NATURE OF KNEES AND ANKLE

1. NATURE OF KNEES AND ANKLE V.S. Berezinsky INFN, Laboratori Nazionali del Gran Sasso

2. PROBLEM of TRANS-KNEE PARTICLES in the RIGIDITY MODELS Rigidity models can be rigidity-confinement models or rigidity-acceleration models (e.g. Biermann SN remnants). The energy of spectrum bending (knee) for nuclei Z Ez = Z Ep, where Ep = 2.5×1015 eV is position of proton knee. EFe= 6.5×1016 eV KASCADE data

3. SECOND KNEEEFe may be related to the second knee(second steepening of the spectrum) Fly’s Eye : ~ 4×1017 eV Akeno : ~ 6×1017 eV HiRes : ~ 7×1017 eV Yakutsk : ~ 8×1018 eV If transition from galactic to extragalactic CR occurs at ankle Ea~1×1019 eV, how the gap between the iron knee, EFe~ 1×1017 eV, (or the second knee, E2~ 1×1018 eV) and the ankle, Ea~ 1×1019 eV,is filled? (Hoerandel 2003)

4. SECOND KNEE and EXTRAGALACTIC PROTONS Second knee automatically appears in the total spectrum (galactic +extragalactic) due to low-energy flattening of extragalactic spectrum, which appears at Ec~ 1×1018 eV.This energy is universal for all propagation modes (rectilinear or diffusive) and it is determined by transition from adiabatic to e+e- -energy losses . g diffusive propagationLemoine 2004, Aloisio, V.B. 2004 rectilinear propagation

5. IS PROTON COMPOSITION of CR at E ≥ 1×1018 eV EXCLUDED by OBSERVATIONS? Hires, HiresMIA, Yakutsk : favour proton compositionFly’s Eye, Haverah Park, Akeno : mixed composition Hires elongation rate

6. DIP as SIGNATURE of PROTONS INTERACTING with CMB (model independent analysis in terms of modification factor)Definition: h(E) = Jp(E)/Jpunm (E) (3) Jp(E) is calculated with all energy losses included. Jpunm (E) - only adiabatic energy losses included. • Dip is stable: • to propagation modes (rectilinear or diffusive), • to variation of source separation (d=1-60 Mpc), • to inhomogeneities in source distribution, • to fluctuations in interaction.

7. DIP: COMPARISON with OBSERVATIONS(assumption Qgen~E-2.7) • AGASA : 19 bins, 2 free parameters, c2=19.06, c2/d.o.f. =1.12, • HiRes : 21 bins, 2 free parameters, c2=19.5, c2/d.o.f. =1.03Conclusions: • At E ≤ 1×1018 eV the new CR component appears (second knee). • The confirmed independent argument for proton composition at 1×1018 ≤E ≤ 4×1019 eV. modification factor

8. DIP and DISCREPANCY between AGASA and HiRes DATA(energy calibration by dip) We have shifted the energies to obtain the best fit to the dip: AGASA : E→kAE (best fit kA=0.90)HiRes : E→kHiRE (best fit kHiR=1.25)

9. ALTERNATIVE EXPLANATION of the DIPis given by galactic component in energy interval1×1018 eV - 1×1019 eV .To obtain good c2 the galactic component Jgal(E) must be taken ad hoc to fit Jobs(E): without detailed propagation model for Jgal(E) it is a “fitting exercise”. Using free parameters for (4 as minimum) one can always have a good (though artificial) fit to Jobs(E). E, eV Extragalactic dip model uses basically one parameter gg=2.7 to describe the complex spectrum. Many models based on the description of CR propagation in the Galaxy predict transition to extragalactic CR at the second knee (Biermann et al. 2003) or below it (Wick, Dermer, Atoyan 2004). The dip in these models has extragalactic origin as in our considerasion.

10. model-dependent analysis TRANSITION from GALACTIC to EXTRAGALACTIC CR in AGN MODEL with QUASI-RECTILINEAR PROPAGATION Assumptions: Spectrum: Emax = 1×1021 eV, Ec ~ 1×1018 eV (free parameter)emissivity:L = 3.5×1021 erg/Mpc3yr luminosity of AGN Lp= L/ ns gives Lp = 3.7×1042 erg/s for Seyferts ns = 3×10-4 Mpc-3 Lp = 3.7×1043 erg/s for powerful AGN ns = 3×10-5 Mpc-3

11. SPECTRA

12. TRANSITION The galactic component at E ≥ 1×1017 eV is assumed to be iron nuclei. The spectrum is found as difference of the total (observed) spectrum and extragalactic proton spectrum (model). Ec is considered as a free parameter in a range (0.3 - 2)×1018 eV

13. TRANSITION from GALACTIC to EXTRAGALACTIC CR in DIFFUSIVE PROPAGATION Assumptions: • power-law Qgen(E) ~ E-2.7 generation spectrum for extragalactic protons • Lp = 3.0×1048 erg/s for source separation d=30 Mpc • Lp = 1.5×1048 erg/s for source separation d=50 Mpc • magnetic field with Kolmogorov spectrum B0 =1 nG on the basic scale lc=1 Mpc • several different regimes in low-energy region (Kolmogorov, Bohm and D(E) ~ E2 ).

14. CONCLUSIONS • Experimentally confirmed dip is a signature of interaction of extragalactic protons with CMB.It should be considered as independent evidence of proton composition at 1×1018 ≤ E ≤ 4×1019 eV. • Dip gives a natural explanation of the second knee: below the low-energy end of the dip (Ec ≈ 1×1018 eV) extragalactic proton spectrum becomesflatter than the measured one, providing thus the transition from galactic to extragalactic cosmic rays.This mechanism works for both rectilinear and diffusive propagation under assumption of unbroken power-law generation spectrum.

15. Transition energy Ec ≈ 1×1018 eV is the universal value, independent of propagation mode, including different diffusion regimes. • Prediction of the shape of the dip is robust. It is practically not modified by all known phenomena: • propagation modes, • inhomogeneities in source distribution, • different distances between sources, • fluctuations in interaction. It makes dip more reliable signature of interaction with CMB than GZK cutoff.

16. In principle, the observed dip can be explained by the galactic component. In the absence of the detailed theory of propagation in galactic magnetic fields, the precise description of the dip shape in this case looks like a formal fitting exercise with many free parameters.