and Cosmology

5.4 Components of an AGN
ity of an AGN. This behavior can be understood by the
following argument. As we have seen, the BLR covers
a broad range in radii around the center, and the physical
conditions in the BLR are “layered”: ions of higher ionization
energy are closer to the continuum source than
those with lower ionization energy. The gas in the BLR
is subject to photoionization, and hence the distribution
of ionization states will depend on the flux of energetic
photons. This flux is ∝ L/r 2 , thus it depends on the luminosity
L of the ionizing radiation and the distance r
for the central source. For a given ionization state, and
thus for a given broad emission line, the value of the
ionization parameter Ξ = L/r 2 should be very similar
in all AGNs. Hence, this argument yields r ∝ L 1/2 .In
fact, direct estimates from sources where the radius was
determined with reverberation mapping confirmed such
a relation, which might be slightly steeper, r ∝ L ∼0.6 .
The value of Ξ can be obtained for those sources for
which reverberation mapping yields a determination of
the size r. These sources are then used to calibrate the
L-r relation for a given line transition. Once this is done,
(5.30) can be applied again, with the radius now determined
from the calibrated value of Ξ and the continuum
luminosity of the AGN. This method can be extended
to high redshifts, if the value of Ξ can be determined
for emission lines which are located in the optical window
at a given redshift, where the MgII and CIV lines
are the most important transitions.
The Eddington Efficiency. Once an estimate for M •
is obtained, the Eddington luminosity can be calculated
and compared with the observed luminosity. The ratio of
these two, ɛ Edd ≡ L/L Edd , is called the Eddington efficiency.
If one can ignore strongly beamed emission, ɛ Edd
should be smaller than unity. For the estimate of ɛ Edd ,
the observed luminosity in the optical band needs to be
translated into a bolometric luminosity, which can be
done with the help of the average spectral energy distribution
of AGNs of a given class. All of these steps
involve statistical errors of a factor ∼ 2 in any individual
object, but when averaged over an ensemble of
sources, they should yield approximately the correct
mean values.
We find that ɛ Edd varies between a few percent to
nearly unity among QSOs. Hence, once a black hole
becomes sufficiently active as to radiate like a QSO, its
luminosity approaches the Eddington luminosity. There
might be a trend that radio-loud QSOs have a somewhat
larger ɛ Edd , but these correlations are controversial and
might be based on selection effects. The fact that ɛ Edd is
confined to a fairly narrow interval implies that the luminosity
of a QSO can be used to estimate M • , just by
setting M • = ɛ Edd M Edd (L). This mass estimate has a statistical
uncertainty of about a factor of ∼ 3 in individual
sources.
The Galactic Black Hole. The Eddington efficiency
of the SMBH in the Galactic center is many orders of
magnitude smaller than unity; in fact, with its total luminosity
of 5 × 10 36 erg/s, ɛ Edd ∼ 10 −8 . Such a small
value indicates that the SMBH in our Galaxy is starved;
the accretion rate must be very small. However, one can
estimate a minimum mass rate with which the SMBH in
the Galactic center is fed, by considering the mass-loss
rate of the stars near the Galactic center. This amounts
to ∼ 10 −4 M ⊙ /yr, enough material to power an accretion
flow with L ∼ 10 −2 L Edd . The fact that the observed
luminosity is so much smaller than this value leads to
two implications. The first of these is that there must
be other modes of accretion which are far less efficient
than that of the geometrically thin, optically thick accretion
disk described in Sect. 5.3.2. Such models for
accretion flows were indeed developed. In these models,
the generated internal energy (heat) is not radiated
away locally, but instead advected with the flow towards
the black hole. The second conclusion is that the central
mass concentration must indeed be a black hole –
a black hole is the only object which does not have
a surface. If, for example, one would postulate a hypothetical
object with M ∼ 3 × 10 6 M ⊙ which has a hard
surface (like a scaled-up version of a neutron star), the
accreted material would fall onto the surface, and its kinetic
and inner energy would be deposited there. Hence,
this surface would heat up and radiate thermally. Since
we have strict upper limits on the radius of the object,
coming from mm-VLBI observations, we can estimate
the minimum luminosity such a source would have. This
estimate is again several orders of magnitude larger than
the observed luminosity from Sgr A ∗ , firmly ruling out
the existence of such a solid surface.
The observed flaring activity of Sgr A ∗ (see
Sect. 2.6.4) yields further information about the properties
of the Galactic SMBH. In particular, the
quasi-periodicity of ∼ 17 min most likely must be iden-
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