Optical spectral changes are not very evident, but our data suggest a spectrum steepening when the source gets fainter, a feature that has already been recognized for other blazars. This behaviour can be interpreted in terms of radiative losses in the electron population of the emitting jet: when the source is bright, cooling can be balanced or overcome by acceleration processes and the resulting spectrum is flatter; when the flux is low, radiative losses dominate and cause a spectral steepening, since the higher-energy ultra-relativistic electrons emitting synchrotron radiation cool faster than the lower-energy ones. However, also a geometrical interpretation of the kind of that presented in Villata & Raiteri (1999; see also Villata et al. 2000) is possible: if a faint state of the source in a given band occurs when the portion of the curved jet emitting in that band becomes less aligned to the line of sight, then a spectral steepening is expected since the higher-frequency emitting portion of the jet departed first from the line of sight.

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{1594Raiterif13.ps}\end{figure}$

Figure 13: Discrete Correlation Function (DCF) between the R data and $14.5\rm ~GHz$ (top) or $8.0\rm ~GHz$ (bottom) data of AO 0235+16; all datasets have been binned over 2 days, while the DCF bin size is 20 days.

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{1594Raiterif14.ps}\end{figure}$

Figure 14: Discrete Correlation Function (DCF) between the 22 and $8.0\rm ~GHz$ data of AO 0235+16; in the bottom panel only data after ${\rm JD}=2450300$ have been considered; both datasets have been binned over 2 days, while the DCF bin size is 20 days.

Discrete autocorrelation function analysis of the optical and radio light curves points out a characteristic time scale for the flux variability of AO 0235+16 of about 11.2 years. However, a deeper insight into the optical and radio light curves aided by DFT analysis and folded light curves reveals that major outbursts occur at roughly half the above time scale, even if one of the events (the 1982 one) appears noticeably delayed.

Indeed, in the best sampled $8.0\rm ~GHz$ light curve, there are five large-amplitude outbursts whose peaks are separated by 2308, 1870, 2007, and 2091 days, giving an average "period" of 2069 $\,\pm\,$ 184 days, i.e. 5.7 $\pm$ 0.5 years. Taking into account that the AO 0235+16 redshift is z=0.94, the relation $P=P_{\rm obs}/(1+z)$ implies that the period in the source rest frame is around 2.8 years. Other characteristic frequencies resulting from the DFT analysis of the radio light curves correspond to periods of 1.8, 2.8, and 3.7years. In the optical, the sparse sampling makes the analysis of variability time scales rather difficult. However, discrete autocorrelation function, DFT, and folded light curves are compatible with a $\sim$ 2069 day periodicity. Such periodicity would not account for the observed big 1979 optical outburst, whose radio counterpart was a rather modest flux increase. The optical autocorrelation analysis puts in evidence also another characteristic time scale of variability of about 1200 days (3.3 years), which corresponds to the time separation between the 1975 and 1979 outbursts, while the DFT of the optical data confirm the 1.8 and 2.8 year periods found in the radio data.

A few previous studies investigated the existence of periodicities in AO 0235+16: Webb et al. (1988) analyzed the optical light curve with the Deeming DFT (Deeming 1975), and derived periods of 2.79, 1.53, and 1.29 years. More recently, Webb et al. (2000) used unequal-interval Fourier transform and CLEAN techniques and obtained periods of 2.7 and 1.2 years for the optical variations. The time scales of long-term optical base-level fluctuations have been studied by Smith & Nair (1995) for three classes of AGNs; they found a best fit period of 2.9 years for AO 0235+16, attributing a moderate confidence to the estimate. The Jurkevic technique and the autocorrelation function were adopted by Fan (2001) for the analysis of the optical light curves, inferring periods of 1.56, $2.95\pm0.25$ , and $5.87\pm 1.3$ years. This last period is highly compatible with what is derived in the present paper. Roy et al. (2000) made a cross-correlation analysis between optical and UMRAO radio data and applied Lomb-Scargle periodograms to the 14.5 and $8.0\rm ~GHz$ light curves to infer a $\sim$ 5.8 year periodicity. Their results are in agreement with what we find in the present paper.

