3.4 The Eddington Limit
Thus the observations require that a luminosity of around 100 times that of the entire Milky Way Galaxy be generated within a region with a diameter only about 1000 times that of the Earth's orbit! (A truly amazing statement.)
The most obvious mechanism for generating such enormous luminosity within such a tiny region of space is an accretion process, but instead of perhaps more familiar compact stars with masses ~M
, the accreting object is required to be a black hole with mass M ~ 108M. The accretion luminosity, L acc, generated by an object of mass M and radius R* is
where 
( = dM/dT) is the accretion rate.
SAQ 2
Question: Why are astronomers forced to infer the existence of supermassive black holes rather than attributing the luminosity of quasars to a very high accretion rate onto a mass M ~ M
Answer
Because the accretion luminosity cannot exceed the Eddington Limit, which is proportional to M.
Sir Arthur Eddington (Figure 6) was responsible for many of the underpinnings of modern astrophysics, including the concept of the limiting Eddington luminosity. Beyond this limit, radiation pressure will cause outflow.
Activity 1: Context: AGN, a developing research field
Read the following extract, which sets the contents of this course in the context of accretion in binary stars.
Observations
Accretion on to stellar mass objects occurs in a wide variety of systems and yields a wide variety of observational behaviour. While there may be many arguments over detailed models, the broad basis of these differences is largely understood. Active galactic nuclei also come in many observed forms. From an observational viewpoint, they can be defined as apparently stellar sources but with non-thermal spectra, and, in cases where they can be determined, significant redshifts. Beyond this, we find a wide variety of properties, which we shall classify in more detail below. But in these cases it is not at all clear how these differences arise, or, indeed, whether one is even dealing with variants of a single basic model. We shall argue that the sources are all manifestations of accretion on to supermassive black holes (of order 108 M), although even this is still not universally accepted. Furthermore, for stellar-mass objects, at least in some cases, we have a complete picture of the system even if some of the details are missing. In no case do we have anything comparable for active galactic nuclei. That is not to say that there are no aspects of active galactic nuclei that are thought to be fairly well understood, but those that are do not include the mechanism of the basic energy source. Thus we have to try to extract from the available data what clues we can to the nature of the central engine. … On the other hand, once one gets beyond the inner engine a consensus appears to be emerging on a standard picture, a so-called unified model, in terms of which one can begin to account for the variety of active galactic phenomena.
Discussion
Apparently stellar in this context means a point source of light, rather than an extended object such as a galaxy.
In describing the observational characteristics of AGN, Frank, King and Raine use the term non-thermal spectrum. This concise term means that the electromagnetic radiation emitted does not have the blackbody spectrum. The blackbody spectrum is physically very simple: its shape is determined by a single parameter, the temperature, T, of the emitting source. However not all sources of light emit blackbody radiation. For example, the electromagnetic radiation emitted by an accelerated electron does not have a blackbody spectrum. We discuss this in Section 7.
Keywords: central engine
Activity 2
Now read the preface of Peterson [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] (An introduction to active galactiv nuclei), omitting the last paragraph.
Phenomenology is a term you may not have encountered before. It is an endeavour which lies somewhere between observation and theory. The observations are described and characterised, and underlying causes are sought, but there isn't a rigorous theory.
Keywords: none
Question 1
What is thought to be the energy source which powers active galaxies? See if you can answer this using the astrophysics terms you have learned, and then try to write another answer using only mainstream physics vocabulary.
Answer
It is thought that accretion onto supermassive black holes powers the emission from active galactic nuclei. In basic physics terms, the electromagnetic radiation is powered by the liberation of gravitational potential energy as matter falls in the gravitational field.
You may also have included some discussion of how the viscosity of the accreting material plays a role in converting kinetic energy into thermal energy and consequently radiation.