A delayed 400 GeV photon from GRB 221009A and implication on the intergalactic magnetic field

The strength of the intergalactic magnetic field (IGMF) is a crucial, yet undetermined, parameter in astrophysics, potentially linked to the universe's origin and evolution, and carrying information about primordial magnetic fields. Accurately measuring the IGMF presents a significant challenge. One promising method involves analyzing the arrival times of gamma rays from extragalactic TeV transients like gamma-ray bursts (GRBs) and blazars. High-energy gamma rays, before reaching Earth, interact with the diffuse infrared background, producing ultra-relativistic electron-positron (e⁺e⁻) pairs. These pairs then scatter off cosmic microwave background (CMB) photons, boosting their energy. Unless the IGMF is extremely weak (≤10⁻²⁰ G), the IGMF significantly influences the arrival time of these secondary gamma rays, providing a means to constrain or directly measure the IGMF strength. This approach has been applied to GRB 940217 and other GRBs, yielding IGMF limits between 10⁻²¹–10⁻¹⁷ G. GRB 221009A, notable for its immense power (~10⁵⁵ erg isotropic equivalent gamma-ray energy), low redshift (z = 0.151), and strong TeV gamma-ray emission, is particularly suitable for this analysis, offering an ideal opportunity to probe the IGMF through its cascade emission. The burst triggered Fermi-GBM and LAT, with LAT detecting strong high-energy emission, and LHAASO observing emission above 10 TeV within roughly 2000 s post-trigger. DAMPE also observed increased counts shortly after the trigger. This paper focuses on analyzing long-term Fermi-LAT data to investigate the possibility of detecting delayed gamma-ray emissions from GRB 221009A and their implications for IGMF.

Previous research utilized the delay in gamma-ray arrival times from extragalactic sources to constrain the IGMF. Plaga (1995) initially proposed this method. Subsequent studies applied this technique to GRB 940217 and other GRBs like GRB 130427A and GRB 190114C, which exhibited powerful very high-energy gamma-ray radiation. These studies provided IGMF limits ranging from 10⁻²¹ to 10⁻¹⁷ G. The unique characteristics of GRB 221009A—its exceptional power, low redshift, and intense TeV emission—make it an especially valuable target for refining these IGMF constraints.

The study analyzed long-term Fermi-LAT data (T₀ + 0.05 - T₀ + 250 days) above 500 MeV within 15 degrees of GRB 221009A's Swift/UVOT localization. Pass 8 R3 data were used, applying quality filters to exclude events from zenith angles > 90° and employing standard data quality cuts. Energy spectral analysis used the Fermitools package and the P8R3_SOURCE_V3 instrument response function. The initial model included galactic and isotropic diffuse emission templates and sources from the Fourth Fermi-LAT source catalog. GRB 221009A was modeled as a point source with a power-law spectral shape. The data were divided into three time intervals (0.05–0.3 days, 0.3–1 days, and 0.3–250 days post-trigger) for unbinned likelihood analysis, with the spectral index fixed at 2 for each energy bin. The spectral energy distributions (SEDs) were calculated for each time interval. To investigate the origin of the delayed 400 GeV photon, two models were considered: the Synchrotron Self-Compton (SSC) model and the cascade emission model. The ELMAG 3.03 package was used for Monte Carlo simulations of the cascade scenario with different IGMF strengths (e.g., 4 × 10⁻¹⁷ G, 1 × 10⁻¹⁶ G, 1 × 10⁻¹⁷ G, 1 × 10⁻¹⁸ G), assuming a turbulent magnetic field with a coherence length of 1 Mpc. The intrinsic energy spectrum of GRB 221009A was modeled as a power law with an index of 2.4. The probabilities of detecting one cascade photon above 100 GeV within the given time intervals were calculated using the simulated spectra and the Fermi-LAT exposure. The sensitivity of ground-based telescopes (H.E.S.S., MAGIC, and CTA) to detect cascade emission was also assessed for different IGMF strengths.

A significant 400 GeV photon was detected by Fermi-LAT at approximately 0.4 days after the GRB 221009A trigger. This photon lacked accompanying prominent low-energy emission. The spatial and temporal coincidence with GRB 221009A was confirmed, with a significance level of 4.4σ. The SEDs for different time intervals showed distinct behaviors, with the later intervals (0.3–1 days and 0.3–250 days) showing only the 400 GeV photon. The SSC model was found to be insufficient to explain the observed 400 GeV photon, particularly in the later time intervals. The cascade emission scenario, with an IGMF strength of about 4 × 10⁻¹⁷ G, provided a more compelling explanation for the delayed 400 GeV photon. The probability of observing one photon above 100 GeV via cascade emission within 0.3-1 days and 0.3-250 days was estimated to be ~2% and ~20.5%, respectively, which is significantly higher than that expected from the SSC model. Monte Carlo simulations using the ELMAG 3.03 package supported the cascade scenario, with the estimated IGMF strength being comparable to lower limits from TeV blazars. The analysis also ruled out weaker IGMF strengths (≤10⁻¹⁸ G). The future potential of Cherenkov Telescopes (CTA) to measure such cascade emission and further constrain the IGMF was discussed. The analysis considered two intrinsic spectral models: a power law (PL) and a power law with an exponential cutoff (PLEcut). Both models support the cascade scenario and the preferred IGMF value.

The detection of the delayed 400 GeV photon from GRB 221009A, coupled with the inadequacy of the SSC model and the strong support from the cascade emission model, provides compelling evidence for an IGMF strength of approximately 4 × 10⁻¹⁷ G. This finding is consistent with previous limits derived from TeV blazar observations. The high optical depth of the universe to high-energy gamma rays indicates the intrinsic spectrum of GRB 221009A likely extends to even higher energies. The cascade emission model, which successfully explains the observed delayed photon, offers strong support for this conclusion. The relatively low probability of observing such a delayed photon within the given timeframe does not invalidate the findings, as it reflects the rarity of such high-energy events resulting from cascade emissions. The use of multiple intrinsic spectrum models to account for uncertainty at energies beyond 13 TeV strengthens the conclusion. While the study focuses on GRB 221009A, the methodology and findings have broader implications for IGMF research and could inform future studies of other high-energy transients.

This study reports the detection of a delayed 400 GeV photon from GRB 221009A, providing strong evidence for an IGMF strength of around 4 × 10⁻¹⁷ G. The cascade emission model, supported by Monte Carlo simulations, offers a more convincing explanation than the SSC model. Future observations with ground-based telescopes like CTA will offer further opportunities to test this estimate and refine our understanding of the IGMF. Further analysis with more detailed modeling of the intrinsic GRB spectrum above 13 TeV would further strengthen this analysis.

The analysis relies on the assumption of a specific IGMF model (turbulent field with a coherence length of 1 Mpc). The intrinsic spectrum of GRB 221009A above 13 TeV is still uncertain, impacting the accuracy of the cascade emission simulations. The low probability of observing the 400 GeV photon via the cascade process, although consistent with the model's predictions, introduces some uncertainty. Future observations with increased sensitivity and improved angular resolution will be essential for validating the IGMF estimate and exploring additional aspects of GRB 221009A’s high-energy emission.