and Cosmology

5. Active Galactic Nuclei
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change substantially over the lifetime of the source,
a total energy can be estimated from the luminosity
and the minimum age,
E 10 47 erg/s × 10 7 yr ∼ 3 × 10 61 erg , (5.8)
however, the assumption of an essentially constant
luminosity is not necessarily justified.
• The luminosity of some AGNs varies by more than
50% on time-scales of a day. From this variability
time-scale, an upper limit for the spatial extent of
the source can be determined, because the source
luminosity can change substantially only on such
time-scales where the source as a whole, or at least
a major part of the emitting region, is in causal contact.
Otherwise “one end” of the source does not
know that the “other end” is about to vary. This
yields a characteristic extent of the central source
of R 1 lightday ∼ 3 × 10 15 cm.
5.3.1 Why a Black Hole?
We will now combine the aforementioned observations
and derive from them that the basic energy production
in AGNs has to be of a gravitational nature. To do this,
we note that the most efficient “classical” method of energy
production is nuclear fusion, as is taking place in
stars. We will therefore make the provisional assumption
(which will soon lead to a contradiction) that the
energy production in AGNs is based on thermonuclear
processes.
By burning hydrogen into iron – the nucleus with the
highest binding energy per nucleon – 8 MeV/nucleon
are released, or 0.008 m p c 2 per nucleon. The maximum
efficiency of nuclear fusion is therefore ɛ 0.8%,
where ɛ is defined as the mass fraction of “fuel” that is
converted into energy, according to
E = ɛ mc 2 . (5.9)
To generate the energy of E = 3 × 10 61 erg by nuclear
fusion, a total mass m of fuel would be needed, where
m is given by
m = E
ɛc ∼ 4 × 2 1042 g ∼ 2 × 10 9 M ⊙ , (5.10)
where we used the energy estimate from (5.8). If the
energy of an AGN was produced by nuclear fusion,
burnt-out matter of mass m [more precisely, (1 − ɛ)m]
must be present in the core of the AGN.
However, the Schwarzschild radius of this mass is
(see Sect. 3.5.1)
r S = 2Gm
c 2
= 2GM ⊙
c 2
m
M ⊙
= 3 × 10 5 cm m M ⊙
∼ 6 × 10 14 cm ,
i.e., the Schwarzschild radius of the “nuclear cinder” is
of the same order of magnitude as the above estimate of
the extent of the central source. This argument demonstrates
that gravitational effects must play a crucial role –
the assumption of thermonuclear energy generation has
been disproven because its efficiency ɛ is too low. The
only known mechanism yielding larger ɛ is gravitational
energy production.
Through the infall of matter onto a central black hole,
potential energy is converted into kinetic energy. If it is
possible to convert part of this inward-directed kinetic
energy into internal energy (heat) and subsequently emit
this in the form of radiation, ɛ can be larger than that of
thermonuclear processes. From the theory of accretion
onto black holes, a maximum efficiency of ɛ ∼ 6% for
accretion onto a non-rotating black hole (also called
a Schwarzschild hole) is derived. A black hole with
the maximum allowed angular momentum can have an
efficiency of ɛ ∼ 29%.
5.3.2 Accretion
Due to its broad astrophysical relevance beyond the
context of AGNs, we will consider the accretion process
in somewhat more detail.
The Principle of Accretion. Gas falling onto a compact
object loses its potential energy, which is first converted
into kinetic energy. If the infall is not prevented, the gas
will fall into the black hole without being able to radiate
this energy. In general one can expect that the gas has
finite angular momentum. Thus it cannot fall straight
onto the compact object, since this is prevented by the
angular momentum barrier. Through friction with other
gas particles and by the resulting momentum transfer,
the gas will assemble in a disk oriented perpendicular to
the direction of the angular momentum vector. The frictional
forces in the gas are expected to be much smaller