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, arXiv0711.3635
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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

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GZK cutoff and anisotropy
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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)

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HiRes cutoff in the spectrum
GZK Statistics

• Expect 42.8 events
• Observe 15 events
• 5 s

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1
9
2
Bergman (ICRC-2005)
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Auger Energy Spectrum 2007
6s
-----------------------------------------
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Arrival directions for Egt57 EeV in Auger 8/13
P0.16
HiRes no signal 2/13 events
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Global energy rescaling
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Arrival directions for Egt40 EeV in HiRes (Egt52
EeV in AGASA)
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Probability of correlation
3 s after penalty on angle M.Kachelriess and
D.S., astro-ph/0512498
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Clustering signal in AUGER 20-25 degree scales
0.5 -1.5 , 70 events, Pierre Auger
Collaboration, ICRC 2007
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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
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Horizon
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50 of protons come from
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Horizon for protons 70 approximations
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Horizon for protons 90
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Horizon for protons
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Simulation with SOPHIA, stochastic energy
losses, Assuming DE/E 20 event by event
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Same true for heavy nuclei Fe
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Simulation by D.Allard
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Minimal UHECR model
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Protons can fit UHECR data
V.Berezinsky, astro-ph/0509069
problem composition ?
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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
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Parameters which define proton flux

• Proton spectrum from one source
• Distribution of sources

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Potential problems

• Shock acceleration predicts 1/Ea with a2-2.2,
  while spectrum fitted with a2.5-2.6
• Linear acceleration even worth
• It is very difficult to accelerate protons to
  E1020 eV. Probably most of sources accelerate
  to lower energies.

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Acceleration of UHECR
A.G.N.
GRB

• Shock acceleration 1/Ea a2-2.2
• Electric field acceleration
  peak at Emax

Radio Galaxy Lobe
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Protons from astrophysical sources

• Most of UHECR with Egt 1019 eV are protons
• Spectrum of single source
• Density of sources and their distribution
• Distribution of maximum energy of sources

Composition HiRes
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Protons from astrophysical objectsmaximum
energy of sources
M.Kachelriess and D.S., hep-ph/0510188
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Protons from astrophysical objectsdensity of
sources
M.Kachelriess and D.S., hep-ph/0510188
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Looking for spectrum of sources
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Spectrum of protons from sources in 100 Mpc
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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 Rlt
  100 Mpc.
• Find all CR within some angle from those
  sources some part is by chance(!)

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How to find probability

• We divide energy range in 2 bins EminltEltE20 and
  EgtE20
• For every source at fixed distance we find
  binomial probability to emit N total CR with n CR
  in bin EgtE20 for all sources with Ngt0 for
  several tested a
• Multiply results for all sources
• Compare results for different a

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Spectrum 1.1 vs 2.7 Egt60 EeV
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100 events Egt60 EeV
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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 Egt60 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