Blazars exhibit strong variability across the entire electromagnetic spectrum, including periods of high-flux states commonly known as flares. The physical mechanisms in blazar jets responsible for flares remain poorly understood to date. Our aim is to better understand the emission mechanisms during blazar flares using X-ray polarimetry and broadband observations from the archetypical TeV blazar Mrk 421, which can be studied with higher accuracy than other blazars that are dimmer and/or located farther away. We studied a flaring activity from December 2023 that was characterized from radio to very high-energy (VHE; E $>0.1$,TeV) gamma rays with MAGIC Fermi -LAT Swift XMM-Newton and several optical and radio telescopes. These observations included, for the first time for a gamma-ray flare of a blazar, simultaneous X-ray polarization measurements with IXPE, in addition to optical and radio polarimetry data. We quantify the variability and correlations among the multi-band flux and polarization measurements, and describe the varying broadband emission within a theoretical scenario constrained by the polarization data. We find substantial variability in both X-rays and VHE gamma rays throughout the campaign, with the highest VHE flux above 0.2,TeV occurring during the IXPE observing window, and exceeding twice the flux of the Crab Nebula. However, the VHE and X-ray spectra are on average softer, and the correlation between these two bands is weaker than those reported in the previous flares of Mrk 421. IXPE reveals an X-ray polarization degree significantly higher than that at radio and optical frequencies, similar to previous results for Mrk 421 and other high synchrotron peaked blazars. Differently to past observations, the X-ray polarization angle varies by ∼100^∘ on timescales of days, and the polarization degree changes by more than a factor of 4. The highest X-ray polarization degree, analyzed in 12,hr time intervals, reaches $26±2%$, around which an X-ray counter-clockwise hysteresis loop is measured with XMM-Newton . It suggests that the X-ray emission comes from particles close to the high-energy cutoff, hence possibly probing an extreme case of the Turbulent Extreme Multi-Zone model for which the chromatic trend in the polarization may be more pronounced than theoretically predicted. We model the broadband emission with a simplified stratified jet model throughout the flare. The polarization measurements imply an electron distribution in the X-ray emitting region with a very high minimum Lorentz factor (γ'_ min ≳10^4), which is expected in electron-ion plasma, as well as a variation of the emitting region size of up to a factor of 3 during the flaring activity. We find no correlation between the fluxes and the evolution of the model parameters, which indicates a stochastic nature of the underlying physical mechanism that likely explains the lack of a tight X-ray/VHE correlation during this flaring activity. Such behavior would be expected in a highly turbulent electron-ion plasma crossing a shock front.

The BL Lacertae object VER J0521+211 underwent a notable flaring episode in February 2020. A short-term monitoring campaign, led by the MAGIC (Major Atmospheric Gamma Imaging Cherenkov) collaboration, covering a wide energy range from radio to very high-energy (VHE, 100 GeV < E < 100 TeV) gamma rays was organised to study its evolution. These observations resulted in a consistent detection of the source over six consecutive nights in the VHE gamma-ray domain. Combining these nightly observations with an extensive set of multi-wavelength data made modelling of the blazar's spectral energy distribution (SED) possible during the flare. This modelling was performed with a focus on two plausible emission mechanisms: (i) a leptonic two-zone synchrotron-self-Compton scenario, and (ii) a lepto-hadronic one-zone scenario. Both models effectively replicated the observed SED from radio to the VHE gamma-ray band. Furthermore, by introducing a set of evolving parameters, both models were successful in reproducing the evolution of the fluxes measured in different bands throughout the observing campaign. Notably, the lepto-hadronic model predicts enhanced photon and neutrino fluxes at ultra-high energies (E > 100 TeV). While the photon component, generated via decay of neutral pions, is not directly observable as it is subject to intense pair production (and therefore extinction) through interactions with the cosmic microwave background photons, neutrino detectors (e.g. IceCube) can probe the predicted neutrino component. Finally, the analysis of the gamma-ray spectra, observed by MAGIC and the Fermi-LAT telescopes, yielded a conservative 95% confidence upper limit of z <= 0.244 for the redshift of this blazar.

