Results on the variability amplitude

The strong dependence of the fractional variability amplitude on the frequency can be seen in Fig. 9.1.

Fvarincreases linearly with the logarithm of the frequency from radio to mm, from optical to UV and in the X-ray band. These trends are representative of the dominant processes responsible for the emission in the different energy bands. However, in some cases the analysis is complicated by the fact that several emission components with different variability properties can contribute to the energy output in the same band and to set them apart is not always possible. In the following sections we try to identify the mechanisms that produce the observed variability amplitude in the different energy ranges.

Radio-millimeter

The variability properties of the radio-millimeter radiation are probably the best understood of the emission of 3C 273, thanks to the noteworthy effort carried out in the past both concerning obser-vations and modelling of the jet emission of this object. As extensively explained in Chapter 7, the radio-mm emission is believed to be synchrotron radiation originating in shocks propagating along the jet. The flaring characteristic of this process can be recognised in the succession of peaks observed in the light curves, with different intensities and durations depending on the wavelength (Fig. 9.3). The steep increase of Fvarfrom 10⁹and 10¹²Hz is well understood as a direct evidence of the evolution of the synchrotron flares. In fact, the higher-energy photons are the first to emerge from the shock and the duration of this synchrotron emission increases with the wavelength. This implies that in the radio band before the complete decay of one flare the next one has already started, giving rise to an intense, radio continuum that is in reality the superposition of several consecutive flares. On the other hand, at higher frequencies, the duration of the flares is shorter than the recurrence time between them and therefore it is possible to observe the quiescent mm emission. This results in an amplitude of the variations that is much larger in the mm and quickly decreases when going to lower frequencies.

The model of Türler et al. (2000), describing the evolution of such synchrotron outbursts, not only represents very well the radio-to-sub-millimeter emission of 3C 273, but allows also to reconstruct the flares at those frequencies where observations were not performed, provided that the shape of the flare is known at a given time and at a given, different frequency. As a consistency check, we use this model to reconstruct long and very well sampled light curves and calculate the corresponding F_var values. As expected considering that the model is the result of the fitting of a sub-sample of our data, the Fvarvalues calculated with the model match very well those calculated with the real light curves (Fig. 9.1).

Infrared

The infrared domain is a good example of a band where several processes significantly contribute to the total emission. Synchrotron flares have been observed at different epochs to stand out on a slower variable, underlying component (Robson et al. 1993). At least part of the IR emission is due to thermal radiation from heated dust (Robson et al. 1983), possibly from different regions with different

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Figure 9.3:3C 273 light curves at 5 GHz, 22 GHz and 3.3 mm.

Figure 9.4:3C 273 light curves in the near-IR H and optical B bands. Synchrotron flares are indicated in blue.

Even without a proper correlation analysis, similar structures can be recognised in the two light curves, with a delay of the IR emission with respect to the optical one (compare for example the 1990–1997 bump in the B curve and the 1991–1998 bump in the H one).

sizes and temperatures (Türler et al. 2006). When the complete IR light curves are considered, Fvar

decreases from the mid- to the near-IR domains, as the synchrotron flares have decreasing intensities and the less variable component is becoming more important.

When the periods of the synchrotron flares are excluded from the IR data sets, the variability properties of the underlying component can be studied in more detail. In particular in the near-IR, where the dust is expected to contribute decreasingly as it approaches its sublimation temperature, F_varincreases linearly with the logarithm of the frequency from 0.04 to 0.1. This suggests the presence of another component whose variability properties are very similar to the optical ones (Fig. 9.4), as it will be seen and discussed in the next section.

Optical-ultraviolet

Following Paltani et al. (1998b), the optical-UV emission can be represented by the superposition of two components, R (which stands for “Red”) andB(for “Blue”), the first one dominating in the optical range and showing smaller variations, and the second one primarily contributing to the UV emission. The total emission from 5×10¹⁴ to 5×10¹⁵ Hz would be determined by the different normalisation of the two components at different frequencies. Due to the variability properties ofR andB, the constant increase of F_varfrom optical to UV can be understood as the transition from the energies whereRis dominant to those where most of the radiation comes fromB. If the amplitude of the variations is well described by this decomposition, the origin of theRcomponent is still under debate (Chapter 7).

The relation between the near-IR and optical emission is important to understand the origin of theR component. The linear relation between Fvar and the logarithm of the frequency observed in the optical-UV appears to be the continuation of a similar trend seen in the near-IR. As dust is not expected to contribute to the optical emission due to sublimation, Ris a good candidate to extend to the near-IR domain and produce the observed radiation. On the other hand, it is necessary to take into account also the synchrotron emission as extrapolated from the mm as a potential contributor in the IR band. In order to test the contribution of the different components, 3 models have been applied to the mm to IR spectral energy distribution:

• Model A: a simple power law fitted to the mm band is extrapolated up to the near-IR.

• Model B: an exponentially cut-off power law is added to theRcomponent and the fit performed in the mm to IR range. Ris modelled with a broken power law as found by Paltani et al. (1998b) and explained in Soldi et al. (2008).

