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Propagation of ultra-high energy cosmic rays in the Universe

Propagation of ultra-high energy cosmic rays in the Universe. Martin Lemoine Institut d’Astrophysique de Paris CNRS, Université Pierre & Marie Curie. Introduction. Ultra-high energy cosmic rays (UHECR) units: 1 EeV ´ 10 18 eV » 1 particle/km 2 /century above 10 20 eV. 2/41.

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Propagation of ultra-high energy cosmic rays in the Universe

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  1. Propagation of ultra-high energy cosmic rays in the Universe Martin Lemoine Institut d’Astrophysique de Paris CNRS, Université Pierre & Marie Curie

  2. Introduction Ultra-high energy cosmic rays (UHECR) units: 1 EeV ´ 1018 eV »1 particle/km2/century above 1020 eV 2/41

  3. Introduction: spectrum at UHE All-particle differential cosmic ray spectrum £ Energy3 Eknee» 2¢1015 eV Esecond knee» 1017.5 eV knee 2nd knee here, Galactic CRs ankle here, extra-Galactic UHECRs Nagano & Watson 00 3/41

  4. Introduction: Galactic and extra-Galactic CRs All-particle differential cosmic ray spectrum £ Energy3 Eknee, Fe» 6¢ 1016 eV Esecond knee» 1017.5 eV knee 2nd knee ? Galactic all-particle ankle change of slope = new component (?) Fe C He H a view from Kaskade 4/41

  5. Energy spectrum at UHE: an end? Where? raw data recalibrated in energy • - Flux at UHE is uncertain ! • AGASA does not see the end of the CR spectrum (?) • HiRes sees the end of the CR spectrum (?) 5/41

  6. Another view of the confusion at UHE 6/41

  7. Chemical composition measurement at UHE HiRes Fly’s Eye Abbasi et al. 04 Xmax : depth (in atmosphere) of maximum shower development model (H) data model (Fe) 7/41

  8. Summary of the introduction… A very brief summary of data at ultra-high energies: a knee at ' 2 1015 eV a second knee at » 1018eV an ankle at » 1019 eV a steepening (or cut-off) at 1020 eV a transition from light (» p) to heavy (» Fe) between 1st and 2nd knee a transition from heavy (» Fe) to light (» p) around 2nd knee - ankle absolute energy scale is uncertain by » 20% in each experiment 8/41

  9. Outline Lecture 1 : Propagation in unmagnetized intergalactic medium – Energy losses Energy losses: GZK (photopion production) pair production cosmological redshift photodisintegration of nuclei Phenomenology of propagated spectra: The ankle and above The 2nd knee and above Secondary products: neutrinos and gamma-rays Lecture 2 : Effects of extra-galactic magnetic fields Particles and cosmic magnetic fields: Charged particle propagation in magnetic fields Origin and distribution of extra-galactic magnetic fields Implications for UHECR phenomenology: homogeneous magnetic fields: effect on spectrum at high and low energy inhomogeneous magnetic fields: some models… 9/41

  10. Greisen – Zatsepin – Kuz’min cut-off Greisen 66, Zatsepin & Kuzmin 66 UHE protons lose energy by interacting with cosmic microwave background photons to produce pions: N + CMB! N’ +  CMB photons hEi» 10-3 eV are seen as -rays in UHECR rest frame… Threshold energy: reaction is permitted when nucleus rest frame cosmic rest frame (=frame where CMB is isotropic) or Energy loss: Interaction length: Energy loss distance: )The Universe is opaque to protons with energy ¸ 6 £ 1019 eV ! 10/41

  11. Greisen – Zatsepin – Kuz’min cut-off Nagano & Watson 00 Pion production losses for different sources redshifts « cosmological distance »: z » 1 GZK cut-off: z=0.032 , d ' 140 Mpc ) highest energy events with E & 1020 eV must originate from within . 100 Mpc !! 11/41

  12. Greisen – Zatsepin – Kuz’min cut-off hot spots counterpart ?! )angular correlations! Cygnus A AGN relativistic jets AGN: E-losses ) Emax . 1019 eV (Protheroe & Szabo 1992, Norman et al. 95) FRII hot spots: Emax» 1020 eV Z B100 G Lkpc (Biermann &Strittmatter 1987) Emax» 1020 eV Z (BR/0.1 G pc) Relativistic jets: (Ostrowski 1998, Casse et al. 2001) 12/41

