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.
