Transcript Presentation

Constraining UHECR source spectrum
from observations in GZK regime
Ultra
High
Energy
\\
Cosmic
Rays
Dmitri Semikoz
APC , Paris & INR, Moscow
with M.Kachelriess and E.Parizot, arXiv:0711.3635
Moscow, May 24, 2008
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

Moscow, May 24, 2008
GZK cutoff and
anisotropy
Moscow, May 24, 2008
The Greisen-Zatsepin-Kuzmin (GZK) effect
Nucleons can produce pions on the cosmic microwave background
2mN m  m
Eth 
 4 1019 eV
4
2

nucleon
pair production energy loss
-resonance
pion production energy loss
multi-pion production
pion production rate
sources must be in cosmological backyard
within 50-100 Mpc from Earth
(compare to the Universe size ~ 5000 Mpc)
Moscow, May 24, 2008
HiRes: cutoff in the spectrum
“GZK” Statistics
3
9
2
1
• Expect 42.8 events
• Observe 15 events
• ~5 s
Bergman (ICRC-2005)
Moscow, May 24, 2008
Auger Energy Spectrum 2007
6s
-----------------------------------------
Moscow, May 24, 2008
Arrival directions for E>57 EeV in
Auger 8/13 P=0.16 %
HiRes: no signal 2/13 events
Moscow, May 24, 2008
Global energy rescaling
Moscow, May 24, 2008
Arrival directions for E>40 EeV in
HiRes (E>52 EeV in AGASA)
Moscow, May 24, 2008
Probability of correlation
3 s after penalty on angle
M.Kachelriess and D.S., astro-ph/0512498
Moscow, May 24, 2008
Clustering signal in AUGER:
20-25 degree scales
~0.5 -1.5 %, ~70 events, Pierre Auger Collaboration, ICRC 2007
Moscow, May 24, 2008
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
Moscow, May 24, 2008
Horizon
Moscow, May 24, 2008
50% of protons come from
Moscow, May 24, 2008
Horizon for protons 70%:
approximations
Moscow, May 24, 2008
Horizon for protons: 90%
Moscow, May 24, 2008
Horizon for protons
-----------------------------
-----------------------------
---------------------------------------------
Simulation with SOPHIA, stochastic energy losses,
Assuming E/E = 20% event by event
Moscow, May 24, 2008
Same true for heavy nuclei:
Fe
----------------------------Simulation by D.Allard
Moscow, May 24, 2008
Minimal UHECR model
Moscow, May 24, 2008
Protons can fit UHECR data
V.Berezinsky, astro-ph/0509069
problem: composition ?
Moscow, May 24, 2008
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
Moscow, May 24, 2008
Parameters which define
proton flux

Proton spectrum from
one source:
A
F (E)  
E
Emin  E  Emax

Distribution of
sources:
D  (1  z ) m3
zmin  z  zmax
Moscow, May 24, 2008
Potential problems:
Shock acceleration predicts 1/E with 22.2, while spectrum fitted with 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.

Moscow, May 24, 2008
Acceleration of UHECR
A.G.N.
GRB
• Shock acceleration:
1/E 2-2.2
• Electric field acceleration:
peak at Emax
Radio
Galaxy
Lobe
Moscow, May 24, 2008
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
F ( E )   ( Emax - E ) / E

n( z )  n0  ( zmax - z )  ( z - zmin )  (1  z )
F ( Emax )   ( E 0 max - Emax ) / Emax

Moscow, May 24, 2008
Protons from astrophysical objects:
maximum energy of sources
M.Kachelriess and D.S., hep-ph/0510188
Moscow, May 24, 2008
Protons from astrophysical objects:
density of sources
M.Kachelriess and D.S., hep-ph/0510188
Moscow, May 24, 2008
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
R< 100 Mpc.
 Find all CR within some angle from those
sources: some part is by chance(!)

Moscow, May 24, 2008
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 
 Multiply results for all sources
 Compare results for different 

Moscow, May 24, 2008
Spectrum 1.1 vs 2.7 E>60 EeV
Moscow, May 24, 2008
100 events E>60 EeV
Moscow, May 24, 2008
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
