Feb. 21st, 2011YongPyong20121 B AYESIAN S TUDY OF UHECR S Wooram Cho Institute of Physics and Applied Physics Yonsei University, Seoul, Korea

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Presentation transcript:

Feb. 21st, 2011YongPyong20121 B AYESIAN S TUDY OF UHECR S Wooram Cho Institute of Physics and Applied Physics Yonsei University, Seoul, Korea Feb. 21 th, YongPyong Resort.

Feb. 21st, 2011YongPyong20122 C ONTENTS  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.  Summary REFERENCE: ARXIV: V1 A BAYESIAN ANALYSIS OF THE 27 HIGHEST ENERGY COSMIC RAYS DETECTED BY THE PIERRE AUGER OBSERVATORY WATSON ET AL.

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. Feb. 21st, 2011YongPyong20123

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. Feb. 21st, 2011YongPyong20124

Feb. 21st, 2011YongPyong eV eV 10 9 ~10 10 eV eV eV TELESCOPE ARRAY EXPERIMENT HOT ISSUE!! GZK cutoff Telescope Array Experiment( Utah, USA) ◆ : Surface Detector

 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. Feb. 21st, 2011YongPyong20126

BAYESIAN ANALYSIS Feb. 21st, 2011YongPyong20127  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: v1 watson et al. r_src : emission rate from src R_bkg : emission rate from bkg

CELESTIAL SPHERE MODEL Feb. 21st, 2011YongPyong20128 Violet : random events Red and Blue : PAO events Science,318,938, Abraham J., et al. Black : VCV AGN

SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong20129 Ref. arXiv: v1 Watson et al. Nc,p : counted number of events in each pixel

SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong Ref. arXiv: v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution

SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong Ref. arXiv: v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution Area of each pixel

SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong Ref. arXiv: v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution Area of each pixel Refraction of arrival direction

SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong Ref. arXiv: v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution Area of each pixel Refraction of arrival direction GZK effect

SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong Ref. arXiv: v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution Area of each pixel Refraction of arrival direction GZK effect

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 Feb. 21st, 2011YongPyong201215

SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong All events from AGN All events from BKG 27 PAO events

SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong F AGN = (UHECR from AGN)/(detected UHECR) F_AGN=1 F_AGN=0F_AGN=4/27

 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. Feb. 21st, 2011YongPyong201218

DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong 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

DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong r -> 1

DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong TA 12 Random 12 X : F_bkg – Fraction of cosmic ray from BKG Y : F_src

DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong TA 12 Random 12 0

DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong TA 12 Random 12 1

DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong TA 12 Random 12 2

 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 Feb. 21st, 2011YongPyong201225

AGN AND UHECR Feb. 21st, 2011YongPyong Violet : random events Red and Blue : PAO events Science,318,938, Abraham J., et al. Black : VCV AGN

AGN AND UHECR Feb. 21st, 2011YongPyong Nc,p : counted number of events in each pixel except Energy spectrum and GZK effect (because energy of each event can be reconstructed)

AGN AND UHECR Feb. 21st, 2011YongPyong Red : VCV AGN Black : Probability of arriving of cosmic ray emitted from AGN

AGN AND UHECR Feb. 21st, 2011YongPyong Likelihood functions and its contour plots Y axis : Events from source / X axis : Events from background Events observed by PAO Y : F_AGN

AGN AND UHECR Feb. 21st, 2011YongPyong Expected figure of Random events Likelihood functions and its contour plots Y axis : Events from source / X axis : Events from background All events are from AGNRandom events Expected figure of AGN events

LINEARITY TEST Feb. 21st, 2011YongPyong 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

MAX. LIKELIHOOD VS F_AGN Feb. 21st, 2011YongPyong PAO case : 1.80E E E-01 Prelim.

MAX. LIKELIHOOD VS F_AGN Feb. 21st, 2011YongPyong PAO case : 1.80E E E-01 Sources should be selected by applying Prelim.

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. Feb. 21st, 2011YongPyong201234

Feb. 21st, 2011YongPyong THANK YOU VERY MUCH. Mr W.R.Cho with Al profiles on the top (2008).

.bak Feb. 21st, 2011YongPyong201236

RE-PRODUCING Feb. 21st, 2011YongPyong Ref. arXiv: v1 Watson et al. Nc,p : counted number of events in each pixel

RE-PRODUCING Feb. 21st, 2011YongPyong 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) Smearing angle=3deg sa=5sa=6 sa=10sa=12 sa=20 F_AGN=9%F_AGN=11% F_AGN=15%

REPRODUCING Feb. 21st, 2011YongPyong sigma_angle/2 Y_maximum point Sum(prob.)F_AGN F_AGN(wat son) E E E E E E E E E E

Feb. 21st, 2011YongPyong  Neutrino fluxes from AGN

BAYESIAN ANALYSIS Feb. 21st, 2011YongPyong Ref. arXiv: v1 Watson et al. r_src : emission rate from src R_bkg : emission rate from bkg Expected figure of Random events Events observed by PAO Likelihood functions and its contour plots Y axis : Events from source / X axis : Events from background