Context. The supernova remnant (SNR) W44 and its surroundings are a prime target for studying the acceleration of cosmic rays (CRs). Several previous studies established an extended gamma-ray emission that is set apart from the radio shell of W44. This emission is thought to originate from escaped high-energy CRs that interact with a surrounding dense molecular cloud complex. Aims. We present a detailed analysis of Fermi-LAT data with an emphasis on the spatial and spectral properties of W44 and its surroundings. We also report the results of the observations performed with the MAGIC telescopes of the northwestern region of W44. Finally, we present an interpretation model to explain the gamma-ray emission of the SNR and its surroundings. Methods. We first performed a detailed spatial analysis of 12 years of Fermi-LAT data at energies above 1 GeV, in order to exploit the better angular resolution, while we set a threshold of 100MeV for the spectral analysis. We performed a likelihood analysis of 174 hours of MAGIC data above 130 GeV using the spatial information obtained with Fermi-LAT. Results. The combined spectra of Fermi-LAT and MAGIC, extending from 100MeV to several TeV, were used to derive constraints on the escape of CRs. Using a time-dependent model to describe the particle acceleration and escape from the SNR, we show that the maximum energy of the accelerated particles has to be ' 40 GeV. However, our gamma-ray data suggest that a small number of lower-energy particles also needs to escape. We propose a novel model, the broken-shock scenario, to account for this effect and explain the gamma-ray emission.

Many of the blazars observed by Fermi actually have the peak of their time-averaged gamma-ray emission outside the ∼ GeV Fermi energy range, at ∼ MeV energies. The detailed shape of the emission spectrum around the ∼ MeV peak places important constraints on acceleration and radiation mechanisms in the blazar jet and may not be the simple broken power law obtained by extrapolating from the observed X-ray and GeV gamma-ray spectra. In particular, state-of-the-art simulations of particle acceleration by shocks show that a significant fraction (possibly up to ≈ 90%) of the available energy may go into bulk, quasi-thermal heating of the plasma crossing the shock rather than producing a non-thermal power law tail. Other “gentler" but possibly more pervasive acceleration mechanisms such as shear acceleration at the jet boundary may result in a further build-up of the low-energy (γ≲ 10^2) electron/positron population in the jet. As already discussed for the case of gamma-ray bursts, the presence of a low-energy, Maxwellian-like “bump” in the jet particle energy distribution can strongly affect the spectrum of the emitted radiation, e.g., producing an excess over the emission expected from a power-law extrapolation of a blazar's GeV-TeV spectrum. We explore the potential detectability of the spectral component ascribable to a hot, quasi-thermal population of electrons in the high-energy emission of flat-spectrum radio quasars (FSRQ). We show that for typical FSRQ physical parameters, the expected spectral signature is located at ∼ MeV energies. For the brightest Fermi FSRQ sources, the presence of such a component will be constrained by the upcoming MeV Compton Spectrometer and Imager (COSI) satellite.

Aims. Mrk 421 was in its most active state around early 2010, which led to the highest TeV gamma-ray flux ever recorded from any active galactic nuclei (AGN). We aim to characterize the multiwavelength behavior during this exceptional year for Mrk 421, and evaluate whether it is consistent with the picture derived with data from other less exceptional years. Methods. We investigated the period from November 5, 2009, (MJD 55140) until July 3, 2010, (MJD 55380) with extensive coverage from very-high-energy (VHE; E>100 GeV) gamma rays to radio with MAGIC, VERITAS, Fermi-LAT, RXTE, Swift, GASP-WEBT, VLBA, and a variety of additional optical and radio telescopes. We characterized the variability by deriving fractional variabilities as well as power spectral densities (PSDs). In addition, we investigated images of the jet taken with VLBA and the correlation behavior among different energy bands. Results. Mrk 421 was in widely different states of activity throughout the campaign, ranging from a low-emission state to its highest VHE flux ever recorded. We find the strongest variability in X-rays and VHE gamma rays, and PSDs compatible with power-law functions with indices around 1.5. We observe strong correlations between X-rays and VHE gamma rays at zero time lag with varying characteristics depending on the exact energy band. We also report a marginally significant (similar to 3 sigma) positive correlation between high-energy (HE; E>100 MeV) gamma rays and the ultraviolet band. We detected marginally significant (similar to 3 sigma) correlations between the HE and VHE gamma rays, and between HE gamma rays and the X-ray, that disappear when the large flare in February 2010 is excluded from the correlation study, hence indicating the exceptionality of this flaring event in comparison with the rest of the campaign. The 2010 violent activity of Mrk 421 also yielded the first ejection of features in the VLBA images of the jet of Mrk 421. Yet the large uncertainties in the ejection times of these unprecedented radio features prevent us from firmly associating them to the specific flares recorded during the 2010 campaign. We also show that the collected multi-instrument data are consistent with a scenario where the emission is dominated by two regions, a compact and extended zone, which could be considered as a simplified implementation of an energy-stratified jet as suggested by recent IXPE observations.

