1. Aspen, April 26, 2005 Tom Gaisser The cosmic-ray spectrum From the knee to the ankle

2. Aspen, April 26, 2005 Tom Gaisser Spectrometers (  A = 1 resolution, good E resolution) Calorimeters (less good resolution) Direct measurements Air showers Air-shower arrays on the ground to overcome low flux. Don’t see primaries directly.

3. Aspen, April 26, 2005 Tom Gaisser Theme of this talk SNR shock model of cosmic-ray origin based on –Energy content –Composition –Spectrum Full spectrum: three energy regions – < PeV (up to the knee) – PeV – EeV (knee – ankle) – > EeV (UHECR) Where is transition from galactic to extra-galactic cosmic rays? –Use spectrum, composition, energy content also to answer questions at high energy

4. Aspen, April 26, 2005 Tom Gaisser Energetics of cosmic rays Total local energy density: –(4  /c) ∫ E  (E) dE ~ 10 -12 erg/cm 3 ~ B 2 / 8  Power needed: (4  /c) ∫ E  (E) /  esc (E) dE galactic  esc ~ 10 7 E -0.6 yrs Power ~ 10 -26 erg/cm 3 s Supernova power: 10 51 erg per SN ~3 SN per century in disk ~ 10 -25 erg/cm 3 s SN model of galactic CR Power spectrum from shock acceleration, propagation Spectral Energy Distribution (linear plot shows most E < 100 GeV) (4  /c) E  (E) = local differential CR energy density

5. Aspen, April 26, 2005 Tom Gaisser 30 Rigidity-dependence Acceleration, propagation – depend on B: r gyro = R/B –Rigidity, R = E/Ze –E c (Z) ~ 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 With characteristic pattern of increasing A Problem: continuation of smooth spectrum to EeV

6. Aspen, April 26, 2005 Tom Gaisser B. Peters on the knee and ankle B. Peters, Nuovo Cimento 22 (1961) 800 Peters cycle: systematic increase of Peters cycle: systematic increase of approaching E max approaching E max should begin to decrease again should begin to decrease again for E > 30 x E knee for E > 30 x E knee

7. Aspen, April 26, 2005 Tom Gaisser Direct measurements to high energy show no strong features below PeV R. Battiston, Rapporteur talk, Tsukuba, 2003 RUNJOB: thanks to T. Shibata ATIC: thanks to E-S Seo & J. Wefel /nucleon)

8. Aspen, April 26, 2005 Tom Gaisser All-particle spectrum: Knee ~3 PeV Tibet E  E/1.23 x 0.1 x 0.01

9. Aspen, April 26, 2005 Tom Gaisser Recent Kascade data show increasing fraction of heavy nuclei with expected cutoff sequence starting at ~3 PeV K-H Kampert et al., astro-ph/0204205 ICRC 2001 (Hamburg) M. Roth et al., Proc ICRC 2003 (Tsukuba) vol 1, p 139 No information > 10 17 eV from original Kascade

10. Aspen, April 26, 2005 Tom Gaisser Models of galactic particles, E >> knee Fine-tuning problem: –continuity of spectrum over factor 300 of energy implies relation between acceleration mechanisms Axford: – reacceleration by multiple SNR Jokipii & Morfill, V ö lk: – reacceleration by shocks in galactic wind (termination shock or CIRs) Erlykin & Wolfendale: –Local source at knee on top of smooth galactic spectrum – (bending of “ background ” could reflect change in diffusion What happens for E > 10 17 eV? –Hillas: component B Völk & Zirakashvili, 28 th ICRC p. 2031 Erlykin & Wolfendale, J Phys G27 (2001) 1005

11. Aspen, April 26, 2005 Tom Gaisser Speculation on the knee Total protons helium CNO Mg… Fe 1 component:  = 2.7, E max = Z x 30 TeV; (Lagage & Cesarsky) or Emax = Z x 1 PeV 3 components  

12. Aspen, April 26, 2005 Tom Gaisser Power needed for knee B-component Integrate to E > 10 18 eV assuming –  esc ~ 2 x 10 7 yrs x E -1/3 – V galaxy ~  (15 kpc) 2 x 200 pc ~ 3 x 10 66 cm 3 –Total power for “ B ” component ~2 x 10 39 erg/s Possible sources – Sources may be nearby – e.g.  -quasar SS433 at 3 kpc has L jet 10 39 erg/s –Eddington limited accretion ~ 2 x 10 38 erg/s –Neutron source at GC ~ 10 38 erg/s

13. Aspen, April 26, 2005 Tom Gaisser Where is transition to extragalactic CR? G. Archbold, P. Sokolsky, et al., Proc. 28 th ICRC, Tsukuba, 2003 HiRes new composition result: transition occurs before ankle Original Fly’s Eye (1993): transition coincides with ankle 3 EeV 0.3 EeV

14. Aspen, April 26, 2005 Tom Gaisser Composition with air showers Cascade of nucleus –mass A, total energy E 0 –X = depth in atmosphere along shower axis –N(X) ~ A exp(X/ ), number of subshowers – E N ~ E 0 / N(X), energy/subshower at X –Shower maximum when E N = E critical –N(X max ) ~ E 0 / E critical –X max ~ ln { (E 0 /A) / E critical } –Most particles are electrons/positrons  from  -decay a distinct component – decay vs interaction depends on depth –N  ~ (A/E  ) * (E 0 /AE  ) 0.78 ~ A 0.22 Showers past max at ground (except UHE) –  large fluctuations –  poor resolution for E, A –Situation improves at high energy and/or high altitude –Fluorescence detection > 10 17 eV Schematic view of air shower detection: ground array and Fly’s Eye