If the major outbursts in AO 0235+16 really occur every $5.7 \pm 0.5$ years, the next one should peak around February-March 2004, and a great observational effort should be undertaken since at least summer 2003 to get more information on the details of the flux behaviour in various bands. Unfortunately, the source is not visible from ground-based optical observatories during springtime because of solar conjunction.

On the other hand, another great effort should be addressed to the theoretical interpretation of such recurrent events, in particular to envisage possible mechanisms that can "disturb" the period. Many models have been proposed to explain the $\sim$ 12 year period inferred from the optical light curve of another well-known BL Lac object, i.e. OJ 287; most of them foresee the existence of a binary black hole system (Sillanpää et al. 1988b; Lehto & Valtonen 1996; Villata et al. 1998; Valtaoja et al. 2000; Abraham 2000). It would be interesting to see whether those models can be adapted to explain the quasi-periodic variability observed in AO 0235+16.

As for the cross-correlation between the optical and radio data, the analysis of the light curves is constrained by the sometimes very sparse optical sampling. However, in general we can say that a radio flux increase always corresponds to each major optical flare; the vice versa is likely true. Such correlation would suggest that the same mechanism is responsible for the optical and radio variations. However, two different behaviours seem to be present: optical and radio fluxes are seen sometimes to reach their maximum values at the same time, while in some cases the higher frequencies lead the lower ones. This would mean that two different mechanisms are presumably at work in the long-term variability. Outbursts occurring simultaneously in all bands may suggest that the synchrotron emission from the radio to the optical band is produced by the same population of relativistic electrons in the same region. But they may also favour the microlensing scenario, which was already suggested for explaining the variability of AO 0235+16 (Stickel et al. 1988; Takalo et al. 1998; Webb et al. 2000; but see Kayser 1988 for a critical discussion). The presence of several foreground objects in the field of the source supports this scenario. One item against this hypothesis is that during the strong flux increase detected in both the optical and radio bands in 1997, the X-ray and $\gamma$ -ray fluxes were not seen in a high state.

On the other hand, the fact that in the radio and optical domains the variations observed at the higher frequencies lead those at the lower ones makes one think to an inhomogeneous jet, where a disturbance travelling downstream enhances first the emission at the higher frequencies and then the emission at the lower ones. An alternative view is given by geometrical models such as the previously mentioned helical model by Villata & Raiteri (1999), if we imagine that the portion of the jet emitting the higher-energy radiation gets closer to the line of sight before that producing the lower-energy flux, as already noted for the spectral changes.

A different interpretation is required to explain the noticeable intraday variability shown by AO 0235+16 in both the optical and radio bands. Indeed, on short time scales, the flux behaviour can be very different with respect to that exhibited on long time scales. Kraus et al. (1999) observed an "unusual" radio event in October 1992, in which the $20\rm ~cm$ maximum preceded the maxima at 3.6 and $6\rm ~cm$ , and the variation amplitude was larger at the lower frequencies. They applied a number of models, both of intrinsic and of extrinsic nature, and concluded that, in any case, the size of the emitting region must be very small, implying a Doppler factor of order 100. Such a high value was subsequently confirmed by Frey et al. (2000) by analyzing VSOP observations of AO 0235+16.

We found several episodes of very fast intraday variability in the radio light curves; in some cases we are in the presence of single points that appear to deviate from the longer trends shown by the data, but there are cases in which the variation is confirmed by more than one point. Calculation of the brightness temperature for the fastest variability events ( $\Delta F / \Delta t > 0.3 ~ \rm Jy\,day^{-1}$ ) in the $14.5\rm ~GHz$ light curve (containing data generally of higher signal-to-noise ratio with respect to the lower frequencies ones) led to values by far exceeding the Compton limit, implying Doppler factors in the range 30-70. Indeed, such results must be taken with caution, since a much better sampling is needed in order to derive reliable Doppler factors from the radio intraday variability.

In conclusion, all the items pointed out by the present work (such as the 5.7 year periodicity, delayed flux variations at lower frequencies, high Doppler factors) would need a further observational effort in the next years, in order to fix them to more precise results.

5 Discussion and conclusions