Axion-like particles (ALPs) are pseudo-Nambu–Goldstone bosons that emerge in various theories beyond the standard model. These particles can interact with high-energy photons in external magnetic fields, influencing the observed gamma-ray spectrum. This study analyzes 41.3 h of observational data from the Perseus Galaxy Cluster collected with the MAGIC telescopes. We focused on the spectra the radio galaxy in the center of the cluster: NGC 1275. By modeling the magnetic field surrounding this target, we searched for spectral indications of ALP presence. Despite finding no statistical evidence of ALP signatures, we were able to exclude ALP models in the sub-micro electronvolt range. Our analysis improved upon previous work by calculating the full likelihood and statistical coverage for all considered models across the parameter space. Consequently, we achieved the most stringent limits to date for ALP masses around 50 neV, with cross sections down to gaγ=3×10−12 GeV−1.

Gamma-ray bursts (GRBs) are explosive transient events occurring at cosmological distances, releasing a large amount of energy as electromagnetic radiation over several energy bands. We report the detection of the long GRB~201216C by the MAGIC telescopes. The source is located at $z=1.1$ and thus it is the farthest one detected at very high energies. The emission above \SI{70}{\GeV} of GRB~201216C is modelled together with multi-wavelength data within a synchrotron and synchrotron-self Compton (SSC) scenario. We find that SSC can explain the broadband data well from the optical to the very-high-energy band. For the late-time radio data, a different component is needed to account for the observed emission. Differently from previous GRBs detected in the very-high-energy range, the model for GRB~201216C strongly favors a wind-like medium. The model parameters have values similar to those found in past studies of the afterglows of GRBs detected up to GeV energies.

The BL Lac 1ES 2344+514 is known for temporary extreme properties (e.g., a shift of the synchrotron SED peak energy $\nu_{synch,p}$ above 1keV). While those extreme states were so far observed only during high flux levels, additional multi-year observing campaigns are required to achieve a coherent picture. Here, we report the longest investigation of the source from radio to VHE performed so far, focusing on a systematic characterisation of the intermittent extreme states. While our results confirm that 1ES 2344+514 typically exhibits $\nu_{synch,p}>$1keV during elevated flux periods, we also find periods where the extreme state coincides with low flux activity. A strong spectral variability thus happens in the quiescent state, and is likely caused by an increase of the electron acceleration efficiency without a change in the electron injection luminosity. We also report a strong X-ray flare (among the brightest for 1ES 2344+514) without a significant shift of $\nu_{synch,p}$. During this particular flare, the X-ray spectrum is among the softest of the campaign. It unveils complexity in the spectral evolution, where the common harder-when-brighter trend observed in BL Lacs is violated. During a low and hard X-ray state, we find an excess of the UV flux with respect to an extrapolation of the X-ray spectrum to lower energies. This UV excess implies that at least two regions contribute significantly to the infrared/optical/ultraviolet/X-ray emission. Using the simultaneous MAGIC, XMM-Newton, NuSTAR, and AstroSat observations, we argue that a region possibly associated with the 10 GHz radio core may explain such an excess. Finally, we investigate a VHE flare, showing an absence of simultaneous variability in the 0.3-2keV band. Using a time-dependent leptonic modelling, we show that this behaviour, in contradiction to single-zone scenarios, can instead be explained by a two-component model.

We perform the first broadband study of Mrk421 from radio to TeV gamma rays with simultaneous measurements of the X-ray polarization from IXPE. The data were collected within an extensive multiwavelength campaign organized between May and June 2022 using MAGIC, Fermi-LAT, NuSTAR, XMM-Newton, Swift, and several optical and radio telescopes to complement IXPE. During the IXPE exposures, the measured 0.2-1 TeV flux is close to the quiescent state and ranges from 25% to 50% of the Crab Nebula without intra-night variability. Throughout the campaign, the VHE and X-ray emission are positively correlated at a $4\sigma$ significance level. The IXPE measurements unveil a X-ray polarization degree that is a factor of 2-5 higher than in the optical/radio bands; that implies an energy-stratified jet in which the VHE photons are emitted co-spatially with the X-rays, in the vicinity of a shock front. The June 2022 observations exhibit a rotation of the X-ray polarization angle. Despite no simultaneous VHE coverage being available during a large fraction of the swing, the Swift-XRT monitoring unveils an X-ray flux increase with a clear spectral hardening. It suggests that flares in high synchrotron peaked blazars can be accompanied by a polarization angle rotation, as observed in some flat spectrum radio quasars. Finally, during the polarization angle rotation, NuSTAR data reveal two contiguous spectral hysteresis loops in opposite directions (clockwise and counter-clockwise), implying important changes in the particle acceleration efficiency on $\sim$hour timescales.

