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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

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

-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)

HiRes: cutoff in the spectrum

“GZK” Statistics

3

Expect 42.8 events

Observe 15 events

~ 5 s

9

1

2

Bergman (ICRC-2005)

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

HiRes: no signal 2/13 events

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

Horizon for protons

-----------------------------

-----------------------------

---------------------------------------------

Simulation with SOPHIA, stochastic energy losses,

Assuming DE/E = 20% event by event

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

A.G.N.

GRB

- Shock acceleration: 1/Ea a=2-2.2
- Electric field acceleration: peak at Emax

Radio

Galaxy

Lobe

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

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

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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