Towards the first detection of strongly lensed HI emission

We report interferometric observations tuned to the redshifted neutral hydrogen (HI) 21cm emission line in three strongly lensed galaxies at $z \sim 0.4$ with the Giant Metrewave Radio Telescope (GMRT). One galaxy spectrum (J1106+5228 at z=0.407) shows evidence of a marginal detection with an integrated signal-to-noise ratio of 3.8, which, if confirmed by follow-up observations, would represent the first strongly lensed and most distant individual galaxy detected in HI emission. Two steps are performed to transcribe the lensed integrated flux measurements into HI mass measurements for all three target galaxies. First, we calculate the HI magnification factor $\mu$ by applying general relativistic ray-tracing to a physical model of the source-lens system. The HI magnification generally differs from the optical magnification and depends largely on the intrinsic HI mass $M_{\rm HI}$ due to the HI mass-size relation. Second, we employ a Bayesian formalism to convert the integrated flux, amplified by the $M_{\rm HI}$-dependent magnification factor $\mu$, into a probability density for $M_{\rm HI}$, accounting for the asymmetric uncertainty due to the declining HI mass function (Eddington bias). In this way, we determine a value of $\log_{\rm 10} (M_{\rm HI}/M_\odot) = 10.2^{+0.3}_{-0.7}$ for J1106+5228, consistent with the estimate of $9.4\pm0.3$ from the optical properties of this galaxy. The HI mass of the other two sources are consistent with zero within a 95 per cent confidence interval however we still provide upper limits for both sources and a $1\sigma$ lower limit for J1250-0135 using the same formalism.