Welcome and thank you all for coming.
In some cases, considerable distances.
It's heartwarming to see so many friends and colleagues, both old and new.
So if we could dim the lights so I can try that.
Okay, very good. So I'm going to talk today about accretion processes in the universe.
I think probably some of you will be hearing about the subject for the first time.
I know that several of you in the audience are among the world's most distinguished researchers in the topic.
So I hope you'll bear with me and indulge a little bit.
I hope you can. So.
Let's begin with the big picture. All structure in the universe.
Stars, galaxies and clusters of galaxies formed as a consequence of accretion.
What is accretion?
Accretion simply refers to the fact or to the process of a dilute gas following on to being concentrated in some kind of a central object.
Stars and planets form in gaseous cocoons and interstellar matter.
Gas streams flow from one star to another in binary systems.
A different type of accretion process and huge collapsed stars.
Black holes, in fact, sit in the centre of galaxies, drawing gas continuously from their surroundings.
Now it must be understood that accretion itself is really all but inevitable.
It can't be stopped. The gas that is accreting is not being blown away by some other accretion event.
Eventually it must collapse to either solids or ultracompact objects known as white dwarfs.
The end states of most stars, which holds itself together with a pressure force similar to those that hold up
atoms and white dwarf star in a sense as a great big atom or a neutron star,
which is like a great big atomic nucleus. I say great big.
But of course, the neutron star itself would fit comfortably within the ring road around Oxford.
You have the mass of the sun. Sometimes it seems a bit like that, even under ordinary circumstances.
Within an area which, as I say, could be comfortably encircled by the ring road or.
The matter could collapse down to the ultimate singularity.
A black hole puncturing spacetime itself.
Now. Allow me to set the tone of the lecture in these early stages by invoking the spirit of Monty Python.
Some of you are of a certain age or sensibility may recover or may remember the Royal Society for putting things on top of other things,
which is really not a bad description of what accretion theorists do.
The sheer numbers have put more things on top of other things than ever before.
This was a good year, so that's a good way to think of astrophysical accretion.
That's what theorists do. They want to figure out how to put things on top of other things now.
In fact, the notion of. Particularly the large scale structure in the universe forming from accretion does have a somewhat more noble line of descent.
There's a very famous quotation from Isaac Newton and later to Richard Bentley.
He writes, If matter were evenly disposed throughout an infinite space.
Newton is trying to figure out now, just by pure thought, no less than the origin of the stars in the universe.
If matter were evenly disposed throughout an infinite space, it could never convene into one mass, but some of it would convene into one mass,
some into another, so as to make an infinite number of great masses scattered great distances from one to another.
Throughout all that infinite space. That's the basic idea.
The pictures we know somewhat more complicated.
And in particular, if we want to understand the first major accretion process, how did the large scale structure of the universe form?
We need to take into account the fact that the universe is expanding.
It began small. It's growing large.
The birth of the universe is in some sense the ultimate anti accretion event.
It's explosive release, which is going on to this day.
Indeed, as we know now, it continues to accelerate.
And within that structure, we need to somehow turn around and re collapse.
This is a difficult problem to form something by self gravity.
We have to start off with a little over density.
It must first before it does anything else, stop expanding with the rest of the universe and only then turn around and collapse back on itself.
This is not so easy. And either a physical. Or a mathematical sense.
The first calculations of how to do this and how small over densities would behave in an expanding
background were done by the Russian physicist Ian Lipschitz using the full machinery of general relativity.
And I've put up the equations there to give you some sense of the complexity of the problem.
If one wants to do it rigorously now, fortunately, it is easy to state the fundamental result in very simple terms.
If the universe grows by a factor of, let's say, F.
The density must go down by a factor of one over f cubed, its ordinary matter being conserved.
Now an embedded growing disturbance and over density does not initially in fact grow.
It too goes down, but only by a factor of one over f squared.
So it's actually decreasing, but relative to the background increasing.
And it's that behaviour which has to turn itself into something more dramatic if we're to get to where we are today.
