Okay. See, here's my outline. I'm going to go about. And John's already touched on the subject,
but I'm going to talk more completely about the connection between quasars and the growth of these black holes at the census of galaxies.
And that's going to lead me on to a quite a long discussion of the physics of the accretion disk, which is the mech,
which is the machine which takes in material dropped into a black hole and processes into into a.
Impact since we're all very interested in impact these days research council driven.
And then I'm going to talk about black hole the connection between black of briefly black holes and stuff formation through cosmic history.
So black hole growth. So as John said, we understand where supernova works, right?
Where black holes of of stellar mass come from.
They're formed in milliseconds when the centre of a star goes unstable and collapses to a black hole.
But we think that the black holes that we see in the middle of galaxies have grown to their present masses.
We don't know what they quite have grown from. Perhaps they've grown from stellar mass black holes, but there are difficulties with that.
But we are pretty sure well, you'll see that there's overwhelming evidence that they have grown gradually to their present large masses.
So they grew. They started small and they grew by feeding.
Now a black hole can swallow us.
The black hole of the middle of the galaxy could swallow the sun just like that hole.
Gulp it. John showed it. Swallowing a star like the sun.
Relatively slowly over a period of a month or so.
But he also explained the rate at which the galaxy can feed stars to a black hole at the centre,
at its centre is simply too insignificant, is too small to allow for significant growth of black holes.
And so we will. We have talked about black holes with masses in excess of ten to the eight solar
masses that are black holes known with masses like ten to the nine solar masses.
And we believe these black holes we have reason to think these black holes existed when the universe was a 15th or so of its present age.
These things have been around for a very long time. They must have formed rather rapidly.
They cannot be formed by eating stars. They must have. They must have grown to their present weight by accreting gas.
So there's a really beautiful argument that a Polish astronomer gave in 1980 to Zoltan to show the connection between quasars and black hole growth.
So what you start by saying is supposing you drop a mass little m into a black hole.
And obviously you were going to get energy M.c squared is then in play in play the rest mass energy
of what you've thrown in is under discussion and suppose you get an amount cappa an efficiency.
So Kepler is dimensionless efficiency. You get an amount of energy Kappa M.c squared out.
We have reason to think. We haven't talked about it today,
but we have great reason to think that copper is a number that varies between something like 0.1 and maybe something like point three,
depending on the spin of the black hole. So it's, it's tense but, but we'll see what value we get for Kepa.
So then what Zoltan showed was that if you ask how much energy is is produced over all of cosmic time in a unit volume.
Then you can obtain that from, from, uh, from just this simple thing here.
So n is the number of sources,
quasars that you see with a flux density is as is measured in something like watts per square metre radian at a redshift z.
So this is the number of this is this is the number of sources per unit volume with this kind of flux density,
with this with this kind of with this kind of redshift.
So any something you can you can you can get simply by counting objects at different flux levels known with a known and measured redshifts,
etc., etc., etc. So then you can do this integral over your data and then you can do this other integral over the redshifts of your data.
And what you end up with is the energy per unit volume that has been emitted by by all these sources over all of cosmic time.
So it's remarkable that just from the observations, without knowing anything much about cosmology,
the absolute bare minimum of cosmology, you can write this down.
So if this energy has per unit, volume has come by this kind of efficiency by dropping by accreting this this mass m that tells
you that there should be a mass density of of the black holes that are built up by this process.
So we're assuming that all the mass in the black hole has been accreted by this process over cosmic time.
You should have a mass density, which is just the energy density that you've measured divided by Kappa C Squared.
And Zoltan, back in this remote time,
1982 predicted what the mass of a black hole should be in the middle of the galaxy by supposing that this this black hole,
mass density, which is so many solar masses per cubic per cubic volume, is divided up amongst the number amongst the galaxies.
So you have a number density of galaxies, of sort of luminosity,
something like the luminosity of our own galaxy, which is very characteristic luminosity.
So you have a number of galaxies per unit volume, you have a mass per unit volume that gives you a mass per galaxy.
That should be the ash obtained by the result of accreting all this material in order to make the luminosity.
So the assumption here is that every galaxies black hole has shone brilliantly as a quasar or whatever is was accumulating this material.
