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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 Wooram Cho Institute of Physics and Applied Physics Yonsei University, Seoul, Korea wrcho@yonsei.ac.kr Feb. 21th, 2012 @ YongPyong Resort. YongPyong2012
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
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
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
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
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
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
CELESTIAL SPHERE MODEL Violet : random events Red and Blue : PAO eventsScience,318,938, Abraham J., et al. Black : VCV AGN YongPyong2012
SIMPLE LIKELIHOOD FUNCTION Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel YongPyong2012
SIMPLE LIKELIHOOD FUNCTION Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel Poisson distribution YongPyong2012
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
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
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
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
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
SIMPLE LIKELIHOOD FUNCTION 27 PAO events All events from BKG All events from AGN YongPyong2012
SIMPLE LIKELIHOOD FUNCTION F_AGN=1 F_AGN=0 F_AGN=4/27 FAGN= (UHECR from AGN)/(detectedUHECR) YongPyong2012
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
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
density distribution and UHECR r -> 1 YongPyong2012
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
density distribution and UHECR TA 12 0 Random 12 YongPyong2012
density distribution and UHECR TA 12 1 Random 12 YongPyong2012
density distribution and UHECR TA 12 2 Random 12 YongPyong2012
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
AGN AND UHECR Violet : random events Red and Blue : PAO eventsScience,318,938, Abraham J., et al. Black : VCV AGN YongPyong2012
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
AGN AND UHECR Red : VCV AGN Black : Probability of arriving of cosmic ray emitted from AGN YongPyong2012
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
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
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
MAX. LIKELIHOOD VS F_AGN Prelim. PAO case : 1.80E-01-9.41E-02+1.34E-01 YongPyong2012
MAX. LIKELIHOOD VS F_AGN Prelim. Sources should be selected by applying PAO case : 1.80E-01-9.41E-02+1.34E-01 YongPyong2012
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
THANK YOU VERY MUCH. Mr W.R.Cho with Al profiles on the top (2008). YongPyong2012
.bak YongPyong2012
RE-PRODUCING Ref. arXiv:1010.0911v1 Watson et al. Nc,p : counted number of events in each pixel YongPyong2012
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
REPRODUCING YongPyong2012
Neutrino fluxes from AGN YongPyong2012
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