and Cosmology

5.4 Components of an AGN
transitions. However, no forbidden transitions are observed
among the broad lines. The classification into
allowed, semi-forbidden, and forbidden transitions is
done by means of quantum mechanical transition probabilities,
or the resulting mean time for a spontaneous
radiational transition. Allowed transitions correspond
to electric dipole radiation, which has a large transition
probability, and the lifetime of the excited state
is then typically only 10 −8 s. For forbidden transitions,
the time-scales are considerably larger, typically 1 s, because
their quantum mechanical transition probability
is substantially lower. Semi-forbidden transitions have
a lifetime between these two values. To mark the different
kinds of transitions, a double square bracket is
used for forbidden transitions, like in [OIII], while semiforbidden
lines are marked by a single square bracket,
like in CIII].
An excited atom can transit into its ground state (or
another lower-lying state) either by spontaneous emission
of a photon or by losing energy through collisions
with other atoms. The probability for a radiational transition
is defined by the atomic parameters, whereas
the collisional de-excitation depends on the gas density.
If the density of the gas is high, the mean time
between two collisions is much shorter than the average
lifetime of forbidden or semi-forbidden radiational
transitions. Therefore the corresponding line photons
are not observed. 6 The absence of forbidden lines is
then used to derive a lower limit for the gas density,
and the occurrence of semi-forbidden lines yields an
upper bound for the density. To minimize the dependence
of this argument on the chemical composition
of the gas, transitions of the same element are preferentially
used for these estimates. However, this is not
always possible. From the presence of the CIII] line and
the non-existence of the [OIII] line in the BLR, combined
with model calculations, a density estimate of
n e ∼ 3 × 10 9 cm −3 is obtained.
Furthermore, from the ionization stages of the lineemitting
elements, a temperature can be estimated,
typically yielding T ∼ 20 000 K. Detailed photoionization
models for the BLR are very successful and are
able to reproduce details of line ratios very well.
6 To make forbidden transitions visible, the gas density needs to be
very low. Densities this low cannot be produced in the laboratory.
Forbidden lines are in fact not observed in laboratory spectra; they
are “forbidden”.
From the density of the gas and its temperature,
the emission measure can then be calculated (i.e., the
number of line photons per volume element). From the
observed line strength and the distance to the AGN, the
total number of emitted line photons can be calculated,
and by dividing through the emission measure, the volume
of the line-emitting gas can be determined. This
estimated volume of the gas is much smaller than the
total volume (∼ r 3 ) of the BLR. We therefore conclude
that the BLR is not homogeneously filled with gas;
rather, the gas has a very small filling factor. The gas in
which the broad lines originate fills only ∼ 10 −7 of the
total volume of the BLR; hence, it must be concentrated
in clouds.
Geometrical Picture of the BLR. From the previous
considerations, a picture of the BLR emerges in which it
contains gas clouds with a characteristic particle density
of n e ∼ 10 9 cm −3 . In these clouds, heating and cooling
processes take place. Probably the most important cooling
process is the observed emission in the form of
broad emission lines. Heating of the gas is provided
by energetic continuum radiation from the AGN which
photoionizes the gas, similar to processes in Galactic
gas clouds. The difference between the energy of a photon
and the ionization energy yields the energy of the
released electron, which is then thermalized by collisions
and leads to gas heating. In a stationary state, the
heating rate equals the cooling rate, and this equilibrium
condition defines the temperature the clouds will attain.
The comparison of continuum radiation and line
emission yields the fraction of ionizing continuum photons
which are absorbed by the BLR clouds; a value of
about 10% is obtained. Since the clouds are optically
thick to ionizing radiation, the fraction of absorbed continuum
photons is also the fraction of the solid angle
subtended by the clouds, as seen from the central continuum
source. From the filling factor and this solid angle,
the characteristic size of the clouds can be estimated,
from which we obtain typical values of ∼ 10 11 cm. In
addition, based on these argument, the number of clouds
in the BLR can be estimated. This yields a typical value
of ∼ 10 10 .
The characteristic velocity of the clouds corresponds
to the line width, hence several thousand km/s. However,
the kinematics of the clouds are unknown. We do
not know whether they are rotating around the SMBH,
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