`Upper-Limit Lensing': Constraining galaxy stellar masses with singly-imaged background sources

Strong gravitational lensing can provide accurate measurements of the stellar mass-to-light ratio $Υ$ in low-redshift ($z$ $\lesssim$ 0.05) early-type galaxies, and hence probe for possible variations in the stellar initial mass function (IMF). However, true multiple imaging lens systems are rare, hindering the construction of large nearby lens samples. Here, we present a method to derive upper limits on $Υ$ in galaxies with single close-projected background sources, where no counter-image is detected, down to some relative flux limit. We present a proof-of-principle application to three galaxies with integral field observations from different instruments. In our first case study, only a weak constraint on $Υ$ is obtained. In the second, the absence of a detectable counter-image excludes stellar masses higher than expected for a Salpeter IMF. In the third system, the current observations do not yield a useful limit, but our analysis indicates that deeper observations should reveal a counter-image if the stellar mass is any larger than expected for a Milky Way IMF. We discuss how our method can help enlarge the current samples of low-$z$ galaxies with lensing constraints, both by adding upper limits on $Υ$ and by guiding follow-up of promising single-image systems in search of fainter counter-images.