A remarkable correlation is found in radio-loud quasars and BLLacs when the directly observed angular motions , \mu , of features ejected in the innermost regions of their jets are plotted on logarithmic scales versus the directly observed 15 GHz flux density , S , of their central engines : an abrupt upper envelope cut-off with a slope of 0.5 is obtained .
This upper envelope and slope can be explained in a simple non-relativistic ejection model if ( a ) , radio-loud quasars are radio standard candles and ( b ) , for the sources defining the cut-off , the features are all ejected with similar speeds .
The upper envelope is then due to the maximum projected velocity seen when the accretion disk is edge-on , and ejections are in the plane of the sky .
In our simple ejection model , where S is a good measure of relative distance , the observed distribution of angular motions can be explained if the radio luminosity of the source is a function of viewing angle , increasing towards face-on .
In this scenario the flux densities of many of the sources with small viewing angles are increased above the detection limit , significantly altering the expected velocity distribution .
This argument can not be used in the cosmological redshift model , where Doppler boosting is then required .
Here we show that when \mu is plotted versus redshift , z , the same upper envelope cut-off is seen .
It is not as sharply defined , since , in this simple model , the \mu upper envelope will be smeared out by sources lying at different cosmological distances , z _ { c } .
Normalizing all sources to the same distance ( 1 Jy ) using the flux density , S , removes this smearing and improves the sharpness of the upper envelope , supporting our assumption that S is a measure of relative distance .
In this model the redshift of quasars can not be a reliable indication of their distance .