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Distant powerful radio sources would be a useful cosmological tool if an intrinsic length-scale or luminosity could be estimated in a way that is independent of the coordinate distance to the source. A model for the propagation of the radio lobes of powerful extended radio sources will be discussed; the model is written in terms of fundamental physical variables such as the luminosity in directed kinetic energy and the ambient gas density, rather than observables, such as the radio power. It will be shown that the fundamental physical variables are simply related to observed quantities.
The application of the model to powerful extended radio sources allows an estimate of the characteristic source sizes that is nearly independent of the de/acceleration parameter $q_o$. The characteristic source sizes estimated in the context of the model may be compared with the observed median source sizes, where each source size is determined directly from the angular extent of the source, the source redshift, and the coordinate distance to the source. The comparison of the model source sizes with the median sizes estimated from the angular source sizes allows an estimate of the de/acceleration parameter $q_o$.
The basic model and method has been applied to one published data set. A flat matter-dominated universe with $q_o = 0.5$ is consistent with the data, though, taken at face value, the data favor a low density universe with $q_o \sim 0$. A low value of $q_o$ implies that either space curvature or a cosmological constant is important at the present epoch. Note that Doppler boosting and beaming of radio emission is unlikely to be important in these systems since the relevant flow velocities are small compared with that of light.
The model also allows an estimate of the ambient gas density and other properties both intrinsic and extrinsic to a radio source. Estimates of these intrinsic and extrinsic properties will be presented and discussed.
This research was supported in part by a U.S. National Science Foundation grant and a National Young Investigator award.
