Improving Accretion Diagnostics for Young Stellar Objects with Mid-infrared Hydrogen lines from JWST/MIRI

We present a comprehensive study of mid-infrared neutral hydrogen (H~\textsc{i}) emission lines in 79 nearby (d $<$ 200 $pc$) young stars using JWST/MIRI. We aim to identify mid-infrared H~\textsc{i} transitions that can serve as reliable accretion diagnostics in young stars, and evaluate their utility in deriving physical conditions of the accreting gas. We identify and measure 22 H~\textsc{i} transitions in the MIRI wavelength regime (5-28 $\mu m$) and perform LTE slab modelling to remove the H\textsubscript{2}O contribution from selected H~\textsc{i} transitions. We find that mid-IR H~\textsc{i} line emission is spatially compact, even for sources with spatially extended [Ne~\textsc{ii}] and [Fe~\textsc{ii}] jets, suggesting minimal contamination from extended jet. Although Pfund~$\alpha$ (H~\textsc{i}~6--5) and Humphreys~$\alpha$ (H~\textsc{i}~7--6) are the strongest lines, they are blended with H$_2$O transitions. This blending necessitates additional processing to remove molecular contamination, thereby limiting their use as accretion diagnostics. Instead, we identify the H~\textsc{i}~(8--6) at 7.502 $\mu m$ and H~\textsc{i}~(10--7) at 8.760 $\mu m$ transitions as better alternatives, as they are largely unaffected by molecular contamination and offer a more reliable means of measuring accretion rates from MIRI spectra. We provide updated empirical relations for converting mid-IR H~\textsc{i} line luminosities into accretion luminosity for 6 different H~\textsc{i} lines in the MIRI wavelength range. Moreover, comparison of observed line ratios with theoretical models shows that MIR H~\textsc{i} lines offer robust constraints on the hydrogen gas density in accretion columns, $n_\mathrm{H} =$10$^{10.6}$ to 10$^{11.2}$ cm$^{-3}$ in most stars, with some stars exhibiting lower densities ($<10^{10}$~cm$^{-3}$), approaching the optically thin regime.