We use analytical methods to develop a mathematical model that expresses the relationship between the linear size of some extragalactic radio sources (EGRS) and their redshift . Result shows that , where . For the purpose of obtaining an empirical relation of similar form, we carry out simple linear regression analyses of the observed linear sizes of these EGRS in our sample against their respective observed redshifts. We obtain an empirical relation of the form, , where and for radio-loud quasars and radio galaxies respectively, with correlation coefficients given by, for each of the sources. The correlation is marginal/slight. Comparing the theoretical and empirical relations, we find that the data show an inverse correlation which is similar to the theory. This suggestively indicates presence of cosmological effects on the size evolution of the radio sources. Moreover, we find that similarity in the behavior of the two sources in the plane, simply supports quasar/galaxy unification scheme in which the different observable properties that characterize these two subclasses of radio sources are aspect-dependent.
Analytical and statistical methods,with some plausible assumptions, have been used in this work to show presence of dense medium around compact steep-spectrum sources in our sample. This is done by carrying out regression analyses using our estimated jet's internal densities and some other source parameters for possible deductions. Results indicate that − and − data (where and are respectively, observed source linear size and ambient medium density) show strong correlations and yield power-law relations of the forms, ~. ±. and ~. ±. . A comparison with obtained theoretical relations suggestively indicates presence of dense gases around these sources. In addition, a simple linear regression analysis of − data shows that jet's particles may be responsible (in addition to the ambient gases) for the observed spectral turnover characteristic of compact steep spectrum sources.
We have used analytical methods in this paper to obtain a mathematical relation that describes relationship between the linear size of compact steep spectrum (CSS) sources and their redshift. Result shows that the source linear size has an inverse power-law dependence on the redshift. Moreover, for the purpose of obtaining an empirical relation that shows relationship between the liner size and the redshift, we carry out simple linear regression analyses on the observed linear sizes of the CSS sources in our sample against their respective observed redshifts. Results of the analyses indicate that the linear sizes of the quasars have direct power law relationship with their respective redshifts; while the converse is the case for their galaxy counterparts. Their correlation coefficients are marginal. In comparison with the obtained theoretical relation, we notice that for the CSS quasars, the linear size-redshift data show an inverse correlation. This is comparable with the theoretical relation. So, it suggests that the dynamical evolution of the source linear sizes may have some cosmological effects on it. However, the converse is the case for the CSS galaxies -the correlation is direct. The possible explanation for this difference is that quasars are observed at higher redshifts than their galaxy counterparts. Hence, the cosmological effects are expected to be more pronounced on the quasars. Furthermore, we use analytical methods again to obtain a theoretical relation that shows relationship between luminosity and redshift. The relation indicates that luminosity of a radio source has an inverse power-law relationship with redshift. This suggestively implies that the intrinsic luminosity of a radio source may be modified by cosmological evolution. Moreover, for the purpose of obtaining an empirical relation for comparison with the theory, we carry out linear regression analysis of observed luminosities against observed redshifts of the CSS quasars and galaxies in our sample. Results show that luminosities have excellent direct power-law relationship with redshifts. However, this is in contradiction to the obtained theory which shows inverse relationship between the two parameters. This excellent direct correlation has been attributable by some authors to strong luminosity selection effects in which samples with high luminosities are found at high redshifts. Therefore, if the selection effects are taken care of, we may be able to see the comparability of the theory with the empirical relation. Hence, we conclude that source radiated power may have some cosmological implications just like we saw in the size/redshift relation.
In this paper, we use analytical methods with some plausible assumptions to develop a mathematical model which may be used to obtain estimate of density of the intergalactic medium (IGM). This relation suggests that the plot of the linear sizes against the bolometric luminosities of the extragalactic radio sources in our sample should be able to furnish us with an estimate of the density of IGM in which the radio sources are domiciled. Moreover, for the purpose of obtaining an empirical relation similar to the theoretical model, we carry out linear regression analysis of linear sizes and luminosities of the 31 radio galaxies in our sample. The regression result shows an empirical relationship between observed source linear sizes and observed bolometric luminosities with slight correlation whose coefficient is 4. Moreover, we compared the theoretical relation and the empirical relation to obtain an estimate of the particle number density of the IGM in which the radio sources are located. The estimate indicates a very low density when compared with the values obtained by authors for the compact steep spectrum (CSS) sources. However, while the linear sizes of the CSS sources are of sub-galactic dimensions -they are located within the interstellar media (ISM) -those of the large extended extragalactic radio sources extend into the intergalactic media. The staggering difference in these obtained densities of IGM and ISM simply supports the general notion that there is a sharp decrease in the density at the IGM-ISM interface. Moreover, using theoretical approach again, with some plausible assumptions, we find another relation which may be used to estimate the ages of extragalactic radio sources. This relation possibly indicates that the plot of the linear sizes against velocities of the radio jets of the radio sources in our sample should be able to supply us with an estimate of the sources' ages. We find from the simple linear regression analysis of linear sizes and jet velocities of the radio galaxies in our sample, a relation with correlation coefficient given as 4, which is also marginal. Comparison of the two relations -theoretical and the empirical relations -gives an estimate of age of the radio sources. The value shows that these large extended extragalactic radio sources are old sources.
In this work, we use analytical methods to describe expansion of Extragalactic Radio Sources (EGRS). Result shows that source size expansion depends on the following parameters: age of the source, lobe internal pressure, ambient medium density, and angle of observation. Moreover, from the analyses, we have shown that the obtained results, and , suggestively implies that and . This shows that since , jet internal pressure exceeds the lobe’s internal pressure. Therefore, for a typical EGRS, this simply indicates that ambient medium density is higher in the jet region than in the region of the lobe. This is expected since the ambient density thins out from the central core to the region where lobe is located. It is in consonance with the notion that for large extended EGRS, lobes are located outside the host galaxies rather than within the host galaxies. Moreover, we can conclude from these results that compact steep spectrum sources have denser ambient medium than their more extended counterparts.
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