  We compare the low redshift (z ~ 0.1) Lyman-alpha forest from hydrodynamical
simulations with data from the Cosmic Origin Spectrograph (COS). We find
tension between the observed number of lines with b-parameters in the range
25-45 km/s and the predictions from simulations that incorporate either
vigorous feedback from active galactic nuclei or that exclude feedback
altogether. The gas in these simulations is, respectively, either too hot to
contribute to the Lyman-alpha absorption or too cold to produce the required
line widths. Matching the observed b-parameter distribution therefore requires
feedback processes that thermally or turbulently broaden the absorption
features without collisionally (over-)ionising hydrogen. This suggests the
Lyman-alpha forest b-parameter distribution is a valulable diagnostic of
galactic feedback in the low redshift Universe. We furthermore confirm the low
redshift Lyman-alpha forest column density distribution is better reproduced by
an ultraviolet background with an HI photo-ionisation rate a factor 1.5-3
higher than predicted by Haardt & Madau (2012).
