Constraining Lorentz invariance viola1ons using the Crab pulsar TeV - PowerPoint PPT Presentation

Constraining Lorentz invariance viola1ons using the Crab pulsar TeV emission Markus Gaug UAB-CERES Universitat Autònoma de Barcelona Spain 35th Interna,onal Cosmic Ray Conference, Bexco, Busan, Korea 1

MAGIC Pulsar data Inter-pulse P2 has been detected significantly up to 1.2 TeV. Joining 19 different observa1on periods Dominated by baseline (N/S ~ 25 !) ~320 hrs from 2007 to 2014: 544 excess events • above 400 GeV 418 above 500 GeV • 2

Lorentz Invariance Viola1on (LIV) • Appears in many quantum gravity models • Leads to a modified dispersion rela,on: E 2 = p 2 + m 2 + f p ; ξ / M Pl ( ) • In low-energy limit, can be expanded: ( ) f p ; ξ / M Pl ) ≈ E Pl ξ (1) p + ξ (2) p 2 + ξ (3) p 3 + ξ (4) p (4) + … ( f p ; ξ / M Pl E 2 E Pl Pl affect affect low-energy physics high-energy physics Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission 3

Lorentz Invariance Viola1on (LIV) • Appears in many quantum gravity models • Leads to a modified dispersion rela,on: E 2 = p 2 + m 2 + f p ; ξ / M Pl ( ) • In low-energy limit, can be expanded: ( ) f p ; ξ / M Pl ) ≈ E Pl ξ (1) p + ξ (2) p 2 + ξ (3) p 3 + ξ (4) p (4) + … ( f p ; ξ / M Pl E 2 E Pl Pl 1 1 E 2 E QG 1 QG 2 Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission 4

Lorentz Invariance Viola1on (LIV) • Appears in many quantum gravity models • Leads to a modified dispersion rela,on: E 2 = p 2 + m 2 + f p ; ξ / M Pl ( ) • Leads to energy-dependent shiQ in pulsar phase: – n=1: linear case ξ=1: subluminal (slower than c) – n=2: quadra1c case ξ=-1: superluminal (faster than c) Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission 5

“Compe11veness” of LIV searches using pulsars - 3 more interes1ng now! 6

Construc1on of a profile likelihood Test sta1s1c: (using profile likelihood ra1o) Work with parameters of interest: MAGIC data: flux ( f ) constrained by addi,onal external spectral index (α) Nuisance parameters: data from FERMI (joint fit) mean pulse posi1on (Φ P2 ) mean pulse width (σ P2 ) 7

Probability Density Func1on for each event Individual event PDF depends on: (fiked) background spectral energy distribu1on h(E’), and PDF of the signal S(E’, Φ’|λ n ;ν) Uses signal normaliza1on g k (which depends on all nuisance parameters!) and background norm b k /τ 8

Probability Density Func1on for pulsar signal PDF of the signal contains the probability to obtain a pulsar event with reconstructed energy E’ and phase Φ’: PDF of the pulse form’: • But tested also asymmetric pulses and Lorentzian shapes • LIV induced phase delay modelled in Δφ(E|λ n ) Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission 9

Results (nuisance parameters) flux normaliza1on spectral index pulse posi1on pulse width Compa1ble with results in Ansoldi et al., A&A 582 (2016) A133 Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission 10

Results (LIV parameter λ) Linear case Quadra1c case Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission 11

Study of systema1cs Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission 12

New constraints 4.5/5.5 Ÿ 10 17 5.3/5.9 Ÿ 10 10 23/11/16 Markus Gaug, Status of LIV paper 13

Conclusions • Crab pulsar is in the game again for LIV! • Diversifica,on of sources important to eliminate source- intrinsic systema,cs. • Interest is now on the quadra,c case for photon ,me-of-flight! • With current data, have almost world-best limits on E QG2 • Future analyses (and combina,ons of likelihood) will reveal nature of the Crab pulses and possibly beder limits than GRBs! Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission 14