A Detailed Investigation of Projection Effects Relevant to the Study of Powerful Classical Double Radio Sources

摘要

A detailed investigation of projection effects involved in the study of classical double sources is presented here. Theoretical calculations of the way projection effects enter empirically determined parameters are studied. It is shown that some parameters, such as the lobe width, are rather insensitive to the projection angle, while other parameters, such as the ambient gas density, are more sensitive. The deviation of the observed value from the true value of any given parameter is usually not significant when the projection angle is greater than about 60° and is significant only at very small projection angle, at which the symmetry axis of the source is pointing close to the line of sight to the observer. Applications of the theoretical model to a sample of classical double radio sources yield the following principal results: 1. A comparison between the radio-loud quasars and the radio galaxies in the sample suggests that their average projection angles are very similar. The average projection angle of the radio-loud quasars in the sample is greater than 35°-40° at the 3 σ level, assuming that the average projection angle of radio galaxies is 70° or above. 2. On average, the low-redshift radio-loud quasars in the sample have much lower lobe surface brightness and lower nonthermal pressure than the low-redshift radio galaxies, a result which cannot be explained by projection effects. This is consistent with the fact that the radio-loud quasars appear to be "fatter" than the radio galaxies, as previously noted by Leahy, Muxlow, & Stephens. 3. The study of departures of the magnetic field strength from that estimated using the minimum-energy conditions suggests that the projection angle of Cygnus A is greater than about 40° (at 3 σ) to 55° (at 2 σ), in agreement with the independent results of Sorathia et al. These departures also indicate that the projection angles of most of the sources in the sample, including galaxies and quasars, are likely to be greater than about 30° (at 3 σ) to 40° (at 2 σ). This result does not depend on any assumptions about the average projection angle of radio galaxies and is consistent with result 1 stated above. Thus, it is very unlikely that projection significantly affects key parameters, such as the ambient gas temperature and density, for the sources studied here.