1 : Preliminaries | 6 : Dynamics I | 11 : Star Formation | 16 : Cosmology |
2 : Morphology | 7 : Ellipticals | 12 : Interactions | 17 : Structure Growth |
3 : Surveys | 8 : Dynamics II | 13 : Groups & Clusters | 18 : Galaxy Formation |
4 : Lum. Functions | 9 : Gas & Dust | 14 : Nuclei & BHs | 19 : Reionization & IGM |
5 : Spirals | 10 : Populations | 15 : AGNs & Quasars | 20 : Dark Matter |
The nuclear gravitational potential is significantly deeper than
anywhere else in the galaxy
For this reason, we find nuclei to be highly unusual environments
(14.1a-e) |
So : the presence of radial anisotropy (+ve _{}) tends to counteract the -ve logarithmic gradients
The sum of the terms inside [ ] could even be zero !
pure radial orbits could, in principal, support a
distribution with an almost empty central cavity
Conclusion :
r_{BH} GM_{BH} / V_{c}^{2} GM_{BH} / ^{2} 1.5 M_{7} _{200}^{-2} pc | (14.2) |
where M_{7} is M_{BH} in units of 10^{7}M_{} (similarly for _{200})
this is equivalent to the radius within which there is equal mass in stars
and the BH
Note : r_{BH} is very small for all but the biggest black holes or the nearest galaxies
Problems : seeing and/or finite aperture size reduces gradients in
luminosity and velocity
this reduces
the terms in the Jeans equation and underestimates M(r) at small r
HST has made a critical contribution in this area, allowing the field to move
forward quite quickly
(though a number of legitimate BH detections had already been achieved
from the ground)
Going a little further : the Schwarzschild radius for the MW black hole is
r_{s} = 0.056 AU (
20 R_{})
Expressing the Sgr A^{*} apparent radio source size in terms
of r_{s} gives 60 × 20 r_{s}
these are upper limits since the measured size of Sgr A^{*}
is set by interstellar scattering
It seems, therefore, that the radio emission originates within a region where
GR effects are significant
Why Sgr A^{*} is such a feeble emitter (in both radio and X-ray) is
still a mystery.
2-body scattering at large radii keeps providing stars of
zero angular momentum to feed the hole
the eating rate is given by :
dN/dt 0.013 per year × M_{BH,7}^{2.33} × n_{c,4}^{1.6} × _{100}^{-5.76} × M_{*,}^{1.06} × R_{*,}^{1.6} | (14.3) |
where the units are indicated by the subscripts (eg n_{c} is in units
of 10^{4} stars pc^{-3})
Note that for main sequence stars :
if AGN luminosity depends on accretion of stars, we might expect :
A simple comparison with the galaxy luminosity function suggests :
an L_{*}
galaxy should have M_{BH}
10^{7.7}M_{} (setting = 0.1)
assuming that BH mass scales with galaxy luminosity, we now expect :
M32 might have M_{BH}
10^{6}M_{}
while M87 might have M_{BH}
10^{8.5}M_{}
in fact, the most luminous QSOs have L 10^{47}
erg/s, suggesting an upper limit :
M_{BH} 10^{9.5}M_{}
(setting L L_{edd})
Conclusion : we expect a range of BH masses : 10^{6}M_{} (very common) - 10^{9.5}M_{} (very rare)