BAYESIAN STUDY OF UHECRS
Wooram Cho
Institute of Physics and Applied Physics
Yonsei University, Seoul, Korea
[email protected]
Feb. 21th, 2012 @ YongPyong Resort.
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CONTENTS
 Introduction
 Ultra High Energy Cosmic Rays(UHECRs)
 Telescope Array(TA) Experiment
 Bayesian Study of UHECRs
 Bayesian Analysis and Likelihood Function
 Density distribution and UHECR
 AGNs(VCV catalogue) and 27 Highest Energy
PAO UHECRs. REFERENCE:
 Summary
ARXIV:1010.0911V1
A BAYESIAN ANALYSIS
OF THE 27 HIGHEST ENERGY COSMIC RAYS
DETECTED BY THE PIERRE AUGER OBSERVATORY
WATSON ET AL.
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INTRODUCTION TO COSMIC RAY
 Primary particle
 Extensive Air Shower
 Ground Detector Array
Experiment
EAS can be detected by ground
detectors,
Detected signals are correlated
with the Primary energy,
type of primary particle and
the arrival direction.
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INTRODUCTION TO COSMIC RAY
 Energy spectrum
 Mass composition
 Source of cosmic ray
EAS can be detected by ground
detectors,
Detected signals are correlated
with the Primary energy,
type of primary particle and
the arrival direction.
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TELESCOPE ARRAY EXPERIMENT
109~1010 eV
1012 eV
1015 eV
Telescope Array Experiment( Utah, USA)
◆: Surface Detector
HOT ISSUE!! GZK cutoff
1019 eV
1020 eV
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 Bayesian Study of UHECRs
 Bayesian Analysis and Likelihood Function
 Bayesian approach
 Full likelihood function in watson’s paper.
 Simple likelihood function
 Density distribution and UHECR
 AGNs(VCV catalogue) and 27 Highest Energy
PAO UHECRs.
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BAYESIAN ANALYSIS
r_src : emission rate from src
R_bkg : emission rate from bkg
 Posterior Probability Distribution(LEFT) is
proportional to Likelihood function(RIGHT),
when prior probability can be approximated to
step function.
 Celestial sphere model of 180(dec)*360(ra)
pixels Ref. arXiv:1010.0911v1 watson et al.
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CELESTIAL SPHERE MODEL
Violet : random events
Red and Blue : PAO events Science,318,938, Abraham J., et al.
Black : VCV AGN
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SIMPLE LIKELIHOOD FUNCTION
Ref. arXiv:1010.0911v1 Watson et al.
Nc,p : counted number of
events in each pixel
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SIMPLE LIKELIHOOD FUNCTION
Ref. arXiv:1010.0911v1 Watson et al.
Nc,p : counted number of
events in each pixel
Poisson distribution
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SIMPLE LIKELIHOOD FUNCTION
Ref. arXiv:1010.0911v1 Watson et al.
Nc,p : counted number of
events in each pixel
Poisson distribution
Area of each pixel
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SIMPLE LIKELIHOOD FUNCTION
Ref. arXiv:1010.0911v1 Watson et al.
Nc,p : counted number of
events in each pixel
Poisson distribution
Area of each pixel
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Refraction of arrival direction
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SIMPLE LIKELIHOOD FUNCTION
Ref. arXiv:1010.0911v1 Watson et al.
Nc,p : counted number of
events in each pixel
Poisson distribution
Area of each pixel
Refraction of arrival direction
GZK effect
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SIMPLE LIKELIHOOD FUNCTION
Ref. arXiv:1010.0911v1 Watson et al.
Nc,p : counted number of
events in each pixel
Poisson distribution
Area of each pixel
Refraction of arrival direction
GZK effect
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SIMPLE LIKELIHOOD FUNCTION
 Remove effect of Energy, Pixel area, arrival
angle error.
 SRC or BKG fills one pixel completely
 UHECR emission rate/each pixel : Constant
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SIMPLE LIKELIHOOD FUNCTION
All events from AGN
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All events from BKG
27 PAO events
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SIMPLE LIKELIHOOD FUNCTION
F_AGN=1
F_AGN=0
F_AGN=4/27
FAGN=
(UHECR from AGN)/(detected UHECR)
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 Bayesian Study of UHECRs
 Bayesian Analysis and Likelihood Function
 Density distribution and UHECR
 Matter can be the source of UHECR
 Density distribution and TA data
 AGNs(VCV catalogue) and 27 Highest Energy
PAO UHECRs.
