Jonathan Bird, Paul Martini, and Christian Kaiser 2007, ApJ, accepted
We determine the maximum lifetime t_max of 52 FRII radio sources found in 26 central group galaxies from cross correlation of the Berlind SDSS group catalog with the VLA FIRST survey. Mock catalogs of FRII sources were produced to match the selection criteria of FIRST and the redshift distribution of our parent sample, while an analytical model was used to calculate source sizes and luminosities. The maximum lifetime of FRII sources was then determined via a comparison of the observed and model projected length distributions. We estimate the average FRII lifetime is 1.5x10^7 years and the duty cycle is ~8x10^8 years. Degeneracies between t_max and the model parameters: jet power distribution, axial ratio, energy injection index, and ambient density introduce at most a factor of two uncertainty in our lifetime estimate. In addition, we calculate the radio active galactic nuclei (AGN) fraction in central group galaxies as a function of several gropu and host galaxy properties. The lifetime of radio sources recorded here is consistent with the quasar lifetime, even though these FRIIs have substantially sub-Eddington accretion. These results suggest a fiducial time frame for energy injection from AGN in feedback models. If the morphology of a given extended radio source is set by large-scale environment, while the lifetime is determined by the details of the accretion physics, this FRII lifetime is relevant for all extended radio sources.
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