrees perfectly with the standard galactic model. In the ankle model transition occurs at E a = 1 × 10 19 eV and the galactic flux at this energy is half of the total in contradiction with standard galactic model. KASCADE HiRes I 3 2 HiRes I 10 10 HiRes II HiRes II 1.5 -1 GeV 1.5 -1 GeV -1 sr -1 sr -2 s 2.5 , m -2 s 2 1 10 10 2.5 , m J(E)E extr. p J(E)E gal. Fe gal. CR extr. p E t r E Fe E t r E b 1 0 10 10 7 8 9 10 9 10 11 10 10 10 10 10 10 10 E, GeV E, GeV
THE DIP and ANKLE TRANSITIONS: MASS COMPOSITION In the dip model transition to proton-dominated component is completed at 1 × 10 18 eV, while in the ankle model at 1 × 10 19 eV. In the range 1 - 10 EeV ankle model predicts iron or mixed composition, while dip model - proton-dominated composition. The elongation rate is most sensitive tool of chemical composition. 900 900 X max , g/cm 2 X max , g/cm 2 800 800 700 700 600 600 500 500 10 8 10 9 10 10 10 11 10 8 10 9 10 10 10 11 E 0 , GeV E 0 , GeV X max ( E ) in the dip model. X max ( E ) in the ankle model.
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