15. Aspen, April 26, 2005 Tom Gaisser New detectors to explore galactic to extra-galactic transition Need > km 2 to reach EeV KASCADE-Grande IceCube (including IceTop) Tunka – 133 “Hybrid” Hi-Res, TA, Auger – below nominal threshold

16. piering Three new kilometer-scale detectors

17. Aspen, April 26, 2005 Tom Gaisser New South Pole station with IceTop Station 21 in foreground

18. Aspen, April 26, 2005 Tom Gaisser IceTop station Two Ice Tanks 2.7 m 2 x 0.9 m deep (scaled-down version of Haverah, Auger) Integrated with IceCube: same hardware, software Coincidence between tanks = potential air shower Local coincidence with no hit at neighboring station tags muon in deep detector Signal in single tank = potential muon Significant area for horizontal muons Low Gain/High Gain operation to achieve dynamic range Two DOMs/tank gives redundancy against failure of any single DOM because only 1 low-gain detector is needed per station ~ 5-10 TeV

19. Aspen, April 26, 2005 Tom Gaisser DOMs in tank before freezing

20. Aspen, April 26, 2005 Tom Gaisser Dec 04: 4 stations, 8 tanks Serap will present IceCube/IceTop on Saturday

21. Aspen, April 26, 2005 Tom Gaisser Importance of locating transition to extra- galactic component: energy content depends on it Composition signature: transition back to protons Uncertainties: 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

22. Aspen, April 26, 2005 Tom Gaisser Power needed for extragalactic cosmic rays (assuming transition at 10 19 eV) Energy in extra-galactic,  CR ~ 2 x 10  erg/cm 3 –Includes extrapolation of UHECR to low energy –  CR = (4  /c)  E  (E) dE = (4  /c){E 2  (E)}  E=10 19 eV x ln{E max /E min } –This gives  CR ~ 2 x 10  erg/cm 3 for differential index  = 2,  (E) ~ E -2 ; significantly more if  > 2, Power required ~  CR /10 10 yr ~ 1.3 x 10 37 erg/Mpc 3 /s –Estimates depend on cosmology + extragalactic magnetic fields: –3 x 10 -3 galaxies/Mpc 3 5 x 10 39 erg/s/Galaxy –3 x 10 -6 clusters/Mpc 3 4 x 10 42 erg/s/Galaxy Cluster –10 -7 AGN/Mpc 3 10 44 erg/s/AGN –~1000 GRB/yr 3 x 10 52 erg/GRB

23. Aspen, April 26, 2005 Tom Gaisser Bahcall & Waxman (GRB) Galactic  extragalactic transition ~ 10 19 eV Assume E -2 spectrum at source, normalize @ 10 19.5 10 45 erg/Mpc 3 /yr ~ 10 53 erg/GRB Evolution ~ star-formation GZK losses included Physics Letters B556 (2003) 1 Bahcall & Waxman hep-ph/0206217

24. Aspen, April 26, 2005 Tom Gaisser Berezinsky et al.: AGN G  E-G transition < 10 18 eV Assume 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 Interpret ankle at 10 19 as –p +  2.7   p + e + + e - Berezinsky, Gazizov, Grigorieva astro-ph/0210095 astro-ph/0410650

25. Aspen, April 26, 2005 Tom Gaisser Questions to ponder How to boost E max to 100 PeV – perpendicular shocks? – self-generated higher magnetic fields? What is the energy-dependence of diffusion? What is the source spectrum? –Are there different slopes for different sources? –How to use the characteristic concave shape of non-linear diffusive shock acceleration? How many sources? How are they distributed?

26. Aspen, April 26, 2005 Tom Gaisser Lessons from the heliosphere ACE energetic particle fluences: Smooth spectrum –composed of several distinct components: Most shock accelerated Many events with different shapes contribute at low energy (< 1 MeV) Few events produce ~10 MeV –Knee ~ Emax of a few events –Ankle at transition from heliospheric to galactic cosmic rays R.A. Mewaldt et al., A.I.P. Conf. Proc. 598 (2001) 165

27. Aspen, April 26, 2005 Tom Gaisser Solar flare shock acceleration Coronal mass ejection 09 Mar 2000 09 Mar 2000

28. Aspen, April 26, 2005 Tom Gaisser SOHO/ LASCO CME of 06-Nov 1997

29. Aspen, April 26, 2005 Tom Gaisser Heliospheric cosmic rays ACE--Integrated fluences: –Many events contribute to low-energy heliospheric cosmic rays; –fewer as energy increases. –Highest energy (75 MeV/nuc) is dominated by low-energy galactic cosmic rays, and this component is again smooth Beginning of a pattern? R.A. Mewaldt et al., A.I.P. Conf. Proc. 598 (2001) 165

30. Aspen, April 26, 2005 Tom Gaisser Questions to ponder How to boost E max to 100 PeV – perpendicular shocks? – self-generated higher magnetic fields? What is the energy-dependence of diffusion? What is the source spectrum? –Are there different slopes for different sources? –How to use the characteristic concave shape of non-linear diffusive shock acceleration? How many sources? How are they distributed?