12. Dark Stars and Black Holes - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This is the first of two lectures on speculations about dark matter composition, before we finally start talking about dark energy. Sean talks about the possibilities for ordinary matter making up the dark matter, while next lecture he will focus on the non-ordinary matter candidates.

It seems like much of the evidence for dark matter we have seen, already implies that it is non-ordinary matter. But since we have not yet found that non-ordinary matter, the theories for dark matter as ordinary continue to be numerous. This is the way science should be working properly. If you view Robert Hazen's Teaching Company course "Origins of Life" you will see this process in full action. Theories are being proposed all the time, the more surprising and testable the better, as Karl Popper said. Some of the most unorthodox are from the very leaders in the field. This is what makes science exciting to me. Sometimes we all need to take a step back and laugh at things. Primordial particle sized black holes? There has to be some right answer(s), so the imagination, creativity, and insight of these scientists are all on display for us.

The leading proposals are reviewed and each one is refuted on grounds of not adding up to enough mass compared to the amount of dark matter needed. It all points to the non-ordinary matter scenario of the next lecture. Supersymmetry theory proposes a natural way of making stable, massive, weakly interacting particles. Axions have similar qualities but are less plausible. Neutrinos are hot dark matter particles, so do not fit in with the leading theories.

We're almost halfway through the lectures, and we've learned an awful lot about the universe. Let's summarize what we've learned so far. We know first that the universe is big and getting bigger. By big, we mean that not only do we live in a galaxy with about 100 billion stars, but we live in a universe evenly distributed with such galaxies. A typical galaxy outside the Milky Way also has 100 billion stars. There may be 100 billion such galaxies in the observable universe, so it's certainly big by any standards.

It's also getting bigger,which means the galaxies are moving apart from each other. We can understand that in terms of Einstein's General Theory of Relativity. The space in between galaxies is itself expanding, pushing galaxies further apart from each other, and stretching the wavelength of light as it travels through empty space, giving rise to the cosmological redshift.

We also have a universe that is full of stuff, yet interestingly there is more stuff in the universe than what we see. We can weigh things in the universe. We can figure out how much mass they have, by using their gravitational fields. So we can take an individual galaxy and weigh it by looking at the motion of stuff outside the galaxy. We find that there continues to be more stuff in the galaxy, even when you can't see stuff anymore. Even when the visible parts of the galaxy stop, there's still more and more mass, as you go further and further out. This is evidence for dark matter.

This evidence is enhanced by looking at clusters of galaxies, at collections of galaxies moving around each other. You can look at both, how fast they're moving, to measure the total mass, you can look at the lensing of light that passes through the cluster, to measure the total mass, you can also look at the profile of x-ray gas in between the galaxies. Any one of these methods gives answers that are consistent with each other, and answers that the total amount of mass in the universe is something like 30% of the critical density you would need to have, to make the universe spatially flat.

So 30% of the critical density is a lot more than we can account for in terms of ordinary matter, in terms of the particles we know from the standard model of particle physics, that make up protons, neutrons, and electrons, the ordinary atoms that make up a table or ourselves. How do we know how much ordinary matter there is in the universe?

We've been emphasizing throughout the last several lectures that we have independent ways of measuring the total amount of ordinary matter in the universe. Two ways in particular are primordial nucleosynthesis, or Big Bang nucleosynthesis, the process by which when the universe was one minute old, it was converting protons and neutrons into helium and other light nuclei. The efficiency with which that happens, the percentage of helium you end up with at the end of the day, depends very much on how many protons and neutrons you have lying around. The more you have, the more helium by weight, you will end up with. So the fact that we have a certain amount of helium, about 24% of the visible mass in the universe, by weight, means that only 5% of the critical density of the universe can be made up by ordinary matter. That's not enough to account for all the mass we need.

Completely independently from that claim, we have the CMB. Slight variations in the temperature of the radiation that comes to us from when the universe first became transparent, 400,000 years after the Big Bang. These slight variations in temperature are all statistical, they are random fluctuations, but different sized regions evolve differently. Some will be enhanced in their temperature fluctuation by moving towards dark matter, some will be suppressed by pulling away from the dark matter, depending on how big that sized region is. So by looking at the distribution of different sized spots on the CMB, we can infer that there must be dark matter, pushing and pulling the ordinary matter we see. We get a consistent answer that's consistent with the claim that 5% is the density of ordinary matter, and 25% is dark matter.

There are other ways of getting similar results, ones that we haven't talked about. For example, you can start with the CMB and assume this is telling you about the primordial perturbations in density, and then let those perturbations evolve to today, to turn into galaxies and large scale structure. You can do this both with pencil and paper, and with a giant computer simulation. You find that in order to make as much structure as we observe on small scales, galaxy sized scales, it must be the case that there is dark matter in the universe, dark matter over and above the ordinary matter we can observe.