And if it's not shining now this just because it's stopped accumulating, it's stopped accumulating the material.
You look inside it and you should see this residue. That's evidence of what of what is achieved.
So you and Trymaine revisited this this idea 21 years after it was originally done,
when the observational data was spectacularly improved by counting from counting the number of quasars that you see in optical bands.
The that led to an estimate.
So that's so that's that's doing the end of S and Z count by counting quasars using optical radiation.
You arrive at a number density of 2.1 by ten to the fifth.
This is point one of Kappa one one whatever.
10% for Kappa Solar masses per cubic parsec.
And for the correlation. So this is an estimate obtained from quasars.
Now let's look at an estimate in the number in the mass density in galactic centre.
Black holes that you get from that correlation between the mass of the black hole and the velocity dispersion of the bulge,
you know how many galaxies there are with which.
And so the Sloan Digital Sky survey measured for millions of galaxies,
the velocity estimates, the velocity dispersion and counted the number of galaxies.
So one knows how many galaxies there are with each velocity dispersion.
And you know from this correlation what size of black hole this thing, this galaxy should contain.
And so that gives you a separate estimate of the mass density in black holes.
And that turned out to be this number here, which is astonishingly in agreement with that number up there.
So that implies that agreement, which is better.
The agreement seems better than it really is because there are some there are
some skeletons in the closet to do with the existence of obscured quasars.
A very large number of quasars are believed to be hidden behind dust, and you can see them only through their X-ray radiation or infrared radiation.
But we'll see. We'll see that these these issues these are technicalities which which means that this agreement is a little bit fortuitous,
but within certainly within factors of of two or so,
there is astonishingly good agreement between the mass density in galactic centre black holes and the radiation emitted by quasars,
which implies that these these black holes formed through rather efficient accretion by material with an efficiency of that sort,
which is sort of efficient ish.
So let's talk now about the physics which leads to the production of radiation, quasar light, etc., when stuff is dropped into a black hole.
So a black hole is just a gigantic drain. And when you tip the washing up water down the sink when you finished with it,
most of the time as it moves towards the axis of the of the plug hole, it has some angular momentum.
So it starts spinning and you get this characteristic vortex.
As the water goes down, it goes down the hole because the water is spinning around the axis of the pipe as it goes down.
And hurricanes and tornadoes depend on exactly the same physics.
The air is drawn inwards because because moist air is moving upwards and has to be replaced by other air coming in horizontally as it moves inwards.
It has some angular momentum, which it conserves, largely conserves.
So it starts to spin fast. So the same happens when gas is dropped on to any compact object, a star or a black hole.
It starts to spin.
And we have here this artist's impression of gas spinning around of what this is supposed to be, a forming a protostar, a forming star.
So this is the solar system at some very early time. So let's just think a little bit about the last thing I want to talk about.
The simplest conceivable model is kind of basic baseline model of an accretion disk.
We imagine that we have a steady state in which mass is flowing inwards towards it's being acquired by the black hole,
the forming star of the neutron stars,
but it's being acquired by some compact object in the middle at a rate down by d t that's that's constant in time.
And as the and as each parcel of gas moves inwards,
it orbits at all times more or less circular because it's not orbiting exactly circular because it's spiralling inwards.
But it's but the inward motion is very small compared to the going in a around motion.
So at all times it's more or less on a circular orbit. And so you can from high school mathematics compute what the energy is of that gas.
It's kinetic and its potential energy. And as it moves inwards it its energy gets more and more negative.
You can also compute from high school mathematics what its ranking of momentum is.
And as it moves in with this angle, momentum j gets smaller and smaller.
So the characteristic view is that here's the black hole.
This is sort of this is cartoon. The matter moves in at some steady rate down by d t this sort of radius here some concept of radius.
And as it moves in it, each parcel of gas has to dump some mangled momentum and some energy.
And the energy that it dumps is going to be, we imagine, is radiated because the disk becomes very hot from this energy being dumped on it.
So it shines and it radiates photons carrying away the energy.
But the photons don't carry away much of the angle of momentum.
The angle momentum has to be laboriously carried outwards by viscous stress, by friction within the disk, which we'll talk about in greater detail.
