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On the whole, unified schemes for radio-loud AGN are very successful. But there remain some potential problems, including disturbing trends in the linear sizes of radio galaxies and quasars, a dependence on redshift of the ratio of quasars to radio galaxies, the lack of superluminal motion in radio galaxies, and the un-FR-I-like radio morphologies of some BL Lac objects. A number of complications also exist, like the need to include evolution in unified schemes (the critical angle separating different AGN classes or the ratio of Ljet / curlyLext may well depend on redshift), even as the relatively simple beaming models adopted so far are underconstrained by existing data. In this section we review known problems for unified schemes and anticipate complications that should be addressed when there are more complete data for larger samples of radio-loud AGN.

8.1 Potential Problems with Unification

8.1.1 Linear Sizes of Blazars and Radio Galaxies

In principle, the linear sizes of radio sources can be used to test unification because blazars oriented at small angles to the line of sight should have systematically smaller large-scale radio structures than radio galaxies in the plane of the sky. Right at the start, however, we must say that conclusions regarding the relative linear sizes of blazars and radio galaxies are extremely murky, having been the subject of quite a number of papers, with often contradictory results (Gopal-Krishna and Kulkarni 1992; Barthel 1989; Kapahi 1987; Kapahi 1989; Kapahi 1990; Barthel and Miley 1988; Onuora 1989; Onuora 1991; Hough and Readhead 1989; Nilsson et al. 1993, and references therein). It turns out that the linear size depends, not unexpectedly, on several factors like radio power and redshift. Even matching these variables, the expected difference in mean linear size is quite modest, only a factor of 2 for an orientation of 30° compared to 90°, while the scatter in intrinsic sizes must be many times that large.

In a recent work, Singal (1993a; see also Singal 1988) studied the linear sizes of a large, heterogeneous sample of radio galaxies (about half of which have redshifts estimated from the magnitude-redshift relation) and quasars. His main result is that both size-luminosity and size-redshift correlations are significantly different for the two classes. In particular, luminosity and size are directly correlated for radio galaxies and inversely correlated for quasars, while the size of radio galaxies falls strongly with redshift and not at all for quasars. According to Singal, the only redshift range for which unification works is 0.5 < z < 1, the interval Barthel (1989) used in his original analysis of the 3CR catalog ostensibly because of the better statistics there. Indeed, for the lowest luminosity bin and z leq 0.4, Singal (1993a) found that the median linear size of quasars is larger than that of radio galaxies, completely opposite to the predictions of the unified scheme.

These results, however, are uncertain and/or contradict other comparable work. One problem with determining linear sizes is that often the radio source morphology is unclear or the source is poorly resolved. In a similar study limited to sources with clear FR II double structures, which by definition have sharp outer boundaries, Nilsson et al. (1993) found quite different results for the dependence of linear size on redshift and luminosity; in direct contrast to Singal (1993a), the median values of the linear size for quasars are (marginally) smaller than for galaxies in all luminosity bins.

Another issue is the use of complete flux-limited samples. The 3CR catalog is excellent for this purpose because it is largely unbiased by beamed flux. From the luminosity function analysis we found quasars (effectively SSRQ) and radio galaxies are divided at thetac ~ 38° (Table 3); the mean angle for SSRQ (between 14° and ~ 38°) is therefore 28° and the mean angle for FR IIs is 66°. The ratio of quasar linear size to radio galaxy linear size, 1.9 for these mean angles, is both small and a very weak function of critical angle. Estimating the critical angle from the numbers of quasars and radio galaxies in the 3CR gives thetac = 44.4 ° (Barthel 1989), with a 1 sigma uncertainty of ± 6.6°; this gives a foreshortening factor of 1.9+0.3-0.2. The foreshortening factor would be much larger were one to compare only FSRQ and FR IIs, but there are too few FSRQ in the 3CR and using the 2 Jy sample would mean incorporating the selection bias of beaming, which is nontrivial.

Another complication is that even modest misalignments between large-scale radio structure and the obscuring torus are enough to confuse the expected linear size trend (Gopal-Krishna et al. 1994). For example, the distributions of observed linear size and bend angle for a large, heterogeneous sample of quasars and radio galaxies are completely consistent with random orientations within and without a cone angle of ~ 50°, respectively, assuming only that the jets have small intrinsic bend angles (ltapprox 25°) and modest intrinsic arm-length differences (Lister et al. 1994a). In sum, considering the many problems and potential complications, it is remarkable that the analysis of linear sizes of quasars and FR IIs gives any sensible results at all.

The comparison of linear sizes of FR I galaxies and BL Lac objects is even more difficult because the amorphous FR I radio structures have no clear outer boundaries. The largest angular sizes of the EMSS BL Lacs are similar to those of B2 FR Is and of a heterogeneous sample of radio-selected BL Lacs (Perlman and Stocke 1993), in apparent contradiction to their unification. This may be due to substantial misalignments between the parsec and kiloparsec scale jets (Perlman and Stocke 1993), which are quite common in BL Lacs (Kollgaard et al. 1992). In that case, a small angle to the line of sight of the VLBI jet does not necessarily imply a very small radio linear size.

In addition, if the bulk Lorentz factors in BL Lac objects are small (Sec. 6.3), the critical angle separating them from FR Is can be quite large. For example, for gamma ~ 2 and f ~ 0.05, thetac ~ 19° (Table 3). The corresponding ratio of projected lengths of BL Lacs and FR Is, evaluated at the mean angle (ignoring beaming) is ~ 3; for the XBL fit in Table 3 it is ~ 2.5.

Figure 21
Figure 21. The apparent velocity relative to the speed of light versus angle to the line of sight for an emitter approaching at relativistic speed. Different curves correspond to different Lorentz factors: from the top down, gamma = 15, 10, 5, 2. The dotted line corr esponds to betaa = 1. Note that betaa is essentially independent of gamma at large angles.

In the end, consideration of linear sizes of radio sources is not a compelling test of unified schemes. Even the oft-stated problem of large deprojected radio sizes - wherein the lengths of superluminal sources and/or one-sided jets as large as ~ 1 Mpc in length (like NGC 6251) are thought to be uncomfortably large when deprojected by their orientation angles - vanishes when one thinks about the numbers. Neither superluminal motion nor one-sidedness require a particularly small angle [Fig. 21 and Eq. (A4), Eq. (A8)], and in fact the expected deprojection correction is only a factor of 2 or so.

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