Connecting galaxies with their haloes -- from parsec to Mpc scales

Abstract: Galaxy evolution is driven by processes occurring across a wide range of scales, from star formation within giant molecular clouds (parsec scales) to outflows and secular evolution across entire galaxies (kpc scales), and the interplay between galaxies, their dark matter haloes, and large-scale structures (Mpc scales). Connecting the distribution of baryonic matter and energy across these scales will remain one of the key challenges for both theoretical and observational astrophysics in the coming decade. A major development towards meeting this challenge has been the growing ability to obtain highly spatially resolved (parsec-scale) integral-field spectroscopic observations (e.g. with VLT/MUSE), as well as to probe the extremely low-surface brightness outskirts of galaxies at large radii and high vertical scale heights. To combine the two regimes, we need a paradigm shift in the way we do spectroscopy on galaxies, especially considering the ongoing and future photometric surveys. The next decade will also bring a revolution in extensive photometric surveys of large areas of the sky, uncovering low surface brightness features around nearby galaxies. However, to fully understand the processes that connect galaxies to their haloes, shape low surface brightness features, and drive secular evolution, spatially resolved spectroscopy will be essential. Here, we outline the need for wide-field spectroscopic observations of statistically significant samples of nearby galaxies and highlight the key questions that can only be addressed with such data