Gebhardt's scaling relationship - from ApJL 539, L13, 2000
43
For this class read on, try chapter 8 in "Galaxies..."
We will discuss the centres of normal and abnormal galaxies, active nuclei and quiescent black holes.
this lecture, same as the last lecture - officially double length
Evidence for supermassive black holes in other galaxies.
Seyfert galaxy
Normal face on spiral
Supermassive black holes come in a range of masses.
Well constrained masses of central massive black holes are in the
million to few billion solar mass range.
There are claims of indirect estimates of black holes with over 20 billion solar masses,
and indirect estimates for black holes with masses substantially less than a million
solar masses (and of course stellar mass black holes).
The mass functions of SMBHs seems to track the mass function of galaxy spheroids.
We don't know how SMBHs form - they could grow by accretion from low mass seeds,
though estimates of QSO luminosity functions suggests most SMBHs spend a short
time in high luminosity accretion phases.
Aside: the time for a black hole mass to double through Eddington rate
accretion is referred to as the Salpeter time, and is about 50 million years, independent of
the black hole mass.
An alternative formation channel is through direct collapse of a compact gas cloud
to a mass close to the final (currently observed) black hole mass.
In this case the typical SMBH gains little additional mass through accretion.
Finally, SMBHs may form through the core collapse and onset of relativistic
instability of compact objects.
If a supermassive star cluster is formed and is bound, then the most massive
stars sink to the centre of the cluster through mass segregation and become
stellar mass black holes (which are also more massive than most of the stars
and continue to segregate as the stars evolve).
Eventually the centre of the cluster has, effectively, a compact sub-cluster
dominated by low mass black holes. This sub-cluster collapses through the
gravothermal instability, but instead of reheating and evaporating, it may
lose more energy through gravitational radiation and collapse to a singularity,
namely a massive black hole.
Emission lines!
a reminder from Bill Keel's catalog
Eddington accretion, AGN luminosity vs galactic luminosity.
What are the black hole masses inferred.
Why are some SMBHs quiescent and how can we tell...
Fraction of galaxies hosting a central supermassive black hole.
Keplerian velocity rise in the centres.
v ~ r-1/2
Keplerian velocity rise may be mimicked by a highly radially
anisotropic stellar population - if there are lots of stars on very
eccentric orbits then we see an apparent rise in velocity at small radii.
Density cusps - adiabatic vs isothermal vs arbitary
rho ~ r-k with k = 1/2 - 5/2
Scaling relationships - MBH vs Mbulge
MBH vs sigmabulge
Gebhardt's scaling relationship - from ApJL 539, L13, 2000
Stars in the cusp around the central black hole are initially on
a range of orbits. Those the come to close to the black hole are ripped to
pieces by the tidal forces and the material swallowed by the black hole.
After everything has settled down, there are no stars on orbits that
come very close to the black hole.
The tidal radius is roughly (MBH/M*)1/3 R*.
There is dynamical relaxation in the stellar cusp, with orbits of stars diffusing
in energy and angular momentum. So some stars are slowly scattered onto orbits that
are going to come within a tidal radius of the black hole, and be ripped to pieces.
Such event release a significant fraction of the stellar mass as energy, and roughly
half the stellar mass is flung out at escape speed, the rest accretes onto the black hole.
We expect this to be observable as a suddent brightening of the (possibly quiescent) black hole.
This may have been serendipitously observed a few times.
The rates at which this occurs are anywhere from every few thousand years to every few
hundred million years, depending on the black hole mass and the properties of the stellar
distribution. We expect it to happen more often around low mass supermassive black holes.
Very high mass black holes swallow stars whole without disruption.
The same process happens to any white dwarfs, neutron stars or low mass black holes mixed in with the stellar population in the centre of the galaxy. These are not tidally disrupted, rather they go into orbits that evolve strongly due to gravitational radiation emission (that may be detectable by LISA) until the coalesce with the big black hole.
Binary black holes form through mergers of galaxies. The central black holes become bound to
each other after dynamical friction has slowed them to be on elliptical orbits within
the surrounding merged galaxy.
Dynamical friction then continues to shrink the orbit of the black hole binary,
until, approximately, the mass in stars within the orbit of the black holes is
comparable to the mass of the black holes. At this point dynamical friction is
ineffecive, and orbit evolution is dominated by sling-shot encounters with individual stars.
Only stars that have orbits that come close to the black holes can interact strongly
with the black holes. ie stars on low angular momentum orbits. These are scattered away,
carrying off angular momentum, thus these stars go into high angular momentum orbits.
The region in phase space where interaction is permitted is referred to as the ``loss-cone''
(it is a cone shaped region in angular momentum space). The loss-cone is emptied by the
scattering, and further orbital evolution halts until star refill the loss-cone.
There are two ways to refill the loss-cone. It can be done slowly through relaxation
of the surrounding stellar population diffusing stars through phase space.
If the potential of the galaxy is lumpy or non-axisymmetric, then there is flow in
angular momentum space, and the loss-cone refills on dynamical time scales as stars stream
into that region of phase space. In which case the orbital evolution of the black hole binary
continues.
To shrink the orbit of the black hole binary by a factor of two, the amount of mass of stars
scattered, has to be roughly equal to the mass of the lower mass black hole!
Eventually, after the orbit has shrunk by many factors of two in radius,
gravitational radiation emission dominates the orbital evolution of the binary, and
the black holes merge. The gravitational radiation emission is low frequency
(milliHerz or lower) but large amplitude and should be detectable by LISA.
The process of supermassive binary black holes merging is slow, so we expect
to see it happening (cf 3C75, or other double-double radio sources, or
double nuclei ``dumbbell'' sources).
In the process of sling-shot scattering stars, a large fraction of the core
mass of the galaxy is thrown onto wide radial orbits. We expect the core of
the galaxy to ``puff out'' and the stellar kinematics to show substantial radial
anisotropy. This is consistent with observed giant elliptical galaxies, which we
may expect to have undergone multiple mergers.
If a second merger occurs before the binary black hole has coalesced, then
we get a triple black hole. These are generally unstable dynamically, and
end in sling-shot ejection of one black hole out of the galaxy, and the resulting
binary black hole will recoil off centre (or to escape) and has to relax to the
centre of the galaxy through dynamical friction, if it is still bound.
Last updated 11/11
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