Astron. Astrophys. 342, 57-68 (1999)

4. The model

The ROSAT HRI observation presented here shows a complex extended X-ray structure surrounding a central point-like source. ROSAT and ASCA spectral analysis reveals that the nucleus is absorbed by a column density cm^-2 similarly to other ROSAT findings for BLRGs (Crawford & Fabian 1995). The unabsorbed luminosity ( erg s^-1) in the 0.1-2.4 keV band and the photon index are typical of steep spectrum radio loud quasars, thus strengthening the hypothesis that we are dealing with a hidden quasar in the nucleus of the radio galaxy in agreement with the unification model.

According to the spectral analysis, the nuclear source contributes % of the total ROSAT PSPC flux while the contribution from a thermal source, if any, cannot exceed % of the total flux. Therefore a large fraction, if not all, of the flux associated with the extended structure should be characterized by a power law spectrum with a slope close to that of the radio emission (). This and the spatial correlation with the overall radio structure suggest that the IC process could be a likely mechanism to generate most of the extended X-ray flux.

However, a considerable fraction (%) of the extended emission flux is confined to the eight-shaped structure (component C in Fig. 5) whose brightness distribution, elongated in a direction at large angle with the radio-axis and falling down radially roughly as , looks very much different from that expected by a simple IC with the CMB photons. As a consequence we have first checked whether this feature could be due to a non spherically symmetric cooling flow. We find that the addition of a cooling flow to an absorbed power law source may give an adequate representation of the combined ROSAT-ASCA spectrum only if a metallicity solar is assumed. Acceptable fits, but worse than those of the partial covering model (Sect. 2), have been obtained with an absorbed power law plus constant or non-constant (s=2, Mushotzky & Szymkowiak 1988) pressure cooling flow models. We derive intracluster gas densities between and, by applying a King's model, cluster luminosities erg s^-1 in the 0.1-2.4 keV band, that is a factor 15-60 larger than the upper limit to any thermal contribution within the ROSAT PSPC extracted radius (Sect. 2). Furthermore, the cluster emission would give out X-rays in excess of the observed HRI background by a factor of 1.5-6 at distance from the nucleus. We conclude that a cooling flow cannot be responsible for the C-component.

We propose that the main features of this component can be explained by the IC scattering of the IR-optical radiation from a hidden quasar with the surrounding relativistic electrons of the radio source, according to the model developed by Brunetti et al. (1997).

4.1. An IC model of component C

The IR-optical emission of the nuclear source, as seen by the relativistic electrons in the radio lobes, is made of two components: the direct radiation from the quasar, for those electrons located within the emission cones (assumed half-opening angle ), plus the reprocessed radiation from the dusty molecular torus surrounding the quasar. In the model we have fixed the inclination of the radio-axis with respect to the sky plane at , close to that inferred from the radio-jet data (Bridle et al.1986), while the direction of the torus axis () is a free parameter constrained by the requirement that the nuclear source is not directly seen by the observer ( cm^-2) and that the IC brightness distribution closely matches the observations (Fig. 6).

Fig. 6. The model's geometry. The direction of the torus axis in spherical coordinates is given by (, ); the jet axis is assumed to lie on the plane. The angle between the line of sight and the torus axis is given by that in the model should be .

As already stated in the Introduction, a relevant parameter for the efficiency of the IC model is the IR radiation from the putative hidden quasar. Unfortunately 3C 219 was not detected in a pointed IRAS observation by Impey & Gregorini (1993) and it has not been observed with ISO. The IR spectral properties of the BLRGs observed by IRAS are poorly known. Heckmann et al. (1994) found that the weighted IRAS 10-86 rest frame spectral index of a sample of 9 BLRGs given by the SUPERSCAMPI procedure is . However, the few detected BLRGs show a large dispersion in the 25-60 spectral indices ranging from -0.47 to +0.44 (Impey & Gregorini 1993, Heckmann et al. 1994, Golombek et al. 1988). By assuming an IR spectral shape consistent with the IRAS upper limits and with the range of observed BLRG spectra and, also, with the predicted spectra of dusty tori models (Pier & Krolik 1992), the 6-100 isotropic IR luminosity of 3C 219 could be as large as erg s^-1.

