MIGHTEE: The evolving radio luminosity functions of star-forming galaxies to $z\sim 4.5$ and the cosmic history of star formation

TL;DR

This work measures the evolving 1.4 GHz radio luminosity functions (RLFs) of star-forming galaxies (SFGs) and AGN using deep MIGHTEE MeerKAT data across the COSMOS and XMM-LSS fields, modeling the total RLF as a sum of SFG and AGN components. By employing a double-parameter evolution: pure luminosity evolution for SFGs (PLE) and pure density evolution for AGN (PDE), and by robustly propagating photometric redshift uncertainties via Monte Carlo methods, the study derives the SFG RLF evolution and infers the cosmic star-formation rate density (SFRD). They find a higher local SFG normalization with a steeper faint-end slope than some earlier works, and strong SFG evolution up to $z\sim2$; the resulting radio-based SFRD is sensitive to the radio–SFR calibration, with a recent SED-based relation (Cook2024) reconciling the radio-derived SFRD with UV–IR tracers. The results highlight the power of radio observations to trace total SFRD and demonstrate that modeling the RLF without requiring per-source classifications can robustly capture the competitive contributions of SFGs and AGN across cosmic time.

Abstract

A key question in extragalactic astronomy is how the star-formation rate density (SFRD) evolves over cosmic time. A powerful way of addressing this question is using radio-continuum observations, where the radio waves are unaffected by dust and are able to reach sufficient resolution to resolve individual galaxies. We present an investigation of the 1.4 GHz radio luminosity functions (RLFs) of star-forming galaxies (SFGs) and Active Galactic Nuclei (AGN) using deep radio continuum observations in the COSMOS and XMM-LSS fields, covering a combined area of $\sim 4\,\mathrm{deg}^2$. These data enable the most accurate measurement of the evolution in the SFRD from mid-frequency radio continuum observations. We model the total RLF as the sum of evolving SFG and AGN components, negating the need for individual source classification. We find that the SFGs have systematically higher space densities at fixed luminosity than found in previous radio studies, but consistent with more recent studies with MeerKAT. We attribute this to the excellent low-surface brightness sensitivity of MeerKAT. We then determine the evolution of the SFRD. Adopting the far-infrared - radio correlation results in a significantly higher the SFRD at $z > 1$, compared to combined UV and far-infrared measurements. However, using more recent relations for the correlation between star-formation rate and radio luminosity, based on full spectral energy distribution modelling, can resolve this apparent discrepancy. Thus radio observations provide a powerful method of determining the total SFRD, in the absence of dust-sensitive far-infrared data.

Figures (14)

• Figure 1: Normalised Redshift distributions for radio sources in the COSMOS (left) and XMM-LSS (right) fields. Each panel shows the normalised redshift histograms for sources with spectroscopic redshifts (spec-z; blue), photometric redshifts where no spec-z is available (phot-z; orange), and radio sources without optical counterparts plotted at $z$>1 (non‑XID; green). Non-XID sources are assigned redshifts using the flux-dependent method described in Section \ref{['sec:opticalcompleteness']} and are shown here restricted to $z$>1.
• Figure 2: Completeness of the 1.4 GHz COSMOS catalogue as a function of input flux density. SKADS (green), modified SKADS (blue), SIMBA (maroon), the mean completeness is the back line. The vertical dashed line marks the uniform flux–density cut at 40 $\mu$Jy; the horizontal dashed line marks 100% completeness. Completeness values exceeding one intermediate flux densities result from noise shifting some sources from adjacent, lower-flux bins into brighter bins Hale_2022.
• Figure 3: Rest-frame 1.4 GHz luminosity versus redshift for COSMOS (left) and XMM–LSS (right). Black points are individual sources. The solid red curve corresponds to the adopted 40$\mu$Jy flux-density cut at the frequency.
• Figure 4: Total 1.4 GHz RLF in ten redshift bins from our photometric redshift PDF-based analysis, including statistically assigned redshifts for the non-XID sources restricted to be at $z>1$. Black hexagons show the $1/V_{\rm max}$ measurements from this work. Red solid and blue dashed curves show the best-fit SF (PLE) and AGN (PDE) components, respectively, with magenta and light-blue bands show their 90 per cent confidence intervals. The yellow, brown and grey dashed curves denote the total, SFG, and AGN RLFs, respectively from Novak_2018. For reference, the $1/V_{\rm max}$ points from Novak_2018 and matthews2024confirmationsubstantialdiscrepancyradio are also shown as green right-pointing and magenta down-pointing triangles, respectively.
• Figure 5: Posterior distributions for the eight parameters of the total RLF model: SFG Schechter function parameters $(\delta, \sigma, \phi_{*}^{\rm SF}, L_{*}^{\rm SF})$, SFG luminosity evolution ($\alpha_L^{\mathrm{SF}}$, $\beta_L^{\mathrm{SF}}$), and AGN density evolution ($\alpha_D^{\mathrm{AGN}}$, $\beta_D^{\mathrm{AGN}}$). Contours show the 68th and 95th percentile confidence regions; vertical lines in the 1D marginals mark the median and 16th/84th percentiles. The SFG (PLE) and AGN (PDE) evolution pairs exhibit the expected anti–correlations, while cross–component couplings remain weak, indicating that the two channels are separately constrained.