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And we now continue our investigation.
How do super-massive black holes generate

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energy and how does it get out?
First of all, the basic mechanism is that

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some material has to get down to the deep
potential well of the central black hole.

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As we've seen earlier from numerical
simulations, a very efficient way to do

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this is in gas reach mergers whereby gas
in colliding or interacting galaxies loses

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energy very rapidly and then sinks to the
bottom of their potential wells.

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This seems to be the best way of fueling
the active nuclei and it's supported by

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many observations.
These are Hubble space telescope images of

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some of the nearby quasars, or really
luminous active nuclei.

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And as you can see, all of them
essentially sit in disturbed looking

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galaxies or sometimes UNC companion
galaxies.

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But let's go back to the numbers.
So, in order to get the observed

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luminosity which are of the order of 10 to
the 44th, 10 to the 46th ergs per second.

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We need really massive black holes or
millions of hundreds of millions of solar

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masses, even billion solar masses have
been detected.

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Now as the mass has been gobbled up, not
all of it has been turned into energy,

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according to mc squared formula.
So there's some efficiency factor which

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I'll denote here as [unknown] and
luminosity is then mass loss rate or mass

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accretion rate m dot times c squared times
[unknown].

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So if you start from very large radii, the
binding energy of some junk or gas far

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away from black hole relative to black
hole is essentially 0.

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Bringing it down to the black hole to some
radius of r requires energy loss that's

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given by the formula for the binding
energy.

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Of course, that is if all of the binding
energy was converted to luminosity, but it

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never is.
And there is again some efficiency.

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Now as you recall, the, from the
discussion of Eddington luminosity.

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It is directly proportional to the mass.
So the more massive black hole gets, the

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more luminous it can get.
And that is a recipe for an exponential

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process and black holes provided a steady
supply of fuel will grow exponentially.

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So considering Schwarzchild black hole,
remember that the smallest stable orbit is

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given by three times the Schwarzchild
radius.

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Given here and plugging this into the
formula we've seen before, we can see that

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the net efficiency, maximum efficiency for
accretion on black hole is of the order of

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17%.
This is just oversimplified calculation

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and doing this more precisely using
general relativity yields efficiency for

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Schwarzschild black hole, 6%.
Now it turns out that the Kerr black

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holes, the rotating black holes, have
smaller smallest out of a stable orbits,

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and therefore they can achieve higher
efficiency, up to 42%, for maximum spin.

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In reality, it's never that much and from
variety of studies we infer that for

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active nuclei at large, the typical or
average efficiency is about 10%.

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So if we take that and ask what kind of
accretion rate is needed in order to power

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a really luminous quasar it turns out to
be couple solar masses per year.

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This is approximately star formation rate
over the entire milky way galaxy.

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A couple solar masses per year worth of
stars are created in, in Milky Way.

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So what will happen with the material that
falls in, it will form accretion disc,

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because that's the smallest energy
configuration for gearing amount of

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angular momentum.
Because it has lost all this binding

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energy, it will get very hot, and
typically the accretion disks peak in

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ultra violet or even soft x-rays, and some
of that will then emerges a thermal

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radiation.
The temperature varies with radius, so it

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won't be simply black body.
But some will also emerge as non thermal

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radiation, and especially if any magnetic
fields are pressed.

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Theoretical consideration yield the
formula that shows the temperature of the

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accretion disk as a function of radius as
shown here.

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And as you can see depends weakly on the
mass accretion rate, m dot, as well as the

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mass of the black hole itself.
And it's almost linear, but not quite,

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with radius.
So Ween's formula expressed in slightly

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different fashion is that peak
temperature, at some peak temperature t.

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The average energy of photons is 2.8
times[UNKNOWN] clustered times the

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temperature.
Turns out that the expected temperatures

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in either parts of accretion disks are of
the order of 100,000 degrees Kelvin.

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Which means that the peak will be far
ultraviolet or maybe soft extra emission.

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This also means that there will be plenty
of ultraviolet photons to ionize gas and

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even to very high ionization levels which
are necessary to get lines like a carbon

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4.
But the other mechanism is due to the free

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electrons moving in magnetic field, its
the synchrotron emission.

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As you probably recall from your study of
physics, chart electric charges moving in

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magnetic field experience Lorentz force
that makes them curve their path.

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If the charge is accelerated or rather
decelerated in this case it has to emit

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some energy and that is the synchrotron
radiation.

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If the electron does not have a huge
energy we can [unknown] trace that with

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Lorenz factor which would be something
familiar from special theory of

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relativity.
Then it will move in circles, and that's

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called cyclotron emission.
This has caused some of the early particle

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accelerators [unknown].
But if it's really highly relativistic

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speed, very close tot he speed of light,
or high Lorentz factors, then it will be

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emitting so called synchrotron radiation.
They have slightly different spectra.

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Simply this radiation mechanism is
responsible for all of the radio emission

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from active galactic nuclei and all of the
high energy emission.

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Thermal is seen from infrared through UV,
there is also synchortron there as well.

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But thermal emission does not count for
either radio or high images.

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Another relativistic effect is that
radiation emitted from a moving source,

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this case electron moving in magnetic
field will be highly beamed.