  13. GZK and the type of sources AGASA: ? New physics ? HiRes: GZK ) cosmological distribution of sources very much suppressed ? quite suppressed ? Is the flux above 1020 eV: a little bit suppressed ? a tiny little bit suppressed ? not really suppressed ? not suppressed at all ? 13/41

  14. Greisen – Zatsepin – Kuz’min cut-off Detailed calculation of pion production losses: … CMB: continuous energy distribution … other radiation fields ? ! can be ignored on large scales In nucleus rest frame (primed variables): f(p’): blackbody of CMB in nucleus rest frame (E’): fractional loss of energy p: interaction cross-section 14/41

  15. Greisen – Zatsepin – Kuz’min cut-off In nucleus rest frame (primed variables): nucleus pc In cosmic rest frame (unprimed variables): cosmic f is Lorentz invariant therefore: with: 15/41

  16. Greisen – Zatsepin – Kuz’min cut-off Finally: with: Energy loss length: (Mpc) pion production (eV) 16/41

  17. Pair production Protons can also lose energy on CMB by pair production: p + CMB! p + e + e+ Reaction is possible if: Fraction of energy lost in each collision: Mean free path:  (10-6 b) E’ (GeV) 17/41

  18. Pair production pair production (Mpc) pion production (eV) 18/41

  19. Redshift (expansion) losses All particles momenta redshift due to cosmological expansion: redshift pair production (Mpc) pion production (eV) 19/41

  20. Energy losses as a function of redshift at high redshift, the cosmic microwave background has higher temperature and density: ) History of the energy of a particle: implicit integro-differential : for solution, see Berezinsky, Gazizov, Grigorieva, PRD74:043005 (2006) 20/41

  21. Energy losses as a function of redshift Energy of a particle as a function of redshift pion production losses pair production losses redshift losses 21/41

  22. Nuclei : photodisintegration losses UHECR nuclei can be partially photodisintegrated by microwave (or infra-red) background photons: A + CMB! (A-X) + X, X= 1,2 or more nucleons threshold energy: energy lost : mean free path: He-4 +  Giant Dipole Resonance E’ » 10-20 MeV (mb) Difficulties: cross-sections not well known) requires theoretical input (Puget et al. 76, Khan et al. 04) IR background not well known 22/41

  23. Nuclei : photodisintegration losses Bertone et al. 02 photodis. on CIRB 10 000 28Si pair production 100 56Fe xloss (Mpc) 12C 4He 1 photodis. on CMB 0.01 1018 1019 1020 1021 1022 Energy (eV) note: pion production off to A x 1020 eV, pair production xlossscales as Z2/A 23/41

  24. Outline Lecture 1 : Propagation in unmagnetized intergalactic medium – Energy losses Energy losses: GZK (photopion production) pair production cosmological redshift photodisintegration of nuclei Phenomenology of propagated spectra: The ankle and above The 2nd knee and above Secondary products: neutrinos and gamma-rays Lecture 2 : Effects of extra-galactic magnetic fields Particles and cosmic magnetic fields: Charged particle propagation in magnetic fields Origin and distribution of extra-galactic magnetic fields Implications for UHECR phenomenology: homogeneous magnetic fields: effect on spectrum at high and low energy inhomogeneous magnetic fields: some models… 24/41

  25. Where does the UHECR component emerge? All-particle differential cosmic ray spectrum £ Energy3 Eknee, Fe» 6¢ 1016 eV Esecond knee» 1017.5 eV knee 2nd knee ? Galactic all-particle ankle Fe C He H 25/41

  26. Transition at the ankle Example: acceleration of UHECRs in gamma-ray bursts with s ' -2.0 Waxman 95, Vietri 95, Milgrom & Usov 95 Galactic Extra-Galactic Waxman & Bahcall 03 )requires a Galactic component to extend to » 1019 eV …. what source? 26/41

