COLIBRE: calibrating subgrid feedback in cosmological simulations that include a cold gas phase

Abstract

We present the calibration of stellar and active galactic nucleus (AGN) feedback in the subgrid model for the new COLIBRE hydrodynamical simulations of galaxy formation. COLIBRE directly simulates the multi-phase interstellar medium and the evolution of dust grains, which is coupled to the chemistry. COLIBRE is calibrated at three resolutions: particle masses of $m_{\rm gas} \approx m_{\rm dm} \sim 10^7$ (m7), $10^6$ (m6), and $10^5~\mathrm{M_\odot}$ (m5). To calibrate the COLIBRE feedback at m7 resolution, we run Latin hypercubes of $\approx 200$ simulations that vary up to four subgrid parameters in cosmological volumes of ($50~\mathrm{cMpc}$)$^{3}$. We train Gaussian process emulators on these simulations to predict the $z=0$ galaxy stellar mass function (GSMF) and size - stellar mass relation (SSMR) as functions of the model parameters, which we then fit to observations. The trained emulators not only provide the best-fitting parameter values but also enable us to investigate how different aspects of the prescriptions for supernova and AGN feedback affect the predictions. In particular, we demonstrate that while the observed $z=0$ GSMF and SSMR can be matched individually with a relatively simple supernova feedback model, simultaneously reproducing both necessitates a more sophisticated prescription. We show that the calibrated m7 COLIBRE model not only reproduces the calibration target observables, but also matches various other galaxy properties to which the model was not calibrated. Finally, we apply the calibrated m7 model to the m6 and m5 resolutions and, after slight manual adjustments of the subgrid parameters, achieve a similar level of agreement with the observed $z=0$ GSMF and SSMR.

Figures (20)

• Figure 1: The Latin hypercube for the Thermal-Kine-tic_var$\mathtt{\Delta T}_{\mathtt{SN}}$var$\mathtt{f}_{\mathtt{E}}$ model. The axes of the panels correspond to different parameters of the model: $m_{\rm BH, seed}$, $f_{\rm kin}$, $n_{\rm H,pivot}$, and $P_{\rm E,pivot}$ (see $\S$\ref{['subsection: selection_theta']} for details). The grey (black) hatched rectangle marks level 1 (level 2) of the hypercube's domain, while light-blue triangles (circles) indicate the sampling for level 1 (level 2), consisting of 40 (8) individual simulations. Together, the simulations from levels 1 and 2 form the training dataset for the Thermal-Kine-tic_var$\mathtt{\Delta T}_{\mathtt{SN}}$var$\mathtt{f}_{\mathtt{E}}$ model, which is used to train the emulators for the $z=0$ GSMF and SSMR.
• Figure 2: The galaxy stellar mass function (GSMF; left) and the median size -- stellar mass relation (SSMR; right) at $z=0$, for the Basic (green) and ThermalKinetic (yellow) models fit to the observed GSMF and SSMR. The dashed and solid curves indicate, respectively, the best-fitting predictions of the emulator and the corresponding simulations with the best-fitting parameters from Table \ref{['table: best-fitting models']}. The shaded yellow regions in the left and right panels indicate the Poisson uncertainty for the GSMF and the $16^{\rm th}$ to $84^{\rm th}$ percentile scatter for the SSMR in the simulation using the ThermalKinetic model, respectively. We convert the green and yellow solid curves into dotted curves where galaxies are poorly resolved ($M_* < 10^9~\mathrm{M_\odot}$) and where the number of galaxies is strongly limited by the finite simulated volume (the number of objects per bin is less than $5$). The vertical solid (dash-dotted) lines show the mass range within which the emulators were trained on the simulations (fit to observational data). The target observational data from 2022MNRAS.513..439D and 2022MNRAS.509.3751H are shown as black squares and circles, respectively. Additionally, the grey hatched region in the right panel indicates the galaxy population-wide scatter in the SSMR from 2022MNRAS.509.3751H. Although the ThermalKinetic model produces a combined fit to the observed GSMF and SSMR that is better than the fit with the Basic model, neither model is particularly satisfactory.
• Figure 3: Posterior distribution of the parameters for the Basic (green) and ThermalKinetic (yellow) models fit to the observed $z=0$ GSMF and SSMR. The $\chi^2_\nu$ values of the fits are shown in the legend. The three contours of each colour indicate $34$, $68$, and $95$ per cent credibility levels. The vertical and horizontal dotted lines indicate the best-fitting values of the model parameters, corresponding to the maximum of the posterior.
• Figure 4: The stellar to halo mass relation (SHMR) at $z=0$ predicted by the trained emulators. The results are shown for the ThermalKinetic model fit to the observed GSMF and SSMR. The individual panels show how the emulated SHMR varies with the BH seed mass ($m_{\rm BH, seed}$; left), the energy in SN feedback in units of $10^{51}$ erg ($f_{\rm E}$; middle), and the fraction of SN energy injected in kinetic form ($f_{\rm kin}$; right). Different colours correspond to different values of each parameter. Only one parameter is varied at a time, while the other parameters are fixed to their best-fitting values as indicated in the legends. The vertical solid lines designate the mass range within which the emulators were trained on the simulations. For reference, each panel shows the data from the semi-empirical models of 2018MNRAS.477.1822M and 2019MNRAS.488.3143B, displayed as black points. Additionally, the middle panel shows the SHMR in the Basic model, also for different values of $f_{\rm E}$ (thin dotted curves). Regardless of the value of $f_{\rm E}$, the SHMR in the Basic model is always too flat compared to the data. This problem is resolved in the ThermalKinetic model for high enough $f_{\rm kin}$.
• Figure 5: Predictions of the best-fitting ThermalKinetic model fit to the observed galaxy stellar mass function (GSMF, purple), galaxy size -- stellar mass relation (SSMR, brown), or to both the GSMF and SSMR (yellow). We show the $z=0$ GSMF (left), the $z=0$ SSMR (middle), and the $z=0$ stellar to halo mass relation (SHMR; right). The emulator predictions are shown as dashed curves, and the results from simulations using the best-fitting parameters are shown as solid curves. The solid curves become dotted at stellar (or halo) masses where galaxies are poorly resolved or where the number of galaxies is small due to the finite simulation volume. The vertical solid and dash-dotted lines carry the same meaning as in Fig. \ref{['fig:basic_and_thermal_kinetic_model_calibration']}. There are no vertical dash-dotted lines in the right panel because we do not fit the model to the SHMR. Fitting only to the observed GSMF (SSMR) results in a good match to the observed GSMF (SSMR) but a poor match to the SSMR (GSMF). Fitting to both observed relations at the same time produces only a reasonable match to the two constraints.