1. Feb. 21st, 2011YongPyong20121 B AYESIAN S TUDY OF UHECR S Wooram Cho Institute of Physics and Applied Physics Yonsei University, Seoul, Korea wrcho@yonsei.ac.kr Feb. 21 th, 2012 @ YongPyong Resort.

2. 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:1010.0911V1 A BAYESIAN ANALYSIS OF THE 27 HIGHEST ENERGY COSMIC RAYS DETECTED BY THE PIERRE AUGER OBSERVATORY WATSON ET AL.

3. 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

4. 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

5. Feb. 21st, 2011YongPyong20125 10 15 eV 10 19 eV 10 9 ~10 10 eV 10 12 eV 10 20 eV TELESCOPE ARRAY EXPERIMENT HOT ISSUE!! GZK cutoff Telescope Array Experiment( Utah, USA) ◆ : Surface Detector

6.  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

7. 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:1010.0911v1 watson et al. r_src : emission rate from src R_bkg : emission rate from bkg

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

9. SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong20129 Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel

10. SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong201210 Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution

11. SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong201211 Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution Area of each pixel

12. SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong201212 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

13. SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong201213 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

14. SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong201214 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

15. 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

16. SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong201216 All events from AGN All events from BKG 27 PAO events

17. SIMPLE LIKELIHOOD FUNCTION Feb. 21st, 2011YongPyong201217 F AGN = (UHECR from AGN)/(detected UHECR) F_AGN=1 F_AGN=0F_AGN=4/27

18.  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

19. DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong201219 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

20. DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong201220 r -> 1

21. DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong201221 TA 12 Random 12 X : F_bkg – Fraction of cosmic ray from BKG Y : F_src 210210 0 1 2

22. DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong201222 TA 12 Random 12 0

23. DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong201223 TA 12 Random 12 1

24. DENSITY DISTRIBUTION AND UHECR Feb. 21st, 2011YongPyong201224 TA 12 Random 12 2

25.  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

26. AGN AND UHECR Feb. 21st, 2011YongPyong201226 Violet : random events Red and Blue : PAO events Science,318,938, Abraham J., et al. Black : VCV AGN

27. AGN AND UHECR Feb. 21st, 2011YongPyong201227 Nc,p : counted number of events in each pixel except Energy spectrum and GZK effect (because energy of each event can be reconstructed)

28. AGN AND UHECR Feb. 21st, 2011YongPyong201228 Red : VCV AGN Black : Probability of arriving of cosmic ray emitted from AGN

29. AGN AND UHECR Feb. 21st, 2011YongPyong201229 Likelihood functions and its contour plots Y axis : Events from source / X axis : Events from background Events observed by PAO Y : F_AGN 210210 0 1 2

30. AGN AND UHECR Feb. 21st, 2011YongPyong201230 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

31. LINEARITY TEST Feb. 21st, 2011YongPyong201231 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

32. MAX. LIKELIHOOD VS F_AGN Feb. 21st, 2011YongPyong201232 PAO case : 1.80E-01 -9.41E-02 +1.34E-01 Prelim.

33. MAX. LIKELIHOOD VS F_AGN Feb. 21st, 2011YongPyong201233 PAO case : 1.80E-01 -9.41E-02 +1.34E-01 Sources should be selected by applying Prelim.

34. 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

35. Feb. 21st, 2011YongPyong201235 THANK YOU VERY MUCH. Mr W.R.Cho with Al profiles on the top (2008).

36. .bak Feb. 21st, 2011YongPyong201236

37. RE-PRODUCING Feb. 21st, 2011YongPyong201237 Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel

38. RE-PRODUCING Feb. 21st, 2011YongPyong201238 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%

39. REPRODUCING Feb. 21st, 2011YongPyong201239 sigma_angle/2 Y_maximum point Sum(prob.)F_AGN F_AGN(wat son) 1.55.00E-021.71E+0622.65 35.05E-036.85E+069.17 18 51.96E-031.92E+079.94 61.50E-032.78E+0711.01 22 107.19E-048.02E+0715.29 31

40. Feb. 21st, 2011YongPyong201240  Neutrino fluxes from AGN

41. BAYESIAN ANALYSIS Feb. 21st, 2011YongPyong201241 Ref. arXiv:1010.0911v1 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