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The cosmic-ray spectrum

The cosmic-ray spectrum. From the knee to the ankle. Spectrometers ( D A = 1 resolution, good E resolution). Air showers. Calorimeters (less good resolution). Air-shower arrays on the ground to overcome low flux. Don’t see primaries directly. Direct measurements. Knee. Ankle.

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The cosmic-ray spectrum

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  1. The cosmic-ray spectrum From the knee to the ankle Tom Gaisser

  2. Spectrometers (DA = 1 resolution, good E resolution) Air showers Calorimeters (less good resolution) Air-shower arrays on the ground to overcome low flux. Don’t see primaries directly. Direct measurements Knee Ankle Tom Gaisser

  3. 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 Tom Gaisser

  4. Spectral Energy Distribution (linear plot shows most E < 100 GeV) (4p/c) Ef(E) = local differential CR energy density Energetics of cosmic rays • Total local energy density: • (4p/c) ∫ Ef(E) dE ~ 10-12 erg/cm3 ~ B2 / 8p • Power needed: (4p/c) ∫ Ef(E) /tesc(E) dE galactic tesc ~ 107 E-0.6 yrs Power ~ 10-26 erg/cm3s • Supernova power: 1051 erg per SN ~3 SN per century in disk ~ 10-25 erg/cm3s • SN model of galactic CR Power spectrum from shock acceleration, propagation Tom Gaisser

  5. 30 Rigidity-dependence • Acceleration, propagation • depend on B: rgyro = R/B • Rigidity, R = E/Ze • Ec(Z) ~ Z Rc • rSNR ~ parsec •  Emax ~ Z * 1015 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 Tom Gaisser

  6. B. Peters, Nuovo Cimento 22 (1961) 800 B. Peters on the knee and ankle <A> should begin to decrease again for E > 30 x Eknee Peters cycle: systematic increase of < A > approaching Emax Tom Gaisser

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

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

  9. M. Roth et al., Proc ICRC 2003 (Tsukuba) vol 1, p 139 K-H Kampert et al., astro-ph/0204205 ICRC 2001 (Hamburg) Recent Kascade data show increasing fraction of heavy nuclei with expected cutoff sequence starting at ~3 PeV No information > 1017 eV from original Kascade Tom Gaisser

  10. Völk & Zirakashvili, 28th ICRC p. 2031 Erlykin & Wolfendale, J Phys G27 (2001) 1005 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, Völk: • 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 > 1017 eV? • Hillas: component B Tom Gaisser

  11. 1 component: a = 2.7, Emax = Z x 30 TeV; (Lagage & Cesarsky) or Emax = Z x 1 PeV Total protons Fe helium CNO Mg… 3 components a=2.7 a=2.4 Speculation on the knee Tom Gaisser

  12. Power needed for knee B-component • Integrate to E > 1018 eV assuming • tesc ~ 2 x 107 yrs x E-1/3 • Vgalaxy ~ p (15 kpc)2 x 200 pc ~ 3 x 1066 cm3 • Total power for “B” component ~2 x 1039 erg/s • Possible sources • Sources may be nearby • e.g. m-quasar SS433 at 3 kpc has Ljet 1039 erg/s • Eddington limited accretion ~ 2 x 1038 erg/s • Neutron source at GC ~ 1038 erg/s Tom Gaisser

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

  14. Composition with air showers • Cascade of nucleus • mass A, total energy E0 • X = depth in atmosphere along shower axis • N(X) ~ A exp(X/l), number of subshowers • EN ~ E0 / N(X), energy/subshower at X • Shower maximum when EN = Ecritical • N(Xmax) ~ E0 / Ecritical • Xmax ~ l ln { (E0/A) / Ecritical } • Most particles are electrons/positrons • m from p-decay a distinct component • decay vs interaction depends on depth • Nm ~ (A/Em)*(E0/AEm)0.78 ~ A0.22 • 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 > 1017 eV Schematic view of air shower detection: ground array and Fly’s Eye Tom Gaisser

  15. New detectors to explore galactic to extra-galactic transition • Need > km2 to reach EeV • KASCADE-Grande • IceCube (including IceTop) • Tunka – 133 • “Hybrid” Hi-Res, TA, Auger • below nominal threshold Tom Gaisser

  16. piering Three new kilometer-scale detectors

  17. New South Pole station with IceTop Station 21 in foreground Tom Gaisser

  18. ~ 5-10 TeV IceTop station • Two Ice Tanks 2.7 m2 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 Tom Gaisser

  19. DOMs in tank before freezing Tom Gaisser

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

  21. Importance of locating transition to extra-galactic component: energy content depends on it • Composition signature: • transition back to protons • Uncertainties: • Normalization point: • 1018 to 1019.5 used • Factor 10 / decade • Spectral slope • a=2.3 for rel. shock • =2.0 non-rel. • Emin ~ mp (gshock)2 Tom Gaisser

  22. Power needed for extragalactic cosmic rays (assuming transition at 1019 eV) • Energy in extra-galactic, CR ~ 2 x 10-19 erg/cm3 • Includes extrapolation of UHECR to low energy • CR = (4/c)  E(E) dE = (4/c){E2(E)}E=1019eV x ln{Emax/Emin} • This gives CR ~ 2 x 10-19 erg/cm3 for differential index  = 2, (E) ~ E-2 ; significantly more if  > 2, • Power required ~ CR/1010 yr ~ 1.3 x 1037 erg/Mpc3/s • Estimates depend on cosmology + extragalactic magnetic fields: • 3 x 10-3 galaxies/Mpc3 5 x 1039 erg/s/Galaxy • 3 x 10-6 clusters/Mpc3 4 x 1042 erg/s/Galaxy Cluster • 10-7 AGN/Mpc3 1044 erg/s/AGN • ~1000 GRB/yr 3 x 1052 erg/GRB Tom Gaisser

  23. Bahcall & Waxman (GRB) Physics Letters B556 (2003) 1 • Galactic extragalactic transition ~ 1019 eV • Assume E-2 spectrum at source, normalize @ 1019.5 • 1045 erg/Mpc3/yr • ~ 1053 erg/GRB • Evolution ~ star-formation • GZK losses included Bahcall & Waxman hep-ph/0206217 Tom Gaisser

  24. Berezinsky et al.: AGN astro-ph/0410650 • G  E-G transition < 1018 eV • Assume a cosmological distribution of sources with: • dN/dE ~ E-2, E < 1018 eV • dN/dE ~ E-g, 1018< E < 1021 • g = 2.7 (no evolution) • g = 2.5 (with evolution) • Need L0 ~ 3 ×1046 erg/Mpc3 yr • Interpret ankle at 1019 as • p + g2.7 p + e+ + e- Berezinsky, Gazizov, Grigorieva astro-ph/0210095 Tom Gaisser

  25. Questions to ponder • How to boost Emax 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? Tom Gaisser

  26. 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. Mewaldtet al., A.I.P. Conf. Proc. 598 (2001) 165 Tom Gaisser

  27. Solar flare shock acceleration Coronal mass ejection 09 Mar 2000 Tom Gaisser

  28. SOHO/ LASCO CME of 06-Nov 1997 Tom Gaisser

  29. 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. Mewaldtet al., A.I.P. Conf. Proc. 598 (2001) 165 Tom Gaisser

  30. Questions to ponder • How to boost Emax 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? Tom Gaisser

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