Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope

We analyze the timing of photons observed by the MAGIC telescope during a flare of the active galactic nucleus Mkn 501 for a possible correlation with energy, as suggested by some models of quantum gravity (QG), which predict a vacuum refractive index ≃1+n(E/MQGn)≃1+(E/MQGn)n, n=1,2n=1,2. Parametrizing the delay between γ  -rays of different energies as Δt=±τlEΔt=±τlE or Δt=±τqE2Δt=±τqE2, we find τl=(0.030±0.012) s/GeVτl=(0.030±0.012) s/GeV at the 2.5-σ   level, and τq=(3.71±2.57)×10−6 s/GeV2τq=(3.71±2.57)×10−6 s/GeV2, respectively. We use these results to establish lower limits MQG1>0.21×1018 GeVMQG1>0.21×1018 GeV and MQG2>0.26×1011 GeVMQG2>0.26×1011 GeV at the 95% C.L. Monte Carlo studies confirm the MAGIC sensitivity to propagation effects at these levels. Thermal plasma effects in the source are negligible, but we cannot exclude the importance of some other source effect.