PG 1553+113 is one of the few blazars with a convincing quasi-periodic emission in the gamma-ray band. The source is also a very high-energy (VHE; >100 GeV) gamma-ray emitter. To better understand its properties and identify the underlying physical processes driving its variability, the MAGIC Collaboration initiated a multiyear, multiwavelength monitoring campaign in 2015 involving the OVRO 40-m and Medicina radio telescopes, REM, KVA, and the MAGIC telescopes, Swift and Fermi satellites, and the WEBT network. The analysis presented in this paper uses data until 2017 and focuses on the characterization of the variability. The gamma-ray data show a (hint of a) periodic signal compatible with literature, but the X-ray and VHE gamma-ray data do not show statistical evidence for a periodic signal. In other bands, the data are compatible with the gamma-ray period, but with a relatively high p-value. The complex connection between the low and high-energy emission and the non-monochromatic modulation and changes in flux suggests that a simple one-zone model is unable to explain all the variability. Instead, a model including a periodic component along with multiple emission zones is required.

Instruments for gamma-ray astronomy at Very High Energies (E>100 GeV) have traditionally derived their scientific results through proprietary data and software. Data standardisation has become a prominent issue in this field both as a requirement for the dissemination of data from the next generation of gamma-ray observatories and as an effective solution to realise public data legacies of current-generation instruments. Specifications for a standardised gamma-ray data format have been proposed as a community effort and have already been successfully adopted by several instruments. We present the first production of standardised data from the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes. We converted 166 h of observations from different sources and validated their analysis with the open-source software Gammapy. We consider six data sets representing different scientific and technical analysis cases and compare the results obtained analysing the standardised data with open-source software against those produced with the MAGIC proprietary data and software. Aiming at a systematic production of MAGIC data in this standardised format, we also present the implementation of a database-driven pipeline automatically performing the MAGIC data reduction from the calibrated down to the standardised data level. In all the cases selected for the validation, we obtain results compatible with the MAGIC proprietary software, both for the manual and for the automatic data productions. Part of the validation data set is also made publicly available, thus representing the first large public release of MAGIC data. This effort and this first data release represent a technical milestone toward the realisation of a public MAGIC data legacy.

The nearby elliptical galaxy M87 contains one of the only two supermassive black holes whose emission surrounding the event horizon has been imaged by the Event Horizon Telescope (EHT). In 2018, more than two dozen multi-wavelength (MWL) facilities (from radio to gamma-ray energies) took part in the second M87 EHT campaign. The goal of this extensive MWL campaign was to better understand the physics of the accreting black hole M87*, the relationship between the inflow and inner jets, and the high-energy particle acceleration. Understanding the complex astrophysics is also a necessary first step towards performing further tests of general relativity. The MWL campaign took place in April 2018, overlapping with the EHT M87* observations. We present a new, contemporaneous spectral energy distribution (SED) ranging from radio to very high energy (VHE) gamma-rays, as well as details of the individual observations and light curves. We also conduct phenomenological modelling to investigate the basic source properties. We present the first VHE gamma-ray flare from M87 detected since 2010. The flux above 350 GeV has more than doubled within a period of about 36 hours. We find that the X-ray flux is enhanced by about a factor of two compared to 2017, while the radio and millimetre core fluxes are consistent between 2017 and 2018. We detect evidence for a monotonically increasing jet position angle that corresponds to variations in the bright spot of the EHT image. Our results show the value of continued MWL monitoring together with precision imaging for addressing the origins of high-energy particle acceleration. While we cannot currently pinpoint the precise location where such acceleration takes place, the new VHE gamma-ray flare already presents a challenge to simple one-zone leptonic emission model approaches, and emphasises the need for combined image and spectral modelling.