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They will merge in a cone and the opening
angle of the cone depends on particle

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energy, the faster it moves, the tighter
the cone.

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So this is what we call relativistic
beaming and we only see the radiation

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that's emitted in our direction.
So what would be the net total emerging

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radiation depends on the distribution of
energies that electrons have, obviously,

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because frequency will depend on the
electron energy in a given magnetic field.

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Of course, magnetic fields in these
environments are not homogeneous either,

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so that further broadens the spectrum.
And the typical emergent spectrum from

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active nuclei is parallel or a combination
of parallels.

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This reflects the parallel distribution of
electron energies.

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There is also a roll over of really high
energies because at some point you run out

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of energy and there is also roll over at
low energies because electrons can then

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absorb the photons emitted by other
electrons.

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So it's called self-absorption cuftoff.
So it looks something like this but over

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large ranges of frequency, it will look
like a really good parallel.

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So oftentimes, we express that this power
is proportional to its frequency to some

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power alpha which tends to be negative
because there is fewer high energy

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photons.
But it's not always a symptom.

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And indeed, when we look at continuum
spectra of quasars in ultraviolet, the

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outer line continuum does seem to be
largely described as a parallel.

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Although not perfectly.
There is a combination of thermal emission

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from the accretion disk as well as
relativistic electrons.

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So now we can understand the very
broad-band energy distribution of active

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nuclei with which we began our discussion.
And here it is plotted over many orders of

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magnitude in frequency or wavelength.
So see that in ultra violet to soft X-rays

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there is a thermal bump from the accretion
disk, hot accretion disk.

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In nearing to find for it, there is
another thermal component, this one comes

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from heated dust.
For example from the Torus that could be

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obscuring active nuclei.
At very high energies, it's pure

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synchroton emission, sometimes the results
of inverse counter emission.

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And in radio it's also pure synchroton
emission.

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There may or may not be radio emission
depending on energy distribution of

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photon, of electrons, of magnetic fields
and so on.

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Now we spoke about rotating black holes
and how threading magnetic field through

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them.
Or through accretion disk will then end up

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with magnetic field being tightly round.
That means it will become very stronger

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and will be collimated very well along the
rotation axis.

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Now that is exactly how particle
accelerators work.

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The charged particles from surrounding
plasma will be accelerated by this

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magnetic field and will move outward.
Because it's always perpendicular to the

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local magnetic lines of force, achieving
relativistic energies and this explains

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presence of jets in active galactic
nuclei.

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Note that if magnetic field is threading
through a black hole, and it could.

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Then that will tap into the rotational
kinetic energy of black hole itself.

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So that these fast electrons are carrying
mechanical energy.

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They are simply particles moving at the
very high speeds, close to the speed of

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light.
And therefore, active nuclei have

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electromagnetic luminosity, radiation from
synchotron or thermal emission.

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But also mechanical luminosity.
They're releasing a lot of mechanical

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energy through these fast particles moving
out typically through the jets.

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And these jets are collimated over very
large range of radii.

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Here it is in radio for Thing familiar
about local galaxy of M87.

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And this is series of consecutive zooms
onto the jet and covers several orders of

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magnitude in scales.
They're collimated because they're moving

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through optimistic speeds and they're very
difficult to derail.

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But eventually they lose enough energy and
the plasma that's being carried out by the

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jet runs out into the environment.
Like intracluster gas, and this is where

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jets then start forming radio lobes.
So radio lobes are powered by the kinetic

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energy of, brought in by these electrons
moving along the jet.

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And they're emitting synchotron radiation
because magnetic field is also trapped in

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the plasma.
The geometry can be very complicated but

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that's the basic physics of it.
So jets are very commonly seen in radio

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sources.
Sometimes they're even seen in visible

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light.
Here is the jet of M87 and it corresponds

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to radio jet as well.
Now in some cases we can actually see the

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obscuring torus.
Here is one of the nearby active galaxies.

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The picture on the left shows an orange
radio emission superimposed an optical

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image.
The picture on the right confusing the

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color now is the optical energy.
And you can see that there is a bright

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central source but also hidden behind what
looks like global [unknown] structure.

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And the jet, sure enough, is orthogonal to
the plane of the obscuring torus, which

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now of course makes perfect sense.
There is another interesting phenomenon

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related to AGN jets and that is Apparent
Superluminal Motions.

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It was noticed that after first precise
radio maps were made, that some of the

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blobs that seemed to travel along the jet
seemed to be moving faster than speed of

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light.
Just knowing how far the galaxy is and so

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on.
So how can that be?

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And there was some discussion of that
where this is actual physical motion,

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productivity's broken or whether this is
just illuminated pattern.

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You can think of it as, if you have a
flashlight and you rotate it very fast on

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some screen far away, the illuminated spot
can move faster than the speed of light.

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But that's not what's going on here.
It turns out this is an optical illusion

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that is specific to relativist motions.
This is a little beyond the scope of this

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class, but just in case that you're
interested to really see in detail, I'm

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including some slides in your PDF stack
that explains how this works.

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Next, we will talk about high-energy,
x-ray, and gamma cosmic backgrounds and

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their origins, which are largely from
active galactic nuclei.