H-alpha as a Tracer of Star Formation in the SPHINX Cosmological Simulations

TL;DR

The paper tackles biases in using Hα as a star formation rate tracer at z>3 by leveraging the SPHINX cosmological simulations to quantify how metallicity and bursty star formation histories affect the SFR–L_{Hα} relation. It introduces two simulation-informed calibrations, including an EW_{Hα}-based form, that reduce the RMSE by up to ~0.06 dex compared with classical calibrations. Applying these calibrations to JWST-era Hα emitters at z ~ 6 modifies the inferred cosmic SFR density by about 12% and steepens the star formation main sequence by ~0.08 in the slope. The work also highlights practical limitations due to dust, IMF, and SPS-model choices, and provides guidance on when and how to apply the new calibrations to observations.

Abstract

The H-alpha (Ha) emission line in galaxies is a powerful tracer of their recent star formation activity. With the advent of JWST, we are now able to routinely observe Ha in galaxies at high redshift (z > 3) and thus measure their star formation rates (SFRs). However, using classical SFR(Ha) calibrations to derive the SFRs leads to biased results because high-redshift galaxies are commonly characterized by low metallicities and bursty star formation histories, affecting the conversion factor between the Ha luminosity and the SFR. In this work, we develop a set of new SFR(Ha) calibrations that allow us to predict the SFRs of Ha-emitters at z > 3 with minimal error. We use the SPHINX cosmological simulations to select a sample of star-forming galaxies representative of the Ha-emitter population observed with JWST. We then derive linear corrections to the classical SFR(Ha) calibrations, taking into account variations in the physical properties (e.g., stellar metallicities) among individual galaxies. We obtain two new SFR(Ha) calibrations that, compared to the classical calibrations, reduce the root mean squared error (RMSE) in the predicted SFRs by $Δ$RMSE $\approx$ 0.04 dex dex and $Δ$RMSE $\approx$ 0.06 dex, respectively. Using the recent JWST NIRCam/grism observations of Ha-emitters at z ~ 6, we show that the new calibrations affect the high-redshift galaxy population statistics: (i) the estimated cosmic star formation rate density decreases by $Δρ$(SFR) $\approx$ 12%, and (ii) the observed slope of the star formation main sequence increases by $Δ$ $\partial$log SFR / $\partial$log M* = 0.08 $\pm$ 0.02.

Figures (7)

• Figure 1: Intrinsic SFR---$L_{\mathrm{H}\alpha}$ relation in the SPHINX$^{20}$ cosmological simulation, color-coded by the stellar metallicity. The SFR values are averaged over $t=10$ Myr, i.e., the typical lifetime of stars traced by $\mathrm{H}\alpha$. The diamonds show the median SFR in the bins of $L_{\mathrm{H}\alpha}^{\mathrm{int}}$, with the error bars showing the standard error on the median. The shaded region indicates the 68% ($1\sigma$) confidence interval. The diagonal lines show the SFR($\mathrm{H}\alpha$) calibrations from the literature, i.e. (top to bottom): the original K98 calibration, the K98 calibration converted to the Kroupa IMF, and two calibrations from T19 calculated for the Kroupa IMF and two different metallicities ($Z_*=Z_\odot$ and $Z_*=0.1Z_\odot$, respectively).
• Figure 2: SFR bias factor ($\Delta_{\mathrm{SFR}}{} \equiv \mathrm{SFR}\left(\mathrm{H}\alpha\right)/\mathrm{SFR}_{10}$) as a function of stellar metallicity (top) and age (bottom) in SPHINX, color-coded by $\mathrm{EW}_{\mathrm{H}\alpha}$. The SFR($\mathrm{H}\alpha$) values are calculated using the T19 calibration ($Z_*=Z_\odot$). The diamonds show the running median, with the error bars indicating the standard error on the median. The shaded region indicates the 68% ($1\sigma$) confidence interval.
• Figure 3: Comparison of the SFR($\mathrm{H}\alpha$) calibrations as a function of the intrinsic $\mathrm{H}\alpha$ luminosity: T19 calibration (gray) and the new SFR($\mathrm{H}\alpha$) calibrations given in \ref{['eq:sfr-calib-lha-corr']} (cyan) and \ref{['eq:sfr-calib-ewha-corr']} (magenta). The vertical axis represents the SFR bias factor ($\Delta_{\mathrm{SFR}}{} \equiv \mathrm{SFR}\left(\mathrm{H}\alpha\right)/\mathrm{SFR}_{10}$; closer to $\log \Delta_{\mathrm{SFR}}{} = 0$ is better). The diamonds show the running median, with the error bars indicating the standard error on the median. The shaded regions indicate the 68% ($1\sigma$) confidence interval.
• Figure 4: Star formation main sequence (SFMS) in the JWST ALT survey Naidu24DiCesare2025 with SFRs calculated using the T19 calibration (gray) and the new SFR($\mathrm{H}\alpha$) calibrations given in \ref{['eq:sfr-calib-lha-corr']} (cyan) and \ref{['eq:sfr-calib-ewha-corr']} (magenta). The diamonds show the running median, with the error bars indicating the standard error on the median. The shaded regions indicate the 68% ($1\sigma$) confidence interval. The dashed lines show the linear regression fits to the SFMS individually for each calibration.
• Figure 5: Same as \ref{['fig:model-int-dsfr']}, but for the observed (i.e., dust-attenuated) $\mathrm{H}\alpha$. In addition to $L_{\mathrm{H}\alpha}$ and $\mathrm{EW}_{\mathrm{H}\alpha}$, two SFR($\mathrm{H}\alpha$) calibrations use the Balmer decrement ($\mathrm{H}\alpha{}/\mathrm{H}\beta{}$) to predict the SFR (orange and light blue). The equations for the new calibrations are given in \ref{['sec:sfr-calib-dust']}.