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Astron. Astrophys. 356, 1-10 (2000)

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5. Discussion

5.1. IR flux and spectral variability

The ISO light curves of May-June 1996 show that the time variability of PKS 2155-304 in the mid- and far-infrared bands is very low or even absent. The flux has not varied significantly in 1996 November and in 1997 May, one year later, and is quite similar to the 1983 IRAS state (Impey & Neugebauer 1988) (Fig. 3), except at 60 µm, where the IRAS flux seems significantly lower. This agreement could support the idea that the infrared flux level of this source is rather stable. We have to wait for future satellite missions to test this statement.

The infrared spectrum from 2.8 to 100 µm is well fitted by a single power law. This is a typical signature of synchrotron radiation, that can explain the whole emission in this wavelength range, excluding important contributions of thermal sources.

The variability in the optical bands is small too, while the simultaneous RXTE light curve (Urry et al. 1998, Sambruna et al. 2000) shows, on the contrary, strong and fast variability at energies of 2-20 keV: the flux varied by a factor 2 on a timescale shorter than a day. This seems to be a common behavior in blazars, for which there is a more pronounced variability at frequencies above the synchrotron peak (Ulrich et al. 1997).

5.2. Contribution of the host galaxy to the IR flux

The absence of variability could be also explained by the contribution, in the IR, of a steady component, such as the host galaxy. The host galaxy of PKS 2155-304 is a large elliptical which is well resolved in near infrared images (Kotilainen et al. 1998), but the pixel field of view of the ISOCAM camera (3" or 6") is too big to resolve it and its contribution is integrated in the flux of the active nucleus.

The magnitude of the host galaxy in the H band is [FORMULA] (Kotilainen et al. 1998). The color of a typical elliptical at [FORMULA] is [FORMULA]=4.6 (Buzzoni 1995), from which we get [FORMULA], which corresponds to a flux [FORMULA] = 0.7 mJy. Mazzei & De Zotti (1994) calculated the flux ratio between the IRAS and the B bands for a sample of 47 elliptical galaxies: their results are [FORMULA], [FORMULA], [FORMULA], [FORMULA]. From these relations we can estimate the host galaxy fluxes in the far-IR at 12, 25, 60 and 100 µm: we have [FORMULA] mJy, [FORMULA] mJy, [FORMULA] mJy, [FORMULA] mJy. If we compare these values with those of Table 6, we see that they are less than 1% of the active nucleus flux, and much less than the uncertainties. We thus conclude that the contribution of the host galaxy to the ISO far-IR flux is negligible.

This fact can be also inferred from the spectral energy distribution (SED), built with the simultaneous data of May 1996 (Fig. 5), that shows that the ISO data lie on the interpolation between radio and optical spectra.

[FIGURE] Fig. 5. Spectral energy distribution of PKS 2155-304. The black data are the simultaneous data of 1996 May: circles are ISO and BVR fluxes (this paper, data of May 27), and EUVE flux (Marshall H.L., priv. comm.); the X-ray spectra are from RXTE (Urry et al. 1998); the [FORMULA]-ray upper limit is from EGRET (Vestrand W.T., priv. comm.). Open grey boxes are data from the multiwavelength campaign of 1994 May (Pesce et al. 1997, Pian et al. 1997, Urry et al. 1997). 1994 ASCA data are from Urry et al. (1997), 1994 EGRET data are from Vestrand et al. (1995), 1996 SAX spectrum is from Giommi et al. (1998), 1996 November RXTE spectrum is from Urry et al. (1998), IRAS data are from Impey & Neugebauer (1988), Mark 6 point is from Chadwick et al. (1999)

5.3. Synchrotron self-absorption

The observed IR spectrum is rather flat, and one can wonder if this is due to a partially opaque emission, i.e. if we have, in the IR, the superposition of components with different self-absorption frequencies, as for the flat radio spectra.

To show that this is not the case, we calculate the self-absorption frequency assuming that the IR radiation originates in the same compact region responsible for most of the emission, including the strongly variable X-ray flux. This is a conservative assumption, since the more compact is the region, the larger is the self-absorption frequency. In the case of an isotropic population of relativistic electrons with a power-law distribution [FORMULA], the self-absorption frequency is given by (e.g. Krolik 1999)


where [FORMULA] is the gamma function, [FORMULA] is the cyclotron frequency, [FORMULA] is the beaming factor, R is the size of the source, [FORMULA], and p is the slope of the electron distribution appropriate for those electrons radiating at the self-absorption energy. In the homogeneous synchrotron self-Compton model, the optical depth [FORMULA] is approximately the ratio of the Compton and synchrotron flux at the same frequency. This ratio can be estimated from the SED (Fig. 5), where the Compton flux is obtained by extending at low frequencies the Compton spectrum with the same spectral index of the synchrotron curve. The upper limit for the [FORMULA]-ray emission in 1996 May corresponds to an upper limit for the value of the optical depth of [FORMULA]. From the ISO spectrum, we have [FORMULA]. Although we cannot a priori determine the other two parameters, namely B and [FORMULA], a reasonable estimate can be derived through the broad band model fitting. In particular if we adopt the values derived by Tavecchio et al. (1998), [FORMULA] G and [FORMULA], we get [FORMULA] Hz. For less extreme values of [FORMULA], [FORMULA] becomes smaller, while much larger values of the magnetic field (making [FORMULA] to increase) are implausible, if the significant [FORMULA]-ray emission is due to the self-Compton process, which requires the source not to be strongly magnetically dominated. The frequency of self-absorption is thus significantly lower then the IR frequencies, implying that the IR emission is completely thin.

5.4. Spectral energy distribution

In Fig. 5 we show the SED of PKS 2155-304 during our multiwavelength campaign, from the far IR to the [FORMULA]-ray band. We also collected other, not simultaneous, data from the literature, especially in the X-ray band, to compare our overall spectrum with previous observations. As can be seen, our IR data fill a hole in the SED and, together with our optical results, contribute to a precise definition of the shape of the synchrotron peak. It is remarkable that although the X-ray state during our campaign was very high (one of the highest ever seen), the optical emission was not particularly bright. Also the upper limit in the [FORMULA]-ray band testifies that the source was not bright in this band.

All this can be explained assuming that the X-ray flux is due to the steep tail of an electron population distributed in energy as a broken power law. The first part of this distribution is flat and steadier than the high energy, steeper part. In this case without changing significantly the bolometric luminosity large flux variations are possible above the synchrotron (and the Compton) peak. An electron distribution with these characteristics can be obtained by continuous injection and rapid cooling (see e.g. Ghisellini et al. 1998). In fact, if the electrons are injected at a rate [FORMULA] between [FORMULA] and [FORMULA], the steady particle distribution will be [FORMULA] above [FORMULA], and [FORMULA] below, until radiation losses dominate the particle escape or other cooling terms (e.g. adiabatic expansion). Electrons with energy [FORMULA] are the ones responsible for the emission at the synchrotron and Compton peaks (as long as the scattering process is in the Thomson limit). Since it is possible to change s without changing the total injected power, large flux variations above the peak are compatible with only minor changes below. This model also predicts that the spectrum below the peak has a slope [FORMULA], which is not far from what we have observed in the far IR.

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Online publication: March 28, 2000