### Become an OU student

Introduction to active galaxies

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

# 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 () occurs at a wavelength given by Wien's displacement law

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, λmax 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.)