The positive velocity shift of absorption transitions tracing diffuse material observed in a galaxy spectrum is an unambiguous signature of gas flow toward the host system .
Spectroscopy probing , e.g. , Na I resonance lines in the rest-frame optical or Mg II and Fe II in the near-ultraviolet is in principle sensitive to the infall of cool material at temperatures T \sim 100 - 10 , 000 K anywhere along the line of sight to a galaxy ’ s stellar component .
However , secure detections of this redshifted absorption signature have proved challenging to obtain due to the ubiquity of cool gas outflows giving rise to blueshifted absorption along the same sightlines .
In this chapter , we review the bona fide detections of this phenomenon .
Analysis of Na I line profiles has revealed numerous instances of redshifted absorption observed toward early-type and/or AGN-host galaxies , while spectroscopy of Mg II and Fe II has provided evidence for ongoing gas accretion onto > 5 \% of luminous , star-forming galaxies at z \sim 0.5 - 1 .
We then discuss the potentially ground-breaking benefits of future efforts to improve the spectral resolution of such studies , and to leverage spatially-resolved spectroscopy for new constraints on inflowing gas morphology .