  27. Spectrum from a cosmological distribution of sources For a continuous distribution of sources: t0: today comoving density of sources (= density today) comoving density of CRs / E interval (=density today) # of CRs injected / Eg / time with: injection energy at t such that Eg=E at t=t0 Emin: minimum E at source : injection index Lcr: CR luminosity (ergs/s) : normalization factor observed differential flux Note: - Lcr may depend on t - ns generally depends on t, e.g. / SFR (star formation rate) … higher by a few at z » 3-4… 27/41

  28. Spectrum from a cosmological distribution of sources Modification factor due to energy losses: =1 if no E-loss and zmax=+1 « dip » due to pair production on CMB GZK cut-off 28/41

  29. Pair production dip ) ankle A population of sources at cosmological distances with ' -2.7: Berezinsky et al. 02 ankle ankle )The ankle might be an effect of propagation in the CMB! Note: assumes existence of a cut-off below 1018 eV 29/41

  30. Ankle = Pair production dip? AGASA AGASA HiRes HiRes if ankle is a dip due to pair production of protons emitted at remote sources: • a GZK cut-off must be clearly seen • the transition between Galactic and extra-Galactic CRs takes place • at lower energies… 30/41

  31. Transition at the second knee low-energy cut-off ! transition between Galactic and extra-Galactic CRs at the second knee ! Berezinsky et al. 04 2nd knee ankle high-E cut-off ? low E cut-off ? however: requires some fine-tuning… physical meaning? Berezinsky et al. 2004: cut-off at injection 31/41

  32. Galactic to extra-galactic CRs at the second knee A two-component view of the all-particle CR spectrum All CR spectrum ! extra-Galactic CRs Galactic CRs Fe C He H 32/41

  33. Nuclei and the transition at the second knee Note: if UHECRs are heavy nuclei (A¸ 2), the pair production dip disappears… Allard et al. 05, Berezinsky et al. 2006 33/41

  34. Pair production dip and heavy nuclei Examples of propagated spectra with different chemical compositions at injection: Berezinsky et al. 2006 Allard et al. 2005 H: 40-50% H: 90% He:10% if protons represent less than » 80% : no dip ) no transition at the second knee… 34/41

  35. Secondary products: neutrinos and gamma-rays Secondary neutrinos and gammas are produced when UHECRs interact with the CMB: (+ multi-pion production) or )GZK cut-off is associated with UHE neutrino e,  and photon production… 35/41

  36. GZK neutrinos spectra Flux of secondary neutrinos: diff. flux # of CRs injected per unit time and unit comoving volume # of  produced per unit CR per unit energy E redshift loss (nearly all GZK neutrinos are produced in immediate vicinity of source) proton CR spectrum neutrino spectra for distances = 10, …, 200 Mpc Engel et al. 2000 36/41

  37. from n decay mostly from GZK GZK neutrinos spectra GZK neutrino spectra for various source evolution models: Allard et al. 06 37/41

  38. GZK neutrinos spectra Allard et al. 06 Waxman & Bahcall limit Engel et al. 00 )GZK neutrinos are likely not to be seen before À1 km3 detectors are built… 38/41

  39. Secondary photons Brunetti et al. 06 GZK photons should be detected from UHECR sources up to distances » 100 Mpc however, if ns» 10-6 Mpc-3) only » 1 source within 100Mpc 39/41

  40. Secondary photons Armengaud et al. 06 one source at 100 Mpc: detection at TeV with HESS 2 40/41

  41. Lecture 1 - Summary Lecture 1 : Propagation in unmagnetized intergalactic medium – Energy losses Hadronic UHECRs lose energy by interaction with the CMB (and possibly CIRB): pion production, pair production, photodissociation. Recent data suggests the existence of the (long awaited) GZK cut-off: sources would lie at cosmological distances, no need for new physics If UHECRs are (mostly) protons, and sources lie at cosmological distances, pair production on the CMB could mimic the ankle in the propagated spectra: the transition between Galactic and extra-Galactic CRs could take place at the 2nd knee: E » 1 EeV … note that recent data also suggests the transition toward a proton dominated composition at UHE, in support of this scenario… … then, the CR injection spectrum should have a powerlaw form with index » 2.6-2.7 down to at least 1018 eV, and a cut-off should be observed below this energy… Alternatively, the transition could take place the ankle if the injection index s » 2.0 – 2.4… … however, this leaves the all-particle spectrum unaccounted for in the region E » 0.5 – 10 EeV… 41/41

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