A Method of Searching for Origins of Cosmic Rays correcting for Galactic Field Deflections and Charge Composition Martin Erdmann, Gero Müller, Martin Urban , Marcus Wirtz martin.urban@rwth-aachen.de
Current status Source Searches The Pierre Auger Collaboration, 2015, ApJ, 804 UHECRs Composition Separate Analyses The Pierre Auger Collaboration, 2015,POS(ICRC 2015) 420 → Point source searches → Large scale anisotropy → Mass composition 2 martin.urban@rwth-aachen.de
Motivation Source Searches The Pierre Auger Collaboration, 2015, ApJ, 804 Galactic Magnetic UHECRs Field Spectrometer Composition The Pierre Auger Collaboration, 2015,POS(ICRC 2015) 420 Galactic magnetic field allows for unified analysis 3 martin.urban@rwth-aachen.de
Galactic Magnetic Field Correction ■ Magnetic field models tuned to Faraday rotation and synchrotron emission measurements 10 Ne at 50 EeV 5 Be at 50 EeV 1 H at 50 EeV ■ Cosmic rays with different rigidities R=E/Z arrive on Earth at different directions ● Source directions can only be found at edge of galaxy ● Magnetic field corrections depend on cosmic ray charges ■ Correction of deflections in magnetic field using a probabilistic approach 4 martin.urban@rwth-aachen.de
Analysis Strategy 5 martin.urban@rwth-aachen.de
Monte Carlo Simulation Monte Carlo simulation Energy spectrum with E -2.6 Most abundant charges: Sources: M87, Cen A & Fornax A smearing: ઠ = 3° Signal fraction: f s = 15 % H, He, C, N, O Rigidity R=E/Z needed for projection to edge of galaxy, but charge? → Assign equal probability for each charge to each cosmic ray 6 martin.urban@rwth-aachen.de
Projection to the edge of the galaxy Galactic magnetic field ■ Regular field by Jansson and Farrar ■ Lensing technique (H.-P. Bretz et al., 2014, Astropart.Phys. 54 110–117) ● Probability to observe cosmic rays originating from (φ,θ) at the Galaxy at direction (φ’,θ’) on Earth ● Rigidity dependent ■ Transposed lens to project to edge of galaxy 7 martin.urban@rwth-aachen.de
Cluster identification Superimposed maps (rigidities) 1000 isotropic simulations probability in pixel [A.U] → accept only directions exceeding 90% probability of orign [A.U] quantile 8 martin.urban@rwth-aachen.de
Clusters and expected arrival directions ■ ■ Search for directions with high arrival probability Use cluster centers as source candidates ■ DBSCAN algorithmus (Ester, M. et al. (1996) KDD-96) ■ Calculate expected arrival directions on Earth using GMF ■ Standard point source search with likelihood ratio 9 martin.urban@rwth-aachen.de < 90 %
Likelihood analysis ■ Model: smearing to account for anticipated signal background cosmic ray direction random fields signal fraction distribution distribution on Earth Isotropy scenario excluded 10 martin.urban@rwth-aachen.de
Charge determination Update charge probabilities using Z fit : most probable charge projected source directions Cosmic Ray E=80 EeV → C = E / R = 8 ■ Charge resolution of ± 2.31 11 martin.urban@rwth-aachen.de
Iterative Procedure Repeat analysis with updated rigidity distributions ■ Sources directions ● improved directional reconstruction ● Additional (unwanted) source candidate ■ Improved charge resolution ± 1.65 12 martin.urban@rwth-aachen.de
Conclusion and Outlook ■ Method to identify source candidates by charge dependent corrections for deflections in GMF ● Search for extragalactic directions ● Evaluation of validity by likelihood ratio method ● Cosmic ray charge resolution ≈ ± 2 ■ Comparison of different magnetic field models ■ Inclusion of uncertainties, i.e. energy, direction ■ Application to data 13 martin.urban@rwth-aachen.de
Backup 14 martin.urban@rwth-aachen.de
Magnetic Field Lenses ■ Backtracking anti-protons from Earth to edge of galaxy ● Using HEALPix scheme with nside=64 175 rigidity bins between 10 17.00 eV and 10 20.49 eV with bin width log 10 (R/V)=0.02 ● ■ Matrices projecting a probability distribution from edge of galaxy on Earth pixel on Earth pixel at galaxy ■ Transposed lens answers question how probable cosmic rays at direction (φ, θ) on earth originate from direction (φ’, θ’) at edge of galaxy 15 martin.urban@rwth-aachen.de
Lens Examples for log 10 R = 18.7 and log 10 R=19.7 16 martin.urban@rwth-aachen.de
Galactic Magnetic Field - Cosmic Ray Flux 17 martin.urban@rwth-aachen.de
Galactic Magnetic Field: Mean Deflections JF12 PT11 18 martin.urban@rwth-aachen.de
Galactic Magnetic Fields: Deflection Variances JF12 PT11 19 martin.urban@rwth-aachen.de
Results for 5 % signal fraction 20 20 martin.urban@rwth-aachen.de
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