So many lines of evidence are pointing us to the conclusion that there's a lot of stuff in the universe that we don't observe directly, and that cannot be accounted for by ordinary atoms, ordinary things that are neutrons, protons, and electrons. We need some form of dark matter. Today's lecture gets down to the nitty gritty and talks about what that dark matter could possibly be. Now the answer that we think is right, is that the dark matter is some new kind of particle, not in the standard model of particle physics, yet is evidence for new physics that we haven't yet detected in the lab.

However, Sean wants us to trust him, and not think he's pulling something over on us, so today we'll consider carefully whether or not we might have made some mistake. Is it possible that the dark matter that we need to explain the motions of things in the universe, might somehow be in the form of stars or gas or dust, collapsed objects that we don't see because they're just too small, but are still made of ordinary stuff.

We're going to day at the end of the day that there's good reason to not believe this is true. Yet we want to go through the possibility, since some of the ordinary matter in the universe is in fact dark. Some of that 5% of the critical density, some of the protons and neutrons, we know we don't see. We don't see the air in the room, or different forms of gas and dust in the universe. In a cluster of galaxies, which we think is big enough to be a fair sample of the universe, we know that most of the ordinary matter is in between the galaxies. How do we know that? Because in the cluster, there's so much stuff that it falls together, heats up, and emits x-rays which you can observe. So you know that in a cluster, most of the ordinary matter is not in the galaxies, but 2/3 of it is in between.

We believe that clusters of galaxies are fair samples of the universe, by which we mean the ratio of stuff in between the galaxies and in the galaxies, should be the same, outside a cluster and inside a cluster. So we believe that even if you have stuff outside clusters of galaxies, which means most galaxies in the universe since most are by themselves, we believe it still should be the case that it's something like 2/3 of the ordinary matter in the universe that is not shining brightly in the form of stars in galaxies, but is in very dilute gas in between.

Yet nevertheless we think that even taking that into account, we don't have enough stuff to make up the dark matter in the universe. So today, we'll talk about different ways you can take ordinary matter and hide it in ways that are not very obvious. So in other words, we're going to talk about dark baryons! Stuff that started life as protons and neutrons, yet has come into a form that's not shining and easy to see, so is hidden from us somehow.

The simplest ways to do this, is to imagine that we have dark stars. A star that is a visible star, a bright star, starts life as a collection of gas and dust, spread across some wide region of the universe, yet is a little bit more dense than its neighboring regions. So just like a galaxy is formed when a whole bunch of stuff comes together under its mutual gravitational pull, stars are formed when stuff comes together under their mutual gravitational pull, in a much smaller region of space.

This same kind of process happens, but with stars, life is actually much more complicated. The process of star formation is one that astronomers don't claim to understand very well. It's a very active area of research in astrophysics right now, because somehow when this cloud of gas collapses, it heats up. Yet instead of bouncing back from the pressure force, it fragments into little tiny stars. Somehow this involves not only the gravitational dynamics of things collapsing, but things like magnetic fields, atomic physics, and the different ways that radiation travels through collapsing gas and dust. It's not a process we claim to understand, but what we can do is go out and look at the end results of that processes.

What are the kinds of stars that we actually see in the universe? The stars like the sun that we see, are easy to see because they're shining, they're giving off radiation. That's because they are so massive, that at the center, the hydrogen from which they are formed is being fused. Just like in the Big Bang, you're taking hydrogen, protons, hydrogen nuclei, and they're fusing together. When you take hydrogen, turn it into deuterium and then helium, you give off energy. The total mass of a helium nucleus is less than the sum of the masses of two protons and two neutrons. So it's able to give off energy by E=mc².

So the question is if there are things like stars, things that are collapsed collections of ordinary matter of gas and dust, and so forth, yet are not shining, maybe they are too small to shine, or something like that? Well yes there are things like that, and you want to ask how many of them are there, what forms do they take, and how do you get them? The simplest way is to start with an ordinary star. Start with a star that is burning its fuel and recognize that there's not an infinite amount of fuel to burn in that star. There's only a finite fuel supply, just like everywhere else. So a star will burn, like the sun for 4.5 billion years, which has another 5 billion years of fuel left, yet eventually will use it up. All that fuel will be turned into heavier elements.

If your star is low mass to begin with, the death of that star is fairly straightforward and calm. It just gives up, doesn't have enough nuclear fuel left, and in the latter stage it becomes big, a puffy red giant that gives off mass slowly into the outer reaches of space, while the core just slowly settles down into what we would call a white dwarf. This is a collection of gas that has been pulled together by its mutual gravity, yet has used up all of its nuclear fuel. So when it uses up its nuclear fuel, the reason why a star is so big in the first place, is because there is pressure created by the temperature that is created by that burning fuel.