So here is a representation of the expanding universe.
And what we want to do is to start off of the region slightly over dance and then let it self accrete.
So as the universe is expanding, the over density has to turn around and accrete if we're going to get the ball rolling.
Now these days, people have done rather sophisticated simulations.
This is the Greco simulation from astronomers in Chile.
It is a simulation which involves 134 million particles.
And in what we'll be looking at here,
it's essentially the growth of this kind of accretion structure with the background expansion taken out of the calculation.
So you're watching the formation of structure relative to this expanding background, and you can see something interesting.
It doesn't tend to form little blobs, nice little spheres, but it.
Forms these elongated filaments and sheets.
And that's really what the large scale structure of the universe looks like when observers go
out and actually look at how the galaxies themselves and the clusters of galaxies are disposed.
You don't see a nice little spherical collapse. Generally, one axis prevails and things tend to be flat.
Gravity makes things flat in this context, not round.
Well, we have a long way to go. We have some idea of how things got get started.
But if we want to move on, we're trying to make the whole universe.
We have to get the galaxies. We have to get the stars. We have to get the planets.
If we want to detach from the expanding universe within a galaxy, there are two principal obstacles that have to be overcome.
One, and I think these are self-evident. If you try to squeeze something, it doesn't like to be squeezed.
There will be an opposing pressure due to the contraction process itself that will continue to grow.
The other very important dynamical consideration is that if there is any angular momentum in the object to begin with when it contracts,
the conservation of angular momentum will cause it to spin more and more rapidly.
And there's an opposing force that results from this which counter effects and eventually prevails over gravity.
Let's take the first one first. Let's consider situations where we have some degree of symmetry in the problem.
Exactly how does the pressure depend upon the density? So P Here is the pressure rho.
The Greek letter Rho stands for the mass density. Proportional to Roe?
No, that's not the relationship.
This would be true for a gas where the temperature remain fixed, but the contraction process itself heats the gas be proportional to ROE squared.
That's a bit too stiff. The correct answer is actually something in between.
So if we want to actually understand what the build-up of the pressure is opposing the accretion,
it helps to think of the molecules in the gas a little bit like a ball bouncing between two walls.
The physics of it is actually very, very similar. So if we imagine a ball.
Moving at velocity V into walls contracting from either side with velocity W each
time the wall strikes the I should say the ball strikes the wall it picks up.
If you can show this, this is a problem we would ask students to do.
The ball picks up a velocity two times, w twice the walls velocity and it comes back, picks up another two to W and so on as the walls contract.
And what you find when you do the calculation is that the product of the separation of the walls l times, the velocity V remains are constant.
And that's the fundamental process that builds up the pressure in a contracting ball of the gas.
I actually have an animation of it. To give you a physical sense.
On how this builds up. So you see the wall bouncing back and forth and boom, boom, boom, bah bah bah bah bah.
So you get a sense that, in fact, you're doing a lot of heating in this process.
And that makes the gas rather stiff. The gas doesn't feel too stiff.
But if you're going to try to contract it uniformly, it's actually extremely stiff.
So how does P depend upon Roe? Well, if we take three simple equations, if we write down that P is Roe v squared,
simply stating that the pressure is the rate of momentum transfer per unit area against the wall.
If we write V times L is a constant which we just found out.
If we write down that mass has conserved the product of the density times,
l cubed is a conserved mass and you can instantly eliminate the velocity and
you find that the pressure is proportional to the density rho the 5/3 power.
That's an interesting kind of an unusual result. It's a funny exponent.
It may not feel that way, but it's a quite the gases are really quite stiff.
Now, interestingly enough. If I tried to do this in relativity, I can go through exactly the same kind of argument.
I have to be a little careful to use momentum instead of velocity,
and it helps to work with the number density instead of the mass density, but it's still basically the same kind of calculation.
What one finds at the end of the day is that the pressure is proportional, not to the 5/3 power of the density,
but the 4/3, which seems like a significant, significant technical difference.
