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

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

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


Gzk cutoff and anisotropy

GZK cutoff and anisotropy


Constraining uhecr source spectrum from observations in gzk regime

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)


Hires cutoff in the spectrum

HiRes: cutoff in the spectrum

“GZK” Statistics

3

Expect 42.8 events

Observe 15 events

~ 5 s

9

1

2

Bergman (ICRC-2005)


Auger energy spectrum 2007

Auger Energy Spectrum 2007

6s

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


Arrival directions for e 57 eev in auger 8 13 p 0 16

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

HiRes: no signal 2/13 events


Global energy rescaling

Global energy rescaling


Arrival directions for e 40 eev in hires e 52 eev in agasa

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


Probability of correlation

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

Clustering signal in AUGER: 20-25 degree scales

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


Clustering signal in auger scan

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

Horizon


50 of protons come from

50% of protons come from


Horizon for protons 70 approximations

Horizon for protons 70%: approximations


Horizon for protons 90

Horizon for protons: 90%


Horizon for protons

Horizon for protons

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

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

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

Simulation with SOPHIA, stochastic energy losses,

Assuming DE/E = 20% event by event


Same true for heavy nuclei fe

Same true for heavy nuclei: Fe

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

Simulation by D.Allard


Minimal uhecr model

Minimal UHECR model


Protons can fit uhecr data

Protons can fit UHECR data

V.Berezinsky, astro-ph/0509069

problem: composition ?


Mixed composition model

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

Parameters which define proton flux

  • Proton spectrum from one source:

  • Distribution of sources:


Potential problems

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

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

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

Protons from astrophysical objects:maximum energy of sources

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


Protons from astrophysical objects density of sources

Protons from astrophysical objects:density of sources

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


Looking for spectrum of sources

Looking for spectrum of sources


Spectrum of protons from sources in 100 mpc

Spectrum of protons from sources in 100 Mpc


How to prepare data

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

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

Spectrum 1.1 vs 2.7 E>60 EeV


100 events e 60 eev

100 events E>60 EeV


Conclusions

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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