The JWST Emission Line Survey (JELS): A narrow-band determination of the H$α$ Luminosity Function and Cosmic Star Formation into the Epoch of Reionization

The recent star-formation activity in galaxies can be optimally traced by the H$α$ emission line, with the resulting H$α$ luminosity function (LF) at a given epoch providing a reliable probe of cosmic star formation. We present the first narrow-band determined H$α$ LF into the Epoch of Reionization (EoR) at $z\sim6.1$, using 39 H$α$ emitters selected from the JWST Emission Line Survey (JELS). The observed and dust-corrected LFs are broadly consistent with recent slitless spectroscopic measurements but show notable discrepancies with predictions from cosmological simulations, likely reflecting differences in emission-line and dust modelling. Fits combining multiple LF datasets help constrain the high-redshift faint-end slope of the H$α$ LF ($-1.79<α_{\rm{Hα}}<-1.62$), but there remains uncertainty in its evolution with redshift. Integrating the JELS dust-corrected H$α$ LFs yields a star-formation rate density of $\log_{10}(ρ_{\rm{SFR_{Hα}}}\,/\,\rm{M_{\odot}\,yr^{-1}\,Mpc^{-3}})=-1.93\,^{+0.14}_{-0.12}$ or $-2.00\,^{+0.16}_{-0.10}$, assuming a continuum-to-line extinction ratios $η_{\rm{dust}}=A_{\rm{cont}}(\rm{6563\,\mathring{A}})/A_{\rm{Hα}}=1$ and 0.44, respectively. Both measurements are consistent within uncertainties with previous results using standard assumptions for the LF integration limit ($L_{\rm{Hα,\,lim}}$) and SFR calibration constant $κ_{\rm{Hα}}$, despite the uncertainties in the dust corrections. We explore the metallicity dependence of $κ_{\rm{Hα}}$ and find $ρ_{\rm{SFR_{Hα}}}$ decreases 0.43 dex compared to the fiducial result and is no longer consistent with UV-determined $ρ_{\rm{SFR}}$ at $z\sim6$. This work highlights the importance of narrow-band surveys in probing the faint H$α$ population and providing new constraints on cosmic star-formation activity into the EoR.