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

Abstract: 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 \simeq 1 + (E/M_{QGn})^n, n = 1,2. Parametrizing the delay between gamma-rays of different energies as \Delta t =\pm\tau_l E or \Delta t =\pm\tau_q E^2, we find \tau_l=(0.030\pm0.012) s/GeV at the 2.5-sigma level, and \tau_q=(3.71\pm2.57)x10^{-6} s/GeV^2, respectively. We use these results to establish lower limits M_{QG1} > 0.21x10^{18} GeV and M_{QG2} > 0.26x10^{11} 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.

• The paper analyzes photon timing from Mkn 501 flares to test quantum gravity effects predicting energy-dependent light speed variations.
• Methodologies using energy cost functions and likelihood functions reveal delays of 0.030–0.048 s/GeV, defining lower bounds for QG mass scales.
• Insights from robust Monte Carlo simulations reinforce constraints on both linear and quadratic quantum gravity models, highlighting prospects for future multi-source studies.

Analysis of Quantum Gravity Effects Using MAGIC Telescope Observations of Mkn 501

The study utilizes photon timings from flares of the active galactic nucleus (AGN) Markarian 501 (Mkn 501) as observed by the MAGIC telescope to investigate potential quantum gravity (QG) effects. These effects, theorized in string-inspired models, suggest modifications in photon propagation due to a posited dispersive vacuum induced by QG fluctuations. The investigation centers on probing possible delays in photon arrival times as a function of energy—a signature of QG effects through a non-trivial refractive index.

Quantum Gravity Models and Refractive Index

The theoretical framework involves hypothesized variations in the speed of light, characterized by a refractive index influenced by QG dynamics. Models predict deviations proportional to photon energy, $E$, occuring linearly or quadratically with scales defined by $M_{\rm QG1}$ and $M_{\rm QG2}$ respectively. Analyzing photons from transiently intense flares in distant AGNs provides a means to test these predictions, given the large propagation path and energy spread, potentially enhancing sensitivity to such subtle effects.

Observational Methodology

The MAGIC telescope's observations over 31.6 hours of flaring activity in Mkn 501, with a detection energy threshold of around 150 GeV, exhibited significant gamma-ray flux variations, with peak flux intensities reaching $(11.0 \pm 0.3) \times 10^{-10}$ cm$^{-2}$s$^{-1}$. Variations were pronounced during short-duration flares, enabling a detailed assessment of energy-dependent timing variations across multiple energy bands.

Analyses and Results

The research applies two analytical methodologies to the data:

1. Energy Cost Function (ECF): This approach evaluates a photon's energy sum over an active flare section to infer time-delay parameters—$\tau_l$ for linear and $\tau_q$ for quadratic dispersions. Results signify a delay of $\tau_l=(0.030 \pm 0.012)$\,s/GeV, resulting in a lower bound for $M_{\rm QG1} > 0.21 \times 10^{18}$\,GeV at 95% C.L. For quadratic dependencies, $\tau_q=(3.71 \pm 2.57) \times 10^{-6}$s/GeV$^2$ was identified, with $M_{\rm QG2} > 0.26 \times 10^{11}$ GeV.
2. Likelihood Function: This statistical technique assesses photon arrival probabilities considering energy spectrum and time delay, yielding $\tau_l = (0.048 \pm 0.021)$s/GeV, reinforcing the ECF results.

Monte Carlo simulations affirmed the method's robustness, successfully recovering simulated propagation delays and returning null results when analyzing non-flaring periods.

Implications and Prospects

These findings suggest a moderate energy-dependent delay consistent with QG models, setting substantial bounds on potential quantum-gravitational mass scales. The results collaborate in expanding previous constraints, particularly on quadratic dispersive effects. Nonetheless, source-specific mechanisms cannot be conclusively ruled out as contributing factors to the observed delays.

Future advancements hinge on increasing the observation of fast, high-luminosity flares from multiple AGN at different redshifts and developing both theoretical understanding and observational methodologies to disentangle intrinsic source processes from QG propagation effects, ultimately refining our comprehension of QG phenomena.