1. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Anatomy of the Cosmic-ray Energy Spectrum from the knee to the ankle

2. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Spectrometers (  A = 1 resolution, good E resolution) Calorimeters (less good resolution) Direct measurements Air showers

3. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser 30 Rigidity-dependence Acceleration, propagation – depend on B: r gyro = R/B –Rigidity, R = E/Ze –E c ~ Z R c r SNR ~ parsec –  E max ~ Z * 10 15 eV – 1 < Z < 30 (p to Fe) Slope change should occur within factor of 30 in energy But spectrum continues smoothly another factor of 30

4. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser B. Peters on the knee and ankle B. Peters, Nuovo Cimento 22 (1961) 800 If the knee is due to an upper cutoff of one population of cosmic rays then the ankle should follow immediately after the knee, reflecting the onset of a new population that extends to higher energy. Instead, the spectrum continues smoothly for at least another factor of 30 before the ankle.

5. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Models of galactic particles, E >> knee Axford: –continuity of spectrum over factor 300 of energy implies relation between acceleration mechanisms – reacceleration by multiple SNR Völk: (see also Jokipii & Morfill) – reacceleration by shocks in galactic wind (analogous to CIRs in heliosphere) Erlykin & Wolfendale: –Local source at knee on top of smooth galactic spectrum – (bending of “background” could reflect change in diffusion @ ~1 pc) Note different composition signatures What happens for E > 10 17 eV? Völk & Zirakashvili, 28 th ICRC p. 2031 Erlykin & Wolfendale, J Phys G27 (2001) 1005

6. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Direct measurements run out of statistics before the knee RUNJOB: thanks to T. Shibata ATIC: thanks to E-S Seo & J. Wefel

7. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Recent Kascade data show increasing fraction of heavy nuclei Note anomalous He / proton ratio in recent Kascade analyses K-H Kampert et al., astro-ph/0204205 ICRC 2001 (Hamburg) M. Roth et al., Proc ICRC 2003 (Tsukuba) vol 1, p 139

8. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Chem. Composition 1 km 2 km Paper in proof at Astropart. Phys. AMANDA (number of muons ) Spase (number of electrons) Iron Proton log(E/PeV)

9. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Large fluctuations in the knee region are worse at sea level Linear plot: green = e+/e-; blue =  Log plot: fluctuations bad at sea level 10 proton showers at 1 PeV

10. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Example: Fluctuations in N , N e at two depths

11. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Primary composition with IceCube N  from deep IceCube; N e from IceTop High altitude allows good energy resolution Good mass separation from N  /N e 1/3 km 2 sr (2000 x SPASE-AMANDA) Covers sub-PeV to EeV energies

12. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Rates of contained, coincident events Area--solid-angle ~ 1/3 km 2 sr (including angular dependence of EAS trigger)

13. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Transition to extra-galactic? Is there a transition between two populations of particles? If so, where is it and what is the evidence? Conflicting evidence from Fly’s Eye (1993) as compared to HiRes (2003) –Fly’s Eye suggests ankle around 3 x 10 18 eV –HiRes + HiRes/MIA transition ~3 x 10 17 eV –Difference has implications for normalization of neutrino flux from extra-galactic sources of UHECR

14. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Change of composition from heavy to light at the ankle ? Original Fly’s Eye (1993): transition coincides with ankle G. Archbold, P. Sokolsky, et al., Proc. 28 th ICRC, Tsukuba, 2003 HiRes new composition result: transition occurs before ankle

15. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Composition from density of muons ρ µ ( 600) vs. E 0 (Akeno, AGASA) consistent with HiRes

16. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Comments Significance of the knee still uncertain –Need better composition measurements to discriminate among models –Analysis using AMANDA II with SPASE needed Large gap in energy between the knee and ankle raises interesting questions – increasing fraction of heavy nuclei 10 15 -10 17 ? – mismatch between location of ankle and change of composition in HiRes data – 10 16.5 to 10 18 of particular interest – IceTop/IceCube may contribute

17. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Energy content of extra-galactic component depends on location of transition Normalization point 10 18 to 10 19.5 used Factor 10 / decade Spectral slope  =2.3 for rel. shock =2.0 non-rel. E min ~ m p (  shock ) 2

18. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser GRB model Assume E -2 spectrum at source, normalize @ 10 19.5 10 45 erg/Mpc 3 /yr ~ 10 53 erg/GRB Evolution like star- formation rate GZK losses included Galactic  extragalactic transition ~ 10 19 eV Bahcall & Waxman, hep-ph/0206217 Waxman, astro-ph/0210638

19. LBL November 3, 2003 selection & comments 14 June 2004 Thomas K. Gaisser Berezinsky et al. AGN Assuming a cosmological distribution of sources with: –dN/dE ~ E -2, E < 10 18 eV –dN/dE ~ E , 10 18 < E < 10 21 –  = 2.7 (no evolution) –  = 2.5 (with evolution) Need L 0 ~ 3×10 46 erg/Mpc 3 yr They interpret dip at 10 19 as –p +  2.7   p + e + + e - Berezinsky, Gazizov, Grigorieva astro-ph/0210095