Study of ultrahigh energy cosmic ray propagation Tom

Study of ultra-high energy cosmic ray propagation Tomáš Fodran 27/09/2019 /13

MOTIVATION & OUTLINE 1) Propagation of proton Cosmic Rays (CR) - Energy losses LIV: Lorentz Invariance Violation CR: Cosmic rays - Energy evolution 2) Lorentz invariance violation (LIV) effects on the proton Cosmic Ray propagation - LIV framework - LIV modified propagation 3) Lorentz invariance violation effects on the proton Cosmic Ray energy spectrum 4) Conclusions 2/13

PROTON ENERGY LOSSES Proton attenuation length λ: Effects of magnetic fields were neglected. . . LIV affects the photomeson production. 3/13

ENERGY EVOLUTION OF PROTON CR Proton energy degrades with the cosmological redshift. 4/13

EFFECTIVE HORIZON OF PROTON CR Units in table: Megaparsecs (Mpc) 5/13

LORENTZ INVARIANCE VIOLATION FRAMEWORK. Assumption: Stecker & Scully (2008) >> LEGEND MPl - Planck Mass (1, 22 x 1028 e. V) μ – particle mass scale (109 e. V) ~ 0 6/13

INELASTICITY (K) Photomeson production: • Inelasticity: Energy loss equation: Energy evolution equation: ϵ - photon energy σ – cross-section γ – Lorentz factor η – threshold photon energy 7/13

INELASTICITY – NO LIV. LEGEND Color map: inelasticity, X-axis: proton energy, Y-axis: photon energy in proton rest 8 8/13

MODIFIED INELASTICITY Values of LIV coefficients in panels: η 2 η 3 η 4 5× 10. − 5 5× 10− 14 5× 10− 5 10− 4 10− 14 10− 5 5× 10− 4 10− 15 10− 6 10− 3 10− 16 10− 7 LEGEND Color map: inelasticity, X-axis: proton energy, Y-axis: photon energy in proton rest frame 9 9/13

EFFECTIVE HORIZON AFFECTED BY 2 nd ORDER LIV COEFFICIENTS Color lines: Proton energy observed on earth 9000 Mpc = redshift 20 10/13

MODIFIED PROTON CR SPECTRA Pierre Auger Observatory LEGEND Г – spectral index ζ – source evolution – -maximal attainable proton energy at source Telescope array Range E (e. V) ζ Γ 0 -6 2. 2 -3 1020, 5 -1023 e. V Step 0. 5 0. 1 100, 5 e. V Sum 13 9 6 702 11/13

THE BEST VALUES OF CHI-SQUARED AS A FUNCTION OF LIV COEFFICIENTS 12/13

CONCLUSIONS • Estimation of the distance of sources - Effective horizon. • LIV effect on Effective horizon - sources further away. • LIV corrections of 2 nd, 3 rd and 4 th order has the same effect on the proton propagation. • Estimation of the upper bound on pion LIV coefficient. • Correlation between the maximal attainable energy at source parameter and LIV coefficients. 13/13

Thank you for your attention