The burning nuclear fusion process, heats up the interior of the star, and that's what keeps it big. When you've used up all the fuel, you don't have any pressure to keep it big anymore, and the star contracts. What is it that stops it from contracting? Well remember way back when we learned about bosons and fermions, we learned that fermions have the property that you can't pack them too tightly. The same reason that this table cannot collapse is because the electrons in the atoms are taking up space. The same thing will be true with a star. If it uses up its fuel and just collapses, eventually it will become the most efficient way to pack the electrons, protons, and neutrons, into a very dense substance.

That substance gives you a star called a white dwarf. It turns out that the electrons are the particles that take up the most space, so they define how big that white dwarf will be. It's the fermi pressure, named after Enrico Fermi of fermion fame, that keeps the white dwarf from shrinking any more. The laws of physics say that there's just nowhere to go. You can't put those electrons on top of each other.

If the star is slightly heavier than that, it will not end up as a white dwarf. It will burn heavier elements into yet heavier elements, in the way that a medium or low-mass star doesn't have access to. In that case, what will eventually happen after it puffs up and becomes a red giant, is that the core will violently collapse. Unlike a low-mass star that just sort of settles down, massive stars undergo a core-collapse, that goes very quickly to a small state, while its outer layers are blown off in a supernova explosion.

Now later in the course, we'll be talking in great detail about how to use supernovae explosions as standard candles to measure the acceleration of the universe. So right now Sean will let us in on a complication. These supernovae, are not those supernovae! There are different ways that stars can explode to become a supernova. This way that we're talking about now, is a core-collapse supernova known as a type II. Another way is what's called a type I supernova, which we'll talk about in later lectures as the ones that give us a standard candle that we use to measure the acceleration of the universe.

A core-collapse supernovae happens when a massive star has burned up its fuel, so the core shrinks and the outer layers are exploded off in what is a type II supernova. So what happens inside? We might have thought that things collapse and will form a white dwarf, since the electrons just can't be squeezed in anymore. This is true, yet there's something else that can happen if these particles have a lot of energy. We know that protons and electrons at these high energies can come together to form a neutron. So a neutron is a smaller particle than an electron. One of the miracles of quantum mechanics is that particles that are higher mass, take up less space. So that's why atoms have sizes that are controlled by their electrons, not by their protons and neutrons. It's the light particles that take up the most space.

So if you want to squeeze things together, but you're prevented from squeezing them because your electrons are taking up space, you do have an out. You have an equal number of protons as you have electrons, because your star is electrically neutral, so those protons can come together with the electrons and form neutrons. The neutrons take up less space, so if you turn off your electrons and protons into neutrons, you get a much more densely packed object, which we call a neutron star.

A neutron star is just a collection of particles that have all been turned into neutrons, and it is so dense that if you start with a several solar-mass star, you can turn it into a neutron star that is only tens of km across, the size of a city here on earth. It's very dense, and thus a high-gravity type of situation.

So you have two different possible end states for big stars. If a star is big, yet not too big, it will end up as a white dwarf. white because the surface is still pretty hot, so it gives off some light, but not very much. White dwarfs are actually very dim. If they are far away, you'd not be able to even see them, so they are candidates for "somewhat dark" matter! Neutron stars are very dim, are not giving off a lot of energy, so they could also be candidates for dark matter.

Finally, what if you had very low-mass stars? So low-mass they were almost closer to being planets than stars. We have in our solar system, gas giant planets, like Saturn and Jupiter. These are not stars because they are not heavy enough to burn nuclear fuel inside. You can imagine objects that come from the condensation of gas and dust, but weigh 100 times the mass of Jupiter. That is not heavy enough to turn on the nuclear fuel and start becoming a star. Such an object is called a brown dwarf, an object which is collapsed gas and dust, star-like in its initial stages, yet never hot enough to begin burning or shining.

So this means we have an entire collection of possibilities for ways to take ordinary matter and squeeze it down into some small, dense object, that doesn't give off a lot of light; a white dwarf, a brown dwarf, or a neutron star. So together, these are all candidates for a certain kind of dark matter. Yet their not the non-baryonic matter of dark matter, since all of these come from ordinary protons and neutrons, They started their lives as ordinary matter, they still count as ordinary matter in terms of nucleosynthesis or the CMB, but they're just ordinary matter hidden in a way that it's hard to find them.

So people have invented a clever nickname for these kind of compact objects; MACHOs (Massive Compact Halo Objects). So last lecture we had WIMPs, and this lecture we get MACHOs. This is not an accident! People have though about this for years. So MACHOs are a candidate for a way to take ordinary matter and hide it. To put it in a form that would be hard to see, and would look kind of like dark matter.

