And we now continue our investigation.
How do super-massive black holes generate
energy and how does it get out?
First of all, the basic mechanism is that
some material has to get down to the deep
potential well of the central black hole.
As we've seen earlier from numerical
simulations, a very efficient way to do
this is in gas reach mergers whereby gas
in colliding or interacting galaxies loses
energy very rapidly and then sinks to the
bottom of their potential wells.
This seems to be the best way of fueling
the active nuclei and it's supported by
many observations.
These are Hubble space telescope images of
some of the nearby quasars, or really
luminous active nuclei.
And as you can see, all of them
essentially sit in disturbed looking
galaxies or sometimes UNC companion
galaxies.
But let's go back to the numbers.
So, in order to get the observed
luminosity which are of the order of 10 to
the 44th, 10 to the 46th ergs per second.
We need really massive black holes or
millions of hundreds of millions of solar
masses, even billion solar masses have
been detected.
Now as the mass has been gobbled up, not
all of it has been turned into energy,
according to mc squared formula.
So there's some efficiency factor which
I'll denote here as [unknown] and
luminosity is then mass loss rate or mass
accretion rate m dot times c squared times
[unknown].
So if you start from very large radii, the
binding energy of some junk or gas far
away from black hole relative to black
hole is essentially 0.
Bringing it down to the black hole to some
radius of r requires energy loss that's
given by the formula for the binding
energy.
Of course, that is if all of the binding
energy was converted to luminosity, but it
never is.
And there is again some efficiency.
Now as you recall, the, from the
discussion of Eddington luminosity.
It is directly proportional to the mass.
So the more massive black hole gets, the
more luminous it can get.
And that is a recipe for an exponential
process and black holes provided a steady
supply of fuel will grow exponentially.
So considering Schwarzchild black hole,
remember that the smallest stable orbit is
given by three times the Schwarzchild
radius.
Given here and plugging this into the
formula we've seen before, we can see that
the net efficiency, maximum efficiency for
accretion on black hole is of the order of
17%.
This is just oversimplified calculation
and doing this more precisely using
general relativity yields efficiency for
Schwarzschild black hole, 6%.
Now it turns out that the Kerr black
holes, the rotating black holes, have
smaller smallest out of a stable orbits,
and therefore they can achieve higher
efficiency, up to 42%, for maximum spin.
In reality, it's never that much and from
variety of studies we infer that for
active nuclei at large, the typical or
average efficiency is about 10%.
So if we take that and ask what kind of
accretion rate is needed in order to power
a really luminous quasar it turns out to
be couple solar masses per year.
This is approximately star formation rate
over the entire milky way galaxy.
A couple solar masses per year worth of
stars are created in, in Milky Way.
So what will happen with the material that
falls in, it will form accretion disc,
because that's the smallest energy
configuration for gearing amount of
angular momentum.
Because it has lost all this binding
energy, it will get very hot, and
typically the accretion disks peak in
ultra violet or even soft x-rays, and some
of that will then emerges a thermal
radiation.
The temperature varies with radius, so it
won't be simply black body.
But some will also emerge as non thermal
radiation, and especially if any magnetic
fields are pressed.
Theoretical consideration yield the
formula that shows the temperature of the
accretion disk as a function of radius as
shown here.
And as you can see depends weakly on the
mass accretion rate, m dot, as well as the
mass of the black hole itself.
And it's almost linear, but not quite,
with radius.
So Ween's formula expressed in slightly
different fashion is that peak
temperature, at some peak temperature t.
The average energy of photons is 2.8
times[UNKNOWN] clustered times the
temperature.
Turns out that the expected temperatures
in either parts of accretion disks are of
the order of 100,000 degrees Kelvin.
Which means that the peak will be far
ultraviolet or maybe soft extra emission.
This also means that there will be plenty
of ultraviolet photons to ionize gas and
even to very high ionization levels which
are necessary to get lines like a carbon
4.
But the other mechanism is due to the free
electrons moving in magnetic field, its
the synchrotron emission.
As you probably recall from your study of
physics, chart electric charges moving in
magnetic field experience Lorentz force
that makes them curve their path.
If the charge is accelerated or rather
decelerated in this case it has to emit
some energy and that is the synchrotron
radiation.
If the electron does not have a huge
energy we can [unknown] trace that with
Lorenz factor which would be something
familiar from special theory of
relativity.
Then it will move in circles, and that's
called cyclotron emission.
This has caused some of the early particle
accelerators [unknown].
But if it's really highly relativistic
speed, very close tot he speed of light,
or high Lorentz factors, then it will be
emitting so called synchrotron radiation.
They have slightly different spectra.
Simply this radiation mechanism is
responsible for all of the radio emission
from active galactic nuclei and all of the
high energy emission.
Thermal is seen from infrared through UV,
there is also synchortron there as well.
But thermal emission does not count for
either radio or high images.
Another relativistic effect is that
radiation emitted from a moving source,
this case electron moving in magnetic
field will be highly beamed.
