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Astron. Astrophys. 355, 880-884 (2000)

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3. Discussion

PKS 2155-304 was observed more than 100 years ago. Griffiths et al. (1979) constructed the annually averaged B light curve up to the 1950's from Harvard photographic collection. But there are only a few observations during the period of 1950-1970. The periodicity obtained here (see Fig. 2) are based on the post-1977 data.

For comparison, we adopted the DCF (Discrete Correlation Function) method to the V measurements. The DCF method, described in detail by Edelson & Krolik (1988) (also see Fan et al. 1998b), is intended for analyses of the correlation of two data sets. This method can indicate the correlation of two variable temporal series with a time lag, and can be applied to the periodicity analysis of a unique temporal data set. If there is a period, P, in the lightcurve, then the DCF should show clearly whether the data set is correlated with the DCF with time lags of [FORMULA] = 0 and [FORMULA] = P. It can be done as follows.

Firstly, we have calculated the set of unbinned correlation (UDCF) between data points in the two data streams a and b, i.e.


where [FORMULA] and [FORMULA] are points in the data sets, [FORMULA] and [FORMULA] are the average values of the data sets, and [FORMULA] and [FORMULA] are the corresponding standard deviations. Secondly, we have averaged the points sharing the same time lag by binning the [FORMULA] in suitably sized time-bins in order to get the DCF for each time lag [FORMULA]:


where M is the total number of pairs. The standard error for each bin is


The resulting DCF is shown in Fig. 3. Correlations are found with time lags of (4.20 [FORMULA] 0.2) and (7.31 [FORMULA] 0.16) years. In addition, there are signatures of correlation with time lags of less than 3.0 years. If we consider the two minima in both the right and left sides of the 7.0-year minimum, then we can say that the periods of 4.16 and 7.0-years found with the Jerkevich method are consistent with the time lags of 4.2-years and 7.3-years found with the DCF method. These two periods are used to simulate the light curve (see the solid curve in Fig. 4).

[FIGURE] Fig. 3. DCF for the V band data. It shows that the V light curve is self-correlated with time lags of 4.2 and 7.31 years. In addition, there are also correlation with time lags of less than 4.0 years.

[FIGURE] Fig. 4. The observed V light curve (filled points) and the simulated V light curve (solid curve) with the periods of 4.16 and 7.0 considered.

It is clear that the solid curve does not fit the observations so well. One of the reasons is that there are probably more than two periods ([FORMULA] 4.2 and [FORMULA] 7.0 years) in the light curve as the results in Fig. 2 and 3 indicate. Another reason is that the derived period is not so significant as Press (1978) mentioned. Press argued that periods in the order of one third of the time span have a high probability of appearing if longer-term variations exist. The data used here have a time coverage of about 16.0 years, i.e., about 3 times the derived periods. Therefore, these are only tentative and should be confirmed by independent work.

From the data, the largest amplitude variations are found for UBVRI bands with I and R bands showing smaller amplitude variations. One of the reasons is from the fact that there are fewer observations for those two bands, another reason is perhaps from the effect of the host galaxy, which affects the two bands more seriously.

In this paper, the post-1970 UBVRI data are compiled for 2155-304 to discuss the spectral index properties and to search for the periodicity. Possible periods of 4.16 and 7.0 years are found.

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© European Southern Observatory (ESO) 2000

Online publication: March 21, 2000