So Fisker's torque carries angular momentum out. It's some steady, some rate.
There's a small flux of angle momentum here and a large flux of angle momentum there.
And the surface of the disk radiates the energy. This is this is our baseline model.
Let's maybe put this on some kind of quantitative basis. The the reason that there is a fiscal tool is because the velocity of the rings.
So we mentally divide the. This is just mentally divided into a series of annually circular annually the interannual.
A moving fast because the Kepler the speed of Kepler orbits goes like one over the square root of radius.
So the inner ones are going fast, the outer ones are going slow, which means that this ring,
as it spins around here, is rubbing on this ring is which is spinning more slowly.
But this and this ring is therefore doing viscous work on this ring.
And this ring is doing viscous work on that ring and so on and so forth.
And that that work is also associated with this ring is twisting this ring and giving angular momentum to it.
So that's why the material in this ring is able to move inwards because it sheds angular
momentum by passing it on to this one and this one passes on to this one and this one,
so on and so forth. But let's think about the energy first.
We have that within within any annulus there is and there is there is the matter is dropping is decreasing its energy.
So when it's that hour plus deal, when it's so the outer edge of one of these rings,
the energy of the mass is minus g m overall plus deal with the factor to the this number here is its gravitational potential energy.
It has it has kinetic energy which is of opposite sine is positive but only of half the size.
So the total energy is is minus a half of this.
So this is the energy it has at the outer edge of an annulus and then the inner edge of the annulus, it has minus a half GM overall.
So the energy that's dropped, that's deposited by a parcel of gas is of mass DM as it passes through.
Here is the difference between these two and it's being dropped at a rate down by d t the rate at which mass is flowing through this annulus.
So that means there is a power rate of a rate of dropping of energy in this annulus which is
given by this where g m overall squared is of course the difference between these two times.
Times delta is the difference between these two. So that's the rate at which matter.
Moving inwards drops energy.
But also there is this business of friction that the each ring has work done on it by the ring that's just interior to it.
And it's it itself does work on the ring that's just outside it.
This is a fundamental this work done is a fundamental part of the of the transfer of an element m outwards,
which is a zeroth order, you know, key, a key part of what's happening.
And when you work out the difference between the work done by this ring and the work that this ring does on that,
which is the which is the sort of surplus this this this this ring here is engaged in a trade.
In some sense, it's picking up energy here, and it's and it's passing it on there.
And the profit, the surplus of one worker over the other work is a profit.
So it's an energy dumped in there. It turns out it's not it's a slightly intricate calculation, but it's done with high school, high school physics.
It turns out that the discus power is three times precisely three times the power that we've just worked out from the matter,
dropping energy as it passes through, directly, dropping this Fisker's work surplus,
this profit on the profits on the handling of a packet of Anglo momentum,
because that's what's happening with we're taking we're buying Anglo momentum here and we're selling it here.
And the energy that comes with it is different. In the two cases we rip off that that surplus and that's three times what we get
from doing a trade in mass where we take in mass here and we jump to dump it up.
Okay. So we have this we have a total power, which is four times the one we just worked out.
And if we equate this total power to the energy that this annulus can radiate per unit time,
so we're going to assume that each annulus radiates like a blackbody.
So it's the Stephan Boltzmann constant times.
T Each of the four is the energy per unit area per unit time, and this is the area of the annulus two pi.
Our delta r is the area of the top surface and there's the bottom surface of the same area.
So this is the total area. So this is the this if it's a temperature t that material and radiating like a black body.
This is the luminous power of an annulus. And we equate this luminous power to the two four times the power worked out on the previous page,
which is then this where the two was on the bottom before is now in the top because of the fall.
We can then for any chosen value of the accretion rate, we can talk about what the what the luminosity is of the disk.
As a function of radius, we can talk about what the temperature of the disk is as a function of radius, but to work this out, I need to,
I need to adopt some value for this and I'm going to adopt values for those stellar mass
black holes and galactic centre black holes which imply that they have a growth time.
They're accumulating material 100 mega year time scales so that they over 100 years
they can double mass because we have reason to think that's a reasonable estimate.
So here is here is a solar mass of black hole of just exactly one solar mass.
So the mass black holes are typically more massive than this by a factor of a few, but not many.
