The Entangling of Supernova Feedback Impacts with Coarsening Simulation Resolution

Technical Summary: The Entangling of Supernova Feedback Impacts with Coarsening Simulation Resolution

Problem Statement
Supernova (SN) feedback is widely recognized as the primary mechanism regulating star formation (SF) and driving galactic outflows. However, the specific channels through which SNe achieve these macroscopic effects remain unclear. While high-resolution simulations can explicitly resolve the thermal expansion and radiative cooling of SN remnants, most galaxy formation simulations operate at lower resolutions. These lower-resolution models rely on "subgrid" approximations that assume the interstellar medium (ISM) conditions within a single gas cell are homogeneous and derivable from the simulation's available data. The central problem addressed is whether coarse-resolution simulations can self-consistently distinguish between the distinct physical impacts of SNe occurring in different environments (e.g., diffuse vs. dense regions) or if the averaging inherent to coarse grids obscures these critical physical processes, leading to mis-estimations of cooling radii and star formation rates.

Methodology
The authors analyze two independent, ultra-high-resolution simulations of isolated dwarf galaxies: LYRA (target gas mass resolution $m_{gas} \sim 4 M_\odot$) and RIGEL ($m_{gas} \sim 1 M_\odot$). Both simulations utilize the moving-mesh hydrodynamics code AREPO and share similar initial conditions (low baryon fraction, $M_{vir} = 2 \times 10^{10} M_\odot$). Crucially, both simulations exclude radiative feedback from young stars to isolate the effects of SN energy injection and radiative cooling.

The study focuses on the immediate environment of individual SN events, defined by the nearest $M_{env}$ of gas to the progenitor star. The authors:

1. Characterized Local Environments: Measured the local gas density ($\rho$) and the change in specific energy ($\Delta e$) for SN events in both simulations.
2. Analyzed Resolution Effects: Systematically "coarsened" the high-resolution data by varying the mass scale of the local environment ($M_{env}$) from $20 M_\odot$ (fine) to $200 M_\odot$ and $2000 M_\odot$ (coarse). This mimics the averaging process of lower-resolution simulations.
3. Correlated with Global Effects: Compared SN properties against galactic outflow rates (energy flux at specific heights above the disk) and local star formation rates (SFR) before and after SN events.
4. Validated with Analytic Models: Compared simulation data against analytic solutions for SN blastwave evolution (e.g., Sedov-Taylor phase, cooling radius estimates from Kim & Ostriker 2015).

Key Contributions and Results

• Bimodal Distribution of SN Environments: The analysis reveals a distinct bimodal distribution in the local densities where SNe occur.

  • Low-Density Mode: SNe occurring in diffuse regions ($n \sim 10^{-4} - 10^{-1} \text{ cm}^{-3}$). These events exhibit large changes in specific energy ($\Delta e$), often exceeding the escape velocity of the disk. They are temporally correlated with galactic outflows and are capable of expanding to kiloparsec scales before radiative losses dominate.
  • High-Density Mode: SNe occurring in dense, star-forming regions ($n \sim 10^4 \text{ cm}^{-3}$). These events show smaller $\Delta e$ changes due to efficient radiative cooling. They effectively disrupt local star-forming clumps on parsec scales but do not drive significant outflows.

• Distinct Feedback Channels: The paper establishes that these two modes drive separate emergent behaviors:

  • Low-density SNe are the primary drivers of galactic outflows (energy injection into the circumgalactic medium).
  • High-density SNe are the primary drivers of direct star formation suppression (disruption of dense gas clouds).
  • Crucially, low-density SNe do not significantly suppress star formation in their immediate vicinity (as the gas is too diffuse to form stars), and high-density SNe do not efficiently drive outflows (as energy is radiated away before the shell can escape the disk).

• The Resolution Threshold: The distinction between these two modes is only preserved at very high resolutions ($M_{env} \lesssim 100 M_\odot$).

  • As $M_{env}$ increases to $200 M_\odot$, the bimodality in density begins to fade.
  • At $M_{env} = 2000 M_\odot$ (typical of many cosmological simulations), the two modes become indistinguishable. The averaging process washes out the density contrast, making it impossible to determine from coarse data alone whether a SN will drive an outflow or suppress star formation.

• Mis-estimation of Cooling Radii: Coarse-resolution density estimates ($\rho_{2000}$) fail to predict the true cooling radius ($r_{cool}$) of a SN.

  • For a given coarse density, the true cooling radius (derived from fine-scale density) can vary by orders of magnitude.
  • Coarse estimates tend to underestimate $r_{cool}$ in low-density environments and fail to capture the bimodal nature of the effect in high-density environments. This undermines subgrid models that rely on local density to decide whether to inject thermal energy or momentum.

• Star Formation Thresholds: When averaging over coarse mass scales ($2000 M_\odot$), regions with average densities as low as $10^{-2} \text{ cm}^{-3}$ can exhibit non-zero star formation rates. This suggests that the high density thresholds ($\rho_{th} \sim 10^3 - 10^4 \text{ cm}^{-3}$) used in high-resolution simulations to mimic molecular clouds may be artificially restrictive when applied to coarse-resolution cells containing mixed phases.

Significance and Claims
The authors conclude that the macroscopic effects of SN feedback are not uniform but are highly dependent on the local, small-scale structure of the ISM. The paper claims that:

1. Self-consistency requires high resolution: Simulations aiming to self-consistently model the dual roles of SN feedback (outflows and SF suppression) must resolve mass scales of $\lesssim 100 M_\odot$ per cell. Below this threshold, the distinct physical channels of feedback are entangled and lost.
2. Subgrid model limitations: Commonly used parameters in coarse-resolution subgrid models, such as the SN cooling radius and SF density thresholds, may require re-evaluation. These models often assume homogeneous ISM conditions within a cell, an assumption that the paper demonstrates leads to significant errors in predicting SN outcomes.
3. Alternative modeling strategies: For simulations that cannot achieve the required resolution, the authors suggest that effective models must mimic the emergent effects of high-resolution results rather than relying solely on local hydrodynamic variables. They highlight "decoupled wind" models (which restrict outflows to low-density gas) and multi-fluid approaches as potential avenues to capture these effects without explicitly resolving the Jeans length of dense clumps.

The paper does not claim that low-resolution simulations are useless, but rather that they cannot self-consistently determine the specific feedback channel (outflow vs. suppression) of a given SN event based on coarse-resolution information alone.