talk at ICRC 2015. Some approaches to Quantum Gravity (QG) predict a modification of photon dispersion relations due to a breaking of Lorentz invariance. The effect is expected to affect photons near an effective QG energy scale. This scale has been constrained by observing gamma rays emitted from variable astrophysical sources such as gamma-ray bursts and flaring active galactic nuclei. Pulsars exhibit a periodic emission of possibly ms time scale. In 2014, the H.E.S.S. experiment reported the detection down to 20 GeV of gamma rays from the Vela pulsar having a periodicity of 89 ms. Using a likelihood analysis, calibrated with a dedicated Monte-Carlo procedure, we obtain the first limit on QG energy scale with the Vela pulsar. In this paper, the method and calibration procedure in use will be described and the results will be discussed. link to proceeding: http://arxiv.org/abs/1509.03545

1. Constraining photon
dispersion relations from
observations of the Vela
pulsar with H.E.S.S
M. Chrétiena,b
, J. Bolmontb
, A. Jacholkowskab
on behalf of the H.E.S.S. Collaboration
34th
International Cosmic Ray Conference
29 July-6 August 2015, Den Haag
a
speaker
b
Université Pierre et Marie Curie, LPNHE, CNRS/IN2P3, Paris

2. 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)
2
d
c
1
En
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

3. Linear phase lag parameter
Lorentz invariance violation leads to a delay in phasogram:
Period (s)
∆Φ = ∆t × P = ϕl × ∆E
linear phase lag parameter (TeV−1
)
Mathieu Chrétien . Photon dispersion relations with Vela . 34th
ICRC . July 2015 3/13

4. 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 area
36 m focal length
Camera:
2048 pixels
3600 images/s
Threshold energy
∼ 20 GeV
Mathieu Chrétien . Photon dispersion relations with Vela . 34th
ICRC . July 2015 4/13

5. 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

6. 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
∞
0
Aeff (E )Λs(E )R(E, E )Fs Φ − ϕlE dE (4)
∞
0
dE : convolution over true energy
Aeff : H.E.S.S. acceptance
Λs : emission spectrum
R : 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

7. 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

8. 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

9. Calibration
Perform toy Monte Carlo simulations of
Vela pulsar Mock data.
Phase lag reconstruction is satisfactory
Confidence intervals are calibrated
They ensure the proper coverage
Systematics are evaluated
template parametrization
spectral index uncertainty
background contamination
etc.
Mathieu Chrétien . Photon dispersion relations with Vela . 34th
ICRC . July 2015 9/13

10. 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

11. Results
Phase lag parameter (1σ):
ˆϕl = −2.0 ± 5.0(stat) ± 3.0(sys) × 10−2
TeV−1
. (5)
95% confidence level limits on quantum gravity energy (d = 294 pc):
El
QG > 3.72 × 1015
GeV, superluminal (6)
El
QG > 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 period
VERITAS observe γ rays > 120 GeV.
Mathieu Chrétien . Photon dispersion relations with Vela . 34th
ICRC . July 2015 11/13

12. Conclusions and prospect
Limits on linear modification of photon dispersion relations due to
Lorentz invariance violation have been obtained with Vela pulsar.
Results are ∼ 1 O.M. below the Crab limit by VERITAS.
but the Crab is faster & farther
VERITAS observe γ ray emission > 120 GeV.
Limits can be improved by:
Better γ/hadron separation
Longer observation.
Considering 240h of Vela observation and extrapolating a power law
spectrum of index Γ=4 up to 400 GeV, a sensitivity of ∼ 1× 1017
GeV
could be reached.
Mathieu Chrétien . Photon dispersion relations with Vela . 34th
ICRC . July 2015 12/13

13. Bedankt voor
uw aandacht!