And so here is the radius in astronomical units, one astronomical unit way out here.
So we're talking about mostly what happens on very small radii.
Here is the radius of the sun. Here is the radius of a white dwarf.
So if when the sun had an accretion disk, which it did when the solar system was forming,
only this part of the diagram was relevant and the characteristic temperatures were less than a thousand degrees.
Kelvin, when the sun becomes a white dwarf,
it will it will have an accretion disk where this bit is relevant and the temperature rise is something like ten to the fifth Kelvin.
And the thing it will be radiating as a in ultraviolet light.
But if it is if it is a black hole, then the here is the actual radius, three kilometres of the sun.
Its whole diagram becomes relevant and it can radiate in hard X-rays up here.
Here is the temperature at the very middle of the sun. Here is the temperature on the surface of the sun to give you some sense of scale.
So that's that encapsulates the characteristics of accreting stellar mass black holes.
If you now change the mass scale to ten to the eighth, but you leave the time of accretion,
the scale, the luck, the timescale of accretion at 100 mega years, 100 million years.
Then the diagram looks like here now we have radius in AEW.
Here is one AEW and the radius is about to AEW here.
Here is. So the crucial thing about this diagram, this is incredibly similar to this diagram, the really boring straight line eye Apollo.
The key thing is that this temperature scale is lower by a factor of 100 than that temperature scale.
So here is the surface temperature of the sun.
So that if you have a galactic centre, a black hole which accretes all the way down to the to the actual radius,
it radiates at temperatures of ten to the 50 K ten to the fifth K.
So only ultraviolet radiation, not x rays.
I mean not hard x rays, soft x rays, ultraviolet radiation.
And there will be lots of and there will be lots of radiation coming out in the optical bands.
Okay. So that's that's an important thing to know.
What about luminosity is this is just this is a plot showing the luminosity for us galactic centre type black hole.
The luminosity that's radiate outside radius are really all we need to know is that that
now the luminosity is that you can achieve if you go all the way to the actual radius,
you can achieve maybe 100 times the luminosity or a few hundred times the luminosity of a whole galaxy.
And, and that to achieve the kind of luminosity, as the John mentioned, ten to the 12.
So the solar luminosity is which which are characteristic of bright quasars and which staggered people in the 1960s.
You have to go in to you have to go into maybe ten A.U., maybe five structural radii.
So you are talking about accretion to the bitter end. I think that's what we need to say there.
Now, you may be impressed by a black hole being able to radiate tens of luminosity of an entire galaxy of 10 to 11 stars.
And that you can see these these things, these quasars are bright enough that you can see them even when they right across the universe.
So as I say, these quasars are seen which have redshifts of six or so.
And when the universe was to more than 200 times denser than it is now, so really is an early time.
This is, in a certain sense, very impressive. But frankly, it's only histrionics.
It's not what makes black holes important. That's what I want to ask you next.
So black holes do have a big impact. These these black holes do, I believe, have a very big impact on the structure of the universe.
But it is not through this histrionics and to understand how they have an impact.
We want to look we need to think bit more carefully about what happens in an accretion disk.
So what provides the all important viscosity? What the accretion disk does is shuffle angular momentum outwards to its angular momentum.
The surface of angle momentum that prevents material disappearing down the structural throat.
And you have to get rid of this angular momentum if the mass is going to move inwards.
And that's what the accretion disk does. It's a machine for shuffling, for carrying an element of out of material to somewhere where it's harmless.
And what actually does this what we're pretty convinced now that it's it's a magnetic
field which does this the thing is that magnetic field lines carry tension.
They're like elastic bands. And when a field line is stretched.
Work is done on the magnetic field and the magnetic field energy goes up, which means that the magnetic field is amplified.
The strength of the magnetic field has to increase, reflecting the work that you've done on the magnetic field and stretching the field line.
A gas in astrophysics is usually can usually be considered to be a perfect conductor.
The scales are very large and the availability of free electrons is always relatively free.
Electrons are usually pretty available. They're very available in an accretion disk.
