3 Discussion

The largest observed amplitude of variability in the infrared bands are $\Delta J = 2\hbox{$.\!\!^{\rm m}$}29$, $\Delta H = 2\hbox{$.\!\!^{\rm m}$}42$, and $\Delta K = 2\hbox{$.\!\!^{\rm m}$}93$. During the same period the largest observed amplitude of variability in the optical bands are: $\Delta U = 3\hbox{$.\!\!^{\rm m}$}39(14.58-17.97)$, $\Delta B = 3\hbox{$.\!\!^{\rm m}$}70 (14.29-17.99)$, $\Delta V = 3\hbox{$.\!\!^{\rm m}$}11 (13.62-16.73)$, $\Delta R = 2\hbox{$.\!\!^{\rm m}$}73(13.26-15.99)$, $\Delta I = 2\hbox{$.\!\!^{\rm m}$}54 (12.56-15.10)$, which are slightly greater than that in the infrared. That result could be due to a larger contamination in the near-infrared by the underlying galaxy or to a better sampling of the light curve in the optical band. BL Lac is rapidly variable in the optical: by a factor of 2.5 over a time scale of 26 hours (Veron 1978), $1\hbox{$.\!\!^{\rm m}$}0$ over about one hour (Weistrop & Goldsmith 1973), $0\hbox{$.\!\!^{\rm m}$}5$ over a few minutes (Weistrop 1973), daily variation as great as $0\hbox{$.\!\!^{\rm m}$}3$ (Caswell et al. 1974), and $0\hbox{$.\!\!^{\rm m}$}56$ over a short time scale of 40 minutes in the B band (Xie et al. 1988); intraday variability of $0\hbox{$.\!\!^{\rm m}$}21$(Heidt & Wagner 1995), a variability by a factor of 2.6 over a time scale of 24 hours was observed in the K band (Impey et al. 1984). Rapid variation in the infrared flux favors a nonthermal mechanism over thermal emission by dust (Cruz-Gonzalez & Huchra 1984). For 3C 66A, De Diego et al. (1997) found that if the largest flux in the infrared is due to thermal processes, then the peak flux suggests that the emitting region is close to light months in diameter while the observed time scales of variability is much shorter. So violent variations in the infrared of BL Lacertae mean that the IR radiation cannot be thermal. In addition, high infrared polarization $P_{\rm IR}=15.1\%$ reported in the H band (Impey et al. 1984) suggests the infrared emission is non-thermal.

As for the spectrum and the brightness of the object, although there is a correlation between B-I and B: $B=(1.31\ \pm\ 0.02)(B-I) +(13.03 \pm 0.1)$ with a correlation coefficient r=0.67 (Fan et al. 1998), there is almost no similar correlation in the infrared, which is probably due to the effect of the underlying galaxy diluting this kind of correlation.

There is a strong correlation between J-H vs. J-K and J-K vs. H-K, but there is almost no correlation between J-H and H-K: $J-K = (1.15 \pm 0.02) (J-H) + 0.70\ \pm\ 0.02$, $H-K = (0.57\ \pm\ 0.003) (J-K) -0.16 \pm 0.01$. Other radio selected BL Lac objects (0219+428, 0422+004, 0735+178, 0829+046 and 1418+546) (Massaro et al. 1995) show similar properties. They show strong color-color correlations both for J-H and J-K and for J-K and H-K, but not for J-H and H-K. We think that one of the reasons is probably due to the fact that J-K has a wider distribution than J-H and H-K. That J-H and H-K concentrate in a small region dilutes the correlation; another reason probably comes from the fact that the spectrum deviates from the power-law.

The long-term (about 20 years) infrared light curves have been presented, there are strong correlations between J-K and J-H as well as H-K. The infrared emission is nonthermal.

Acknowledgements

This work is supported by the National Pandeng Project of China.