Constraining photondispersion relations fromobservations of the Velapulsar with H.E.S.SM. Chrétiena,b, J. Bolmontb, A. Jacholkowskab

on behalf of the H.E.S.S. Collaboration34th International Cosmic Ray Conference29 July-6 August 2015, Den Haag

aspeakerbUniversité Pierre et Marie Curie, LPNHE, CNRS/IN2P3, Paris

Quantum gravity (QG)

Some approaches to QG predict a Lorentz invariance violation.Photon dispersion relation is energy dependent.

c′ ≈ c ×[1± n + 1

2

(E

EQG

)n], n =

{1 linear correction,2 quadratic correction

(1)

EQG is the QG energy scale to be constrained.Expected . EPlanck=1.2×1019 GeV.

Photons acquire a relative time delay:

∆t∆En ' ±

(1 + n)

2dc

1En

QG, (2)

Variable/transient/periodic γ rays emitters : GRBs, AGNs, pulsars.

Constraints on linear term are presented using data from Vela pulsar.

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 2/13

Linear phase lag parameter

Lorentz invariance violation leads to a delay in phasogram:

Period (s)

∆Φ = ∆t × P = ϕl ×∆Elinear phase lag parameter (TeV−1)

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 3/13

The 5th H.E.S.S. telescope

A 28 m diameter telescope were added to the H.E.S.S. array in 2012.

Dish:614 m2 mirror area36 m focal length

Camera:2048 pixels3600 images/s

Threshold energy∼ 20 GeV

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 4/13

Detection of Vela pulsar

Stacking data from March 2012 to April 2014 lead to 11σ significance.∼ 10000 pulsed γ rays in P2 from ∼ 20 GeV up to 120 GeV.

See M. Gajdus’s talk in Parallel GA16 H.E.S.S. session.

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 5/13

The method

Introduced by Martinez & Errando and adapted to pulsars in the following.A maximum likelihood is computed over all events in dataset:

L(ϕl) =∏

i

P(Ei ,Φi ;ϕl). (3)

P(E ,Φ,ϕl) includes two contributions:Background (mis-reconstructed γ rays)Pulsed signal distribution:

Ps(E ,Φ;ϕl) = C∫ ∞

0Aeff (E?)Λs(E?)R(E ,E?)Fs

(Φ− ϕlE?

)dE? (4)

∫∞0 dE? : convolution over true energy

Aeff : H.E.S.S. acceptanceΛs : emission spectrumR : Point spread function (energy bias & resolution)Fs : phasogram as it would be measured without Lorentz invariance violation

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 6/13

Application on Vela dataset

Spectrum from (ON-OFF) distribution."Template" phasogram is parametrized at the lowest energies.

An asymmetrical Lorentzian gives the best significance (same as Fermi).

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 7/13

Application on Vela dataset

The phase lag is negligeable!

Errors calibration is mandatory.

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 8/13

Calibration

Perform toy Monte Carlo simulations ofVela pulsar Mock data.

Phase lag reconstruction is satisfactory

Confidence intervals are calibratedThey ensure the proper coverage

Systematics are evaluatedtemplate parametrizationspectral index uncertaintybackground contaminationetc.

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 9/13

Summary of systematics

Change in ϕl (10−2/TeV) Change in ϕl (10−2/TeV)

lower bound upper bound

Fs < 1 < 0.6

Spectral index < 1 < 0.4

Zenith dispersion < 2 < 0.7

Background < 0.8 < 0.3

Calibration curve < 0.2 < 0.2

Acceptance < 1 < 1

Energy resolution < 0.6 < 1

Energy bias < 0.3 < 1

Energy reconstruction < 1 < 1

Total < 3 < 3

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 10/13

Results

Phase lag parameter (1σ):

ϕ̂l =(−2.0± 5.0(stat) ± 3.0(sys)

)× 10−2 TeV−1. (5)

95% confidence level limits on quantum gravity energy (d = 294 pc):

E lQG > 3.72× 1015 GeV, superluminal (6)

E lQG > 3.95× 1015 GeV, subluminal (7)

Results are ∼ 1 O.M. below the Crab limits by VERITAS

Possible explanations:Factor ∼ 10 from distance.Factor ∼ 3 from periodVERITAS observe γ rays > 120 GeV.

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 11/13

Conclusions and prospect

Limits on linear modification of photon dispersion relations due toLorentz invariance violation have been obtained with Vela pulsar.Results are ∼ 1 O.M. below the Crab limit by VERITAS.

but the Crab is faster & fartherVERITAS observe γ ray emission > 120 GeV.

Limits can be improved by:Better γ/hadron separationLonger observation.

Considering 240h of Vela observation and extrapolating a power lawspectrum of index Γ=4 up to 400 GeV, a sensitivity of ∼ 1× 1017 GeVcould be reached.

Mathieu Chrétien . Photon dispersion relations with Vela . 34th ICRC . July 2015 12/13

Bedankt vooruw aandacht!