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Constraining UHECR source spectrum from observations in GZK regime

Constraining UHECR source spectrum from observations in GZK regime. Dmitri Semikoz APC , Paris & INR, Moscow. with M.Kachelriess and E.Parizot, arXiv:0711.3635. Overview:. GZK cutoff and anisotropy Horizon for protons and iron Model: protons from point-like sources

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Constraining UHECR source spectrum from observations in GZK regime

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  1. Constraining UHECR source spectrum from observations in GZK regime Dmitri Semikoz APC , Paris & INR, Moscow with M.Kachelriess and E.Parizot, arXiv:0711.3635

  2. Overview: • GZK cutoff and anisotropy • Horizon for protons and iron • Model: protons from point-like sources • Can we find spectrum from 2-3 events per source? • Conclusions

  3. GZK cutoff and anisotropy

  4. pair production energy loss -resonance pion production energy loss multi-pion production pion production rate The Greisen-Zatsepin-Kuzmin (GZK) effect Nucleons can produce pions on the cosmic microwave background  nucleon • sources must be in cosmological backyard within 50-100 Mpc from Earth (compare to the Universe size ~ 5000 Mpc)

  5. HiRes: cutoff in the spectrum “GZK” Statistics 3 Expect 42.8 events Observe 15 events ~ 5 s 9 1 2 Bergman (ICRC-2005)

  6. Auger Energy Spectrum 2007 6s -----------------------------------------

  7. Arrival directions for E>57 EeV in Auger 8/13 P=0.16 % HiRes: no signal 2/13 events

  8. Global energy rescaling

  9. Arrival directions for E>40 EeV in HiRes (E>52 EeV in AGASA)

  10. Probability of correlation 3 s after penalty on angle M.Kachelriess and D.S., astro-ph/0512498

  11. Clustering signal in AUGER: 20-25 degree scales ~0.5 -1.5 %, ~70 events, Pierre Auger Collaboration, ICRC 2007

  12. Clustering signal in AUGER: scan 2% after scan and penalty between 7 and 23 degrees Pierre Auger Collaboration, ICRC 2007 Statistically limited at the moment. If real, connection to LSS and EGMF

  13. Horizon

  14. 50% of protons come from

  15. Horizon for protons 70%: approximations

  16. Horizon for protons: 90%

  17. Horizon for protons ----------------------------- ----------------------------- --------------------------------------------- Simulation with SOPHIA, stochastic energy losses, Assuming DE/E = 20% event by event

  18. Same true for heavy nuclei: Fe ----------------------------- Simulation by D.Allard

  19. Minimal UHECR model

  20. Protons can fit UHECR data V.Berezinsky, astro-ph/0509069 problem: composition ?

  21. Mixed composition model D.Allard, E.Parizot and A.Olinto, astro-ph/0512345 Problems: 1) escape of the nuclei from the source 2) How to accelerate Fe in our Galaxy

  22. Parameters which define proton flux • Proton spectrum from one source: • Distribution of sources:

  23. Potential problems: • Shock acceleration predicts 1/Ea with a=2-2.2, while spectrum fitted with a=2.5-2.6 • Linear acceleration even worth • It is very difficult to accelerate protons to E=1020 eV. Probably most of sources accelerate to lower energies.

  24. Acceleration of UHECR A.G.N. GRB • Shock acceleration: 1/Ea a=2-2.2 • Electric field acceleration: peak at Emax Radio Galaxy Lobe

  25. Protons from astrophysical sources • Most of UHECR with E> 1019 eV are protons • Spectrum of single source • Density of sources and their distribution • Distribution of maximum energy of sources Composition HiRes

  26. Protons from astrophysical objects:maximum energy of sources M.Kachelriess and D.S., hep-ph/0510188

  27. Protons from astrophysical objects:density of sources M.Kachelriess and D.S., hep-ph/0510188

  28. Looking for spectrum of sources

  29. Spectrum of protons from sources in 100 Mpc

  30. How to prepare data: • Take sources with some density • Propagate protons and deflect them in extragalactic and galactic magnetic fields • Convolve result with experimental exposure and take into account energy resolution. This produce CR dataset. • Take sources within some distance from Earth R< 100 Mpc. • Find all CR within some angle from those sources: some part is by chance(!)

  31. How to find probability: • We divide energy range in 2 bins: Emin<E<E20 and E>E20 • For every source at fixed distance we find binomial probability to emit N total CR with n CR in bin E>E20 for all sources with N>0 for several tested a • Multiply results for all sources • Compare results for different a

  32. Spectrum 1.1 vs 2.7 E>60 EeV

  33. 100 events E>60 EeV

  34. Conclusions • When sources of UHECR will be found, one can try to find acceleration spectrum of sources even 2-3 events come from any individual source • Typical number needed is 100 events with E>60 EeV to reject 1.1 from 2.7 at 99% C.L. in 95 % of cases. • In most of cases individual source would give up to 4 events in this dataset

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