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Bayesian Study of UHECRs

Bayesian Study of UHECRs. Wooram Cho Institute of Physics and Applied Physics Yonsei University, Seoul, Korea wrcho@yonsei.ac.kr Feb. 21 th , 2012 @ YongPyong Resort. Contents. Introduction Ultra High Energy Cosmic Rays(UHECRs) Telescope Array(TA) Experiment Bayesian Study of UHECRs

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Bayesian Study of UHECRs

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  1. Bayesian Study of UHECRs Wooram Cho Institute of Physics and Applied Physics Yonsei University, Seoul, Korea wrcho@yonsei.ac.kr Feb. 21th, 2012 @ YongPyong Resort. YongPyong2012

  2. 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. • Summary REFERENCE: ARXIV:1010.0911V1 A BAYESIAN ANALYSIS OF THE 27 HIGHEST ENERGY COSMIC RAYS DETECTED BY THE PIERRE AUGER OBSERVATORYWATSON ET AL. YongPyong2012

  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. YongPyong2012

  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. YongPyong2012

  5. TELESCOPE ARRAY EXPERIMENT 109~1010 eV 1012 eV 1015 eV 1019 eV 1020 eV Telescope Array Experiment( Utah, USA) ◆: Surface Detector HOT ISSUE!! GZK cutoff YongPyong2012

  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. YongPyong2012

  7. 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. YongPyong2012

  8. CELESTIAL SPHERE MODEL Violet : random events Red and Blue : PAO eventsScience,318,938, Abraham J., et al. Black : VCV AGN YongPyong2012

  9. SIMPLE LIKELIHOOD FUNCTION Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel YongPyong2012

  10. SIMPLE LIKELIHOOD FUNCTION Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution YongPyong2012

  11. 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 YongPyong2012

  12. 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 YongPyong2012

  13. 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 YongPyong2012

  14. 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 YongPyong2012

  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 YongPyong2012

  16. SIMPLE LIKELIHOOD FUNCTION 27 PAO events All events from BKG All events from AGN YongPyong2012

  17. SIMPLE LIKELIHOOD FUNCTION F_AGN=1 F_AGN=0 F_AGN=4/27 FAGN= (UHECR from AGN)/(detectedUHECR) YongPyong2012

  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. YongPyong2012

  19. 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 Jascheet al. UHECRs can be generated in dotted pixels YongPyong2012

  20. density distribution and UHECR r -> 1 YongPyong2012

  21. density distribution and UHECR TA 12 -1 Y : F_src Random 12 2 1 0 X : F_bkg – Fraction of cosmic ray from BKG 0 1 2 YongPyong2012

  22. density distribution and UHECR TA 12 0 Random 12 YongPyong2012

  23. density distribution and UHECR TA 12 1 Random 12 YongPyong2012

  24. density distribution and UHECR TA 12 2 Random 12 YongPyong2012

  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 YongPyong2012

  26. AGN AND UHECR Violet : random events Red and Blue : PAO eventsScience,318,938, Abraham J., et al. Black : VCV AGN YongPyong2012

  27. AGN AND UHECR Nc,p : counted number of events in each pixel except Energyspectrum and GZK effect (because energy of each event can be reconstructed) YongPyong2012

  28. AGN AND UHECR Red : VCV AGN Black : Probability of arriving of cosmic ray emitted from AGN YongPyong2012

  29. AGN AND UHECR Y : F_AGN 2 1 0 Events observed by PAO 0 1 2 Likelihood functions and its contour plots Y axis : Events from source / X axis : Events from background YongPyong2012

  30. 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 YongPyong2012

  31. 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 YongPyong2012

  32. MAX. LIKELIHOOD VS F_AGN Prelim. PAO case : 1.80E-01-9.41E-02+1.34E-01 YongPyong2012

  33. MAX. LIKELIHOOD VS F_AGN Prelim. Sources should be selected by applying PAO case : 1.80E-01-9.41E-02+1.34E-01 YongPyong2012

  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. YongPyong2012

  35. THANK YOU VERY MUCH. Mr W.R.Cho with Al profiles on the top (2008). YongPyong2012

  36. .bak YongPyong2012

  37. RE-PRODUCING Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel YongPyong2012

  38. RE-PRODUCING Smearing angle=3deg sa=5 sa=6 F_AGN=9% F_AGN=11% sa=20 sa=10 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) YongPyong2012

  39. REPRODUCING YongPyong2012

  40. Neutrino fluxes from AGN YongPyong2012

  41. BAYESIAN ANALYSIS r_src : emission rate from src R_bkg : emission rate from bkg Ref. arXiv:1010.0911v1 Watson et al. 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 YongPyong2012

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