But as most astrophysicists, I should say, I hope all astrophysicists know, it actually has extremely profound consequences, as we will see.
Summarise. How does P depend upon Roe?
If I try to make gas accrete without loss of energy, either the pressure is proportional to density for the 5/3 for an ordinary gas,
or to the 4/3 if the particles are moving near the speed of light in relativity.
So armed with this knowledge, we can really start to think about how to put things on top of other things.
We can start to try to make matter in the universe. Accrete.
Well, it seems to me there are two types of interesting spherical accretion processes.
Processes where we have a high degree of symmetry.
Nothing depends upon direction. Everything is just moving radially, accreting on to some kind of a central object.
One is known as bond, the accretion. I won't talk too much about bond the accretion in this lecture.
It's kind of a technical subject. It's an interesting problem from a mathematical point of view,
probably a little bit too idealised, I think, to be of profound astrophysical significance.
So the second type of accretion process, which I will discuss, may not strike you as an accretion process at all.
But I would like to think of stars. Ordinary stars like the Sun as a sort of extended accretion event, because in fact,
the sun, even as we speak, is in fact at least the core of the sun.
I have to make that distinction. It's actually getting smaller and smaller with time at a very slow rate.
But there's no question that the core of the sun is contracting, which comes.
And it's quite interesting to think of stars in this way as kind of these extended accretion events.
So to understand what's going on, it's imagining we have a gigantic ball of gas.
If we make it too big, I take the same amount of mass and spread it over to bigger volume.
It'll gather itself back up by its own self gravity, but only to a certain point.
Because if I now take the gas and try to squeeze it, we know what's going to happen.
The density will excuse me. The pressure will rise.
Like the density to the 5/3 power. And ultimately the pressure will push back harder and the gravity can attract.
In effect, the pressure force is going like one over the size cubed.
The gravitational force no more than one over R squared. So if it's not too big, not too small.
I have a just right point on the just right point, Goldilocks point.
Is the far. Now, a very interesting question is what happens if we squeeze so hard and those molecules are like that
ball hitting the wall that we just saw and it's going so fast that it's approaching the speed of light.
Well, we know what happens then when the pressure is proportional to the density, to the 4/3 power.
That's not an idle thought.
Exercise actually happens in the course of real stars.
The core mass exceeds 1.4 times the mass of the sun.
In that case, the pressure force and the gravity force behave similarly.
They are both one over r squared forces, and if the mass is in excess of 1.4 solar masses, the pressure is unable to push back.
Accretion wins, gravity wins.
And there's 1.4 solar masses as a very important number in astrophysics.
It's known as the Chandrasekhar limit. Stellar cores with masses in excess of 1.4 solar masses ultimately will lose the battle to accretion.
To summarise, here is a star. If I make it too big for its mass.
Dad. The gravity rig gathers its two big. If I squeeze it down too much, the star is too small.
Pressure inflates. Just right.
The real star. It's optimising something.
Now, in fact, the first serious models of stars in the 19th century by Calvin and Helmholtz were explicit accretion models.
Accretion was actually invoked. The idea was that the star was squeezing itself.
The whole star was contracting. It was heating up.
But rather than having the pressure go like the density to the 5/3 power, the energy leaked out and there was an energy loss.
And the energy loss to the star was our game.
That was the origin of the stars luminosity.
The source of a star's energy in the view of Kelvin and Helmholtz is the contraction itself,
the work done to do the contraction and the release of the potential energy of the star.
Half of the liberated energy is released as heat.
And if that is so, the star does its arithmetic and always stays at the just right point to maintain its equilibrium.
It's a very elegant model. There you have it in schematic form.
Now there is ultimately a problem with the model.
The lifetime of a star like the Sun would only be 10 million years.
Ten to the seven years. Well, for Calvin in particular, this was not a problem.
This was a feature. Calvin used this result together with arguments pertaining to the cooling of the earth, to argue explicitly,
and I would say vehemently against the geological sedimentation timescales in the late 19th century for the age of the earth,
and thus indirectly against Darwinian evolution.
