Periodic Reporting for period 1 - TEL-STARS (Turbulent and Explosive Lives of Massive Stars) Reporting period: 2021-01-01 to 2022-06-30 Summary of the context and overall objectives of the project Stars are the basic building blocks of the visible Universe and have produced almost all chemical elements heavier than helium. Massive stars with luminosities of up to several million times that of our Sun are cosmic powerhouses. Their immense radiation, strong stellar winds and powerful supernova (SN) explosions helped to re-ionise the Universe after the Dark Ages, drive the evolution of galaxies and laid the foundation for life as we know it. Massive stars end their lives in spectacular SNe and leave behind neutron stars (NSs) and black holes (BHs) that open the door to physics that is inaccessible otherwise on Earth. NSs are made of ultra-compact matter and some, so-called magnetars, are supposed to host the strongest magnetic fields in the whole Cosmos. Thanks to large transient surveys and the detection of gravitational waves (GWs) from merging NSs and BHs, massive star research is shifting into the focus of modern astrophysics. An accurate understanding of the lives and final fates of massive stars is essential, yet large gaps remain.Most stars are not alone but have a companion with whom they orbit in a binary-star system. While stars evolve, they grow in size and mass transfer from one star to the other may begin. In about a quarter of cases, such a phase leads to the coalescence of both stars. Magnetic fields may be generated in mergers, possibly explaining the more than 70-year-old mystery of the origin of strong magnetic fields in some massive stars. When magnetic massive stars explode in SNe, they may form highly-magnetic NSs, thereby offering a solution to the origin of the strongest magnets in the Universe. It is unclear whether and how SN explosions are affected by previous binary mass exchange. For example, the famous SN 1987A is best explained by a merger product and also Eta Carinae, a star that became the second brightest star in the night sky during its great eruption in ~1840, might be the result of merging stars. For these reasons, we conduct the first three-dimensional (3D), magnetohydrodynamic (MHD) simulations of stellar mergers. They will allow us to better understand these complex physical phases and emerging phenomena such as strong magnetism. Furthermore, we make detailed models of various binary mass-transfer phases, map out the binary-star parameter space that leads to stellar mergers and develop computationally cheaper, simplified merger models. We can then follow the evolution of a large set of models up to the SN stage to better understand the diversity of SNe and other transients. Every model must be checked against observations for validation. To this end, we will develop machine-learning techniques to compare our models to observations of stars and be able to use the observations to inform the modelling. The project will open new possibilities for massive star research, solve some long-standing questions and offer plentiful extensions. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far We have focused on three of the four main objectives. First, we began to explore different stellar-merger situations with 3D MHD simulations. Simulations are running and will continue to do so. A paper on the outcome of our first large merger simulations is in a mature state.Second, we successfully developed the physical model and numerical setup to compute a grid of binary stars with a one-dimensional, stellar evolution code. The first grid is almost complete and the analysis of the results has begun.Third, we have developed a semi-analytic model of neutrino-driven core-collapse SNe and successfully applied it to our models. We explored how envelope stripping of stars in binary systems influences their further evolution up to core collapse (Schneider et al. 2021, A&A). Envelope stripping affects the core evolution of stars such that they explode more easily and rather form NSs than BHs. NS formation is possible in single stars initially less massive than 35 solar masses while this limit increases to 70 solar masses in stripped stars. Also, the ensuing SN is more energetic and produces more nickel. Our work naturally explains the apparent non-existence of BHs beyond ~20 solar mass in Galactic X-ray binaries. For GW astronomy, our results revise down predictions of the merger rates of BH-BH and NS-BH systems because fewer stars will form BHs. We have also finished a study on the pre-SN interior structures of gainers of binary mass exchange and are currently writing up a paper.Fourth, we started to explore different machine-learning techniques to identify those methods best suited for our purposes. Feed-forward neural networks seem to be the current front-runner, but a final verdict is yet to be made.As part of the main objectives, we study in collaboration with others at the host institute the common-envelope (CE) phase of binary stars. In a CE event, a smaller star is engulfed by the envelope of a giant star and a large fraction of the envelope might be ejected. For the first time, we reached full envelope ejection in a simulation and observed bipolar outflows launched by strong magnetic fields that were produced in the CE phase (Ondratschek et al. 2022, A&A Letters). This simulation explains how some iconic planetary nebulae likely formed and received their asymmetric structures. We also expanded our work to CE situations with massive stars, which is key in the evolution of GW merger events (Moreno et al., A&A in press). We are currently using these CE simulations to develop simplified models of the CE phase for use in stellar evolution codes with the help of a drag-force algorithm. The first results give hope that a predictive theory for CE events in stellar evolution codes might be within reach. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) We could successfully apply our gained knowledge to problems beyond our planned goals. In Hirai et al. 2021, MNRAS, we found a way by which an initially stable triple system becomes unstable and induces a stellar merger. The merger outcome closely resembles Eta Carinae and its impressive Homunculus nebula. Again involving stellar mergers in triple star systems (Stegmann et al. 2022, Phys. Rev. D), we showed how one can explain the small mass ratios observed in some double BH mergers. Thanks to our expertise, we were able to help interpret the discovery of stellar-mass BH around a massive star outside the Milky Way Galaxy (Shenar et al. 2022, Nature Astronomy). Theory predicts that a few per cent of all massive stars should have such a dark companion, but they are difficult to find.We expect to finish our exploration of 3D MHD simulations of stellar mergers within the time frame of the project. With the help of these simulations, we will make new simplifying models of stellar mergers for use in stellar evolution codes as well as study the evolution of merged stars from right after the merger phase until the SN stage. The analysis of the grids of binary star models will shed light, e.g. on which binary stars are expected to merge and will allow for detailed comparisons to observations. In combination with simplified merger models, we can then explore the properties of a large set of merged stars. Our work on the pre-SN evolution of binary products is already in a mature state and we plan to keep exploring and expanding the scope because we have identified new, beyond the state-of-the-art questions that our models can probably explain. Work on the fourth objective will start later this year except for the above-mentioned exploratory work already done. Birth of a magnetic massive star in a stellar merger. Colour indicates the magnetic field strength.