So you can treat the accretion disk is made up of a perfect conductor and it's
easy to show that when you have a magnetic field line inside a perfect conductor,
the field line is trapped with respect to the fluid or the fluid is trapped with respect to the magnetic field line,
depending on who you consider to be the boss. So if the feel, if the fluid stretches in some way, the field line within it has to stretch too.
So here we have, I hope, a.
A baby film which shows so what we have here is a black hole and here we have around is an accretion disk that you can't see.
What you can see is a series of.
Magnetic field lines. Which I've just drawn. I've just drawn.
Going out radially. And then.
If you animate this thing, each each point on the field line is moving around here with capillary and speed,
and the inner points go around faster than the outer points.
And so what was a radial arrangement of field lines becomes a tangential, a more and more tangential array of field lines.
And also these field lines are getting longer and longer. They're being stretched.
So. The field lines, the trap.
Yeah. Okay. So. So the field lines are constantly stretched, and that means the field is amplified.
So. It doesn't matter how weak the magnetic field was originally.
Through this stretching, this endless stretching that's inherent in the sheer of the flow within the accretion disk,
the field is going to be amplified until it is strong enough for its back reaction.
The tension that it provides to modify the flow.
And that means that the field will inevitably be amplified until it becomes capable of transporting angular momentum outwards.
And I hope for that figure. You can imagine that it is going to transform Anglicanism outwards because the magnetic tension is pulling backwards
on the on the particles that were a small radius and pulling forwards on the particles which are at large radius.
So it's clearly transporting angry momentum outwards.
Now field lines provide tension along there along their length, but they exert pressure perpendicular to their length.
So. So here's a field line on detention, but and here's another field line on detention.
And there's a pressure that that provided by the magnetic field that operates between these two.
So here we have a field line. Here's here's the here we have a field line that's near the mid plane of the accretion disk.
And I've drawn this. So it has a very slight a very slight upward curving this.
This very slight upward curving this enables the plasma, encourages the plasma.
So there's a sort of gravitational field down here towards the mid plane of the disk that the yellow is supposed to represent,
the plasma which is surrounding the field line.
And this plasma can't move perpendicular to the field line, but it can slide along the field line.
So this because of this slight arching of the field line, the plasma begins to roll gently.
Downhill here, downhill here. And the amount of plasma in this region here decreases and the amount of plasma here in here increases.
But then that makes that that means so here we have this have been a thinning of the plasma here.
But that encourages this. It means there's less weight acting holding down the field line because the plasma contains the mass,
the field is providing force, but not any significant mass.
So if you take away some of the mass here, this magnetic pressure will cause this to arch up.
But then that encourages this flow downhill towards the wings.
So that's shown here where almost all the plasma has flown away from flowed away from here down to down to these foot points here.
So you have an instability here. This is the Parker instability that leads a straight field line to become a looped field line.
We can't see this in an accretion disk, but you can see it most beautifully in action in the sun.
This is an ultraviolet picture of the sun. And you see these loops here.
So these these loops are field lines. They're illuminated by relativistic electrons which are trapped along the field lines.
So it's kind of a it's kind of a fortunate chance that you can actually see the field lines, but you can see that they form these loops.
Now, another key piece of magnetic physics now plays a role, which is that when you have a field line going this way and a field line going that way,
and if they come close, then you can have a rearrangement here,
which so that this field line which used to go to that South Pole,
starts to go to this South Pole and corresponding the field line that used to go to this pole goes to that pole.
So you have this reconnect. But this is reconnection, which is a sort of discontinuous process occurs at this at this moment here leading to this.
But when you compare the geometry from here to here to here to here,
you find that this the field lines have grown shorter as a result of going from here to here.
And I said that when field lines are stretched, the magnetic energy is increased.
Correspondingly, when they shorten, the magnetic energy is decreased.
So the magnetic energy over here is less than the magnetic energy over here.
And where is the energy go? All the energy has gone in the violent heating of the of particles,
the raising to the production of energetic particles at this moment of reconnection.
So when feels. When? When, when. So the the.
The. The constant movement of the foot lines of the easily we've got these loops forming
as as the Parker instability pushes field lines above the the plane of the disc and
then the the differential rotation within the disc is bringing is bringing oppositely
directed field lines ODIs or oppositely directed field lines close to one another.