Among other critics, was, in fact, T.H. Huxley.
Who criticise the work on the grounds that Calvin had hidden in and unwarranted assumptions in the calculations.
The mathematics was correct. The assumptions were in error, which in fact turned out to be exactly the case.
But I doubt for reasons that actually could have foreseen, Calvin and Helmholtz did get the basics right.
These guys were not going to screw up at that level. But what they did not and could not get right was the fact when the contraction process hits,
the gas above 10 million degrees tended the seven degrees.
Nuclear reactions are triggered, providing a profound feedback.
Greatly slowing, but in fact not absolutely stopping the core contraction.
The sun will last not ten to the seven years. Not 10 million years, but 10 billion years.
Now on our to do list, I talked a bit about pressure forces and accretion.
I like to talk about.
Rotational forces and the build-up of opposing centrifugal force and how objects in the universe manage to accrete even when they're rotating.
So in reality, accreting gas cannot fall directly onto a central mass.
Always falls in with some angular momentum.
As I've said, as the gas contracts it grows or the rotational energy grows like one over R squared, the gravitational energy like one over R.
It's a situation similar to the pressure. At small distances.
The opposing force is growing much more rapidly than the gravitational force,
and less angular momentum is extracted from the elements of fluid somehow and transported outward.
Sustained accretion is simply impossible. Well, how does accretion occur?
The gas has to lose angular momentum and generally can do so as we'll see.
But it's a process that happens very slowly. Radiation is much more efficient.
The gas cools under these circumstances.
It is natural for the gas to flatten and cool, but maintain a reservoir of angular momentum.
In which the centrifugal force v squared over r balances the gravitational force
GM over r squared where m is the central mass r is location within the disk.
So we speak of an accretion disk.
We can see today we can see accretion disks.
They can be imaged. Here is a an accretion disk.
The colours that you see which is forming around a star in a dark cloud in the constellation cepheus the well
what you're looking at is heat emission coming from the star and then you see some white lines in the picture.
And those are thought to come from a shockwave, from a much larger accretion process which is raining down on the disk itself.
Here's a rather dramatic edge on view of a disk around a forming star on the left.
You see the disk itself, a rather thick looking disk.
It looks a little bit like a Frisbee coming at you on the right.
It's taken through a filter in which the disk emission has been suppressed.
And you can see reflection from the central star quite easily popping out of the top.
We can even see evidence of disks inside the nuclei of galaxies.
This is a picture of a dusty Taurus and a little bright spot, which is actually an inner accretion disk in the core of an active galaxy.
So we can see these things.
Now, interestingly, even before we had any hope were before the days of adaptive optics and before the days of the Hubble telescope.
Discs were already an iconic presence in astrophysics, intimately associated with high energy physics astrophysics, excuse me.
And the search for black holes in particular.
The two gentlemen that you see, Roger Penrose, emeritus, Ralph Spall, professor of mathematics at the University of Oxford, and Stephen Hawking,
Lucasian, professor of mathematics at the other place, were in fact instrumental in making black holes part of the fabric of physics.
They proved that under rather general circumstances, it was inevitable that black holes had to form these punctures in space.
Time were inevitable, and it didn't require such unusual conditions.
I think that was the surprising thing and this was quite an exciting result in the 1960s,
and astrophysicists were in a mad scramble to try to find evidence for the existence of black holes.
Now, black holes, you recall, are black because they don't emit anything.
So the problem is, how do you see them? Well, the thought was that many black holes may be surrounded by accretion disks.
And by looking at the accretion disks, you could gather evidence for the existence of the black hole itself.
Now, they had a rather rough history. You remember this Chandrasekhar limit that I mentioned a few slides back.
Well, Chandrasekhar's advisor Arthur Eddington had a few choice words to say about his students work.
Referring to the Chandrasekhar limit. Dr. Chandrasekhar has gotten this result before, but he has rubbed it in in his last paper.
Various accidents may intervene to save the star from collapsing to a singular point a puncture in space time.
But I want more protection than that. I think there should be a law of nature to prevent the star from behaving in this absurd way.
