One of the most direct ways to test the connection between the emissions at different wavelengths is studying their time correlation. The presence of a correlation and, possibly, the analysis of the time delays are powerful tools to understand the origin of the different emissions. Already from the definition of cross-correlation function (Eq. (9.8)) it is possible to see that the main difficulty in this kind of analysis is represented by the available data that need to come from simultaneous observations, possibly on long time scales, for different energy bands. A few of such campaigns have been carried on for 3C 273 and have given interesting results in different energy domains.
9.3.1 Some of the previous works on 3C 273 correlations
The long, well sampled light curves available in the radio-mm band allowed a detailed study of the temporal and spectral evolution of the synchrotron flares, followed by the definition of a phe-nomenological jet model that well represents the variations observed in this energy domain (Türler et al. 1999a, 2000). In this case the cross-correlation analysis shows an increasing delay between the light curves, when going from higher to lower frequencies indicating the already discussed scenario
Cross-correlations and time delays 137
Figure 9.17:Left:example of cross-correlation in the radio band, where the delay of the 22 GHz emission on the 5 GHz one is represented. Circles are obtained with the DCF analysis and the thick line is calculated with the ICF method.Right:average time delay of the radio-to-mm light curves as a function of the frequency. The 0.8 mm light curve is assumed to have average delay equal to 0, and the lower energies follow with positive delays up to 2.2 years.
(Sect. 7) where the emission from the shock propagating along the jet starts at higher energies and slowly evolves towards lower ones. In Fig. 9.17 (left panel), an example of cross-correlation function is shown for the 5 and 22 GHz light curve, showing the delay of the second curve on the first one.
The peak of the correlation coefficient at about –1.5 years indicates that the 5 GHz emission follows the 22 GHz one after∼1.5 years. In order to show the full radio-to-mm evolution of the synchrotron flares, we display in Fig. 9.17 (right panel) the average delay of the emission in the 2.5 GHz to 0.8 mm band. Every point is calculated as the average of the delays between that specific light curve and all the others (always in the radio-mm) and then it is added to the average delay at 0.8 mm, as the 0.8 mm radiation is the first one to be emitted within those considered in this plot.
Thanks to the 20 years of observations with the International Ultraviolet Explorer (IUE) satellite and to the long-term monitoring of several optical telescopes, Paltani et al. (1998b) were able to characterise the variability properties of the optical and UV emission and their inter-connections.
Among the other results, they found a very good correlation between the optical and UV light curves and within the UV ones, with the longer wavelengths following the shorter with delays of a few days.
The correlation and the associated delays can be well explained by a reprocessing model, where an external X-ray source, rather than internal dissipation of gravitational energy, is heating up the reprocessing zone and the further parts (i.e. at larger lags) are also the colder ones.
Using the same optical-UV data and the results of the observations performed by BATSE, Paltani et al. (1998a) found strong correlations between the optical-UV and the hard X-rays, both showing two peaks, one at 0 lag and the other at about 1.5 years. The 0 lag peak is dominant in the optical-X-ray correlation and the 1.5 years lag is dominant in the UV-optical-X-ray one (see Fig. 11 in Soldi et al.
2008). This seems to indicate that theRcomponent (dominant in the optical, but still contributing in the UV) correlates at 0 lag with the X-rays, whereas theBcomponent anticipates them by 1.5 years.
Two simultaneous near-IR and medium X-ray (3–20 keV) campaigns have been carried out in 1996–1997 and 1999 to study the correlation in these two bands of the emission of 3C 273 (McHardy et al. 1999, 2007). During both periods, a high correlation has been detected between the flaring activity of the IR and the X-ray emissions, suggesting that during these episodes we observe the X-rays produced by the synchrotron self-Compton (SSC) process on IR seed photons. As these
observations were not scheduled at a particular time, McHardy et al. proposed that the SSC process dominates most of the time the X-ray emission.
9.3.2 Our correlation study
Due to the latest updates, some of the light curves have been considerably extended, allowing further studies of the time correlations. In particular, the major improvements are seen in the IR and X-ray data sets that now significantly overlap with light curves in other energy bands. We therefore concentrate on the IR and X-ray correlations with other bands and analyze only the cases where there is a sufficiently dense sampling during at least 4-year overlap of the light curves. We use both the DCF and ICF methods to compute the cross-correlation and use their consistency as a criterion for the robustness of the results. We define for the following sections the medium X-rays as the range between 5 and 20 keV, where most of the last 10 years of data come from RXTE observations. We consider hard the X-rays above 20 keV and use for the correlation only the data collected by BATSE.
To discuss our correlation results, we use the 5 keV and the 20–70 keV light curves as representative of the medium and hard X-rays, respectively.