Then this reconnection process happens which accelerates particles, the accelerated particles, then bang into nearby other particles of the plasma,
and the plasma becomes heated,
and soon the region above and below the disc becomes too hot to be confined by the gravitational field of the disc in the black hole.
So you get hot regions generating in the in the you get very hot plasma forming in the region above and below the disc.
Just as in the sun. In the sun the temperature rises by orders of magnitude from the temperature underneath here,
which is rather dark because we're looking at ultraviolet radiation,
which is actually the photosphere the the part of the what what we with with our naked eye see of the sun.
The temperature rises to about 100,000 degrees significantly above the surface of the sun.
The sun can't contain that hot plasma and it flows away from the sun in the solar wind.
The same thing must happen off of the two surfaces of an accretion disk.
The next thing the magnetism does for you is arrange that this flow perpendicular away from the accretion disk is culminated.
Bye bye. Physics that we don't fully understand, but is certainly to do with magnetic pressures of this magnetic field contained in this material,
which is which is too hot, too hot, too hot to handle, too hot to contain.
It flows away from the accretion disk and as it flows away from the accretion disk, the field lines tend to be stretched.
And also this material, of course, is rotating.
Everything is rotating with the accretion disk. So this stuff gets the field lines get pulled out somehow like this into some kind of a spiral.
This is not properly understood. I mean, it's we can't exactly model it,
but we're pretty sure this is what happens so that the flow off the disk becomes not a sort of quasi spherical flow,
like the flow out of the sun to the solar wind.
It becomes a strongly correlated wind that runs along the spin axis, the two along the spin axis of the disk in the two directions.
So it's an amazing fact. It's a it's an empirical fact that this.
I mean, this qualitative discussion illustrates the decreasing objects are actually detectable not by evidence of inflow.
It's extremely hard to find any evidence of inflow in any accreting object.
What is always very evident is outflow.
So here is here is a protostar sitting inside here you can't see it because it's obscured by the accretion disk.
There's a protostar, a young star, so as the sun once was,
which is accreting material from a disk which you don't see properly, what you see is its illuminated surfaces here.
So the protostar light coming out of the protostar, which doesn't come directly to us,
it scatters off material above and below the accretion disk here and comes to us.
So here is this accreting protostar is this Protostar with this accretion disk and here is here is a jet of material that's flowing at something.
What's typical this is this is a hub here. Objects. That's what these things are, these accreting protostars.
This stuff is coming off at maybe a couple of hundred kilometres a second.
It's quite cold. This is the ordered outflow from the system.
So this is just a boring protostar nothing relativistic.
Here is this is SS four, three, three, which is an accreting stellar mass black hole, which is in a binary star.
So here's the binary companion, here's the black hole, here's the accretion disk.
And this thing is shooting out at about the third of the speed of light gas, which is quite cold.
It's it's cold enough to form to contain hydrogen atoms which emit HL for radiation.
That's how this thing was detected originally.
So it's shooting out these jets and then this disk is processing in the because it senses the gravitational field of this neighbour.
So the spin axis of this system is, is constantly processing, moving around the cone.
And as it moves around a cone, you get this, you get this pattern form.
This is a radio picture. This is this is radio radiation from relativistic electrons.
But the point is that this is this the at the time that material was shot out, the jet was looking in this direction.
At the time that this was shot out, the jet was looking in this direction.
As the as the jet moves around and the material moves away from the jet, you get this characteristic corkscrew effect.
So this is this is called a emitted emission from a accreting soda mass black hole.
And this is column is emission from an accreting galactic mass black hole.
This is this is in the radio. So Cygnus A the scale of this thing is bigger than the scale of a galaxy.
It's something like 50 killer parsecs somewhere inside here,
way too small to be seen to be strictly speaking, seen there is the there is the accreting black hole.
And then there are these two two jets which have different intensities, largely because they're moving mildly relativistic.
So. So these accreting objects manifest themselves by.
To a large extent. I mean, what makes them really clear is that they're spewing stuff out in a jet.
Once you recognise that these jets exist, you have to completely revisit your picture of how an accretion disk works.
Because the picture I was the baseline picture I was peddling was that you had mass going in,
angular momentum going out and radiation only going perpendicularly to the disk.