To estimate the IR luminosity of the hidden quasar we first notice that the monochromatic luminosities of a sample of low redshift () radio galaxies are on the average times smaller than those of a sample of quasars in the same redshift interval (Heckmann et al. 1992). By applying Pier & Krolik (1992) models to the adopted geometrical configuration of 3C 219 we predict an IR luminosity a factor 3-7 lower than seen from a face-on quasar, depending on the torus parameters. If these ratios and the upper limits for the observed IR luminosity of 3C 219 are adopted, the 6-100 rest frame upper limit on the luminosity of the hidden quasar would be erg s^-1.

We have also tried to estimate the luminosity of the hidden quasar by following a different approach.

If a mean optical-X-ray spectral index (; Brunner et al. 1994) is adopted, then from the 0.1-2.4 keV rest frame luminosity of erg s^-1 () of the unabsorbed nuclear source, and a typical optical spectral index (Richstone & Schmidt 1980), we derive a 350-650nm rest frame luminosity erg s^-1. A similar value ( erg s^-1) is obtained by making use of the correlations between the radio, optical and X-ray powers of radio loud quasars (Browne & Murphy 1987, Kembhavi 1993).

Since Heckmann et al. (1992, 1994) have shown that the 6-100 rest frame luminosity of radio loud quasars is a factor 6-8 larger than the 350-650nm rest frame optical luminosity, we find an expected 6-100 luminosity erg s^-1, larger but close to the upper limit derived in the first estimate previously discussed.

As a consequence in the IC model described below we will adopt a 6-100 luminosity erg s^-1 for the 3C 219 hidden quasar, which corresponds to an IR-optical 100-0.35 rest frame luminosity of erg s^-1 if typical IR-optical spectral parameters are assumed (Brunetti et al. 1997).

In our model computations, we assume an emission pattern of the reprocessed IR radiation close to that predicted by the theoretical models of Pier & Krolik (1992). It should be stressed, however, that, due to the smoothing made by the PSF of the ROSAT HRI, a precise knowledge of this pattern is not crucial. A possible additional beamed IR emission (Hes et al. 1995) has not been taken into account, but being it directional anyway it would affect the calculation only in a small fraction of the radio-volume.

In order to get some insight into the spatial distribution of the relativistic particles, we have constructed a 3D contour of the radio-volume by making use of the weakest isophote in the 1.4 GHz-VLA map of Clarke et al. (1992). The radio galaxy volume is assumed to be symmetric around the line joining the mid-points of the weakest radio isophote at each fixed distance from the nucleus. We have deprojected the structure with the inclination angle and obtained a virtual 3D model of the radio galaxy. Obviously, this is a rather crude approximation as might be indicated by the complex structure of the radio isophotes. Given the spectral properties of the hidden quasar and those of the relativistic electrons, a numerical code computes the total IC soft X-ray luminosity and brightness distribution projected on the plane of the sky. In order to obtain a map to be compared with that derived from the observations, the contribution from the IC scattering of the CMB photons and the observed background level were added to the theoretical matrix, the brightness distribution was convolved with the ROSAT HRI PSF and smoothed with the same gaussian function used for the data (Sect. 3).

As a first approximation we consider an uniform distribution of the relativistic particles and an electron spectrum extended to lower energies with the slope indicated by the radio spectral index, not modified by radiative and adiabatic losses.

One can distinguish two regions in the X-ray brightness distribution of the model (Fig. 7): at small distances from the nucleus (comparable with the minor axis of the radio galaxy) the X-ray emission distribution depends mainly on the nuclear radiation field, the X-ray axis being that of the quasar illumination cone; at larger distances from the nucleus the X-ray distribution is mainly determined by the distribution of the relativistic particles and the X-ray emission tends to be more and more aligned with the radio structure. The IC X-ray flux from the far lobe can be considerably larger than that from the near one depending on the inclination of the radio-axis on the sky plane. As shown by Brunetti et al. (1997) in the case of ellipsoidal radio galaxies, the predicted ratio for an inclination can range up to , depending on the relative contribution due to the IC scattering of the CMB photons and on the luminosity of the hidden quasar. This may explain the larger extension of the observed brightness distribution toward the northern lobe. At larger distances from the nucleus, where the nuclear photon energy density becomes lower than that of the CMB, the IC with the CMB dominates the X-ray flux and the resulting X-ray brightness distribution becomes aligned with the radio-axis.

