The EAGLE simulations of galaxy formation: calibration of subgrid physics and model variations

TL;DR

The paper investigates how calibrated subgrid physics in the EAGLE simulations shape galaxy populations. By calibrating to the $z=0.1$ galaxy stellar mass function (GSMF) and central BH scaling, the authors present four calibrated models and nine single-parameter variations to dissect the roles of star formation feedback and AGN feedback. They show that reproducing the GSMF alone can yield unrealistically compact galaxies unless additional constraints (e.g., correct galaxy sizes) are enforced, highlighting the impact of numerical radiative losses and the need for density- or metallicity-dependent feedback efficiencies. The results demonstrate that low-mass galaxies are chiefly controlled by stellar feedback while high-mass systems are regulated by BH/AGN feedback; the models converge on realistic stellar mass densities and star formation histories when calibrated against multiple observables. Overall, the work underscores the importance of calibrating subgrid prescriptions against diverse diagnostics to obtain physically plausible galaxy populations in cosmological simulations.

Abstract

We present results from thirteen cosmological simulations that explore the parameter space of the "Evolution and Assembly of GaLaxies and their Environments" (EAGLE) simulation project. Four of the simulations follow the evolution of a periodic cube L = 50 cMpc on a side, and each employs a different subgrid model of the energetic feedback associated with star formation. The relevant parameters were adjusted so that the simulations each reproduce the observed galaxy stellar mass function at z = 0.1. Three of the simulations fail to form disc galaxies as extended as observed, and we show analytically that this is a consequence of numerical radiative losses that reduce the efficiency of stellar feedback in high-density gas. Such losses are greatly reduced in the fourth simulation - the EAGLE reference model - by injecting more energy in higher density gas. This model produces galaxies with the observed size distribution, and also reproduces many galaxy scaling relations. In the remaining nine simulations, a single parameter or process of the reference model was varied at a time. We find that the properties of galaxies with stellar mass <~ M* (the "knee" of the galaxy stellar mass function) are largely governed by feedback associated with star formation, while those of more massive galaxies are also controlled by feedback from accretion onto their central black holes. Both processes must be efficient in order to reproduce the observed galaxy population. In general, simulations that have been calibrated to reproduce the low-redshift galaxy stellar mass function will still not form realistic galaxies, but the additional requirement that galaxy sizes be acceptable leads to agreement with a large range of observables.

Figures (12)

• Figure 1: The fraction of the energy budget due to type II SNe feedback that is used for thermal heating, $f_{\rm th}$, in the FBconst, FB$\sigma$, FBZ and Ref models. The FBconst model, represented by the dashed grey line, adopts $f_{\rm th}=1$, independent of local conditions. $f_{\rm th}$ declines smoothly as a function of $T_{\rm DM}$ in the FB$\sigma$ model (equation \ref{['eq:fth(T)']}), and as a function of $Z$ in the FBZ model (equation \ref{['eq:fth(Z)']}). The upper axis is aligned and scaled such that both FB$\sigma$ (upper axis) and FBZ (lower axis) are described by the dark blue curve (no physical correspondence between $T_{\rm DM}$ and $Z$ is implied by this alignment). The Ref model adds a density dependence to FBZ (equation \ref{['eq:fth(Z,n)']}), such that for stars forming from gas with $n_{\rm H}<n_{\rm H,0}$ the $f_{\rm th}$ function is shifted to lower values (e.g. cyan curve for $n_{\rm H}=n_{\rm H,0}/3$) and vice versa (e.g. red curve for $n_{\rm H}=3n_{\rm H,0}$).
• Figure 2: Left: The $z=0.1$ GSMF of the calibrated L050N0752 simulations, FBconst (red), FB$\sigma$ (green), FBZ (cyan) and Ref (dark blue). Curves are drawn with dotted lines where galaxies are comprised of fewer than 100 star particles, and dashed lines where the GSMF is sampled by fewer than 10 galaxies per bin. Data points show measurements with $1\sigma$ error bars from the SDSS Li_and_White_09 and GAMA Baldry_et_al_12_short surveys. The simulations each reproduce the observed number density of galaxies at fixed mass to $< 0.31\,{\rm dex}$, a precision unprecedented for hydrodynamical simulations. Right: To illustrate convergence as the simulation volume is varied, the Ref model at intermediate resolution is shown in volumes of $L=25$, $50$ and $100\,{\rm cMpc}$. The Ref-L050N0752 (dark blue) and Ref-L100N1504 (red) GSMFs are consistent for $M_\star \lesssim 10^{11.5}\,{\rm M}_\odot$. The GSMF of Ref-L025N0376 is consistent with that of its larger counterparts for $M_\star < 10^{9.5}\,{\rm M}_\odot$, but samples large-scale structures poorly owing to its small volume, imprinting "wiggles" on the GSMF.
• Figure 3: The sizes, at $z=0.1$, of disc galaxies in the four simulations that were calibrated to reproduce the present-day GSMF. Sizes from the Ref-L100N1504 (presented by S15) are also shown (yellow curve), to demonstrate consistency between volumes. Size, $R_{50}$, is defined as the half-mass radius (in proper kpc) of a Sérsic profile fit to the projected, azimuthally-averaged stellar surface density profile of a galaxy, and those with Sérsic index $n_{\rm s}<2.5$ are considered disc galaxies. Curves show the binned median sizes, and are drawn with dotted lines below a mass scale of 600$m_{\rm g}$, and a dashed linestyle where sampled by fewer than 10 galaxies per bin. The $1\sigma$ scatter about the median of Ref is denoted by the blue shaded region. The solid and dotted grey lines show the median and $1\sigma$ scatter of sizes for $n_{\rm s}<2.5$ galaxies inferred from SDSS data by Shen_et_al_03, whilst grey data points and error bars show sizes of blue galaxies inferred by Baldry_et_al_12_short from GAMA data. Only the Ref model successfully reproduces the observed GSMF and galaxy sizes at $z=0.1$.
• Figure 4: Face-on (left) and edge-on (right) projections, at $z=0.1$, of the galaxy formed within the same $M_{200} \sim 10^{12}\,{\rm M}_\odot$ halo in the four simulations that were calibrated to reproduce the present-day GSMF. Each image subtends a field of view of $100\,{\rm pkpc}$, and is a composite of SDSS $u$-, $g$- and $r$-band emission maps generated with the radiative transfer software skirt. The overall size of the optical envelope of the galaxy is similar in each case, but the distribution and dynamics of the stars differ markedly between Ref and the other models. In the latter, the galaxy forms an unrealistically compact bulge component at early epochs and exhibits too little ongoing star formation (blue-coloured concentrations) in the extended disc. Consequently, only in Ref does the galaxy exhibit an effective radius, $R_{50}$, that is consistent with the observed size-mass relation for disc galaxies.
• Figure 5: The evolution of the comoving stellar mass density of the calibrated EAGLE models. Data points correspond to measurements from several observational surveys spanning $0 < z < 4$ (see text for details). Although the models each broadly reproduce the observed GSMF at $z=0.1$, they exhibit markedly different star formation histories, and the FBconst model in particular forms too much stellar mass at early times. Taking the observations at face value, only the Ref model is broadly consistent with the observational constraints for $z\lesssim 2$.