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 E z = Z E p, where E p = 2.5×10 15 eV is position of proton knee. E Fe = 6.5×10 16 eV KASCADE data

3 SECOND KNEE E Fe may be related to the second knee (second steepening of the spectrum) Fly’s Eye : ~ 4×10 17 eV Akeno : ~ 6×10 17 eV HiRes : ~ 7×10 17 eV Yakutsk : ~ 8×10 18 eV If transition from galactic to extragalactic CR occurs at ankle E a ~1×10 19 eV, how the gap between the iron knee, E Fe ~ 1×10 17 eV, (or the second knee, E 2 ~ 1×10 18 eV) and the ankle, E a ~ 1×10 19 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 E c ~ 1×10 18 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. rectilinear propagation diffusive propagation Lemoine 2004, Aloisio, V.B 

5 IS PROTON COMPOSITION of CR at E ≥ 1×10 18 eV EXCLUDED by OBSERVATIONS? Hires, HiresMIA, Yakutsk : favour proton composition Fly’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:  (E) = J p (E)/J p unm (E) (3) J p (E) is calculated with all energy losses included. J p unm (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 Q gen ~E -2.7 ) AGASA : 19 bins, 2 free parameters,     2 /d.o.f. =1.12, HiRes : 21 bins, 2 free parameters,  2 =19.5,  2 /d.o.f. =1.03 Conclusions: At E ≤ 1×10 18 eV the new CR component appears (second knee). The confirmed independent argument for proton composition at 1×10 18 ≤E ≤ 4×10 19 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→k A E (best fit k A =0.90) HiRes : E→k HiR E (best fit k HiR =1.25)

9 ALTERNATIVE EXPLANATION of the DIP is given by galactic component in energy interval 1×10 18 eV - 1×10 19 eV. To obtain good  2 the galactic component J gal (E) must be taken ad hoc to fit J obs (E): without detailed propagation model for J gal (E) it is a “fitting exercise”. Using free parameters for (4 as minimum) one can always have a good (though artificial) fit to J obs (E). Extragalactic dip model uses basically one parameter  g =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. E, eV

10 model-dependent analysis TRANSITION from GALACTIC to EXTRAGALACTIC CR in AGN MODEL with QUASI-RECTILINEAR PROPAGATION Assumptions: Spectrum: E max = 1×10 21 eV, E c ~ 1×10 18 eV (free parameter) emissivity: L = 3.5×10 21 erg/Mpc 3 yr luminosity of AGN L p = L / n s gives L p = 3.7×10 42 erg/s for Seyferts n s = 3×10 -4 Mpc -3 L p = 3.7×10 43 erg/s for powerful AGN n s = 3×10 -5 Mpc -3

11 SPECTRA

12 TRANSITION The galactic component at E ≥ 1×10 17 eV is assumed to be iron nuclei. The spectrum is found as difference of the total (observed) spectrum and extragalactic proton spectrum (model). E c is considered as a free parameter in a range ( )×10 18 eV

13 TRANSITION from GALACTIC to EXTRAGALACTIC CR in DIFFUSIVE PROPAGATION Assumptions: power-law Q gen (E) ~ E -2.7 generation spectrum for extragalactic protons L p = 3.0×10 48 erg/s for source separation d=30 Mpc L p = 1.5×10 48 erg/s for source separation d=50 Mpc magnetic field with Kolmogorov spectrum B 0 =1 nG on the basic scale l c =1 Mpc several different regimes in low-energy region (Kolmogorov, Bohm and D(E) ~ E 2 ).

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 1×10 18 ≤ E ≤ 4×10 19 eV. Dip gives a natural explanation of the second knee: below the low-energy end of the dip (E c ≈ 1×10 18 eV) extragalactic proton spectrum becomes flatter 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 E c ≈ 1×10 18 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.