Evidence for a maximum jet efficiency for the most powerful radio galaxies

We use new mid-infrared (mid-IR) photometry from the Spitzer Space Telescope to study the relations between low-frequency radio luminosity density L-nu 151 (MHz), mid-IR (12 mu m rest frame) luminosity nu L-nu 12 (mu m) and optical emission-line ([O II]) luminosity L-[O II], for a complete sample of z similar to 1 radio galaxies from the 3CRR, 6CE, 6C*, 7CRS and TOOT00 surveys. The narrow redshift span of our sample (0.9 < z < 1.1) means that it is unbiased to evolutionary effects. We find evidence that these three quantities are positively correlated. The scaling between nu L-nu 12 (mu m) and L-[O II] is similar to that seen in other active galactic nuclei samples, consistent with both nu L-nu 12 (mu m) and L-[O II] tracing accretion rate. We show that the positive correlation between nu L-nu 12 (mu m) and L-nu 151 (MHz) implies that there is a genuine lack of objects with low values of nu L-nu 12 (mu m) at high values of L-nu 151 (MHz). Given that nu L-nu 12 (mu m) traces accretion rate, while L-nu 151 (MHz) traces jet power, this can be understood in terms of a minimum accretion rate being necessary to produce a given jet power. This implies that there is a maximum efficiency with which accreted energy can be chanelled into jet power and this efficiency is of the order of unity.