But now that's not at all what happens,
what your picture has to be that at every radius there is material boiled off the surface of the accretion disk.
And as that material goes out, it's carrying mass, it's carrying energy in the flow, mechanical energy, kinetic energy of the flow.
And it is carrying angular momentum because this stuff isn't flowing purely away from the it's not only moving down the spin axis,
it's also moving around the spin axis,
not moving away from the spin axis because the magnetic field is is wrapping around it and forcing it back onto the spin axis.
So it's a it's a it's a twisting it's a corkscrew thing.
So we're losing mass energy and angular momentum from the surface of the disc at every radius.
So this so so there's an advection of mass and angular momentum inwards.
There is a viscous transport of angular momentum outwards, and there is sort of a loss of angle momentum here.
So what's the consequence of all this? Well, one consequence is that what makes it into the black hole is only can be can
potentially be only a small fraction of what's dumped on the disc at a large radius,
because much of what's dumped at large radius can be shot out in the jet.
So since it's sort of a piece of self sacrifice, a small amount of mass sacrifices itself in all the order that many much mass maybe free.
And there's a flow of there's still a vicious flow of angular momentum outwards, but there's also this loss of angular momentum here.
The luminosity of the disk is going to be smaller than previously advertised because because the for the mass that
joins the energy released by the mass that joins the black hole is not only radiated from the surface of the disk,
it's also pumped into the, uh, into the jet.
So the system has acquired a mechanical power output in addition to its luminous power output.
So the luminous power output will be smaller per unit accretion per unit mass added to the black hole than we previously estimated.
Okay. So we're now very much guided by observations because our ability to compute this stuff is very limited.
The observations indicate that the mechanical power can can insert and can quite often significantly exceed the radiative power,
so less energy can be radiated from the disk surface than is pumped into the jet.
This jet production process could be very, very efficient.
Also very interesting is that systems can switch rapidly between modes in which most of the power goes into mechanical output.
And a lot of the power is is is relatively.
Produced. And you can you can study this.
What this sort of switching process has to be studied mostly has to be studied in the context of Sotomayor's black holes,
objects like SS four, three, three.
Because the time, the characteristic timescale of a black hole is proportional to its mass right it schwarzschild radius is proportional to its mass.
The speed of light is always the same. The characteristic timescale is the structural radius divided by the speed of light.
So an object like sigma say that I showed you a picture of an accreting galactic
nucleus has a achieves or changes in 100 mega years by as much as we expect this four,
three, three to change by in maybe a couple of years.
So if you want to study, if you want to understand the time variability of black holes, you want to focus on these micro quasars.
They're called objects like this four through three solar mass accreting black holes.
And they tell us that that can be this rapid switching between the relatively in the mechanically efficient mode.
So finally, very finally, black holes and star formation.
This is a plot of the estimates of the rate at which stars have formed in logarithmic scale.
The rate at which stars are formed is a function of redshift in the past.
So it rose until redshift of two and has fallen steeply since then by a factor of more than ten.
This down here is a plot which reproduces this is this curve here is fitted to the data points.
This black curve is the same is the same curve shown on the same plot of redshift versus a rate.
So the masses per year sort of thing per megaparsec. Per cubic megaparsec.
And then also on this diagram on here,
MADDOW and Dickinson have added the an estimate of the rate at which black holes have been accreting obtained from X-ray radiation.
That's the black curve, except that they've multiplied they've scaled the actual measurements by a factor of a thousand.
Remember, John said that the masses of black holes in the middle of galaxies are characteristically 1000/1000 of the mass of the stars in the galaxy.
So here we see a very concrete indication that black hole, well,
this this rate of accretion by black holes to within the errors is pretty much the same as the as the estimate of the rate of the formation of stars.
So this suggests that black holes, these black holes have grown.
Uh, uh, on the same time trajectory as the stars are formed.
First rising, then falling. And that's presumably because the the the black hole accretion in the radiative li efficient mode that we see
with the quasars is what's being plotted here depends upon heating having a high availability of cold gas.
Star formation depends on the high availability of cold gas.
And what we're looking here is a plot of the availability of cold gas suitable for either making stars or making a nuclear black hole.
Both things happening simultaneously. But why?