Fig. 7. The model predicted X-ray isophotes (contours) are superposed on the VLA 1.4 GHz map (gray-scale). The inclination of the radio-jet axis on the sky plane is , while for the torus axis and . The isophotes are on the same scale as those of Fig. 5, starting from the 0.24 level, and reproduce fairly well the C-component.

The model reproduces fairly well the observed brightness in the extended inner regions where the IC emission is dominated by the scattering of the radiation from the nuclear source (Fig. 5 and Fig. 7).

The required inclination of the dusty torus is such that its axis makes an angle of with the radio-axis and with the line of sight. Large tilts between the radio and dusty lane/torus axis for a number of radio galaxies have been discovered with ground based telescopes (Möllenhoff et al. 1992) and more recently with HST observations (Ford et al. 1994, de Juan et al. 1996). It also follows that the distribution of the relativistic particles within the C-component is uniform, at least on the smoothing scale ( Kpc).

The required relativistic electron density can be compared with that derived by the minimum energy (equipartition) argument. Since relativistic electrons with energies much lower () than those of the synchrotron (radio) electrons dominate our IC model, we apply the equipartition equations given by Brunetti et al. (1997) for a fixed low energy cut off in the electron spectrum (in this paper and ). The equipartition magnetic field strength evaluated by assuming the minimum energy condition over all the radio-volume and equal energy density between negatively and positively charged particles is G (with standard equipartition formulae it would be G).

Our model requires a density of relativistic particles such that G, i.e. 3.3 times smaller than the equipartition value. The minimum energy hypothesis is not fulfilled, the energy in the particles being a factor 10 larger than in the equipartition case. In the case of Fornax A, Feigelson et al. (1995) also found a similar, although smaller, departure from the equipartition condition, while in the case of the radio galaxy PKS 1343-601 (Cen B), Tashiro et al. (1998) find that the energy density of the relativistic particles (), equally distributed between negative and positive charges, is a factor larger than that of the magnetic field. With the parameters given in Tashiro et al. paper, by including the energy contribution of mildly relativistic particles (), we derive a ratio between particle and magnetic field energy densities, that is a value of the same order as that found in the case of 3C 219.

4.2. The external components

The simple model discussed so far cannot explain the rather complex structure seen in the external regions where the IC scattering of the quasar's photons becomes more and more negligible. The IC scattering of the CMB photons may explain the observed features under the assumption that there are deviations from the assumed uniformity and simple 3D geometry of the spatial distribution of the relativistic particles. In general, variations of a factor 2-2.5 in the relativistic electron column densities in excess of those of our model would be sufficient to give the observed X-ray brightness distribution. There is some evidence that this might be the case.

Let us consider first the N-component. Both the radio brightness (Fig. 5) and the 1.4-5 GHz spectral index distributions (Clarke et al. 1992) indicate the possible presence of a flow of relativistic particles toward the E-W direction from the northern hot-spot to the N-component, which coincides with a region of steeper radio spectral index.

Since at the position of the N-component our basic IC model predicts a number of counts 3/4 that of the background (of which 20% from the IC scattering of the nuclear photons), the observed signal can be generated by an increase of a factor 2.5 in the number of relativistic electrons. We have tested this hypothesis under the assumption that the back-flow might provide the required enhancement in the density of relativistic particles leaving the magnetic field strength unchanged, i.e. a factor 3.3 lower than the equipartition value of Sect. 4.1. By assuming an electron injection spectrum and radiative losses, we find a synchrotron radio brightness of the western part of the north lobe and a 1.4-5 GHz spectral index both consistent with Clarke et al. (1992) findings. The implied age of the particles reservoir would be years. (For these calculations we have used the SYNAGE package of Murgia & Fanti, 1996).