Eddington did not mince words. This was 1935, and in our meeting, I wish I had been a fly on the wall there.
Well, black holes are ubiquitous now in theory and in the even in some sense in a real sense and observations today,
this was far from so as we've just seen in the 1930s, and it was far more so in the 1960s.
And an important impetus for the development of accretion.
This theory was as a means to search for black holes.
Why? How did this get started? Well, it really began in 1962 with the birth of X-ray astronomy.
Two seminal figures in that field, Riccardo Giacconi and Bruno Rossi.
And they had the bright idea simply to strap a couple of Geiger counters into the payload of a rocket and send it up and see what they could see.
And much to everyone's surprise, they found a sky full of X-rays.
Orders of magnitude more than anybody thought at the time.
What is the significance of this for accretion? Well, black holes are invisible.
How does one search for them? The answer is in close binary systems.
Two stars in orbit around one another.
When the stars are close enough, matter is drawn from the normal star into an accretion disk around the black hole.
It's the disk we observe as a proxy for the whole itself.
So this is the physical picture that astronomers have in mind.
So you have a more or less normal star. It's very, very close to a black hole.
If in fact the black hole is close enough, it can actually pull matter off of the star.
And because of the presence of relative angular momentum and accretion, disk must form.
And the accretion disk itself, as we'll see in our modelling, can get very, very hot.
In the course of its accretion. The disk must somehow dissipate.
The rotational energy of the gas doesn't dissipate angular momentum.
It has to move angular momentum outwards, but it dissipates the energy and radiates it.
If we dissipate the rotation of the gas, that will allow it to slow down and spiral inwards.
The accretion process can continue, but like an automobile brake where we're trying to stop differential rotation, the gas becomes very, very hot.
Indeed, it is a generic source of X-rays, which is why X-ray astronomy is the vehicle to search for these black holes.
So are there truly black holes with disks around them?
Well, the transformational year was 1968.
Jocelyn Bell Burnell, who I wish could have been in the audience tonight.
She's judging the Physics Olympiad in London. Jocelyn is a visiting professor in the department here in the Astrophysics Department.
As a graduate student in Cambridge, she discovered radio pulsars.
That's a radio pulsar. Radio pulsars, when they were discovered, are radio signals coming from space at incredibly precise intervals,
more precise than any clock on earth could measure.
And when they were found, it was stunning.
There was even speculation that it was a sign of extraterrestrial intelligence.
Until the sky turned out to be full of water.
Well, very quickly, within a few months of the discovery, Tommie Gold identified pulsars with rotating neutron stars,
these very compact objects that would rotate as a result very, very rapidly without any dissipative process slowing them down.
It was the only clock anybody could think of. That would have the accuracy.
To produce these radio signals and exactly how the radio signals are produced is still a complicated problem that's not completely understood.
Later on in the same year in the Crab Nebula, in the Constellation, the crab, a fantastically rapid pulsar, was discovered.
Going around once every 30 milliseconds and there was nothing that could go around that fast and be an astronomical source except a neutron star.
And in fact, there were other very, very powerful and compelling arguments that link the rotating neutron stars with pulsars.
Now in rotating neutron star is practically a rather a neutron star in itself is practically a black hole.
So if neutron stars were real, it's just a relatively small leap to have gravity become the ultimate vector and leave behind a black hole.
So this was powerful evidence for the existence of these objects.
And after 1968, they were taken extremely seriously.
More than ever, it was important to understand the physics of accretion disks.
What makes the friction in an accretion disk?
How does it slow down? The earth goes around the sun.
The planets go around the sun. They don't spiral under the sun.
Why is it that gas spirals in to a central object?
It's not just a matter of a gas being a continuous fluid.
When you work out the details, you still have difficulties.
Big difficulties. Well, for more than 20 years,
the best that theorists could do was to account for this so-called anomalous friction by adding an ad hoc term to the fundamental equations.
Just saying something was making friction in the disk.
Perhaps there was some sort of a subtle instability in the disk.
