4.1. FR I and FR II galaxies
FR Is have been defined as having low radio brightness regions further away from the galaxy than the high brightness regions (edge-darkened morphologies), while FR II have high brightness regions further away from the galaxies than the low-brightness regions, i.e. they are the classical double radio sources with edge-brightened lobes (). The Fanaroff-Riley classification is somewhat subjective; although most objects can be assigned without ambiguity to one or the other classes, there are a number of intermediate objects which are difficult to classify (). FR Is generally have a 178 MHz luminosity below ~ 2.5 1033 erg s-1 Hz-1 while FR IIs are stronger than this value (); the division in power between the two classes is however not sharp, but when radio sources are plotted as points in the radio luminosity-optical luminosity plane, the Fanaroff-Riley break becomes very sharp, with the break radio power approximately proportional to the optical luminosity squared, ranging from 3 1031 erg s-1 Hz-1 for MR = - 21 to 4 1033 erg s-1 Hz-1 for MR = - 24 at 1400 MHz ().
Most radio galaxies contain a jet and a flat spectrum radio core.
FR IIs jets are generally one sided (). The depolarization of the lobes is systematically stronger on the counter-jet side, suggesting that the visible jet is on the near side of the source indicating that the jet asymmetry is due to the presence of relativistic beaming (; ). The large jet-counterjet brightness ratio observed in radio loud QSOs requires characteristic jet speeds > 0.6 c on kiloparsec scales ().
At parsec-scales, FR Is also have one-sided jets implying relativistic speeds (v/c ~ 0.9); these jets decelerate to non relativistic speeds within ~ 2 kpc from the nucleus becoming symmetrical (; ). At kpc-scales, they are most probably turbulent, subsonic flows with velocities of the order of 1 000-10 000 km s-1 (; ). In the FR I source 3C264.0, the jet seems to be relativistic ( ~ 5 where = (1 - 2)-0.5 is the Lorentz factor and = v/c) near the nucleus (< 300 pc) (); apparent superluminal transverse motion has been measured in the FR Is M87 () and B21144+35 ().
The kinematic Doppler factor
of a source moving in a
direction making an angle
to the line of sight and
having an intrinsic Lorentz factor
is defined as:
[ (1 -
If S0 is the unbeamed flux of the nucleus,
the observed value for the
same object having its intrinsically symmetric jet making an angle
the line of sight would be
If S0 is the unbeamed flux of the nucleus, the observed value for the same object having its intrinsically symmetric jet making an angle with the line of sight would be ():
with p = 3 + or p = 2 + for a single sphere or a continuous jet respectively, being the spectral index (S -) (). For a given value of , the maximum value of S/S0 is obtained for = 0°; for relativistic jets and small values of , S() ~ S0 p; S/S0 is minimum for = 90°, in which case, S/S0 = 2 -p; the ratio of the maximum to the minimum value of S/S0 is 2 (1 - )-p which is equal to 80 000 if p = 2 and = 10. Fig. 5 shows the change of the boosting factor S/S0 with the angle for various values of .
Figure 5. Changes of the boosting factor S/S0 with the viewing angle , for various values of .
We call R the flux ratio of the core to the extended components and R0 the value of R for an unbeamed source. In FR Is and FR IIs, the core luminosity is correlated with the extended radio power, the median value of R decreasing from 10-1 to 10-3 when the extended radio power (at 1400 MHz) increases from 1030 to 1034 erg s-1 Hz-1; the dispersion is however large (; ; ; ). Part of this dispersion is due to the fact that the jets are randomly oriented with respect to the line of sight (). The observed values of R span a wide range of values; the most lobe-dominated sources have ratios as low as R ~ 10-5; in contrast, the most core dominated sources can have R ~ 103 ().
As the extended emission of radio sources is unbeamed, statistically the ratio of the observed R value of any single object to the median value of R for radio objects having the same extended radio power will be a rough estimate of the enhancement factor (note however that the median value of R which is equal to R(60°) is not equal to R0).
For NLRGs, is larger on average than ~ 60° as objects with < 60° would generally appear as BLRGs or QSOs (). For this reason, QSOs and BLRGs tend to have relatively more powerful radio cores (by about a factor of ten) than NLRGs having the same extended luminosity (; ; Hardcastle et al. 1998).
Monte Carlo simulations of the Ptot vs Pcore diagram showed that the minimum Lorentz factor is below ~ 3.0 for FR Is sources () and above ~ 3.0 for FR IIs (; ). Wall & Jackson (1997) chose to model the Doppler beaming of the FR I and the FR II populations with a single Lorentz factor and a single intrinsic flux ratio R0 for each parent population and took p=2; Monte Carlo simulations gave R0 = 0.01 and = 10.3 for the FR Is and R0 = 0.004 and = 20 for the FR IIs. So, although these studies give significantly different values for the Lorentz factors, they agree on the fact that they are smaller in FR Is than in FR IIs.
Spatial and spectral measurements show that both resolved (thermal) and unresolved X-ray emission in FR Is are common, although the relative strength and size of the resolved component varies between objects; the thermal extended emission comes either from hot galactic corona or from intracluster gas; the unresolved X-ray component correlates well with the core radio emission (; ). The nuclear components do not seem to show any sign of absorption ().