Evolution of Hα Equivalent Widths from z ~ 0.4-2.2: implications for star formation and legacy surveys with Roman and Euclid

We investigate the `intrinsic' Hα EW distributions of z ~ 0.4 - 2.2 narrowband-selected Hα samples from HiZELS and DAWN using a forward modeling approach. We find an EW - stellar mass anti-correlation with steepening slopes -0.18±0.03 to -0.24+0.06-0.08 at z ~ 0.4 and z~ 2.2, respectively. Typical EW increases as (1+z)^1.78+0.22-0.23 for a 10¹⁰ M_ emitter from 15+2.4-2.3{A} (z ~ 0.4) to 67.7+10.4-10.0{A} (z ~ 2.2) and is steeper with decreasing stellar mass highlighting the high EW nature of low-mass high-z systems. We model this redshift evolving anti-correlation, W₀(M,z), and find it produces Hα luminosity and SFR functions strongly consistent with observations validating the model and allowing us to use W₀(M,z) to investigate the relative contribution of Hα emitters towards cosmic SF. We find EW₀ > 200 {A} emitters contribute significantly to cosmic SF activity at z ~ 1.5 - 2 making up ~ 40% of total SF consistent with sSFR > 10-8.5 yr⁻¹ (~ 45 - 55%). Overall, this highlights the importance of high EW systems at high-z. Our W₀(M,z) model also reproduces the cosmic sSFR evolution found in simulations and observations and show that tension between the two can simply arise from selection effects in observations. Lastly, we forecast Roman and Euclid grism surveys using W₀(M,z) including observational efficiency and limiting resolution effects where we predict ~ 24000 and ~ 30000 $0.5 < z < 1.9$ Hα emitters per deg⁻², respectively, down to >5×10⁻¹⁷ erg s⁻¹ cm⁻² including 107.2 - 8 M_ galaxies at $z > 1$ with EW₀ >1000{A}. Both Roman and Euclid will enable us to observe with unprecedented detail some of the most bursty/high EW, low-mass star-forming galaxies near cosmic noon.