We set it up in a certain way. It wouldn't maintain the configuration.
That was speculation. And then these sort of instabilities resulted in a large internal friction because they would trigger turbulence.
And turbulence with all of its mixing would be highly dissipative.
They even gave this kind of a discourse process, the sort of friction resulting from rubbing of adjacent orbits in the disk.
It's called the viscosity. They call this viscosity alpha viscosity.
Now the most successful implementation of this Alpha Formalism by Shakira in San Diego.
Gave quite useful predictions. And in fact, some of the most interesting predictions required this ad hoc term to be added to the equations.
But then the results turned out to be independent of it.
An interesting set of mathematical affairs.
Many results would depend upon this artificial term that was not well understood, but only in a very marginally dependent way.
Still absent any understanding of what was really going on in the fluids, matters remained entirely unsatisfactory.
If you did a calculation. This is what you would find.
There would be your unperturbed orbit. You would do a perturbation, and the perturbation would look like this.
You would go back and forth. Nothing very exciting would happen when you disturb the gas.
Well, the prevailing approach, I would say circa 1980.
Don't worry. Be happy. Some, however, were a bit more nettled.
And this is a wonderful quotation by Professor Kip Thorne, one of the leading theorists of the 1970s, one of fact,
one of the leading relativists who was extremely active at the frontlines of the search for black holes.
And he was extremely nettled, he said. The chief stumbling block at this point is the friction in the disk.
We do not know whether the friction is generated by turbulence in the spiralling gas by magnetic fields.
We haven't talked about magnetic fields. But I will come back to them.
Or by a combination of turbulence and magnetic fields.
December 1974, evidently.
Astronomers have been doing this thing kind of thing for a while.
It turns out, as I was reading this book by Dorothy Sellers, by the way,
an excellent read for scientists, if you've not seen it, the documents in the case at one point,
one of the characters in the book utters, I hate being accounted for, as though I were some incalculable quantity in an astronomical equation.
Evidently, this was something that astronomers were forced to do from time to time.
It is a remarkable fact, however.
That if we consider the effects of an electrical current being present in the flow it and let me remind you especially in a disk around a black hole,
these are completely ionised gases. These are gases where there are ions and electrons that are free to move around.
And if that's the case, it turns out that the dynamical, the rotational properties of the fluid are dramatically altered.
The system is in fact completely destabilised.
If the rotation rate is faster on the inside than on the outside, which almost all rotating systems are if they're not in a state of uniform rotation.
Differentially rotating systems are prone to this instability, which is now known as the magneto rotational instability, instability.
And if you look at the dates, you notice it had precursors in the literature dating back to the 1950s.
And that's an interesting question as to why it wasn't appreciated earlier.
And the answer seems to be that the work itself was extremely mathematical,
and neither of the earlier authors made any real attempt to elicit the physics of the instability itself.
And so, although it was in a classic textbook by Chandrasekhar for many, many years, it just stayed on people's shelves,
completely unappreciated until John Hawley and I went back totally unaware of the earlier work founded on our own,
and then traced it back to these earlier origins.
So if we take another look at Professor Thorne's quotation back in 1974, we're now in a position to answer him.
The answer to his question is yes. Turbulence, magnetic fields.
Combination of turbulence and magnetic fields. Yes. In fact, we now know that it is the magnetic field itself that introduces the turbulence.
To understand this, we can go back to the work of Professor Hans Al-Fayed, who won a Nobel Prize for eliciting this in the 1970s.
And in fact, it really is remarkable.
Many of us have worked with these equations long enough now that it's sort of second nature to us.
But it's amazing that we can do anything at all with a magnetic field in a gas.
I think you have a gas which is full of electrons and electrons are doing electron things.
And then you have the ions and the ions behave a different set of equations.
They have their iron things that they're doing, they're moving in different ways.
And if they don't have the same velocities, if there's a difference between the ions and electrons, you get a current,
and then the current makes magnetic fields, and then the magnetic fields act back on the ions and electrons and it seems a hopeless can of worms.