• Model C: we add to Model B an isothermal grey-body¹ to model the presence of dust. The temperature and size of the dust emitting region are fitted, whereas the dust emissivity index and the wavelength at which the optical depth equal 1 are fixed to the values found by Türler et al. (2006), i.e. 1.5 and 10µm, respectively.

1An isothermal grey-body at temperature T emits at the observed frequencyνobsa flux density given by:

F^obs_ν (νobs)=(1+z) AdustD⁻²_L (1−e^−τν) B^em_ν (νem,T ) (9.6) where B^em_ν (νem,T ) is the Planck function for a black body at temperature T, DLis the luminosity distance, Adustis the area of the projected source,τνis the optical depth that can be expressed as a function of the dust emission indexβand the frequency at which the optical depth equals 1,τν=(νem/ντ=1)^β. This model does not take into account the source geometry (Polletta et al. 2000; Türler et al. 2006).

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Figure 9.5: 3C 273 average SED from mm to UV fitted in the mm-IR range with different models, which include a simple or cut-off power law (dashed line), theR component (dotted line) and a grey-body (dotted curve). The Bcomponent (dot-dashed line) is also shown. The continuous line indicates the sum of the different components contributing to the total model.Top left:SED fitted with Model A (excluding the periods of synchrotron flares). Top right: SED fitted with Model B (excluding the synchrotron flares). Bottom left:

SED fitted with Model C (excluding the synchrotron flares).Bottom right:SED fitted with Model C (including the synchrotron flares).

The fit with Model A can explain the far- and mid-IR emission, but predicts fluxes in the near-IR two times higher than those observed (top left panel in Fig. 9.5). Therefore, there is the need of a cut-off in the synchrotron emission extrapolated from the mm band. This is introduced in Model B, together with the R component, and results in a reduced chi-squaredχ²_red = 1.5, mainly due to the deviation of the model in the near-IR band from the data points (top right panel in Fig. 9.5). This suggests the need of an additional component in this energy range to model the dust contribution.

The inclusion of a grey-body in Model C improves significantly the fit, resulting in a χ²_red = 0.36 and a F-test probability PF−test = 2× 10⁻⁴ (bottom left panel in Fig. 9.5). We found a slope of the power law of Γ = 0.74± 0.06 with a cut-off at ν_c ≃ 5.1× 10¹³Hz. The dust emitting area is found to be A_dust = 1.5±0.5 pc² with a temperature of T_dust = 1156± 92 K. The same model is applied to the light curves including the synchrotron flares and similar parameters are obtained:

Γ =0.68±0.08,ν_c≃5.4×10¹³Hz, Adust=1.35±1.30 pc²and Tdust=1178±196 K, indicating that the dust component is not well constrained in this case (bottom right panel in Fig. 9.5). The difference between the dust parameters obtained here and those reported by Türler et al. (2006) (Adust =0.6 pc², Tdust= 1620 K) could be due to variability of the dust, but are more likely caused by the uncertainty on the extrapolation of the mm emission at higher frequencies due to the strong variability of the

synchrotron component. We want to notice also that the near-IR dust emission is more complicated than the one-zone, one-temperature model used here, as we will see with the correlation analysis for example (Sect. 9.3.2). In addition dust is expected to contribute along the whole IR spectrum, but a further modelling is not possible here, as the average spectrum in the far- and mid-IR is dominated by the synchrotron emission, even outside synchrotron flares.

X-rays

There are apparently two different variability behaviours when the amplitude of the variations in the X-ray band is studied. Fvar shows a slowly increasing trend in the 0.1–10 keV range and at higher energies it steeply increases, more than doubling the value it had at soft-medium X-rays when it reaches a few hundred keV. Different variability properties in the medium and hard X-rays are found also by the study of the characteristic time scales of the variations (Sect. 9.2) and by the cross-correlation analysis (Sect. 9.3).

It has been observed that the X- and gamma-ray emission of 3C 273 shares properties that are common of Seyfert galaxies and of blazars, as the occasional detection of an iron Kαemission line (e.g. Yaqoob & Serlemitsos 2000) and the presence of a break in the spectrum around 1 MeV (Johnson et al. 1995). Since these two components are likely to contribute, with different normalisations, to the whole X-ray spectrum of 3C 273, 10–20 keV could represent a transition energy between the dominance of the less variable Seyfert and the more variable blazar contributions. On the other hand, a single component characterised by at least two parameters varying independently could also explain the observed properties. In the single-component scenario, the 2 to 500 keV spectrum could be produced, for example, by a single power law pivoting at low X-ray energies. Then the variations at medium X-rays would be dominated by the variation in the low-energy flux of this component, whereas the variations at hard X-rays would rather be due to the variation of the photon index. The long time-scale variations of the photon index (Fig. 13 in Soldi et al. 2008) and of the hard X-ray emission (Fig. 9.19) could support this decomposition.