and Cosmology

3. The World of Galaxies
110
angular radius of ∼ 6 × 10 −6 arcsec. Current observing
capabilities are still far from resolving scales of order
r S , but in the near future VLBI observations at very
short radio wavelengths may achieve sufficient angular
resolution to resolve the Schwarzschild radius for the
Galactic black hole. The largest observed velocities of
stars in the Galactic center, ∼ 5000 km/s ≪ c, indicate
that they are still well away from the Schwarzschild radius.
However, in the case of the SMBH in our Galactic
center we can “look” much closer to the Schwarzschild
radius: with VLBI observations at wavelengths of 3 mm
the angular size of the compact radio source Sgr A ∗ can
be constrained to be less than 0.3 mas, corresponding to
about 20r S . We will show in Sect. 5.3.3 that relativistic
effects are directly observed in AGNs and that velocities
close to c do in fact occur there – which again is
a very direct indication of the existence of a SMBH.
If even for the closest SMBH, the one in the GC,
the Schwarzschild radius is significantly smaller than
the achievable angular resolution, how can we hope to
prove that SMBHs exist in other galaxies? Like in the
GC, this proof has to be found indirectly by detecting
a compact mass concentration incompatible with the
mass concentration of the stars observed.
The Radius of Influence. We consider a mass concentration
of mass M • in the center of a galaxy where
the characteristic velocity dispersion of stars (or gas)
is σ. We compare this velocity dispersion with the characteristic
velocity (e.g., the Kepler rotational velocity)
around a SMBH at a distance r, givenby √ GM • /r.
From this it follows that, for distances smaller than
r BH = GM •
σ 2 ∼ 0.4
(
M•
10 6 M ⊙
) (
σ
100 km/s
) −2
pc ,
(3.32)
the SMBH will significantly affect the kinematics of
stars and gas in the galaxy. The corresponding angular
scale is
θ BH = r BH
D
∼ 0 . ′′ 1
( )
M•
(
σ
) ( −2 D
10 6 M ⊙ 100 km/s
) −1
,
1Mpc
(3.33)
where D is the distance of the galaxy. From this we immediately
conclude that our success in finding SMBHs
will depend heavily on the achievable angular resolution.
The HST enabled scientists to make huge progress
in this field. The search for SMBHs promises to be successful
only in relatively nearby galaxies. In addition,
from (3.33) we can see that for increasing distance D the
mass M • has to increase for a SMBH to be detectable
at a given angular resolution.
Kinematic Evidence. The presence of a SMBH inside
r BH is revealed by an increase in the velocity dispersion
for r r BH , which should then behave as σ ∝ r −1/2
for r r BH . If the inner region of the galaxy rotates,
one expects, in addition, that the rotational velocity v rot
should also increase inwards ∝ r −1/2 .
Problems in Detecting These Signatures. The practical
problems in observing a SMBH have already been
mentioned above. One problem is the angular resolution.
To measure an increase in the velocities for small
radii, the angular resolution needs to be better than
θ BH . Furthermore, projection effects play a role because
only the velocity dispersion of the projected stellar distribution,
weighted by the luminosity of the stars, is
measured. Added to this, the kinematics of stars can be
rather complicated, so that the observed values for σ
and v rot depend on the distribution of orbits and on the
geometry of the distribution.
Despite these difficulties, the detection of SMBHs
has been achieved in recent years, largely due to the
much improved angular resolution of optical telescopes
(like the HST) and to improved kinematic models.
3.5.2 Examples for SMBHs in Galaxies
Figure 3.24 shows an example for the kinematical
method discussed in the previous section. A long-slit
spectrum across the nucleus of the galaxy M84 clearly
shows that, near the nucleus, both the rotational velocity
and the velocity dispersion change; both increase dramatically
towards the center. Figure 3.25 illustrates how
strongly the measurability of the kinematical evidence
for a SMBH depends on the achievable angular resolution
of the observation. For this example of NGC 3115,
observing with the resolution offered by space-based
spectroscopy yields much higher measured velocities
than is possible from the ground. Particularly interest-