And in reality, it turns out to be remarkably simple.
Because if we take into account the fact that this gas behaves like an excellent electrical conductor.
It turns out that the magnetic field lines of force.
You should think of these lines of force as kind of physical things.
These are the lines that you see when you take a bar magnet and sprinkle it with iron filings.
You see these characteristic patterns or merge those magnetic lines of force, act as though they were painted in, frozen in to the gas.
If the gas swirls around the magnetic field, lines of force swirl around as well.
Moreover, if we take one of these magnetic lines of force and we bend it.
It acts like a taut spring. Its physical effect is to provide attention.
Like a plucked spring. Excuse me. A plucked string.
Or even more simply, when you have a magnetic field present, the fluid elements feel like they are hooked together by a spring.
Hook is a good word to use in that context because they obey Hooke's law.
They feel an attractive force. I try to separate them, which is proportional to their separation.
So magnetic fields are difficult to think of it difficult for me to think of when I've been struggling with them for decades.
I find it easier to think of the masses on springs as something I can understand.
So imagine we have two masses connected by a spring in orbit around the star.
What will happen? You're going to be surprised if you haven't seen this before.
Let's focus in on the process. Let's take a close up view of those two masses.
And we have a mass which is orbiting a little bit farther out, rotating a little bit more slowly.
So it has a small arrow. And then I have another mass over here which is going faster.
My rotational centre is down here and they're hooked by this spring.
The spring is pulling back on this inner mass, which is trying to go faster,
but it is losing its angular momentum to the outer mass, which is moving more slowly.
What will happen under those circumstances?
Well, the inner mass will spiral in the outer mass will acquire the angular momentum and start to spiral out.
And the spring will stretch. But that just makes the connection between them, the talk between them even more powerful.
That's the basis of the instability. If you put a weak spring, I mean, this is a purely mechanical process between two masses in orbit.
It doesn't hook them together. It makes them fly apart.
And that's the basis of the origin of turbulence in these disks when even a very weak magnetic field is present.
If we go back to the case of the magnetic field, here's a schematic picture.
The field lines are pointing upwards. Here's my equilibrium.
If I imagine bending those lines and then letting the equations take over and let it evolve, this is what I find.
When I actually do the simulation, things start to slide.
And of course, a real disk doesn't do that indefinitely.
I have pieces of the disks going out. They encounter other pieces of the disk coming in and it becomes happily a turbulent mess.
That's what we want. That's the origin of the friction.
Once we knew this, it was actually embarrassingly easy to simulate on a computer.
Here is. A doughnut starting off from an initial condition, which is not a disc like condition, but it is threaded by a magnetic field.
And on the left there is a meridian, meridian or slice.
From the right side. You're viewing it from above, and you're looking at how the density evolves in a disk which is subject to this instability.
And it does precisely what it should do.
Mixes different fluid elements. Makes the disk hot.
It fits the bill perfectly. It's even possible to get more dramatic looking outflows now on the left side of this picture.
I'll let this run. I have presented a diagram which displays curves known as echoey potential surfaces.
That sounds complicated.
Aqui Potential surfaces are simply the surfaces that if I were to make the disc out of water, that would be the surfaces that the water would fill up.
I could potential surfaces on the earth like the ocean, follow spherical shells in a disc.
They follow unusual shapes because you have both gravity and strong rotation to contend with.
And one of the things that is interesting is that there are some surfaces which are quite happy and are completely bound.
They look like teardrops and then other surfaces near the disc where you get a
significant well which open up and extend to infinity so that you can have an outflow.
And this is a. An excellent example of exactly that process of material that has come in through the body of
the disk and then managed to hop on to one of these other surfaces and turns into an outflow.
So. One of the ubiquitous properties that we see with disks is not only accretion itself into a central object,
but a lot of material is coming out both in jets and winds.
And this is something that even if you didn't want to put it into, this simulation emerges extremely naturally.
So there's something right about this explanation. You're getting many, many things out that you didn't put in.
Let me summarise. In preparing this talk.
