Imladris: a detailed and flexible model for galaxy simulations with individual stars

Abstract

Coupling stellar feedback to the evolution of individual stars, as opposed to averaging over the initial mass function (IMF), substantially improves the fidelity of galaxy formation simulations by capturing stochastic population effects. Existing treatments can typically only operate at a narrow mass resolution range, limiting their applicability. We present Imladris, a detailed model for star formation and stellar feedback with individual stars. At high resolution, each star can be represented by its own particle ("star-by-star"). At coarser resolution, star particles represent specific realisations of stellar populations sampled from the IMF. Both methods share a unified implementation of stellar feedback tied to the individually tracked stars, including supernovae, stellar winds and radiation. Imladris has been optimised for both computational efficiency and memory footprint. We demonstrate the model with idealised galaxy simulations ($M_\mathrm{vir}\sim10^{10}-10^{11}\,\mathrm{M_\odot}$) spanning a baryonic mass resolution range of $2.5-1000\,\mathrm{M_\odot}$. Without re-calibration, the time-averaged star formation rate (SFR), galactic wind mass and energy loadings close to the disc are converged up to a resolution of $20\,\mathrm{M_\odot}$ within a factor of 1.1, 1.1 and 1.3, respectively, and 1.4, 1.6 and 2.5 up to $100\,\mathrm{M_\odot}$. Above this, SFRs become more bursty, while loading factors increase substantially. This is linked to resolution-dependent supernova clustering, which represents a fundamental barrier to convergence for any scheme attempting to model a self-consistent stellar feedback-regulated interstellar medium. Regardless, the ability to deploy the scheme across a wide range of resolutions (and to carry out in-depth resolution convergence studies) makes Imladris a powerful tool for numerical investigations of galaxy formation.

Figures (15)

• Figure 1: For the fiducial m10 simulations, the distributions of ZAMS masses of all individually tracked stars (specifically the mass-normalised logarithmic IMF). The m10mg2.5 resolution simulation tracks individual stars down to $2.5\,\mathrm{M_\odot}$, all others down to $5\,\mathrm{M_\odot}$. Below this mass, stars are still sampled from the full IMF (the dashed line) but their individual masses are not recorded. All simulations lie on top of the input IMF, with deviations entirely consistent with Poisson noise, indicating that the IMF sampling in both discrete population and solo mode perfectly reproduces the input IMF without bias, independently of mass resolution.
• Figure 2: Visualisation of the m10mg2.5 simulation after 800 Myr. Panels have side length 4 kpc (recall the initial gas disc scale length is 1.1 kpc). Top left: Face-on total gas surface density (projected $\pm2$ kpc from the disc mid--plane). Bottom left: As top left, but viewed edge--on (note different colourbar range). Top centre: The mid--plane gas temperature (i.e. this is a slice, not a projection). Bottom centre: Edge-on mass--weighted metallicity projection (i.e. this is the surface density of metals divided by the total gas surface density). Top right: Surface density of newly formed stars (i.e. not including the stellar disc present in the initial conditions). This is made by smoothing the mass of the star particles (which are point masses) with a Gaussian kernel with $\sigma = 20$ pc. Over-plotted are the locations of all stars with a mass greater than $8\,\mathrm{M_\odot}$ (note that all stars more massive than $2.5\,\mathrm{M_\odot}$ are represented by individual particles in this simulation). Stellar mass is indicated by both marker size and colour (using a logarithmic scaling), with the smallest, reddest marker in the image representing an $8\,\mathrm{M_\odot}$ star and the largest, bluest marker representing a $69.4\,\mathrm{M_\odot}$ star (the most massive star in the galaxy at this particular moment). Bottom right: The mid--plane (i.e. a slice) interstellar radiation field intensity from 6--13.6 eV, expressed in Habing units.
• Figure 3: Visualisation of the m11mg20 simulation after 800 Myr. Panels have side length 8 kpc and are as \ref{['fig:wlm_2.5_image']}, with different colourbar ranges. The (logarithmic) scaling of the marker size for massive stars also differs from \ref{['fig:wlm_2.5_image']}. At this particular point in the simulation, the most massive star in the galaxy is $137.8\,\mathrm{M_\odot}$, represented with the largest, bluest marker.
• Figure 4: Visualisation of all of the fiducial simulations of the m10 system at 800 Myr. Resolution coarsens from left to right. The top and middle rows show the total gas surface density, projected face-on and edge-on, respectively. Note that the colour scale differs for these two projections in order to achieve an appropriate dynamic range to highlight details. The bottom row shows the gas temperature at the disc mid-plane; this is a slice rather than a projection. While all simulations produce an ISM with clumps, filaments and hot bubbles, fine structure is smoothed out at coarser resolution in favour of larger, monolithic structures.
• Figure 5: Visualisation of all of the fiducial simulations of the m11 system at 800 Myr. Resolution coarsens from left to right. The top and middle rows show the total gas surface density, projected face-on and edge-on, respectively. Note that the colour scale differs for these two projections in order to achieve an appropriate dynamic range to highlight details. The bottom row shows the gas temperature at the disc mid-plane; this is a slice rather than a projection.