and Cosmology

5. Active Galactic Nuclei
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Binary QSOs. The connection between the activity of
galaxies and the presence of close neighbors is also seen
from the clustering properties of QSOs. In surveys for
gravitational lens systems, pairs of QSO images have
been detected which have angular separations of a few
arcseconds and very similar redshifts, but sufficiently
different spectra to exclude them being gravitationally
lensed images of the same source. The number of binary
QSOs thus found is considerably larger than the
expectation from the large-scale correlation function of
QSOs. This conclusion was further strengthened by an
extensive analysis from the QSOs in the Sloan Digital
Sky Survey (see Sect. 8.1.2). The correlation function of
QSOs at separations below ∼ 30h −1 kpc exceeds that of
the extrapolation of the correlation function from larger
scales by a factor of 10 or more. Hence it seems that
the small-scale clustering of QSOs is very much enhanced,
say compared to normal galaxies, which could
be due to the triggering of activity by the proximity
of the neighbor: in this case, both galaxies attain a perturbed
gravitational potential and start to become active.
5.4.6 The Black Hole Mass in AGNs
We now return to the determination of the mass of the
central black hole in AGNs. In Sect. 5.3.5, a lower limit
on the mass was derived, based on the fact that the
luminosity of an AGN cannot exceed the Eddington
luminosity. However, this estimate cannot be very precise,
for at least two reasons. The first is related to the
anisotropic appearance of an AGN. The observed flux
can be translated into a luminosity only on the assumption
that the emission from the AGN is isotropic, and
we have discussed several reasons why this assumption
is not justified in many cases. Second, we do not
have a clear idea what the ratio of AGN luminosity to
its Eddington luminosity is. It is clear that this ratio
can vary a lot between different black holes. For example,
the black hole at the center of our Galaxy could
power a luminosity of several 10 44 erg/s if radiating
with the Eddington luminosity – and we know that the
true luminosity is several order of magnitudes below
this value.
M • from Reverberation Mapping. A far more accurate
method for estimating the black hole mass in AGNs
comes from reverberation mapping which we described
in Sect. 5.4.2. The principal quantity that is derived from
this technique is the size r of the BLR for a given atomic
line or for a given ionization state of a chemical element.
Furthermore, the relative line width Δλ/λ can be
measured, and can be related to the characteristic velocity
dispersion σ in the BLR, σ = c Δλ/λ. Assuming
that the gas is virialized, or moving on Keplerian orbits
around the black hole, the mass of the latter can be
estimated to be
M • ≈ r σ 2 /G , (5.30)
where the difference between random motion and circular
orbits corresponds to a factor of order 2 in this
estimate. Thus, once reverberation mapping has been
conducted, the black hole mass can be estimated with
very reasonable accuracy.
However, this is a fairly expensive observing technique,
requiring the photometric and spectroscopic
monitoring of sources over long periods of time, and
it can therefore be applied only to relatively small samples
of sources. Furthermore, this technique is restricted
to low-luminosity AGNs, since the size of the BLR, and
thus the time delay and the necessary length of the monitoring
campaign, increases with the black hole mass.
We might therefore want to look at alternative methods
for estimating M • .
M • from Scaling Relations. When applied to a set
of nearby Seyfert 1 galaxies, for which reverberation
mapping has been carried out, one finds that the black
hole mass in these AGNs satisfies the same relation
(3.35) between M • and the velocity dispersion σ e of
the bulge as has been obtained for inactive galaxies.
This scaling relation then yields a useful estimate of
the black hole mass from the stellar velocity dispersion.
Unfortunately, even this method cannot be applied to
a broad range of AGNs, since the velocity dispersion of
stars cannot be measured in AGNs which are either too
luminous – since then the nuclear emission outshines
the stellar light, rendering spectroscopy of the latter
impossible – or too distant, so that a spatial separation
of nuclear light from stellar light is no longer possible.
However, another scaling relation was found which
turns out to be very useful and which can be extended
to luminous and high-redshift sources. The size of the
BLR correlates strongly with the continuum luminos-