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Abstract The Cherenkov Telescope Array (CTA) is a next-generation ground-based observatory for gamma-ray astronomy at very high energies. The Large-Sized Telescope prototype (LST-1) is located at the CTA-North site, on the Canary Island of La Palma. LSTs are designed to provide optimal performance in the lowest part of the energy range covered by CTA, down to ≃20 GeV. LST-1 started performing astronomical observations in 2019 November, during its commissioning phase, and it has been taking data ever since. We present the first LST-1 observations of the Crab Nebula, the standard candle of very-high-energy gamma-ray astronomy, and use them, together with simulations, to assess the performance of the telescope. LST-1 has reached the expected performance during its commissioning period—only a minor adjustment of the preexisting simulations was needed to match the telescope’s behavior. The energy threshold at trigger level is around 20 GeV, rising to ≃30 GeV after data analysis. Performance parameters depend strongly on energy, and on the strength of the gamma-ray selection cuts in the analysis: angular resolution ranges from 0.°12–0.°40, and energy resolution from 15%–50%. Flux sensitivity is around 1.1% of the Crab Nebula flux above 250 GeV for a 50 hr observation (12% for 30 minutes). The spectral energy distribution (in the 0.03–30 TeV range) and the light curve obtained for the Crab Nebula agree with previous measurements, considering statistical and systematic uncertainties. A clear periodic signal is also detected from the pulsar at the center of the Nebula.

Abstract Gamma-ray astronomy has become one of the main experimental ways to test the modified dispersion relations (MDRs) of photons in vacuum, obtained in some attempts to formulate a theory of quantum gravity. The MDRs in use imply time delays that depend on the energy and that increase with distance following some function of redshift. The use of transient, or variable, distant and highly energetic sources already allows us to set stringent limits on the energy scale related to this phenomenon, usually thought to be of the order of the Planck energy, but robust conclusions on the existence of MDR-related propagation effects still require the analysis of a large population of sources. In order to gather the biggest sample of sources possible for MDR searches at teraelectronvolt energies, the H.E.S.S., MAGIC, and VERITAS collaborations enacted a joint task force to combine all their relevant data to constrain the quantum gravity energy scale. In the present article, the likelihood method used to combine the data and provide a common limit is described in detail and tested through simulations of recorded data sets for a gamma-ray burst, three flaring active galactic nuclei, and two pulsars. Statistical and systematic errors are assessed and included in the likelihood as nuisance parameters. In addition, a comparison of two different formalisms for distance dependence of the time lags is performed for the first time. In a second article, to appear later, the method will be applied to all relevant data from the three experiments.