4 Discussions

We have presented some new results of CCD photometry for three BL Lac objects in 1993-1998. During our observation OJ 287 was in the stage of a large periodic outburst which consisted of at least two peaks. Almost all the observations obtained over consecutive nights detected intranight variations. In 1995 and 1996 BL Lac kept in faint states, with fewer and smaller rapid flares and flickers. On the contrary, in late 1997 BL Lac was at the stage of a large outburst, accompanied with much more large amplitude rapid flares and fluctuations. Previous observation by Webb et al. (1988) also showed similar variability behaviour. Over the interval from 4 January 1981 to 15 December 1985, BL Lac was faint at $15.6 \leq B\leq 17.2$ mag and occurred with relatively little flaring activity, while in 1970-1981 when BL Lac was much brighter, 1-2 mag flares occurred frequently (see Fig. 1 of Webb et al. 1988). PKS 0735+178 was almost at its faint end from 1994 to early 1998. Over this time interval, the intraday variations and microvariations in PKS 0735+178 were rare and the amplitude was very small, except a rapid darkening of $\sim\! 0.4$ mag on 24 January 1995. On the contrary, in 1970-1986 when the source was brighter than 16.5 mag in the B band at most time, Webb et al. observed many large rapid flares (see Fig. 1 and Table 3 of Webb et al. 1988). PKS 2155-304 (see Fig. 8 of Pian et al. 1997) and S5 0716+714 (see Fig. 2 of Wagner et al. 1996) also exhibited similar variability behaviours as BL Lac and PKS 0735+178, with more rapid flares in the bright state than in the faint state. Other BL Lac objects probably showed this variability behaviour too. But what causes this difference?

It is now widely believed that the continua emission of blazars mainly originates in the relativistic jet and is boosted by relativistic beaming,

S=S₀D⁴,

where S is the observed flux, S₀ the intrinsic flux, and D the Doppler factor,

$$D=\frac{1}{\gamma(1-\beta\cos\theta)},$$ (3)

$\theta$ is the angle of the jet orientated from the line of sight, $\beta =v/c$, c is the speed of light, v is the speed of the jet, $\gamma =(1-\beta^{2})^{-1/2}$.Suppose the orientation of the relativistic jet in a BL Lac object is not fixed in some cases and varies by a small amplitude with the time. According to Eqs. (3) and (2), this may cause the variation of Doppler factor D and hence the variation of observed flux S. That is to say, the observed variability in a BL Lac object can be divided into two components, one is the intrinsic flux variations of S₀ caused by randomly occurring, radiating decaying shocks or other motions in the relativistic jet and amplified by relativistic beaming, the other is the contributions from geometric variations of the orientation of the jet. As mentioned in the Introduction section, the difference between the periodicity in long timescale variability and the irregularity of short timescale variability suggests that the former have a different origin from the later. It is natural to deduce that the intrinsic flux variations of S₀ caused by randomly occurring shocks is just the irregular short time scale variations, the long time scale variability is thus caused by the variation of Doppler factor D, and the outburst states and low states, which provide the base-levels for small flares or flickers, are the states that $\theta$ varies to near the maximum and minimum, respectively. Therefore, when staying in low states, BL Lac objects have smallest Doppler factors, the intrinsic flares are least boosted, and the smaller ones will not be enhanced large enough to be observed. That is why BL Lac, PKS 0735+178, S5 0716+714 and PKS 2155-304 were less active and exhibit fewer small flares and flickers when they were in faint states.

The relativistic jet model above expanded can also explain the stable colour found during the periodic outburst in OJ 287 (Sillanp$\ddot{\rm a}\ddot{\rm a}$ et al. 1996b), since the motion of the orientation of a jet do not change the emission mechanism. Takalo et al. found that for both 3C 66A and OJ 287 the observed total amplitude of variations $\bigtriangleup f_{\nu}$ depends on the observing frequency approximately as $\nu^{-1}$ in the optical-infrared regime (Takalo et al. 1996), i.e.,

$$\bigtriangleup f_{\nu}\propto \nu^{-1}.$$ (4)

This phenomena can also be explained. The total amplitude of variations, according Eq. (2), is

$$\bigtriangleup f_{\nu}=S_{0}(D_{\rm max}^{4}-D_{\rm min}^{4}).$$ (5)

For blazars which are dominated by nonthermal emission, we have

$$S_{0}\propto \nu^{-\alpha},$$ (6)

where $\alpha$ is the spectra index. We thus have

$$\bigtriangleup f_{\nu}\propto S_{0}\propto \nu^{-\alpha}.$$ (7)

For 3C 66A, the average spectra index in the optical-infrared regime is $\alpha = 1.0$ (Takalo et al. 1996), thus the total amplitude of variations is $\bigtriangleup f_{\nu} \propto \nu^{-1}$.For OJ 287, the average spectra index in the optical-infrared regime is $\alpha = 1.26$ (Kidger 1995) or $\alpha = 1.20 \,\pm \,0.13$ (Cruz-Gonzalez & Huchra 1984), thus the total amplitude of variations approximately is $\bigtriangleup f_{\nu} \propto \nu^{-1}$.

If the motion of the orientation of a jet is precession and nutation (like the motion of the pole of the earth), that is to say the motion is periodic, the periodicity of long timescale is naturally an exhibition of this periodic motion. However, whether the variation of the orientation is possible needs further investigation to search for physical basis for it.

Acknowledgements

We are grateful to National Science Foundation of China and Yunnan Province for their support of this work.