It was kind of fun to remember what the big problems were when I was a graduate student.
Not that long ago. I hope I'm.
1970s, late 1970s. And in fact, there has really been major historical progress.
We have seen the origin of large scale structure in the universe via the tiny fluctuations that missions like
WMAP more recently Planck have revealed all these little tiny specks essentially correspond to fluctuations.
Really fluctuations in the radiation,
but they're tracing fluctuations in the matter that will eventually grow into the large scale structure that has made the universe what it is.
We can see that these are tiny fluctuations and part intended.
The four part content of a five. But we still don't know how to make galaxies.
I can't give you a lecture on how galaxies are made. We don't even understand a lot of simple accretion processes.
I'm embarrassed to say we don't understand how hot gas accretes within clusters of galaxies.
Galaxies cluster together in groups with thousands of members.
They say gas in a galaxy spills out. It occupies the space in between the galaxies emitting X-rays, and it's behaving in a way we don't understand.
We seem to have kind of a carbon problem again in the sense that there's a heat source which is keeping the gas hot that we don't understand.
An embarrassing theoretical failure, one that I myself have spent time working on.
Here's a lovely picture. This is the centre of the galaxy and what you see in these kinds of rings.
These are stars that are whose orbits have been tracked.
These are the proper motions of the stars near the centre of the galaxy.
Look at this orbit. It's incredibly elliptical.
It's almost like a straight line in and out. These are the actual orbits.
This is the cleanest evidence that we have, that there is a black hole in the centre of the galaxy.
You can determine the mass quite accurately 4.6 million solar masses in a region on the scale of the size of the solar system.
It's got to be a black hole. It's quiet as a whisper.
There's nothing going on. At one point, black holes were invoked to explain things called quasars.
The brightest objects in the room in the in the universe.
They were incredibly luminous. If you had a black hole present, fireworks resulted.
My previous part of this lecture was to explain why the disks around black holes emit X-rays 4.6 million solar masses and little the galaxy.
Nothing. It's not understood. Our understanding of many observational facts surrounding black hole accretion sources is minimal or nil.
The disks are constantly erupting and quieting down and changing their spectral appearances completely.
There's a famous example. Here's a black hole candidate and there is a spectrum.
This is called a state power law. Seven months later, the spectrum looks like this.
Now, this spectrum, we don't understand. We do understand this is pretty much what you would get from an accretion disk.
Here. The spectrum seems to be dominated by a population of relativistic particles.
And why within a period of seven months we should go from one to the other,
completely changing, at least the radiative state of the disc is not understood.
So there will be a lot to keep people like me, I hope, gainfully employed for a while.
Parasitology. Oh, this is an embarrassment. It's like all my failures in front of my eyes.
But a stellar accretion disk or a major town challenge.
Too big to succeed. Big disk is bad.
It rotates slowly, it's cold, it's dusty, and it's incredibly neutral.
And it's very difficult to see how magnetic fields can work in a situation like this.
It appears as though it can just barely do it. But the physics is not well understood.
There really is a long way to go. At the same time, things are not all bleak.
The combination of, I would say, improved physical analysis and what is truly dazzling progress in computational power allows us to do,
among other things I should say,
three dimensional general relativistic magneto, hydro, dynamical, turbulent disk calculations of an accreting disk around a rotating core black hole.
For those of you who know what those words means, that is simply stunning.
We are in an era we may not be able to do that calculation well, but we can do it and get some kind of results out of it and.
It will only get better with time and I think it's quite exciting.
You just saw in this earlier calculation with the jet emerging, we start with any old kind of random initial equilibrium.
Let the magneto rotational instability run and it turns into a cat.
Larry and Jeff, excuse me, kept Larry in disk with the jet popping out of it right where it should be.
So this is progress. This really is progress. And just remember.
That's what the universe would look like without accretion.
Without accretion, the universe would be a big, boring bag of gas doing nothing hurtling into oblivion.
So let's be glad some of us are taking the trouble to put things on top of other things.
Thank you very much.