In order to estimate the uncertainties on the calculated cross-correlations, we perform simulations with the bootstrap procedure. 1000 simulated data sets for each light curve are cross-correlated to as many data sets at another wavelength. Then, at each time lag we build the distribution of the correlation coefficients obtained and consider as the uncertainty at this lag the standard deviation of the Gaussian fit.
Medium and hard X-rays
One of the first results of this analysis is the lack of a strong correlation between the medium and hard X-rays. The correlation function shows repeated oscillations and in addition the ICF and DCF methods give discordant results at some time lags (for example at 0 lag, see Fig. 11 in Soldi et al.
2008). Together with the different level of variability amplitude and the different maximum time scales, the lack of correlation between the medium and hard X-rays seems to indicate important differences in the variability properties of the X-ray emission above and below ∼ 20 keV. We are therefore justified to study individually the correlation of the medium and hard X-rays with the other energy bands.
Medium X-rays
• With radio-mm No correlation is found between the medium X-rays and the radio-mm emis-sion (Fig. 11 in Soldi et al. 2008), suggesting that the bulk of the medium X-rays is not related to the jet. The correlation found by McHardy et al. (1999, 2007) between the IR and the medium X-rays might be a secondary effect that is dominating the X-ray emission only during isolated flares.
• With optical-UV Only a small subsets of X-ray points overlap with the optical-UV light curves, preventing from applying a proper correlation analysis. On the other hand, as one of the most common scenarios to connect the soft/medium X-ray and optical-UV emissions, i.e. repro-cessing, predicts a correlation at short lags, we select the data subsets for which X-ray and optical-UV observations were performed within one day and apply a Spearman test to check for the presence of a correlation. We apply this procedure to all light curves from 0.1 to 10 keV.
Cross-correlations and time delays 139
Figure 9.18: Correlation of the X-ray and optical-UV light curves for data taken within one day. For each plot, the value of the Spearman correlation coefficient and the associated probability for random occurrence are indicated.
Figure 9.19: Example of correlations of the radio-mm data sets with the hard X-rays, and relative light curves.
The error bars of the BATSE light curve are omitted for better clarity and the vertical dotted lines indicate the peak of the synchrotron flares discussed in the text. Top left: correlation of the 20–70 keV curve with the 15 GHz one (points: DCF method; thick line: ICF method). Positive delays indicates that the higher-energy emission follows the lower-energy one.Top right:20–70 keV (triangles) and 15 GHz (circles) light curves in the range covered by the hard X-ray data. Bottom left: correlation of the 20–70 keV curve with the 0.8 mm one.Bottom right:20–70 keV and 0.8 mm light curves.
We choose the 3000 Å light curve as representative of the UV band and the U, V and B in the optical, as they have more overlapping with the X-ray data sets. No significant correlation is found apart from the 1 keV – 3000 Å case and from a marginal correlation for the 5 keV – B data sets (Fig. 9.18).
Hard X-rays
• With radio-mm A correlation is found between the 5–37 GHz curves and the hard X-rays (top left panel in Fig. 9.19), with the higher radio frequencies leading and the X-rays correlating at about 0 lag with the 5 GHz emission. The delays are consistent with those obtained with cross-correlations within the radio band. The hard X-ray cross-cross-correlations with the mm band show a significant peak at ∼ −2.5 years (bottom left panel in Fig. 9.19), which is in contradiction with the radio-mm correlations discussed in Sect. 9.3.1. Looking at the light curves, it appears
The X-ray spectral variability 141 that the radio-mm correlation with the hard X-rays is due to the matching of the strong peak characterising the BATSE light curve with one determined synchrotron flare. If in the radio band the flare peaking at 15 GHz in November 1991 is within the time period covered by BATSE and gives origin to the correlation (top right panel in Fig. 9.19), in the mm this flare occurred earlier and therefore outside the BATSE coverage. As a consequence the peak in the correlation between the hard X-rays and the mm is due to the correspondence with the following bright flare peaking in 1997 at 0.8 mm (bottom right panel in Fig. 9.19). Therefore, it is difficult to say if there is a direct correlation between the hard X-ray and the jet emission, or if the correlation we observe is only due to chance occurrence. On the other hand, there is no evidence of a correlation at small lags between the hard X-rays and the mm, which would be expected if the high-energy emission was radiated during the Compton phase of the shock in the jet, phase which is shortly anticipating the onset of the synchrotron emission.
IR and optical-UV
A correlation is found between the optical-UV and the near-IR light curves, with a positive delay of on average 1 year of the IR emission (Fig. 10 in Soldi et al. 2008). The delay is increasing from 0.8 to 1.2 years with the wavelength of the IR data set, clearly suggesting that the IR radiation comes from dust heated up by the optical-UV flux at different temperatures depending on the distance from the optical-UV source.