One of the surprises discovered when improved telescopes made it possible to see very old galaxies is that galaxies formed much more rapidly after the Big Bang than simulations had expected. One reason the simulations were inaccurate is that their model of mechanical feedback from supernovaes was flawed. An improved method of simulating this has resolved the paradox.
Philip F. Hopkins, et al. "How To Model Supernovae in Simulations of Star and Galaxy Formation" (July 21, 2017)We study the implementation of mechanical feedback from supernovae (SNe) and stellar mass loss in galaxy simulations, within the Feedback In Realistic Environments (FIRE) project. We present the FIRE-2 algorithm for coupling mechanical feedback, which can be applied to any hydrodynamics method (e.g. fixed-grid, moving-mesh, and mesh-less methods), and black hole as well as stellar feedback. This algorithm ensures manifest conservation of mass, energy, and momentum, and avoids imprinting 'preferred directions' on the ejecta. We show that it is critical to incorporate both momentum and thermal energy of mechanical ejecta in a self-consistent manner, accounting for SNe cooling radii when they are not resolved. Using idealized simulations of single SNe explosions, we show that the FIRE-2 algorithm, independent of resolution, reproduces converged solutions in both energy and momentum. In contrast, common 'fully-thermal' (energy-dump) or 'fully-kinetic' (particle-kicking) schemes in the literature depend strongly on resolution: when applied at mass resolution ≳100M⊙, they diverge by orders-of-magnitude from the converged solution. In galaxy-formation simulations, this divergence leads to orders-of-magnitude differences in galaxy properties, unless those models are adjusted in a resolution-dependent way. We show that all models that individually time-resolve SNe converge to the FIRE-2 solution at sufficiently high resolution (<100M⊙). However, in both idealized single-SNe simulations and cosmological galaxy-formation simulations, the FIRE-2 algorithm converges much faster than other sub-grid models without re-tuning parameters.