and Cosmology

3.6 Extragalactic Distance Determination
it is statistically highly significant, but the deviations
of the data points from this power law are considerably
larger than their error bars. An alternative way to express
this correlation is provided by the relation M/L ∝ L 0.25
found previously – see (3.27) – by which we can also
write M • ∝ Mbulge 0.9 .
An even better correlation exists between M • and the
velocity dispersion in the bulge component, as can be
seen in the right-hand panel of Fig. 3.28. This relation
is best described by
M • = 1.35 × 10 8 M ⊙
(
σ e
200 km/s
) 4
, (3.35)
113
Fig. 3.27. The Seyfert galaxy NGC 4258 contains an accretion
disk in its center in which several water masers are embedded.
In the top image, an artist’s impression of the hidden disk
and the jet is displayed, together with the line spectrum of the
maser sources. Their positions (center image) and velocities
have been mapped by VLBI observations. From these measurements,
the Kepler law for rotation in the gravitational field
of a point mass of M • = 25 × 10 6 M ⊙ in the center of this galaxy
was verified. The best-fitting model of the central disk is
also plotted. The bottom image is a 20-cm map showing the
large-scale radio structure of the Seyfert galaxy
the SMBH is located (see Fig. 3.28, left). Here, the
bulge component is either the bulge of a spiral galaxy
or an elliptical galaxy as a whole. This correlation
is described by
M • = 0.93 × 10 8 M ⊙
(
LB,bulge
10 10 L B⊙
) 1.11
; (3.34)
where the exact value of the exponent is still subject to
discussion, and where a slightly higher value M • ∝ σ 4.5
might better describe the data. The difference in the results
obtained by different groups can partially be traced
back to different definitions of the velocity dispersion,
especially concerning the choice of the spatial region
across which it is measured. It is remarkable that the
deviations of the data points from the correlation (3.35)
are compatible with the error bars for the measurements
of M • . Thus, we have at present no indication of an
intrinsic dispersion of the M • -σ relation.
In fact, there have been claims in the literature that
even globular clusters contain a black hole; however,
these claims are not undisputed. In addition, there may
be objects that appear like globular clusters, but are in
fact the stripped nucleus of a former dwarf galaxy. In
this case, the presence of a central black hole is not
unexpected, provided the scaling relation (3.35) holds
down to very low velocity dispersion.
To date, the physical origin of this very close relation
has not been understood in detail. The most obvious
apparent explanation – that in the vicinity of a SMBH
with a very large mass the stars are moving faster than
around a smaller-mass SMBH – is not conclusive: the
mass of the SMBH is significantly less than one percent
of the mass of the bulge component. We can therefore
disregard its contribution to the gravitational field in
which the stars are orbiting. Instead, this correlation has
to be linked to the fact that the spheroidal component
of a galaxy evolves together with the SMBH. A better
understanding of this relation can only be found from
models of galaxy evolution. We will continue with this
topic in Sect. 9.6.