Modelling the nebular emission of galaxies across cosmic time with COLT

TL;DR

This work significantly advances galaxy-scale nebular emission modelling by integrating a thermal equilibrium solver and a metal-level population solver into COLT, a Monte Carlo radiative transfer post-processing tool. The coupled RT, ionization, and temperature framework enables self-consistent computation of nebular line and continuum emission from simulated galaxies across cosmic time, validated against Cloudy benchmarks and applied to both local (LMC-like) and high-redshift (thesan-zoom) systems. Key contributions include the ability to model nebular continuum (free-free, free-bound, two-photon) and a broad metal-line library with CHIANTI data, as well as robust tests (CIE, Strömgren spheres) and realistic mock observations. The results demonstrate COLT’s capability to reproduce observed emission-line ratios (e.g., O32, R3) and morphologies, positioning it as a powerful tool for interpreting JWST-era nebular spectroscopy and guiding future explorations of ISM physics across cosmic history.

Abstract

Extragalactic nebular emission has long been a workhorse probe of the processes driving galaxy evolution, but the richness of JWST spectroscopy has shifted the bottleneck from data acquisition to physical interpretation and modelling. In this context, we present a major update to the Monte Carlo radiative transfer code COLT to facilitate self-consistent modelling of nebular line and continuum emission from simulated galaxies. We introduce a new thermal equilibrium solver that iteratively couples to the existing ionization solver and radiation field to compute effective gas temperatures by accurately balancing photoionization heating, radiative and dielectronic recombination, collisional ionization, charge exchange, metal and primordial line cooling, free-free emission, and Compton scattering. To prevent over-cooling where non-equilibrium hydrodynamics dominate, we introduce a Courant-limited cooling prescription tied to each cell's sound-crossing time, preserving temperatures in the diffuse halo while allowing physically motivated cooling in the interstellar medium (ISM). Applied to an isolated local galaxy simulation, the equilibrium solver reshapes the ISM phase space by reducing spuriously excessive lukewarm ($T=10^3-10^4$K) gas and better resolving warm ionized and cold neutral phases, while leaving the CGM largely intact. We further implement a level population solver based on modern atomic data, enabling accurate cooling and emissivities for a large library of UV to infrared metal lines, together with newly implemented primordial nebular continuum emission from free-free, free-bound, and two-photon processes. Finally, by applying COLT to the high-redshift THESAN-ZOOM simulations, we reproduce observed emission-line ratios, establishing COLT as a robust framework for forward modelling nebular emission across cosmic time.

Figures (11)

• Figure 1: A schematic overview of the colt post-processing workflow, including new features introduced in this work. User-defined inputs and simulation data set the simulation parameters, including gas and dust properties and source SEDs. The core code loop begins with ionizing radiation sampled from sources being transported through the gas, which accumulates photoionization and photoionization heating rates. These rates, along with rates for collisional ionization, radiative and dielectronic recombination, and charge exchange, are then plugged into the ionization solver to find the equilibrium ionization states. These initial states are then fed into the thermal equilibrium solver, which uses a root-finding algorithm (see text for details) to balance heating and cooling due to photoionization heating, radiative and dielectronic recombination, collisional ionization, charge exchange, metal and primordial line cooling, free-free emission, and Compton scattering. The updated, converged temperature and ionization states alter the transport of ionizing radiation, and so we iterate the core code loop until the change in the total number of hydrogen recombinations ($\int\alpha_\text{B} n_e n_\mathrm{HII}\, \text{d}V$) is less than a user-defined tolerance. After this joint convergence of the radiation field, ionization, and temperature, line emissivities are evaluated with the level-population solver and, where requested, non-ionizing stellar and nebular continuum is transported to produce mock observables (e.g., maps, IFS cubes, integrated spectra, profiles, sizes) alongside cell-level (ion fractions, temperatures, heating/cooling rates, escape/absorption fractions), star-level (escape/absorption/integrations), photon-level (paths/scattering), and binned (radial, angular, HEALPix) statistics.
• Figure 2: The ionization states of gas in collisional ionization equilibrium (CIE) as a function of temperature for distributions He, C, N, O, Ne, Si, S, and Fe from colt (solid) and Cloudy (dashed), evaluated from $T=10^3$ K to $T=10^8$ K at a fixed density of $\mathrm{n_H}=100\,\mathrm{cm^{-3}}$. Photoionization, molecules, dust, and induced processes are disabled. The agreement between the codes is overall excellent across the range of temperatures. Fe shows the largest overall offset, with a mean absolute error of 6.1%, and the mean absolute error for other ions is $\lesssim$5% (see text).
• Figure 3: Emissivity versus temperature for a set of nebular emission lines, computed in the same CIE set-up as Fig. \ref{['fig:CIE_test']} with colt (solid) and Cloudy (dashed). We show CIII]$\lambda$1907,1909 Å, [NII]$\lambda$6550,6585 Å, [OII]$\lambda$3727,3730 Å, [OIII]$\lambda$4364 Å, [OIII]$\lambda$5007 Å, and [SII]$\lambda$6718,6733 Å, all of which have emissvities calculated with our newly implemented level population solver. Agreement is excellent across the full temperature range, demonstrating the accuracy of our level population solver, with mean absolute fractional errors of $\lesssim$3.5% for all lines (see text). We also show the emissivities of H$\alpha$ and H$\beta$, which are calculated using tables assuming the Case B approximation Storey:1995aa, and show similarly good agreement (see text).
• Figure 4: Spherically symmetric H-only Strömgren test comparing colt (solid) and Cloudy (dashed). The ionizing source is a BPASS v2.2.1 SED for an IMF-averaged 5 Myr stellar population with a metallicity of $Z=0.02$ and mass of $10^{4.7}\,\mathrm{M_\odot}$. We show the equilibrium temperature (upper panel) and the fractional abundance of hydrogen ions as a function of radius (lower panel). The agreement between the codes is excellent, with both codes recovering a sharp ionization front and decreasing temperature with radius. Outside the ionized zone, temperatures diverge because colt’s network currently lacks molecular cooling, which suppresses further cooling. This difference is not relevant for the minimally metal-enriched ISM regime which we target.
• Figure 5: Metal-enriched Strömgren test comparing colt (solid) and Cloudy (dashed). We use the same setup as for Fig. \ref{['fig:stromgren_hydrogen_test']}, except we use HII region abundances (apart from He) and we change the ionizing source to a BPASS v2.2.1 SED for an IMF-averaged 3 Myr stellar population with a metallicity of $Z=0.006$. We show the equilibrium temperature (upper left panel), fractional abundance of oxygen ions (upper central panel), and [OIII]$\lambda$5007 Å / H$\beta$ ratio (upper right panel) as a function of radius. In the lower panel, we show the intrinsic spectrum of the Strömgren sphere, which includes high-EW emission lines and a Balmer jump. The agreement between the codes is excellent, which shows the combined accuracy of our ionization solver, radiation transport, thermal equilibrium solver, level population solver, nebular continuum, and cooling/heating rates.