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

1 35th Interna,onal Cosmic Ray Conference, Bexco, Busan, Korea

MAGIC Pulsar data

Inter-pulse P2 has been detected significantly up to 1.2 TeV. Joining 19 different

• bserva1on 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)

3

• Appears in many quantum gravity models
• Leads to a modified dispersion rela,on:
• In low-energy limit, can be expanded:

E 2 = p2 + m2 + f p;ξ / MPl

( )

f p;ξ / MPl

( )

f p;ξ / MPl

( ) ≈ EPlξ (1) p +ξ (2) p2 + ξ (3)

EPl p3 + ξ (4) E 2

Pl

p(4) +…

affect affect low-energy physics high-energy physics

Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission

Lorentz Invariance Viola1on (LIV)

4

• Appears in many quantum gravity models
• Leads to a modified dispersion rela,on:
• In low-energy limit, can be expanded:

E 2 = p2 + m2 + f p;ξ / MPl

( )

f p;ξ / MPl

( )

f p;ξ / MPl

( ) ≈ EPlξ (1) p +ξ (2) p2 + ξ (3)

EPl p3 + ξ (4) E 2

Pl

p(4) +…

Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission

1 EQG1 1 E 2

QG2

Lorentz Invariance Viola1on (LIV)

5

• Appears in many quantum gravity models
• Leads to a modified dispersion rela,on:
• 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)

E 2 = p2 + m2 + f p;ξ / MPl

( )

Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission

“Compe11veness” of LIV searches using pulsars

6

more interes1ng now!

• 3

Construc1on of a profile likelihood

Work with parameters of interest: Nuisance parameters:

flux (f)

spectral index (α) mean pulse posi1on (ΦP2) mean pulse width (σP2)

constrained by addi,onal external data from FERMI (joint fit)

MAGIC data:

7

Test sta1s1c: (using profile likelihood ra1o)

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’|λn;ν) Uses signal normaliza1on gk (which depends on all nuisance parameters!) and background norm bk/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’:

9

PDF of the pulse form’:

• But tested also asymmetric pulses and Lorentzian shapes
• LIV induced phase delay modelled in Δφ(E|λn)

Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission

Compa1ble with results in Ansoldi et al., A&A 582 (2016) A133

Results (nuisance parameters)

10

flux normaliza1on spectral index pulse posi1on pulse width

Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission

Quadra1c case

Results (LIV parameter λ)

11

Linear case

Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission

Study of systema1cs

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

New constraints

23/11/16

Markus Gaug, Status of LIV paper 13

4.5/5.5Ÿ1017 5.3/5.9Ÿ1010

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 EQG2
• Future analyses (and combina,ons of likelihood) will reveal

nature of the Crab pulses and possibly beder limits than GRBs!

14 Markus Gaug, Constraining LIV using the Crab Pulsar TeV emission