So why has this fallen? It's fallen because the availability of cold gas has decreased.
Is that because the availability of gas is decreased? Not a bit of it.
The universe has made very little progress at turning gas into stars and galaxies.
Most of the universe's ordinary matter lies in the intergalactic medium,
between galaxies and in clusters of galaxies like this one here, the Virgo cluster imaged in X-rays.
We see this. This intergalactic gas is dense enough.
We can actually see it by the thermal X-ray emission that it produces.
And what you find here is that in these so-called cool, cool clusters,
which are the majority of clusters of galaxies, is the temperature of the X-rays falls,
the temperature of the gases emitting the X-rays falls by about a factor three between sort of this zone here typical zone.
And, and as you approach the, uh, the black hole which sits in the middle of m87 in the middle there.
So as you, as you move inwards, the temperature of the gas falls by about a factor of three.
The density of the gas zooms up enormously because it's compressed by extra gravitational field.
And the time in the time required for the gas in here to cool to absolute zero by radiating X-rays and then optical UV light.
And the optical light is much shorter than the age of the universe. You might say so.
So when people first saw this in the 1970s, late 1980s, around 1980, they assumed that there was a steady flow of material from the outside in.
It got cooler and cooler and cooler and then eventually formed stars or something, or maybe was accreted by the black hole.
Well, we now know that's not the case because the temperature drops by about a factor of three.
But there are there's an absence of emission lines coming from material that's cooler than, say, a factor of three.
So you don't see loads of material at temperatures of a million degrees K or less.
So the material is not succeeding in cooling. It is radiating, but it is not cooling.
Why is it not cooling? This is a radio map of the same galaxy.
So this is what? This is what the Virgo cluster of galaxies looks like in synchrotron radiation produced by relativistic electrons.
This is a large scale picture.
There's a jet coming out, it's banging into the intergalactic medium, it at some 1020 killer parsec distances and and dumping energy in it.
This is here we have a series of beautiful blow up. So what you can do with radio interferometry.
So you you see on extremely small scales this is the jet coming out of the black hole at the centre of Messier 87,
which has a mass of nearly 5 billion solar masses. It's a really it's a really beefy black hole in it is draw.
It is what what is this? It's not a very luminous source.
It is not a quasar. So it's this black hole has switched into into its mechanical mode.
It's putting out energy mechanically, which we can trace by looking at this synchrotron radiation.
This mechanical energy is being carried to regions of relatively low density by the jets.
And there is is heating up the surrounding plasma and preventing that surrounding plasma cooling below
a million degrees C because he can't cool below a million degrees C it can't form stars and it's.
The rate at which this black hole accretes material should increase steeply with declining temperature at the centres.
This is a very stable process if the gas in the middle gets a little bit cooler.
The rate of of accretion by the black hole should go up strongly.
It should go like the minus five halves power of the temperature.
The the that means that the jets will ramp up to greater power, keep the gas in the middle.
And so you have a stabilisation process. I made the black hole in the middle of of m87 is stabilising this intergalactic gas in
exactly the same way that the nuclear reactor at the middle of the sun stabilises the sun.
If the middle of the sun is a bit denser, it heats up and the rate of the rate of nuclear reaction zooms up.
That releases energy, which causes the middle of the sun to expand a bit.
And so that sort of that's why the middle of the sun is a stable thing.
So what's that? What's the bottom line on this? The bottom line on this is that is that it's these galactic centre black holes
which are responsible for setting the upper limits on the masses of galaxies.
So as the universe clustering within the universe is preceded, the the distributed, the number of dark matter halos is a function of mass.
This is log masses is the number of logarithm of the number of dark matter halos has
been a curve like this which has had which is moved to bigger and bigger masses.
So at earlier times it was looking something like this and then something like this.
So it's moved to bigger and bigger masses as the clustering has proceeded.
And for a while galaxies tagged along, mirroring this growth of clustering.
But then these black holes switch from their readily efficient mode to their to
their readily radioactively inefficient and mechanically efficient mode and,
and prevented the formation of galaxies with masses of ten to the 13, ten to the 14th, and ten to the 15 solar masses.
So the so they have they have set their imprint on the universe as a whole through this mechanical process that we don't entirely understand.
Thank you.