[Paper Review] A thermal-kinetic subgrid model for supernova feedback in simulations of galaxy formation

Evgenii Chaikin, Joop Schaye+4 more|arXiv (Cornell University)|Nov 9, 2022

Astrophysics and Star Formation Studies4 citations

TL;DR

This paper introduces a thermal-kinetic subgrid model for supernova feedback in galaxy formation simulations, combining high-temperature thermal energy injections with low-velocity kinetic kicks to suppress spurious radiative losses and enhance feedback efficiency. The model achieves excellent convergence across resolution scales and reproduces observed star formation rates, velocity dispersions, and mass loading factors in Milky Way-mass and dwarf galaxies.

ABSTRACT

We present a subgrid model for supernova feedback designed for cosmological simulations of galaxy formation that may include a cold interstellar medium (ISM). The model uses thermal and kinetic channels of energy injection, which are built upon the stochastic kinetic and thermal models for stellar feedback used in the OWLS and EAGLE simulations, respectively. In the thermal channel, the energy is distributed statistically isotropically and injected stochastically in large amounts per event, which minimizes spurious radiative energy losses. In the kinetic channel, we inject the energy in small portions by kicking gas particles in pairs in opposite directions. The implementation of kinetic feedback is designed to conserve energy, linear and angular momentum, and is statistically isotropic. To test the model, we run simulations of isolated Milky Way-mass and dwarf galaxies, in which the gas is allowed to cool down to 10 K. Using the thermal and kinetic channels together, we obtain smooth star formation histories and powerful galactic winds with realistic mass loading factors. Furthermore, the model produces spatially resolved star formation rates (SFRs) and velocity dispersions that are in agreement with observations. We vary the numerical resolution by several orders of magnitude and find excellent convergence of the global SFRs and wind mass loading. We show that large thermal-energy injections generate a hot phase of the ISM and modulate the star formation by ejecting gas from the disc, while the low-energy kicks increase the turbulent velocity dispersion in the neutral ISM, which in turn helps suppress star formation.

Motivation & Objective

• To develop a subgrid feedback model that accurately reproduces observed galaxy properties—especially star formation rates and galactic winds—despite limited numerical resolution.
• To address the inefficiency of purely thermal feedback models, which suffer from excessive radiative cooling losses in low-resolution simulations.
• To explore how kinetic feedback, particularly low-velocity kicks, can suppress star formation by increasing turbulent velocity dispersion in the neutral ISM.
• To achieve numerical convergence of key galaxy observables across multiple resolution levels, ensuring robustness in cosmological simulations.

Proposed method

• Implement a thermal feedback channel that injects energy stochastically in large, isotropic bursts to minimize radiative energy losses, using a delayed cooling approach.
• Introduce a kinetic feedback channel that injects momentum via paired gas particle kicks in opposite directions, conserving energy, linear, and angular momentum.
• Use a statistical isotropy framework for both channels to ensure physical realism and avoid directional biases in feedback effects.
• Calibrate the model using a fraction $ f_{ m kin} $ of kinetic energy injection and a characteristic kick velocity $ riangle v_{ m kick} $, with $ f_{ m kin} = 0.1 $ and $ riangle v_{ m kick} = 50 $ km s$^{-1} $ as fiducial values.
• Run isolated simulations of Milky Way-mass and dwarf galaxies with gas cooling down to 10 K to test feedback efficacy and convergence.
• Analyze spatially resolved star formation rates, H i velocity dispersions, and wind mass loading factors to compare with observational data.

Experimental results

Research questions

• RQ1 Can a combined thermal-kinetic feedback model reproduce the observed Kennicutt-Schmidt star formation relation in isolated galaxies with varying resolution?
• RQ2 How does the balance between thermal and kinetic energy injection affect the turbulent velocity dispersion and star formation suppression in the neutral ISM?
• RQ3 What is the optimal combination of $ f_{ m kin} $ and $ riangle v_{ m kick} $ to achieve convergence in star formation rates and wind mass loading across resolution scales?
• RQ4 To what extent do low-energy kinetic kicks increase turbulent velocity dispersion and reduce local star formation efficiency without disrupting global galaxy properties?
• RQ5 How do the thermal and kinetic channels complement each other in sustaining realistic galactic winds and suppressing overcooling in dense gas?

Key findings

• The thermal-kinetic model produces smooth star formation histories and realistic galactic winds with mass loading factors consistent with observations.
• The model shows excellent convergence of global star formation rates and wind mass loading across several orders of magnitude in numerical resolution.
• A small but non-zero kinetic fraction ($ f_{ m kin} o 0.1 $) is essential to reproduce the correct slope of the Kennicutt-Schmidt relation; purely thermal or purely kinetic models fail to match observations.
• Low-energy kicks ($ riangle v_{ m kick} = 50 $ km s$^{-1} $) increase the turbulent velocity dispersion in the neutral ISM by a factor of a few, suppressing local star formation without reducing total SFR.
• For $ riangle v_{ m kick} o 10^2 $ km s$^{-1} $, galaxy properties such as SFR and wind mass loading become insensitive to further decreases in kick velocity, indicating convergence.
• Spatially resolved H i velocity dispersions from the model agree well with observations from Zhou et al. (2017) and Law et al. (2022), especially for $ f_{ m kin} = 0.1 $ and $ 0.3 $.