  We present Herschel observations of 22 radio galaxies, selected for the
presence of shocked, warm molecular hydrogen emission. We measured and modeled
spectral energy distributions (SEDs) in 33 bands from the ultraviolet to the
far-infrared to investigate the impact of jet feedback on star formation
activity. These galaxies are massive, early-type galaxies with normal
gas-to-dust ratios, covering a range of optical and infrared colors. We find
that the star formation rate (SFR) is suppressed by a factor of ~3-6, depending
on how molecular gas mass is estimated. We suggest this suppression is due to
the shocks driven by the radio jets injecting turbulence into the interstellar
medium (ISM), which also powers the luminous warm H2 line emission.
Approximately 25% of the sample shows suppression by more than a factor of 10.
However, the degree of SFR suppression does not correlate with indicators of
jet feedback including jet power, diffuse X-ray emission, or intensity of warm
molecular H2 emission, suggesting that while injected turbulence likely impacts
star formation, the process is not purely parameterized by the amount of
mechanical energy dissipated into the ISM. Radio galaxies with shocked warm
molecular gas cover a wide range in SFR-stellar mass space, indicating that
these galaxies are in a variety of evolutionary states, from actively
star-forming and gas-rich to quiescent and gas-poor. SFR suppression appears to
have the largest impact on the evolution of galaxies that are moderately
gas-rich.