Let us consider now the S-component. Our basic IC model predicts a number of counts, of which 35% from the IC scattering of the nuclear photons, close to that of the background. Here an enhancement of a factor of 2 in the density of relativistic electrons would be sufficient to account for the observed X-ray flux.

We notice that the S-component lies in a region between the radio jet and the southern hot-spot where there is evidence of a systematic steepening of the radio spectral index and where the magnetic field lines surround a lobe of brighter radio emission, being perpendicular to the line joining the radio-jet with the hot-spot itself (see the polarization map in Clarke et al. 1992). This may suggest a strong interaction between two relativistic plasmas, one of which a back-flow from the hot-spot.

We have also considered the possibility that the S and N-components are of thermal origin. The contribution of these components to the total X-ray flux is 15% and we know from the spectral analysis that at most 10% of the total flux can be thermal ( keV). Thus it is possible that at least one of these components is of thermal origin. From the rotation measure (RM) and depolarization maps Clarke et al. (1992) find that an external clumpy medium is responsible for the observed RM and depolarization features. For the sake of clarity we present in Fig. 8 the X-ray brightness overlayed onto the depolarization map.

Fig. 8. The X-ray image of Fig. 5 (yellow contours, same levels) superposed on the high frequency (6 and 18 cm) depolarization map (color-scale) of 3C 219. This has been obtained from the plate of Clarke et al. (1992) by digitizing and transforming in FITS format. The scale level is in arbitrary units with the most depolarized regions in red. The blue contours represent the 22 cm total intensity (see Clarke et al.1992). The coincidence between a region of high depolarization and the S-component is striking.

The coincidence of the S-component with the depolarization structure transverse to the radio-axis is striking, while a spotted distribution of moderate depolarization is also observed on the southern part of the N-component. On the other hand, we notice that the X-ray isophotes of the northern radio lobe appear to carefully avoid regions of larger depolarization. This is a somewhat contradictory result. Therefore, we have concentrated our attention on the S-component only.

Let us suppose that, according to the spectral analysis of Sect. 2, the source is surrounded by a magnetized thermal plasma with a temperature 1.5 keV and in pressure equilibrium with the relativistic plasma. In our non-equipartition model the pressure inside the radio lobes is dyne cm^-2 and the resulting external gas density would be cm^-3. The strength of the S-component entails an emission measure pc cm^-6, that is a depth of the emission region kpc, much larger than the observed feature. The thermal model may be eased by assuming that the gas is highly clumped. We find that a structure with an overall size 50 kpc, a filling factor of a few percentage points and clumps with a mean size 1 kpc may account for the observed X-ray intensity and depolarization (). A detailed model would require the knowledge of the RM structure function (Tribble, 1991). We tentatively conclude that a thermal origin of the S-component cannot be ruled out.

Finally, we notice that the hot-spots are not detected at the sensitivity level of our HRI observation. While the binning and smoothing procedures used to enhance the HRI image statistics give a convolved PSF much larger than the southern hot-spot dimension, thus depressing any upper limit on the X-ray flux from the hot-spot itself, the convolved PSF is comparable with the northern hot-spot extension. The northern hot-spot has been resolved at 1.4 GHz with an angular size of 12 arcsec (Clarke et al. 1992). From the analysis of the digitized 1.4 GHz map of 3C 219 we derive a radio flux 250 mJy contributed by the hot-spot within a circular region of 90 arcsec², comparable with our X-ray beam size, and compute an equipartition () magnetic field strength G. The 2- upper limit of the X-ray brightness of the hot-spot is erg s^-1 cm^-2 arcsec^-2. This allows us to set an upper limit to the density of the relativistic electrons Compton scattering the CMB photons and a lower bound to the magnetic field of G, which is a factor of 4.8 lower than the equipartition value. Therefore, a deviation from the equipartition condition in the hot-spot as well as in the lobes cannot be ruled out.

© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998
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