Evolution of H α equivalent widths from z ∼ 0.4 - 2.2: implications for star formation and legacy surveys with <i>Roman</i> and <i>Euclid</i>

ABSTRACT Past studies have investigated the evolution in specific star formation rate (sSFR) and its observational proxy (H $\alpha$ equivalent width; EW) up to $z \sim 6$; however, such measurements may overestimate the typical sSFR/EW at a given redshift due to selection effects. We investigate the ‘intrinsic’ (selection and observational effects corrected) H $\alpha$ EW distributions of $z \sim 0.4 - 2.2$ narrowband-selected H $\alpha$ samples from High-z Emission Line Survey (HiZELS) and Deep and Wide Narrowband survey (DAWN) using a forward modelling approach where we assume an ‘intrinsic’ exponential EW distribution, apply selection and filter effects, and compare with observed H $\alpha$ EW distributions. We find an ‘intrinsic’ EW–stellar mass anticorrelation, EW$_0 \propto M^\gamma$, with steepening slopes $\gamma = -0.18\pm 0.03$ to $-0.24^{+0.06}_{-0.08}$ at $z \sim 0.4$ and $z\sim 2.2$, respectively. At $10^{10}$ M$_\odot$, we find EW$_0 \propto (1+z)^{1.78^{+0.22}_{-0.23}}$ and a steeper evolution with decreasing stellar mass highlighting the high EW nature of low-mass, high-z systems. We model this redshift evolving EW–stellar mass anticorrelation, $W_0(M,z)$, and find it produces H $\alpha$luminosity and SFR functions strongly consistent with observations. Our $W_0(M,z)$ model suggests EW$_{\mathrm{0}}$$&amp;gt; 200$ Å emitters contribute $\sim 40$ per cent to overall cosmic SF at $z \sim 1.5 - 2$, consistent with sSFR $\gt 10^{-8.5}$ yr$^{-1}$ (makes up $\sim 45 - 55$ per cent of cosmic SF at $z \sim 2$) and highlights the importance of high EW systems at high-z. Our $W_0(M,z)$ model also reproduces the cosmic sSFR evolution found in both simulations and observations (including selection limits), such that selection effects in observations may explain the disagreement. Lastly, we forecast Roman and Euclid grism surveys using our $W_0(M,z)$ model including limiting resolution and observational efficiency effects. We predict $\sim 24\,000$ and $\sim 30\,000$$0.5 &amp;lt; z &amp;lt; 1.9$ H $\alpha$ emitters per deg$^{-2}$, respectively, down to $F_{\rm {H\alpha }+\rm {[N{{\small II}}]}} &amp;gt; 5\times 10^{-17}$ erg s$^{-1}$ cm$^{-2}$ including $10^{7.2 - 8}$ M$_\odot$ galaxies at $z &amp;gt; 1$ with EW$_{\mathrm{0}}$$&amp;gt; 1000$ Å. Both Roman and Euclid will observe some of the most bursty/high EW, low-mass star-forming galaxies near cosmic noon in unprecedented detail.