The recently discovered population of faint FR0 radiogalaxies has been interpreted as the extension to low power of the classical FRI sources. Their radio emission appears to be concentrated in very compact (pc-scale) cores, any extended emission is very weak or absent and VLBI observations show that jets are already mildly or sub-relativistic at pc scales. Based on these observational properties we propose here that the jets of FR0s are strongly decelerated and disturbed at pc scale by hydrodynamical instabilities.}{With the above scenario in mind, we study the dynamics of a low-power relativistic jet propagating into a confining external medium, focusing on the effects of entrainment and mixing promoted by the instabilities developing at the jet-environment interface downstream of a recollimation shock. We perform a 3D relativistic hydrodynamical simulation of a recollimated jet by means of the state-of-the-art code PLUTO. The jet is initially conical, relativistic (with initial Lorentz Factor $\Gamma$=5), cold and light with respect to the confining medium, whose pressure is assumed to slowly decline with distance. The magnetic field is assumed to be dynamically unimportant. The 3D simulation shows that, after the first recollimation/reflection shock system, a rapidlygrowing instability develops, as a result of the interplay between recollimation-induced instabilities and Richtmyer-Meshkov modes. In turn, the instabilities promote strong mixing and entrainment that rapidly lead to the deceleration of the jet and spread its momentum to slowly moving, highly turbulent external gas. We argue that this mechanism could account for the peculiarities of the low-power FR0 jets. For outflows with higher power, Lorentz factor or magnetic field, we expect that the destabilizing effects are less effective, allowing the survival of the jet up to the kpc scale, as observed in FRIs.

Flat spectrum radio quasars (FSRQs) constitute a class of jetted active galaxies characterized by a very luminous accretion disc, prominent and rapidly moving line-emitting cloud structures (broad-line region, BLR), and a surrounding dense dust structure known as dusty torus. The intense radiation field of the accretion disc strongly determines the observational properties of FSRQs. While hundreds of such sources have been detected at GeV energies, only a handful of them exhibit emission in the very-high-energy (VHE, E greater than or similar to 100 GeV) range. This study presents the results and interpretation derived from a cumulative observation period of 174 h dedicated to nine FSRQs conducted with the Major Atmospheric Gamma-ray Imaging Cherenkov telescopes from 2008 to 2020. Our findings indicate no statistically significant (>= 5 sigma) signal for any of the studied sources, resulting in upper limits on the emission within the VHE energy range. In two of the sources, we derived quite stringent constraints on the gamma-ray emission in the form of upper limits. Our analysis focuses on modelling the VHE emission of these two sources in search for hints of absorption signatures within the BLR radiation field. For these particular sources, constraints on the distance between the emission region and the central black hole are derived using a phenomenological model. Subsequently, these constraints are tested using a framework based on a leptonic model.

We present the first multi-wavelength study of Mrk 501 including very-high-energy (VHE) gamma-ray observations simultaneous to X-ray polarization measurements from the Imaging X-ray Polarimetry Explorer (IXPE). We use radio-to-VHE data from a multi-wavelength campaign organized between 2022-03-01 and 2022-07-19. The observations were performed by MAGIC, Fermi-LAT, NuSTAR, Swift (XRT and UVOT), and several instruments covering the optical and radio bands. During the IXPE pointings, the VHE state is close to the average behavior with a 0.2-1 TeV flux of 20%-50% the emission of the Crab Nebula. Despite the average VHE activity, an extreme X-ray behavior is measured for the first two IXPE pointings in March 2022 with a synchrotron peak frequency >1 keV. For the third IXPE pointing in July 2022, the synchrotron peak shifts towards lower energies and the optical/X-ray polarization degrees drop. The X-ray polarization is systematically higher than at lower energies, suggesting an energy-stratification of the jet. While during the IXPE epochs the polarization angle in the X-ray, optical and radio bands align well, we find a clear discrepancy in the optical and radio polarization angles in the middle of the campaign. We model the broad-band spectra simultaneous to the IXPE pointings assuming a compact zone dominating in the X-rays and VHE, and an extended zone stretching further downstream the jet dominating the emission at lower energies. NuSTAR data allow us to precisely constrain the synchrotron peak and therefore the underlying electron distribution. The change between the different states observed in the three IXPE pointings can be explained by a change of magnetization and/or emission region size, which directly connects the shift of the synchrotron peak to lower energies with the drop in polarization degree.

