Results on the characteristic time scales of the variations

The AC function and the SF analyses allow different definitions of variability time scales. Among them we have chosen to characterise the AC function with the time at which AC = 0 (τ_AC=0 ≡ τ₀), and the SF with the maximum variability time scale (τmax). These definitions describe different time scales and it is difficult to say in what relation they are, because it is hard to identify physically what time scale they refer to. Therefore, we choose to discuss in more detailτ_max, as it is a commonly used definition of a characteristic time scale and thus can be more easily compared to the values available in the literature. We use insteadτ₀ to confirm the trends observed withτ_maxand in order to have an indication of the behaviour ofτ₀in the IR band, where the SF analysis does not allow a measurement

Figure 9.13: Top: τ0 (as calculated from the auto-correlation) as a function of the frequency (circles). The stars represent the data sets that do not include the synchrotron flares. Bottom: τmax (as calculated from the structure function) as a function of the frequency. The dashed line is the best fit to the radio-mm data (see text).

ofτ_maxwith the data available at the moment.

In Fig. 9.13 the values ofτ₀ andτ_max are reported as a function of the frequency. The different behaviours and trends are discussed in the following sections.

Radio to IR

From radio to mm, the maximum time scale of variabilityτ_maxsteeply decrease from values of a few years down to values of a few months (bottom panel in Fig. 9.13). A similar trend is observed for τ₀(top panel). This can be interpreted as due to the typical evolution of synchrotron flares that start as short flares at higher energies (optical-IR) and progressively evolve on longer time scales while moving to lower energies. A study of the long-term variability in the radio band has been carried out by Hovatta et al. (2007) for a sample of AGN observed during ∼ 25 years. Our values ofτ_max and α^SF obtained at 22 and 37 GHz are in complete agreement with their results for 3C 273. In the

The characteristic time scales of the variations 133 IR band, when the periods of the synchrotron flares are excluded from the analysis, a slower varying component appears, with characteristic time scales τ₀ about a factor of 2 larger than those found including the flares.

Being the decreasing trend of the characteristic time scale connected to the evolution of the syn-chrotron flares, one can assume thatτ_maxrepresents an upper limit to the cooling time tcoolof electrons through this emission process. This results in an estimate of the lower limit of the magnetic field of B_min ≥ 0.089±0.003 Gauss (see Soldi et al. 2008 for details). Using the time scales of submm-cm and IR flares, Courvoisier et al. (1988) and Robson et al. (1993) have obtained values of the magnetic field in the range B∼0.4−1 Gauss, consistent with our result.

Optical-ultraviolet

In the optical-UV range,τ_maxdecreases with frequency, as it is expected due to the decreasing contri-bution of theRcomponent in this band, where instead theBcomponent is dominant and shows larger amplitude and shorter variability time scales thanR(Paltani et al. 1998b). Maximum time scales of

∼3.9 and 0.5 years are characteristic of the optical and UV structure functions, respectively. τ_max in the UV band was already found by other studies of 3C 273 UV variability (Paltani et al. 1998b;

Favre et al. 2005). The same trend is observed whenτ₀ versus νis considered and no differences are observed in the optical when the synchrotron flares are excluded (these points are not reported in Fig. 9.13 for better clarity).

The UV SF fitting results in slopes between 0.9 and 1.2 which are consistent with those expected in the frame of the disk instability (DI) model (Kawaguchi et al. 1998). In this model, the optical-UV variability is produced by occasional flare or blob formation caused by instabilities in the disc atmosphere. As the dominant UV emission of 3C 273 is thought to be related to the disc, we limit the discussion here to the UV band. The DI model can also explain the increase of the amplitude of the variations with the frequency in the UV band (Fig. 9.1) with an alternative solution to the scenario with the two-competing components (Rand B). In fact, the avalanche that is at the origin of the variability would start in the outer regions of the disc and drift to the inner regions covering a larger fraction of the disc. This would explain then the fact that the cooler outer regions, emitting at lower energies, are less variable than the hotter central regions (Kawaguchi et al. 1998). However, the expected time delays as a function of wavelength for this model are not discussed by Kawaguchi et al. (1998).

Alternative variability models, as the starburst or the gravitational microlensing ones, do not rep-resent well the slopes of the UV SF (Kawaguchi & Mineshige 1999, Hawkins 1993), even though the latter model is found to well represent the optical SF variability of quasar with z> 0.5, whereas the DI model better explains the variability of Seyfert with z < 0.3 (Hawkins 2002). It is not sur-prising though that 3C 273 follows more the Seyfert behaviour due to its low redshift and its double Seyfert-blazar spectral properties.

X-rays

The long and well sampled X-ray light curves available for 3C 273 allow for the first time an accurate structure function analysis and determination ofτ_max. We describe here in detail the study performed and its results.

