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The radio bridge shape of very powerful extended (FR II) radio sources has been studied in detail; the sample used here includes 12 radio galaxies and six radio-loud quasars with redshifts between 0 and 1.8. Specifically, the width and radio surface brightness of the radio bridge are measured as a function of distance from the radio hot spot on each side of each source. The width as a function of distance from the hot spot agrees very well with theoretical predictions based on the standard model of bridge growth, in which the bridge expands laterally because of a blast wave driven by the large pressure difference between the relativistic plasma in the radio hot spot and surrounding radio lobe and the adjacent ambient gas. The simple assumptions that go into the theoretical prediction are that the lobe radio power and width (measured in the vicinity of the radio hot spot) are roughly constant over the lifetime of a given source, and that the rate at which the bridge lengthens, referred to as the lobe propagation velocity, is roughly constant over the lifetime of a source. These three assumptions appear to be consistent with other independent studies of very powerful extended radio sources of the type studied here, within the present (rather large) observational uncertainties. The radio surface brightness as a function of distance from the hot spot agrees surprisingly well with a simple model in which the radio bridge undergoes adiabatic expansion in the lateral direction, assuming that the initial lobe radio power and lobe width are time independent for a given source. That is, the observed lobe surface brightness and width, and the width as a function of position along the radio bridge, are used to predict the radio surface brightness as a function of position along the radio bridge, assuming adiabatic expansion of the bridge in the lateral direction. The predicted and observed surface brightness along the bridge agree surprisingly well. This suggests that there is little reacceleration of relativistic electrons within the radio bridge and that the backflow velocity of relativistic plasma within the bridge is small compared with the lobe advance velocity. These results are consistent with implications based on the bridge shape and structure discussed by Alexander & Leahy since we consider only very powerful FR II sources here. The Mach number with which the radio lobe propagates into the ambient medium can be estimated using the structure of the radio bridge; this Mach number is the ratio of the lobe propagation velocity to the sound speed of the ambient gas. The lateral expansion of the bridge is driven initially by a blast wave. When the velocity of the blast wave falls to a value of the order of the sound speed of the ambient medium, the character of the expansion changes, and the functional form of the bridge width as a function of position exhibits a break, which may be used to estimate the ratio of the lobe advance velocity to the sound speed of the ambient gas. We observe this break in several sources studied here. The Mach number of lobe advance depends only upon the ratio of the width to the length of the bridge as a function of position, which is purely geometric. Typical Mach numbers obtained range from about 2 to 10 and seem to be roughly independent of redshift and the total size (core-lobe separation) of the radio source. The Mach number can be used to estimate the temperature of the ambient gas if an independent estimate of the lobe propagation velocity is available. Lobe propagation velocities estimated using the effects of synchrotron and inverse Compton aging of the relativistic electrons that produce the radio emission are combined with the Mach numbers in order to estimate ambient gas temperatures. The temperature obtained for Cygnus A matches that indicated by X-ray data for this source. Typical temperatures obtained range from about 1 to 20 keV. This temperature is characteristic of gas in clusters of galaxies at low redshift, which is interesting since we show in a companion paper that the ambient gas density in the vicinity of the same sources is similar to that observed in low-redshift clusters of galaxies. The temperature and density estimates of the ambient gas in the vicinity of any given source are combined to estimate the cooling time of the gas, which indicates whether or not the source is likely to be in a cooling flow region. It does appear that many of the sources may be in regions that would be defined as "cooling flow regions," since, for many sources, the cooling time is less than the age of the universe at the redshift of the source. It has been pointed out by Carilli et al. that the magnetic field strength in Cygnus A is likely to be about 0.3 of the minimum-energy value. We repeat the two independent tests discussed by Carilli et al. for Cygnus A and add a third independent test. All three tests suggest an offset from equipartition or minimum-energy conditions that are consistent with the Carilli et al. result; we obtain an offset of about 0.25. Furthermore, it is shown in a companion paper that all sources are likely to have a similar offset; the source-to-source dispersion in the offset must be less than about 15%.

Radio Bridge Structure and Its Application to Estimate the Mach Number and Ambient Gas Temperature of Powerful Sources