They will merge in a cone and the opening
angle of the cone depends on particle
energy, the faster it moves, the tighter
the cone.
So this is what we call relativistic
beaming and we only see the radiation
that's emitted in our direction.
So what would be the net total emerging
radiation depends on the distribution of
energies that electrons have, obviously,
because frequency will depend on the
electron energy in a given magnetic field.
Of course, magnetic fields in these
environments are not homogeneous either,
so that further broadens the spectrum.
And the typical emergent spectrum from
active nuclei is parallel or a combination
of parallels.
This reflects the parallel distribution of
electron energies.
There is also a roll over of really high
energies because at some point you run out
of energy and there is also roll over at
low energies because electrons can then
absorb the photons emitted by other
electrons.
So it's called self-absorption cuftoff.
So it looks something like this but over
large ranges of frequency, it will look
like a really good parallel.
So oftentimes, we express that this power
is proportional to its frequency to some
power alpha which tends to be negative
because there is fewer high energy
photons.
But it's not always a symptom.
And indeed, when we look at continuum
spectra of quasars in ultraviolet, the
outer line continuum does seem to be
largely described as a parallel.
Although not perfectly.
There is a combination of thermal emission
from the accretion disk as well as
relativistic electrons.
So now we can understand the very
broad-band energy distribution of active
nuclei with which we began our discussion.
And here it is plotted over many orders of
magnitude in frequency or wavelength.
So see that in ultra violet to soft X-rays
there is a thermal bump from the accretion
disk, hot accretion disk.
In nearing to find for it, there is
another thermal component, this one comes
from heated dust.
For example from the Torus that could be
obscuring active nuclei.
At very high energies, it's pure
synchroton emission, sometimes the results
of inverse counter emission.
And in radio it's also pure synchroton
emission.
There may or may not be radio emission
depending on energy distribution of
photon, of electrons, of magnetic fields
and so on.
Now we spoke about rotating black holes
and how threading magnetic field through
them.
Or through accretion disk will then end up
with magnetic field being tightly round.
That means it will become very stronger
and will be collimated very well along the
rotation axis.
Now that is exactly how particle
accelerators work.
The charged particles from surrounding
plasma will be accelerated by this
magnetic field and will move outward.
Because it's always perpendicular to the
local magnetic lines of force, achieving
relativistic energies and this explains
presence of jets in active galactic
nuclei.
Note that if magnetic field is threading
through a black hole, and it could.
Then that will tap into the rotational
kinetic energy of black hole itself.
So that these fast electrons are carrying
mechanical energy.
They are simply particles moving at the
very high speeds, close to the speed of
light.
And therefore, active nuclei have
electromagnetic luminosity, radiation from
synchotron or thermal emission.
But also mechanical luminosity.
They're releasing a lot of mechanical
energy through these fast particles moving
out typically through the jets.
And these jets are collimated over very
large range of radii.
Here it is in radio for Thing familiar
about local galaxy of M87.
And this is series of consecutive zooms
onto the jet and covers several orders of
magnitude in scales.
They're collimated because they're moving
through optimistic speeds and they're very
difficult to derail.
But eventually they lose enough energy and
the plasma that's being carried out by the
jet runs out into the environment.
Like intracluster gas, and this is where
jets then start forming radio lobes.
So radio lobes are powered by the kinetic
energy of, brought in by these electrons
moving along the jet.
And they're emitting synchotron radiation
because magnetic field is also trapped in
the plasma.
The geometry can be very complicated but
that's the basic physics of it.
So jets are very commonly seen in radio
sources.
Sometimes they're even seen in visible
light.
Here is the jet of M87 and it corresponds
to radio jet as well.
Now in some cases we can actually see the
obscuring torus.
Here is one of the nearby active galaxies.
The picture on the left shows an orange
radio emission superimposed an optical
image.
The picture on the right confusing the
color now is the optical energy.
And you can see that there is a bright
central source but also hidden behind what
looks like global [unknown] structure.
And the jet, sure enough, is orthogonal to
the plane of the obscuring torus, which
now of course makes perfect sense.
There is another interesting phenomenon
related to AGN jets and that is Apparent
Superluminal Motions.
It was noticed that after first precise
radio maps were made, that some of the
blobs that seemed to travel along the jet
seemed to be moving faster than speed of
light.
Just knowing how far the galaxy is and so
on.
So how can that be?
And there was some discussion of that
where this is actual physical motion,
productivity's broken or whether this is
just illuminated pattern.
You can think of it as, if you have a
flashlight and you rotate it very fast on
some screen far away, the illuminated spot
can move faster than the speed of light.
But that's not what's going on here.
It turns out this is an optical illusion
that is specific to relativist motions.
This is a little beyond the scope of this
class, but just in case that you're
interested to really see in detail, I'm
including some slides in your PDF stack
that explains how this works.
Next, we will talk about high-energy,
x-ray, and gamma cosmic backgrounds and
their origins, which are largely from
active galactic nuclei.