Radiation from a dusty torus

Chiaberge et al. [42] have suggested that tori do not exist in FR-I sources, or they must have a very thin geometry. This conclusion results from the correlation found between optical and radio cores of some FR-I sources. However, the sample used in this analysis represents only just under half of the FR-I galaxies tabled by Zirbel and Baum [43], and one needs additional observations of the polarized optical spectrum to reach a firm conclusion about this [44]. Nevertheless, these results could be interpreted as suggesting that perhaps there is a correlation between a flat infrared torus and a flat distribution of BLR clouds as suggested by Maiolino [39]. We do not know what mechanism, other than accretion, could cause such a flattening of the BLR and the torus. However, such a flattening might be understood in terms of a non-homogeneous spherical shell of BLR or dust in which the polar caps above and below the disk plane are much more diluted than the equatorial belt. Zier and Biermann [45] have shown that the caps of a spherical layer of dust could be diluted so much, that even a dense torus would have a doughnut shape.

We have already discussed some aspects related to the infrared radiation from ubiquitous dusty tori in quasars. Unification schemes for AGN generally involve the following components: Kerr black hole, a relativistic accretion disk, jets, broad line clouds and a dusty torus. For blazars the situation appears at first sight to be a little different, and we wonder why that might be. There are two issues which should be considered in connection with dusty tori in blazars. Firstly, since there is no direct evidence of any thermal emission from tori we should consider what indirect evidence (at any wavelength) there is about the existence of dust in the centres of host galaxies. Secondly, we should consider what kind of torus geometry would fit observations made at different wavelengths best.

Since unification schemes propose that FR-I and BL Lacs are related, FR-I sources being the mis-oriented counterparts of BL Lacs [14], we have searched the literature for information about dust structures associated with blazars/BL Lacs/FR-I. We note that Blazejowski et al. [38] required an external IR photon field from a torus scattered by relativistic jet electrons, in addition to those in the SSC model, in order to fit $\gamma$-ray spectra of OVV quasars observed by EGRET. A key to the existence of tori in blazars could come from establishing a link between the torus and the BLR. For example, when there is no detection of direct optical emission, the interpretation of spectro-polarimetric data on FR-I objects with strong evidence for infrared obscuration ([15] and references therein) could suggest the existence of a BLR hidden by a thick torus. In this case, the observed polarized broad lines would be the result of scattering into the line of sight by free electrons in zones whose shape and orientation is determined by the torus' inner geometry. Hence, the detection of free electron scattering regions should be a good diagnostic of torus geometry. Falcke et al. [11] proposed that the opening angle of the torus might play a critical role in the FR-I and FR-II dichotomy - a closed torus covering a large fraction of $4 \pi$ steradians, as seen from the black hole, would obscure the internal activity of FR-I objects.

de Koff et al. [46] have discussed how the properties of the dust depend upon the radio properties of the object, and found that FR-II, which are powerful radio galaxies, have a rather clumpy dust distribution, and they suggest that this translates into a large opening angle of the torus. A less powerful radio jet (such as those in FR-I) would only slowly disperse the dust, and this type of obscuration might contribute to the deceleration of FR-I jets by entraining the material from the torus.

We consider first the FR-I galaxy Centaurus A. Alexander et al. [33] explain the IR spectrum of Cen A using a combined model of infrared emission from startbursts, cirrus clouds and an AGN-type torus. A compact optically thick torus with $r_{\rm out,torus}=3.6$ pc and an opening angle of $\phi=30^{\circ}$ would account for the observed flux. Centaurus A appears as a concentrated IR source in the H band [47] within a scale of tens of pc. No optical emission has been observed from the central source and, as Falcke et al. [11] suggested, this source may have a closed torus hiding the BLR which has not been detected even in polarized flux. Israel et al. [48], Rydbeck et al. [49] and Turner et al. [50] concluded that there is a dense nuclear torus with diameter $< 230$ pc. It is also interesting that Bryant et al. [47] show a clear picture of a warped dust lane obscuring the nuclear source - the radio jet being perpendicular to a large-scale torus which seems to be inclined with respect to the plane of the dust-lane.

Turning now to other FR-I radio galaxies, 3C218 (Hydra A) also shows evidence for a nuclear obscuration [51]. 3C270 is another FR-I radio galaxy for which a broad $H_{\alpha }$ emission line has been detected [52]. Ferrarese et al. [53] proposed that its nucleus is surrounded by a dust torus with a diameter of 120 pc and optical depth $\tau \approx 1$. An inclination angle of $20^{\circ}$ between the axis of the torus and the line of sight would be in accordance with the detection of un-obscured nuclear optical emission [30].

Possible evidence against tori in blazars comes from the FR-I radio galaxy M87, which seems to have a very low IR flux which cannot be explained with a standard torus model [54]. The torus in this source could be very diluted, and heated less as a result of the extremely low accretion activity of M87 [13] such that its emission is dwarfed by the jet emission.