Context. Extreme TeV BL Lacs are a class of blazars with unique spectral and temporal features that are not easily reproducible using standard one-zone models based on single shock acceleration. To account for their peculiar properties, we elaborated a two-step acceleration model in which a recollimation shock and the subsequent downstream turbulence energize non-thermal electrons. Aims. We applied the model to a sample of extreme TeV BL Lacs with well-characterized spectral energy distributions. Since we used several sources, we automatized the exploration of the parameter space. This allowed us to derive the parameter distributions and study the correlations among them. Methods. We numerically solved a system of two coupled nonlinear differential equations to obtain the non-thermal particles and turbulence spectra. We calculated the spectral energy distribution via the synchrotron self-Compton emission model. The automatization of the parameter space exploration is possible through a Markov chain Monte Carlo (MCMC) ensemble sampler, in our case emcee. Results. We derived well-defined posterior distributions for the parameters, showing that the model is well constrained by available data and demonstrating the suitability of our method. The cross-correlations among some of the physical parameters are not trivial. Therefore, we conclude that MCMC sampling is a key instrument for characterizing the complexity of our multiparameter phenomenological model.

In recent years, a new generation of optical intensity interferometers has emerged, leveraging the existing infrastructure of Imaging Atmospheric Cherenkov Telescopes (IACTs). The MAGIC telescopes host the MAGIC-SII system (Stellar Intensity Interferometer), implemented to investigate the feasibility and potential of this technique on IACTs. After the first successful measurements in 2019, the system was upgraded and now features a real-time, dead-time-free, 4-channel, GPU-based correlator. These hardware modifications allow seamless transitions between MAGIC's standard very-high-energy gamma-ray observations and optical interferometry measurements within seconds. We establish the feasibility and potential of employing IACTs as competitive optical Intensity Interferometers with minimal hardware adjustments. The measurement of a total of 22 stellar diameters are reported, 9 corresponding to reference stars with previous comparable measurements, and 13 with no prior measurements. A prospective implementation involving telescopes from the forthcoming Cherenkov Telescope Array Observatory's Northern hemisphere array, such as the first prototype of its Large-Sized Telescopes, LST-1, is technically viable. This integration would significantly enhance the sensitivity of the current system and broaden the UV-plane coverage. This advancement would enable the system to achieve competitive sensitivity with the current generation of long-baseline optical interferometers over blue wavelengths.

The Lorentz Invariance Violation (LIV), a proposed consequence of certain quantum gravity (QG) scenarios, could instigate an energy-dependent group velocity for ultra-relativistic particles. This energy dependence, although suppressed by the massive QG energy scale E_QG, expected to be on the level of the Planck energy 1.22 × 10^19 GeV, is potentially detectable in astrophysical observations. In this scenario, the cosmological distances traversed by photons act as an amplifier for this effect. By leveraging the observation of a remarkable flare from the blazar Mrk 421, recorded at energies above 100 GeV by the MAGIC telescopes on the night of April 25 to 26, 2014, we look for time delays scaling linearly and quadratically with the photon energies. Using for the first time in LIV studies a binned-likelihood approach we set constraints on the QG energy scale. For the linear scenario, we set 95% lower limits E_QG>2.7×10^17 GeV for the subluminal case and E_QG> 3.6 ×10^17 GeV for the superluminal case. For the quadratic scenario, the 95% lower limits for the subluminal and superluminal cases are E_QG>2.6 ×10^10 GeV and E_QG>2.5×10^10 GeV, respectively.

Aims. LST-1, the prototype of the Large-Sized Telescope for the upcoming Cherenkov Telescope Array Observatory, is concluding its commissioning in Observatorio del Roque de los Muchachos on the island of La Palma. The proximity of LST-1 (Large-Sized Telescope 1) to the two MAGIC (Major Atmospheric Gamma Imaging Cherenkov) telescopes permits observations of the same gamma-ray events with both systems. Methods. We describe the joint LST-1+MAGIC analysis pipeline and use simultaneous Crab Nebula observations and Monte Carlo simulations to assess the performance of the three-telescope system. The addition of the LST-1 telescope allows the recovery of events in which one of the MAGIC images is too dim to survive analysis quality cuts. Results. Thanks to the resulting increase in the collection area and stronger background rejection, we find a significant improvement in sensitivity, allowing the detection of 30% weaker fluxes in the energy range between 200 GeV and 3 TeV. The spectrum of the Crab Nebula, reconstructed in the energy range ~60 GeV to ~10 TeV, is in agreement with previous measurements.