How to model supernovae in simulations of star and galaxy formation

Philip F. Hopkins, Andrew Wetzel, Dušan Kereš, Claude André Faucher-Giguère, Eliot Quataert, Michael Boylan-Kolchin, Norman Murray, Christopher C. Hayward, Kareem El-Badry

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


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 SN 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-SN simulations and cosmological galaxy-formation simulations, the FIRE-2 algorithm converges much faster than other sub-grid models without re-tuning parameters.

Original languageEnglish (US)
Pages (from-to)1578-1603
Number of pages26
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
StatePublished - Jun 21 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmology: Theory
  • Galaxies: Active
  • Galaxies: Evolution
  • Galaxies: Formation
  • Stars: Formation


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