New Analytic Solutions for Galaxy Evolution: Gas, Stars, Metals, and Dust in Local ETGs and Their High-z Star-forming Progenitors

We present a set of new analytic solutions aimed at self-consistently describing the spatially averaged time evolution of the gas, stellar, metal, and dust content in an individual star-forming galaxy hosted within a dark halo of a given mass and formation redshift. Then, as an application, we show that our solutions, when coupled to specific prescriptions for parameter setting (inspired by in situ galaxy-black hole coevolution scenarios) and merger rates (based on numerical simulations), can be exploited to reproduce the main statistical relationships followed by early-type galaxies and their high-redshift star-forming progenitors. Our analytic solutions allow one to easily disentangle the diverse role of the main physical processes regulating galaxy formation, quickly explore the related parameter space, and make transparent predictions on spatially averaged quantities. As such, our analytic solutions may provide a basis for improving the (subgrid) physical recipes presently implemented in theoretical approaches and numerical simulations and can offer a benchmark for interpreting and forecasting current and future broadband observations of high-redshift star-forming galaxies.