Evaluating star formation rates at z = 5

TL;DR

This work investigates biases in inferring star formation rates at $z=5$ by applying full 3D radiative transfer to two zoom-in simulations (NewHorizon and NewCluster) and generating synthetic tracers for $\mathrm{H}\alpha$, IR, UV, and $[\mathrm{CII}]$ emission. By comparing tracer-derived SFRs to true SFRs averaged over $10$ or $100\,\mathrm{Myr}$, the authors quantify calibration- and geometry-driven scatter: $\mathrm{H}\alpha$ SFRs are most sensitive to dust attenuation and the dust-to-metal ratio, with attenuation curves (e.g., $k_{\mathrm{H}\alpha}/k_{\mathrm{H}\beta}$) playing a crucial role; IR SFRs track long-timescale star formation but suffer from UV photon leakage and burstiness; a hybrid $\mathrm{IR} + \mathrm{UV}$ estimator reduces scatter to $\sim0.27$ dex and mitigates attenuation corrections. The $L_{[\mathrm{CII}]}$–SFR relation is steeper than some prior work ($\sim1.4$) with substantial scatter driven by metallicity and gas density, and the deficit is not universal. The results provide practical benchmarks for interpreting high-$z$ SFR indicators and highlight the need for realistic dust physics and sampling when using IR and line tracers in observational surveys.

Abstract

Inferring the star formation rates (SFR) in high redshift galaxies remains challenging, owing to observational limitations or uncertainties in calibration methods that link luminosities to SFRs. We utilize two state-of-the-art hydrodynamical simulations NewHorizon and NewCluster, post-processed with the radiative transfer code Skirt, to investigate the systematic uncertainties and biases in the inferred SFRs for z=5 galaxies; an epoch where galaxies build-up their stellar mass. We create synthetic observables for widely-used tracers: Halpha nebular line, [CII] 158 micron fine-structure line, total infrared (IR) continuum luminosity, and hybrid (IR + UV). We find that Halpha-inferred SFRs, time-averaged over 10 Myr, are sensitive to the choice of calibration and exhibit substantial scatter driven by dust attenuation, viewing angle, and dust-to-metal ratio. Adopting a steeper attenuation curve reduces this scatter significantly but does not fully eliminate systematic uncertainties. IR continuum-based SFRs trace intrinsic SFRs time-averaged over 100 Myr timescales when a well-sampled continuum emission between restframe 8 and 1000 micron is available and underestimate them with typical approaches when IR data are limited. Nevertheless, IR SFRs display a considerable scatter, largely due to UV photon leakage and strong variations in the star formation history. When UV data are available, hybrid (IR + UV) SFRs provide a more robust estimate, reducing scatter compared to IR-based SFRs while avoiding explicit attenuation corrections. Finally, we derive a [CII]-SFR relation finding a steeper relation than previous studies, however with significant scatter linked to gas density and metallicity. Overall, IR-, hybrid-, and [CII]-based tracers remain more robust than Halpha against variations in optical depth.

Figures (15)

• Figure 1: Projection of the gas mass (left) and post-processed Skirt output of the H$\alpha$ (middle) and [Cii] (right) emission of the most and least massive NewCluster (top two rows) and NewHorizon (bottom two rows) galaxies in a face-on configuration. The bar shows the physical scale of each source in kpc.
• Figure 2: Integrated spectral energy distribution of one representative NewCluster galaxy as produced by the Skirt radiative transfer simulations assuming a dust-to-metal ratio of 16%. Left: Full SED in the observed frame, shown for both the face-on (black) and edge-on (teal) configurations, spanning wavelengths from the ultra-violet to the millimeter. Shaded vertical regions show the coverage of ALMA bands 3, 7, and 9, and the dashed line demonstrates the JWST IFU range. Right: Examples of continuum-subtracted emission lines extracted from the same SED.
• Figure 3: H$\alpha$-derived SFRs using Eq. \ref{['eq:halpha-reddy22']} versus SFR$_{\rm 10\,Myr}$ for NewCluster (black squares) and NewHorizon (red circles) simulated galaxies. The identity line is shown in black, the purple and orange dotted lines show the best-fit of the H$\alpha$-derived SFRs using the conversion of reddy2022 and murphy2011, respectively (see Sect. \ref{['section:halpha-sfr']} for details). In the top left corner, the slopes and offsets are shown with the same color code as the lines, and the scatter $\sigma$ of the inferred SFRs.
• Figure 4: Same as Fig. \ref{['fig:sfr-halpha']}, for the IR-inferred SFRs versus time-averaged SFR over 100 Myr. The SFRs are derived using kennicutt1998 conversion (Eq. \ref{['eq:sfr-lir']}) and the best fit is the purple dashed line.
• Figure 5: Same as Fig. \ref{['fig:sfr-halpha']}, for the Hybrid-inferred SFRs (IR + UV) versus time-averaged SFR over 100 Myr. The SFRs are derived using the conversion in Eq. \ref{['eq:sfr-hybrid']} and the best fit is the purple dashed line.