Discovery of Hydrogen Radio Recombination Lines at z=0.89 towards PKS 1830-211

We report the detection of stimulated hydrogen radio recombination line (RRL) emission from ionized gas in a $z=0.89$ galaxy using 580--1670 MHz observations from the MeerKAT Absorption Line Survey (MALS). The RRL emission originates in a galaxy that intercepts and strongly lenses the radio blazar PKS 1830-211 ($z=2.5$). This is the second detection of RRLs outside of the local universe and the first clearly associated with hydrogen. We detect effective H144$\alpha$ (and H163$\alpha$) transitions at observed frequencies of 1156 (798) MHz by stacking 17 (27) RRLs with 21$\sigma$ (14$\sigma$) significance. The RRL emission contains two main velocity components and is coincident in velocity with HI 21 cm and OH 18 cm absorption. We use the RRL spectral line energy distribution and a Bayesian analysis to constrain the density ($n_e$) and the volume-averaged pathlength ($\ell$) of the ionized gas. We determine $\log( n_e ) = 2.0_{-0.7}^{+1.0}$ cm$^{-3}$ and $\log( \ell ) = -0.7_{-1.1}^{+1.1}$ pc towards the north east (NE) lensed image, likely tracing the diffuse thermal phase of the ionized ISM in a thin disk. Towards the south west (SW) lensed image, we determine $\log( n_e ) = 3.2_{-1.0}^{+0.4}$ cm$^{-3}$ and $\log( \ell ) = -2.7_{-0.2}^{+1.8}$ pc, tracing gas that is more reminiscent of H II regions. We estimate a star formation (surface density) rate of $\Sigma_{\mathrm{SFR}} \sim 0.6$ M$_{\odot}$ yr$^{-1}$ kpc$^{-2}$ or SFR $\sim 50$ M$_{\odot}$ yr$^{-1}$, consistent with a star-forming main sequence galaxy of $M_{\star} \sim 10^{11}$ M$_{\odot}$. The discovery presented here opens up the possibility of studying ionized gas at high redshifts using RRL observations from current and future (e.g., SKA and ngVLA) radio facilities.