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DENSITY DISTRIBUTION AND
UHECR
Z:Y:X
Dec:z:ra:delta(color),
(z<0.03)
Binned dec:ra
density distribution is reconstructed from SDSS
Mon. Not. R. Astron. Soc. 409, Jens Jasche et al.
UHECRs can be generated in dotted pixels
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DENSITY DISTRIBUTION AND
UHECR
r -> 1
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DENSITY DISTRIBUTION AND
UHECR
TA 12
-1
Y : F_src
2
Random 12
1
0
0
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2
X : F_bkg – Fraction of
cosmic ray from BKG
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DENSITY DISTRIBUTION AND
UHECR
TA 12
0
Random 12
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DENSITY DISTRIBUTION AND
UHECR
TA 12
1
Random 12
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DENSITY DISTRIBUTION AND
UHECR
TA 12
2
Random 12
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 Bayesian Study of UHECRs
 Bayesian Analysis and Likelihood Function
 Density distribution and UHECR
 AGNs(VCV catalogue) and 27 Highest Energy
PAO UHECRs.
 My likelihood function
 Linearity test
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AGN AND UHECR
Violet : random events
Red and Blue : PAO events Science,318,938, Abraham J., et al.
Black : VCV AGN
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AGN AND UHECR
Nc,p : counted number of
events in each pixel
except Energy spectrum
and GZK effect
(because energy of each
event can be reconstructed)
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AGN AND UHECR
Red : VCV AGN
Black : Probability of arriving of cosmic ray
emitted from AGN
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AGN AND UHECR
Y : F_AGN
2
Events
observed by
PAO
1
0
0
1
2
Likelihood functions and its contour plots
Y axis : Events from source / X axis : Events from background
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AGN AND UHECR
All events are from AGN
Random events
Expected figure
of AGN events
Expected figure
of Random events
Likelihood functions and its contour plots
Y axis : Events from source / X axis : Events from background
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LINEARITY TEST
Likelihood functions and its contour plots
Y axis : Events from source / X axis : Events from background
Z=0.003 , F_AGN=0 ~ F_AGN=1
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MAX. LIKELIHOOD VS F_AGN
PAO case : 1.80E-01
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Prelim.
+1.34E-01
-9.41E-02
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MAX. LIKELIHOOD VS F_AGN
Prelim.
Sources should be
selected by applying
PAO case : 1.80E-01
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+1.34E-01
-9.41E-02
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SUMMARY
 Summary
 By Applying Bayesian statistics, correlation
between AGN and UHECR can be estimated using
Maximum likelihood estimator.
 Plan




Linearity test will be done.
This study will be applied to TA data.
Density distribution will be applied to this study.
Large Scale Structure study.
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THANK YOU VERY MUCH.
Mr W.R.Cho
with Al profiles on the top (2008).
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 .bak
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RE-PRODUCING
Ref. arXiv:1010.0911v1 Watson et al.
Nc,p : counted number of
events in each pixel
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RE-PRODUCING
Smearing angle=3deg
sa=5
sa=6
F_AGN=9%
sa=10
F_AGN=11%
sa=20
sa=12
F_AGN=15%
Likelihood functions and its contour plots
Y axis : Events from source / X axis : Events from background
27 PAO events, gamma = 3.6 , various sigma_angle/2(sa)
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REPRODUCING
sigma_angle/2
Y_maximum Sum(prob.
point
)
F_AGN
F_AGN(wats
on)
1.5
5.00E-02
1.71E+06
22.65
3
5.05E-03
6.85E+06
9.17
5
1.96E-03
1.92E+07
9.94
6
1.50E-03
2.78E+07
11.01
22
10
7.19E-04
8.02E+07
15.29
31
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 Neutrino fluxes
from AGN
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BAYESIAN ANALYSIS Ref. arXiv:1010.0911v1 Watson et al.
r_src : emission rate from src
R_bkg : emission rate from bkg
Events observed by
PAO
Expected figure
of Random events
Likelihood functions and its contour plots
Y axis : Events from source / X axis : Events from background
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