At kiloparsec scales, starburst activity dominates the infrared emission, but as one goes deeper into the nucleus of the galaxy, de Koff et al. [46] found that well organized dust structures were present in FR-I galaxies in the 3CR catalog, and this could indicate that the flow of matter towards the nucleus is rather steady in FR-I, allowing the formation of distinct torus features. These structures tended to be sharply defined small-scales disks with radii less than $\sim 2.5$ kpc. The detection of large-scale dusty features (sometimes shaped as bars or dust-lanes) suggests that there could be an association between a small-scale infrared torus, such as those in Seyfert galaxies, and a large-scale torus sometimes identified with the dust structure of the galaxy. The structure of the nuclear torus could then depend on the large-scale dust distribution - well-organized kpc dust structures could extend inward towards smaller scales (small-scale torus surrounded by large-scale torus). We define this as a symbiosis between the large and small scale dusty features [16].

The above discussion leads us to the conclusion that dust could be present everywhere, even in FR-I objects where the torus cannot easily be detected. Since FR-I and BL Lacs are thought to be similar (apart from orientation) and there is some evidence of BLR and torus activity in FR-I, we postulate that the linkage between BLR and tori in quasars discussed by Chiaberge et al. [30] may apply also in blazars. We shall calculate next the optical depth for $\gamma$-$\gamma$ absorption in the infrared radiation field of tori.

We know that the IR emission from the torus is strongly related to the activity of the central object. The inner radius depends on $L_{\rm disk}$, and is given by the sublimation radius of the dust [55]:

$$R_{\rm in, torus} \approx T_{1500}^{-2.8} L_{\rm disk,46}^{1/2}~pc$$ (11)

where $L_{\rm disk}=10^{46} L_{\rm disk,46}$ erg/s, and $T_{1500}$ is the dust temperature in units of 1500 K (the dust sublimation temperature is taken to be 1500 K). The inner torus radius is plotted in Fig. 8 versus disk luminosity for three dust temperatures.

We start with a torus centred on the black hole, symmetric about the jet axis, and having a rectangular cross section with full height $h$, and inner and outer radii $R_{\rm in, torus}$ and $R_{\rm out,torus}$. We shall discuss how $\tau _{\gamma \gamma }$ changes for different scales of tori, e.g., simulating an open torus by having either a rectangular cross section or a rectangular cross section with the inner edges cut away at angle $\phi$ (see Fig. 9).

As discussed earlier, in the context of the symbiosis between jets and accretion disks, an increase in jet power could be at the expense of disk luminosity. A lower disk luminosity at UV frequencies would reduce the heating of the inner surface of the dusty torus, causing the inner radius of the torus, given by Eq. 11, to be small (Fig. 8). This implies that fat dusty tori ( $R_{\rm in,torus} \ll h$) could exist in AGN with very low central activity such as blazars, and this would be in accordance with the closed torus model discussed by Falcke et al. [11]. On the other hand, for a ``cold torus'' with $T<1000$ K, the inner radius would be far from the nucleus for a given luminosity (see Fig. 8). Such inefficient heating of the dust would probably describe best the torus in M87 which seems to be a peculiar object in that it has an extremely low mass accretion rate.

Figure 8: $R_{\rm in, torus}$ vs. $L_{\rm disk}$ for three different dust temperatures: $T=1500$ K (solid curve), 1000 K (dashed curve), 700 K (dotted curve).

Due to its size, the energy density of the infrared photons remains fairly uniform inside the torus. A flat torus (i.e., $R \gg h$) could approximate the models proposed by Chiaberge et al. [42]; see the discussion from the previous section and comments by Maiolino et al. [39] about a flattened BLR distributions. Although flat tori have not been detected, and we are uncertain about the stability of such a configuration of dust, we believe that it is an interesting possibility. For simplicity we model in this section a torus with a single black body temperature such that the IR intensity is constant within the solid angle subtended by the torus. We shall extend the work of Protheroe & Biermann [17] for different torus geometries. Fig. 9 illustrates the geometry for interaction, at points A and B, of $\gamma$-rays with IR photons emitted from the surfaces of the torus.

Figure 9: Torus cross-sections considered: rectangle, rectangle with edges cut away at angle $\phi$, the opening angle in this case (see text). $\gamma$-rays at point A interact with any photons emitted from the inner surface of the torus (between points 1 to 3). Gamma-rays at point B (above the torus) also interact with any photons emitted from the upper surface (between 3 to 4).

