4.4.2. Brightness temperature and variability of the core

Kellermann et al. (1998) have used the Very Long Baseline Array at 15 GHz to image the structure of 132 strong compact AGNs, including 15 BLLs, 12 BL/HPQs and 31 HPQs, and derived the maximum brightness temperatures T (all T's listed in their table 3 are low by a factor of ten; Kellermann (1998), private communication). Many of the measured angular diameters are not larger than the nominal resolution, therefore the derived brightness temperatures are often lower limits.

observed with VLBI at 22 GHz 140 compact extragalactic radio sources, including 14 BLLs, 11 BL/HPQs and 42 HPQs. Meaningful values of the brightness temperature have been obtained for 9 BLLs, 9 BL/HPQs and 32 HPQs.

Fig. 6 shows the histograms of the observed brightness temperatures for the BLLs, BL/HPQs and HPQs separately for the two samples. It appears that the distributions of brightness temperatures are significantly different for BLLs and HPQs and that the distribution for the BL/HPQs is very similar to that of the HPQs. In fact, on average, the brightness temperatures for BL/HPQs are slightly higher than those of HPQs, in agreement with the assumption that BL/HPQs are extreme cases of HPQs with, on average, larger boosting factors.

Figure 6. Distributions of the brightness temperature of blazar radio cores as measured by Möllenbrock et al. (1996) and Kellermann et al. (1998)(after correction by a factor of ten; see text), plotted separately for the HPQs, BL/HPQs and BLLs.

Lähteenmäki & Valtaoja (1999) have used 22 and 37 GHz continuum flux data to derive variability time-scales and associated brightness temperatures T for a sample of 25 HPQs, 11 BL/HPQs and 10 BLLs. The variability time-scale is defined as = dt / d[ln(S)] ([71]). Again, the brightness distribution of the BL/HPQs is much more similar to that of the HPQs than to that of the BLLs: the brightness temperatures of the 7/9 BLLs are lower than 3 10¹² K; on the other hand, only 1/25 HPQ has such a low T, while 3/11 BL/HPQs have a low T.

The brightness temperatures derived from variability are systematically larger than those obtained directly from VLBI measurements because of the different dependence on the Doppler factor: T_VLBI = T₀ and T_var = T₀ ³ , i.e. T_var = T_VLBI ² (Lähteemäki et al. 1999).

Readhead (1994) and [240] showed that the maximum intrinsic brightness temperature is the equipartition value ~ 5 10¹⁰ K rather than the inverse Compton value ~ 10¹² K. [239] computed the boosting Doppler factor using the equation: = (T / 10^10.7)^1/3 ([49]); they found that generally the BLLs have a Doppler factor < 3 (except for OJ425, PKS1413+135 and S52007+77), while for HPQs and BL/HPQs, is in the range 4-25.

Hughes et al. (1992) have made a structure function analysis of the total flux density at centimeter wavelengths of 51 core dominated objects, including 12 BLLs, 6 BL/HPQs and 12 HPQs; they estimated a characteristic time-scale of variability (in the observer's frame) for each object; the distributions for the BL/HPQs and the HPQs are similar, while the distribution for the BLLs is significantly different; the median value is ~ 1 yr for both BL/HPQs and HPQs; it is ~ 3 yr for BLLs. There are 4/12 BLLs, 5/6 BL/HPQs and 10/12 HPQs with a time-scale smaller than 2.5 year. The one BLL with a very small time-scale (log(t) = -0.5) is PKS0048-09.

Smith & Nair (1995) have determined the rest-frame time-scale of variation of the base level of the optical light-curve of a sample of 36 BLLs; they found that objects with z > 0.4 (i.e. basically what we call BL/HPQs) have a mean rest-frame time-scale of 2.42 yr, while the mean time-scale for objects with z < 0.4 is 6.61 yr.

Heidt & Wagner (1996) have studied the optical intraday variability of 26 objects from a complete sample of 34 BLLs. The activity parameter I (in % per day) shows a bimodal distribution; eleven objects display an I between 3 and 27, while 15 have I < 3. Twelve of these objects are BL/HPQs, seven having I > 3, while only 4/14 BLLs have such a high variability index. There is therefore a correlation between fast optical variability and the presence of broad emission lines. The four BLLs with I > 3 are: PKS0426-380 and S41749+70 which both have a high luminosity extended radio component (see table 5), S50716+714 and OQ530. Heidt & Wagner have noted that low redshift (z < 0.4) objects have on average lower values of I than high z objects which is a similar effect since high z BLLs either have broad emission lines or may be extreme cases of HPQs with a very high amplification of the featureless continuum.

51 AGNs, all flat spectrum radio sources, including 7 BLLs, 7 BL/HPQs and 13 HPQs, are known to be sources of high-energy -rays (100 MeV). 77% (10/13) of the HPQs are variable in -rays while 71% (5/7) of the BL/HPQs and 28% (2/7) of the BLLs (S50716+71 and PKS2155-304) are variable ([305]).

It is clear that BLLs have lower brightness temperatures and are less variable on the average than both HPQs and BL/HPQs.