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Abstract The extent to which turbulence mixes gas in the face of recurrent infusions of fresh metals by supernovae (SN) could help provide important constraints on the local star formation conditions. This includes predictions of the metallicity dispersion among metal-poor stars, which suggests that the interstellar medium was not very well mixed at these early times. The purpose of thisLetteris to help isolate, via a series of numerical experiments, some of the key processes that regulate turbulent mixing of SN elements in galactic disks. We study the gas interactions in small simulated patches of a galaxy disk with the goal of resolving the small-scale mixing effects of metals at parsec scales, which enables us to measure the turbulent diffusion coefficient in various galaxy environments. By investigating the statistics of variations ofαelements in these simulations, we are able to derive constraints not only on the allowed range of intrinsic yield variations in SN explosions but also on the star formation history of the Milky Way. We argue that the observed dispersion of [Mg/Fe] in metal-poor halo stars is compatible with the star-forming conditions expected in dwarf satellites or in an early low-star-forming Milky Way progenitor. In particular, metal variations in stars that have not been phase-mixed can be used to infer the star-forming conditions of disrupted dwarf satellites. 

Abstract The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA’s first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultra-compact stellar-mass binaries, massive black hole binaries, and extreme or interme-diate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.