5.2 The obscuring torus

If an AGN consisted solely of the central engine, observers would see X-rays and ultraviolet radiation from the hot accretion disc (accounting for the 'the big blue bump' in Figure 17) and, apart from the jets, very little else. To account for the strong infrared emission from many AGNs, the model includes a torus of gas and dust that surrounds the central engine.

The dust particles - which are usually assumed to be grains of graphite - will be heated by the radiation from the engine until they are warm enough to radiate energy at the same rate at which they it receive it. As dust will vaporise (or sublimate) at temperatures above 2000 K, the cloud must be cooler than this.

Question 11

Assuming that dust grains radiate as black bodies, estimate the range of wavelengths that will be emitted from the torus.

Note: A black-body source at a temperature T has a characteristic spectrum in which the maximum value of spectral flux density (Fλ) occurs at a wavelength given by Wien's displacement law

Answer

Wien's displacement law relates the temperature of a black body to the wavelength at which the spectral flux density has its maximum value. In this case, the dust grains on the inner edge of the torus will be at 2000 K, so their peak emission will be at

So, λ_max is about 1.5 μm.

Grains further from the engine will be cooler, and their emission will peak at longer wavelengths, so the torus can be expected to radiate in the infrared at wavelengths of 1.5 μm or longer. (Note that although the spectrum emitted by dust grains is not a black-body spectrum, it is similar enough for the above argument to remain valid.)

So such a dust cloud will act to convert ultraviolet and X-ray emission from the engine into infrared radiation, with the shortest wavelengths coming from the hottest, inner parts of the cloud.

From a very simple dust cloud model, it is easy to understand why AGNs so often emit most of their radiation in the infrared. Almost certainly, dust heated by the engine is observed in most AGNs, although the dust may be more irregularly distributed than in our simple model, and the torus may have gaps in it. Some small amount of the infrared radiation will generally come from the engine itself, though, and in BL Lacs it is probable that most of the infrared radiation comes from the engine. The variability that was discussed in Section 4.2 applies to radiation from the engine at X-ray and optical wavelengths (and sometimes at radio wavelengths). The infrared emission from the torus is thought to vary much more slowly, as you would expect from the greater extent of the torus.

Note that this torus is not the same as the accretion disc surrounding the black hole, though it may well lie in the same plane and consist of material being drawn towards the engine.

It is possible, using a simple physical argument, to make a rough estimate of the inner radius of the torus by asking how far from the central engine the temperature will have fallen to 2000 K, the maximum temperature at which graphite grains can survive before being vaporised.

If the engine has a luminosity, L, then the flux density at a radius r from the engine will be L/4r². A dust grain of radius a will intercept the radiation over an area a² (Figure 33) and, if no energy is reflected, the power absorbed will be

Figure 33: A spherical dust grain of radius a will intercept radiation over an area πa²

The temperature of the dust grain will rise until the power emitted by thermal radiation is equal to the power absorbed. If the grain behaves as a black body we can write

where σ is the Stefan-Boltzmann constant (σ = 5.67 × 10⁻⁸ W m² K⁻⁴).

Here we assume that the temperature of the grain is the same over its whole surface, which would be appropriate if, for instance, the grain were rotating. Next, we make the power absorbed equal to the power radiated

Finally, if we divide both sides by a², the radius a is cancelled out (as it should - the size of the dust grain should not come into it) and we can rearrange for r to get:

This distance is called the sublimation radius for the dust.

Question 12

Calculate the dust sublimation radius, in metres and parsecs, for an AGN of luminosity 10³⁸ W. (Assume that dust cannot exist above a temperature of 2000 K.)

Answer

From Equation 3.7 we have

Thus, according to this calculation, the radius of the inner edge of the dust torus is 1.5 × 10¹⁵ m or 0.05 pc. (A more rigorous calculation, which takes account of the efficiency of graphite grains in absorbing and emitting radiation, gives a radius of 0.2 pc.)

For typical luminosities, the inner edge of the torus is three or four orders of magnitude (i.e. 1000 to 10 000 times) bigger than the emitting part of the accretion disc which is contained within the central engine in Figure 31. Even so, the torus cannot be resolved even in high-resolution images. However there is evidence in several galaxies of a much more extensive disc of gas and dust that encircles the AGN. It has been suggested, although not proven, that these discs provide a supply of material that can spiral down into the central regions of the active galaxy - passing into the torus, through the accretion disc, and eventually falling into the black hole itself.One example of such a disc is found in the radio galaxy NGC 4261 which is shown in Figure 34.

The digitized Sky Survey was produced at the Space Telescope Science Institute under US Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions. The Second Palomar Observatory Sky Survey (POSS-II) was made by the California Institute of Technology with funds from the National Science Foundation, the National Aeronautics and Space Administration, the National Geographic Society, the Sloan Foundation, the Samuel Oschin Foundation, and the Eastman Kodak Corporation. The Oschin Schmidt Telescope is operated by the California Institute of Technology and Palomar Observatory. Supplemental funding for sky-survey work at the STScI is provided by the European Southern Observatory; Figure 34b: L. Ferrarese (Johns Hopkins University) and NASA. ©

The digitized Sky Survey was produced at the Space Telescope Science Institute under US Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions. The Second Palomar Observatory Sky Survey (POSS-II) was made by the California Institute of Technology with funds from the National Science Foundation, the National Aeronautics and Space Administration, the National Geographic Society, the Sloan Foundation, the Samuel Oschin Foundation, and the Eastman Kodak Corporation. The Oschin Schmidt Telescope is operated by the California Institute of Technology and Palomar Observatory. Supplemental funding for sky-survey work at the STScI is provided by the European Southern Observatory; Figure 34b: L. Ferrarese (Johns Hopkins University) and NASA.

Figure 34: The radio galaxy NGC 4261 (also known as 3 C 270) is about 31 Mpc away. (a) An optical image that shows the elliptical host galaxy, with contours of radio emission overlaid (in red). The full extent of the radio lobes is about 76 kpc. (b) An optical image from the Hubble Space Telescope of the central regions of NGC 4261, which reveals the presence of a disc of obscuring dust that is about 250 pc in diameter

On the left (Figure 34a) you can see a radio image of the jets, superimposed on an optical image of the host galaxy. The highly magnified image (Figure 34b), taken with the Hubble Space Telescope, shows a dark obscuring disc silhouetted against the stellar core of the elliptical host galaxy. This disc is about 250 pc across and very much bigger than the sub-parsec structures that make up the AGN itself. Note that its plane is perpendicular to the axis of the radio jets shown on the left of the figure. Thus the jets seem to be aligned along the rotation axis of the disc, and this lends support to the ideas of jet formation that were outlined in Section 4.7.