The 10-year observations of RXTE constitute one of the best sampled and longest coverage of an AGN in the X-rays. We build the structure functions in the 4–9 and 9–20 keV bands using the PCA

Figure 9.14: SF in the 4–9 keV (open circles) and 9–20 keV range (filled triangles) built withRXTE/PCA data. Both curves have been renormalised to the expected value of the respective upper plateau (continuous line). The dashed lines indicate the expected values of the lower plateaus for the 4–9 (lower line) and 9–20 keV (upper line) range. The vertical dotted lines indicate the break time scaleτbreakfor the fitting of the 4–9 keV curve andτmaxof both SFs.

light curves provided by the RXTE archive, after rebinning them to 1000-second bins. In both energy bands the main features of a SF are present: the lower and upper plateau are very well defined and one or two power laws represent a good fit to the curve in between (Fig. 9.14). The flattening of the SF at large time lags happens for both energy bands at a timeτ_max∼0.22 years. This corresponds to the maximum time scale of variability of the source in the observed period, though variability on much longerτthan the sampled 10 years is of course possible. At small time lags, in both energy bands it is possible to detect variability down to time scales of a few hours. In particular, the 4–9 keV SF flattens at a smallerτ(2.7 hours) than the 9–20 keV one (7 hours), indicating that the noise level of the 4–9 keV light curve is lower and allows us to investigate shorter time scales. The 4–9 keV SF is best fitted with a broken power law, with break atτ_break ∼ 2.2 days and slopes of 0.90±0.07 and 0.57±0.03, before and after the break, respectively. Even if a hint of a steepening is also present in the 9–20 keV SF atτ_break, the curve is well fitted with a single power law with a slope of 0.51±0.02, as the possible time break is too close to the time scales at which the noise starts dominating the curve. Following the relation proposed by McHardy et al. (2006) between the break time of the power density spectrum, the black hole mass and the bolometric luminosity (see Chap. 6), we would expect for 3C 273 a break time at 3 days (using MBH= 6.5×10⁹M⊙and Lbol = 6×10⁴⁶erg s⁻¹), which is close to the value found with the SF analysis, indicating that also 3C 273 follows this relation. The different slopes found below and above∼2 days could be a hint that two different processes contribute on different time scales. As no further steepening of the curves to a slope of 2 are observed when the SF rises from the noise, the lowest time scales sampled do not correspond to the minimum variability time scales.

The characteristic time scales of the variations 135

Figure 9.15:SF in the 4–9 keV range for the sub-samples withd f >0(filled up-triangles) andd f <0(open down-triangles). The expected values of the upper and lower plateaus are indicated by the continuous and dashed lines, respectively.

Interesting information can be obtained also from the distributions of flux ratios dr and flux differ-ences d f calculated for all the couples of points in the RXTE light curves. Even though the maximum variations in amplitude are observed in the 9–20 keV data set, with drmax = 5.8 (drmax = 3.7 for the 4–9 keV band), the 4–9 and 9–20 keV light curves show on average the same variability with an average factor<dr>≃1.3, confirming the result obtained with the Fvarparameter. Since the average flux differences< d f >are slightly negatives in both bands, we build the SFs using only the d f < 0 or d f > 0 values in order to check for the signature of asymmetry in the X-ray flare profiles³ (see for example de Vries et al. 2005). The d f < 0 and d f > 0 SFs do not show significant differences (Fig. 9.15), therefore suggesting the symmetry of the brightening and decaying phases of X-ray flares.

In alternative, the negative<d f >could be due either to the uneven sampling (maybe favoring in the monitoring programme the periods immediately after the flares) or to a global decreasing trend of the light curve, implying in both cases more observational time spent during decreasing states. The latter possibility seems to be supported by the fact that the average of d f is found to be positive forτ <3 years and negative for 3< τ <10 years.

At higher energies, BATSE also provided a 10-year coverage of the high-energy emission of 3C 273. As BATSE light curves are rebinned to 1 month, the SFs built with these data sample a shorter time frame than the RXTE ones, going from 1 month to 10 years. Even though BATSE SFs are less well defined than those below 20 keV, interesting information can be obtained about the vari-ability behaviour of 3C 273 at hard X-rays. The 20–70 and 70–430 keV SFs show a very similar shape, both reaching the upper plateau at a time of about 1.3–1.4 years, significantly longer than that observed below 20 keV with RXTE. The same trend is observed for the characteristic time scaleτ₀. Before the plateau, the BATSE SFs have a slope of 0.3±0.1 and 0.4±0.1 below and above 70 keV, respectively. Due to the similarities of the two SFs, we summ up these data sets in order to obtain

3d f has been defined so that d f >0 indicates a brightening of the source.

Figure 9.16: SF in the 20–430 keV range (open squares) calculated with BATSE data. For comparison, the 9–20 keVRXTESF is also shown (filled triangles). Both curves have been renormalised to the expected value of their respective upper plateaus (continuous line). The dashed line indicates the expected value of the lower plateau for the 20–430 keV range. The vertical dotted lines indicateτmaxof the 9–20 keV curve (∼0.22years) and of the 20–430 keV SF (∼1.3years).

a higher signal-to-noise ratio and calculate a 20–430 keV SF (Fig. 9.16). The maximum variability time scale is still≥1.3 years and below this time the curve has a slope of 0.48±0.12, consistent with what is obtained in the 9–20 keV range. The steeper slope of the summed SF could be an effect of the increased signal-to-noise. In fact, as pointed out by de Vries et al. (2003), the larger the measurement noise of the light curve, the flatter the SF.