Constraining uhecr source spectrum from observations in gzk regime
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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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Constraining UHECR source spectrum from observations in GZK regime

Dmitri Semikoz

APC , Paris & INR, Moscow

with M.Kachelriess and E.Parizot, arXiv:0711.3635


  • 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

GZK cutoff and anisotropy

pair production energy loss


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


  • sources must be in cosmological backyard

    within 50-100 Mpc from Earth

    (compare to the Universe size ~ 5000 Mpc)

HiRes: cutoff in the spectrum

“GZK” Statistics


Expect 42.8 events

Observe 15 events

~ 5 s




Bergman (ICRC-2005)

Auger Energy Spectrum 2007



Arrival directions for E>57 EeV in Auger 8/13 P=0.16 %

HiRes: no signal 2/13 events

Global energy rescaling

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

Probability of correlation

3 s after penalty on angle

M.Kachelriess and D.S., astro-ph/0512498

Clustering signal in AUGER: 20-25 degree scales

~0.5 -1.5 %, ~70 events, Pierre Auger Collaboration, ICRC 2007

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


50% of protons come from

Horizon for protons 70%: approximations

Horizon for protons: 90%

Horizon for protons




Simulation with SOPHIA, stochastic energy losses,

Assuming DE/E = 20% event by event

Same true for heavy nuclei: Fe


Simulation by D.Allard

Minimal UHECR model

Protons can fit UHECR data

V.Berezinsky, astro-ph/0509069

problem: composition ?

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

Parameters which define proton flux

  • Proton spectrum from one source:

  • Distribution of sources:

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.

Acceleration of UHECR



  • Shock acceleration: 1/Ea a=2-2.2

  • Electric field acceleration: peak at Emax




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

Protons from astrophysical objects:maximum energy of sources

M.Kachelriess and D.S., hep-ph/0510188

Protons from astrophysical objects:density of sources

M.Kachelriess and D.S., hep-ph/0510188

Looking for spectrum of sources

Spectrum of protons from sources in 100 Mpc

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(!)

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

Spectrum 1.1 vs 2.7 E>60 EeV

100 events E>60 EeV


  • 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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