A unified constraint on the Lorentz invariance violation from both - PowerPoint PPT Presentation

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion A unified constraint on the Lorentz invariance violation from both short and long GRBs YUNGUO – JIANG Institute of High Energy Physics, Chinese Academy of Sciences, 100049 Beijing, China May 23, 2012 Based on the work arXiv: 1201.3413, to appear in Astroparticle Physics. Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Fermi satellite observation • Gamma-Ray Burst Monitor (GBM) : 8 KeV – 40 MeV, Large Area Telescope (LAT): 30 MeV – 300 GeV. Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Fermi satellite observation • Gamma-Ray Burst Monitor (GBM) : 8 KeV – 40 MeV, Large Area Telescope (LAT): 30 MeV – 300 GeV. Figure: GRB 080916, The Fermi LAT Figure: GRB 090510, Ackermann et al. and GBM Collaborations, Science, ApJ, 716 :1178 323 :1688 Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Fermi satellite observation • An interesting Feature: GeV photons arrive later than MeV photons. Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Fermi satellite observation • An interesting Feature: GeV photons arrive later than MeV photons. Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Explanations • Lorentz Invariance Violation (LIV) • Quantum gravity effects: D-foam; Loop gravity • Finsler geometry: DSR Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Explanations • Lorentz Invariance Violation (LIV) • Quantum gravity effects: D-foam; Loop gravity • Finsler geometry: DSR • GRB models • Magnetic-dominated baryon-loaded jet (M´ esz´ aros & Rees, ApJ 733(2011)L40) • Acceleration time ( Duran & Kumar, MNRAS,412(2011)512) • Optical depths (Bo´ snjak & Kumar, MNRAS,421(2012)L39) Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Explanations • Lorentz Invariance Violation (LIV) • Quantum gravity effects: D-foam; Loop gravity • Finsler geometry: DSR • GRB models • Magnetic-dominated baryon-loaded jet (M´ esz´ aros & Rees, ApJ 733(2011)L40) • Acceleration time ( Duran & Kumar, MNRAS,412(2011)512) • Optical depths (Bo´ snjak & Kumar, MNRAS,421(2012)L39) • Our Recipe (Chang&Jiang&Lin, arXiv:1201.3413) ∆ t obs = ∆ t LIV + ∆ t int . Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Magnetic jet model, Bo´ snjak & Kumar • Bulk Lorentz factor � ( r / r 0 ) 1 / 3 r 0 � r � r s , for Γ( r ) ≈ η for r � r s . • Optical depth � ∞ dr ′ τ T ( r ) = 2Γ 2 σ T n Γ , r where n ≃ L / 4 π r 2 m p Γ c 3 σ 0 . • MeV emission r p ≈ 1 . 36 × 10 5 L 3 / 5 52 σ − 3 / 5 r − 3 / 5 , 0 , 3 0 , 7 r 0 where L 52 ≡ L / 10 52 erg · s − 1 , σ 0 , 3 ≡ σ 0 / 10 3 , and r 0 , 7 ≡ r 0 / 10 7 cm. Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Magnetic jet model • Spectra of background photons: � β − 1 1 � β − 2 �� E p L > p n ′ γ ( > E ) = , 4 π r 2 Γ c β − 1 E (1 + z ) E p • Optical depth of High Energy photons � σ γγ � E p E 0 � β − 1 � β − 2 L > p τ ± ( E 0 , r ) = . 4 π r Γ 2 (1 + z ) 3 − 2 β E p c Γ 2 m 2 e c 4 β − 1 • GeV emission radius r γγ ( E 0 ) ≈ 4 . 13 × 10 6 L 0 . 41 > p , 52 E 0 . 08 p , − 6 E 0 . 49 0 , − 4 r − 0 . 41 (1 + z ) 0 . 57 0 , 7 r 0 • Intrinsic time delay � 1 / 3 � 1 / 3 � ∆ t = 3 r 0 (1 + z ) �� r γγ ( E 0 ) � r p . − 2 c r 0 r 0 Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion LIV Effects • LIV induced time delay � ∆ E ∆ t LIV = 1 + n � n D n , M n c 2 2 c � z (1 + z ′ ) n dz ′ D n ≡ c . Ω M (1 + z ′ ) 3 + Ω Λ H 0 � 0 • For n = 1, ∆ E D 1 M 1 c 2 = c . ∆ t LIV • A statistical method ∆ t obs ∆ E D 1 1 + z = a LIV K ( z ) + b , K ( z ) ≡ (1 + z ) c Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion LIV Effects Figure: Linear fit of GRBs, E QG = (2 ± 0 . 2) × 10 17 GeV. Shao & Xiao, & Ma, arXiv:0911.2276 Questions: • Dependence of GeV photons selection. • GeV photons are emitted earlier. Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion LIV effects and GRB models • Considering the GRB models ∆ t LIV = ∆ t obs − ∆ t int , • Estimation of b ∼ ∆ t int / (1 + z ), b ≃ 0 . 08 r 0 . 86 0 . 7 L 0 . 14 > p , 52 E 0 . 03 p , − 6 E 0 . 16 0 , − 4 (1 + z ) 0 . 19 M 1 c 2 GRB ∆ t obs ∆ t LIV K ( z ) E low E high MeV GeV s s s · GeV GeV 4.50 × 10 18 10.02 × 10 19 080916c 100 13.22 12.94 0.24 7.02 × 10 18 9.73 × 10 19 090510 100 31 0.20 0.14 3.38 × 10 18 9.94 × 10 19 090902b 100 11.16 9.5 0.10 6.20 × 10 18 9.59 × 10 19 090926 100 19.6 21.5 0.20 Table: r 0 , 7 is chosen as 16.7, 0.1, 28.7 and 55.0 for GRB 080916c, GRB 090510, GRB 090902b and GRB 090926, respectively. Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion LIV effects and GRB models 8 GRB 090510 7 GRB 090926 6 ∆ t LIV / (1+z) / (10 −2 sec) 5 GRB 080916c 4 3 GRB 090902b 2 1 0 0 1 2 3 4 5 6 7 8 K(z) / (10 18 sec ⋅ GeV) Figure: The plot of ∆ t LIV / (1 + z ) vs. K ( z ) for four Fermi -detected GRBs. • Quantum gravity scale M 1 c 2 ∼ 1 . 0 × 10 20 GeV Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Discussion and conclusion • Without GRB models, the LIV effects are not conclusive. • The quantum energy scale is 10 20 GeV. • r 0 can be predicted by time delay of GeV photons in the magnetic jet model. Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Discussion and conclusion • Without GRB models, the LIV effects are not conclusive. • The quantum energy scale is 10 20 GeV. • r 0 can be predicted by time delay of GeV photons in the magnetic jet model. • Quantum gravity theories are ruled out? • Are GRB models trustable? Yunguo Jiang IHEP

Introduction Magnetic jet model Test of LIV effects A combination analysis Conclusion Thank you! Yunguo Jiang IHEP