Accretion rates are smaller in blazars than in quasars. Since the thickness of the torus is related to the accretion inflow and disk luminosity (through radiation pressure effects) [56] one expects tori in FR-I to be thinner, diluted, and/or less efficiently heated - as is probably the case in M87. Therefore, we have varied $h$ between $1$ pc and $3$ pc, $R_{\rm in, torus}$ between $0.1$ pc and 1 pc, and $R_{\rm out,torus}$ between 2 pc and 10 pc. The optical depth from $z=0$ to infinity, for $\gamma$-rays traveling along the jet axis, is shown in Fig. 10 where we have compared the case of a torus with $R_{\rm in, torus}=0.1$ pc (solid curves) with a torus having $R_{\rm in, torus}=1$ pc (dashed curves) for three different torus heights $h$. We find that more $\gamma$-rays with energies around $10^{2.5-3.5}$ GeV would be absorbed by $\gamma$-$\gamma$ interactions when the torus comes closer to the central source. We also find that an open torus geometry ($\phi >0$) can significantly modify $\tau _{\gamma \gamma }$ as shown in Fig. 11(a) where it is again seen to have the greatest effect near the pair production threshold. If the torus has a large outer radius, then more IR photons from the upper surface of the torus are available for interaction with $\gamma$-rays along the jet. For example, for an extended torus with $R_{\rm out, torus}=10$ pc the absorption of photons with energy above 2 TeV is larger (compare dotted line with upper solid curve in Fig. 11a). As noted previously by Protheroe and Biermann [17], we can see that for photon energies above about several hundreds of GeV the opacity is large enough such that no TeV $\gamma$-rays can emerge if the source is near the centre of the torus.

Figure 10: Optical depths for $\gamma$-rays traveling along the jet axis from $z=0$ to infinity in the torus IR radiation ($T=1000$ K) for $r_{\rm out}=2$ pc and $r_{\rm in}=0.1$ pc (solid curves) or $r_{\rm in}=1$ pc (dashed curves). Results are show for three torus heights: $h=1$ pc (lower curves), $h=2$ pc (middle curves), $h=3$ pc (upper curves).

Figure 11: Optical depths for $\gamma$-rays traveling along the jet axis from $z=z_0$ to infinity in the torus IR radiation. (a) $T=1000$ K, $z_0=0$, $r_{\rm in}=0.1$ pc, $r_{\rm out}=2$ pc, $h=3$ pc and with the torus inner edge cut away at angle $\phi =0^\circ$ (upper solid curve), $10^\circ$, $30^\circ$, $50^\circ$ (lower solid curve). Dotted curve is for $r_{\rm out}=10$ pc and $\phi =0^\circ$. (b) $r_{\rm in}=0.1$ pc, $r_{\rm out}=2$ pc, $h=1$ pc, $\phi =0^\circ$, $T=1000$ K (solid curves) or $T=100$ K (dotted curves), for $z_0=0.01$ pc (upper curves), 0.1 pc (middle curves), and 0.5 pc (lower curves)

Risaliti et al. [57] have shown that a torus is stable if the mass of the dust in the torus does not exceed the dynamical mass flowing toward the center. This constrains the outer torus radius, $R_{\rm out,torus}$, to have values less than 10 pc for a column density of dust along the line of sight that intersects the obscuring medium of $N\approx 10^{24}$ cm$^{-2}$. FR-I objects could have diluted tori with column densities of $N\approx 10^{22}$ cm$^{-2}$, or lower, but still be optically thick, and this would impose a upper limit of $\sim 100$ pc for the torus' outer radius. However, Maiolino et al. [58] interpret their data as suggesting that the inner parts of tori are much denser than the outer parts, and find a gradient in the torus' covering factor that would give $R_{\rm out, torus}< 20$ pc for Seyfert galaxies. The covering factor plays a crucial role in these models, as well as the gas mass enclosed within the torus [57]. For simplicity, we take a value of 10 pc as the maximum radius of the dust torus which could be relevant to our analysis.

In Fig. 11(b) we show how the optical depth depends on the distance of $\gamma$-ray emission region along the jet. So far, we have assumed that the torus radiates as a perfect black body. However, if the torus is patchy or not optically thick at IR wavelengths we may have diluted black body radiation, $u_{\rm IR} \approx \eta_{\rm IR} a T^4$ erg/cm$^3$, where $a$ is the radiation constant. All our curves would be multiplied by $1/\eta_{\rm IR}$ in this case. Alternatively, for a poor heating mechanism related to a low luminosity of the accretion disk the dust could be heated to lower temperatures, e.g. $T\approx 100$ K, and this results in reducing the GeV to TeV opacity considerably, with the pair production threshold $\gamma$-ray energy increasing as $\sim 1/T$ as illustrated in Fig. 11(b) by the dotted curves. We note however, that Blazejowski et al. [38] require $\eta_{IR} \approx 0.3$ to fit $\gamma$-ray spectra of OVV quasars with an external inverse Compton model, and this still allows for significant TeV $\gamma$-ray absorption in this type of blazar. Extremely low values of $\eta_{IR}$ may apply in objects such as M87.