So we'll now give arguments that have nothing to do with Big Bang nucleosynthesis or the CMB, as to why MACHOs are not a huge part of that 25% of the universe we really think is not ordinary matter. Even if we didn't know from nucleosynthesis or the CMB, that the dark matter was not ordinary, could it be possible to rule out that possibility by ruling out these candidates, one after another? Sean would like to argue that yes, this is indeed the case.

So first, lets consider white dwarfs and neutron stars. White dwarfs and neutron stars are dim. If our galaxy were filled with many of them, they would act much like dark matter. They would be hard to see, they don't interact with each other, they don't run into each other that much, and they're very dense so that you can pack a lot of mass into these kinds of objects. The problem is we only have very specific channels for creating white dwarfs and neutrons stars. First, you have to make a big star, one that shines and eventually gives off its nuclear fuel to condense into a white dwarf or neutron star.

In the process of condensation, these stars give off a lot of mass, so it's a minority of the original mass of the star, that ends up in the form of a white dwarf or a neutron star. Most of the original mass of the star, gets ejected into interstellar space. So if you're trying to imagine that the universe is full of white dwarfs and neutron stars, then you're imagining that there's all of this stuff having been ejected into interstellar space, during the process of forming these white dwarfs and neutron stars.

That ejected mass just isn't there. We would be able to see it because it would have heavy elements in it, and be observed in the spectra of different objects. Yet it's just not observed. So in other words, there's no way to efficiently take ordinary matter and convert any substantial fraction of it into white dwarfs and neutron stars. There's no way that we know of.

For brown dwarfs, it's a little bit more complicated. The brown dwarf is not something you get by the end of a star, but something you create at the beginning as a very low-mass star. So how do we know there are not a lot of brown dwarfs in the universe? Well there could be, yet our most reasonable extrapolations say there are not. We can figure out how many stars are made as a function of their mass. You can observe the stars we do see, and see how many "very massive" stars there are, how many "medium mass" stars there are, and how many "not so massive" stars there are. From this, we can extrapolate to how many brown dwarfs there probably are. It turns out that the most reasonable extrapolations we have, say that there shouldn't be that many brown dwarfs out there.

Now Sean is the first to admit that this is not an air-tight argument. We could certainly very well be surprised. After all, if the alternative is new laws of physics, we should be thinking very hard. So what we can do, is come up with an absolutely new way of constraining the number of MACHOs in the universe, regardless of how they were made. We want to go out there and look for condensed star-like objects, even without knowing where they could come from.

The way to do that is to use gravitational lensing. Just like we used before to weigh galaxies and clusters, we can look for these tiny star-like objects, using gravitational lensing. The good news about MACHOs that lets us look for them using lensing, is that they move. The amount of lensing due to one tiny little white dwarf, or brown dwarf, or neutron star, is very little. You would not be able to notice a big deflection of a background object. However, if we get an exact alignment, so that a white dwarf is right in between us and a background star, than it will focus the light a little bit, and that background star will appear a little bit brighter than without the lens. It's just like putting a magnifying glass up to the sun, which makes it look brighter if you're right there at the point where things are focused on you.

The problem there is, of course, how would you know if something were right in the middle of you? The good news there is that things move around. These star-like objects, these MACHOs, are moving through the halo of our galaxy, or in between our galaxy and other galaxies, so we can look at a whole bunch of background stars at once, and wait for these events of the MACHO going in front of the background star. The brightness of that background star will be seen to go up and then back down, doing so in very specific ways. It will go up and down in a perfectly symmetric way, and absolutely independent of what color you observe. Every wavelength of light coming from that star will be amplified and then go back down again, in precisely the same way.

So there are projects going on to search for these microlensing events, and they have indeed found them. We see such data from one of these projects, a light curve, the amount of light that is coming from a single background star. They observe literally millions of stars, waiting for a coincident brown dwarf, or white dwarf to go by. Here we see the light going up and down, perfectly symmetric. This is a wonderful candidate for a microlensing event.

The point is that you look at millions of stars, waiting for these microlensing events. You find that there are not nearly enough of them to account for what we need to be the dark matter of the universe. So it's not a matter that we don't know how to make them. If there were enough brown dwarfs, white dwarfs, or neutron stars, to be a substantial fraction of the dark matter, you would have seen them using microlensing, and you don't.

There is of course, another way to make very dense stuff in the universe, and that is a black hole. If you have white dwarfs as the end-points of medium mass stars, neutron stars as the end-points of more massive stars, you can then ask what happens if we squeeze those neutrons together even more? Within the standard model of particle physics, there really is no place to go when you squeeze those neutrons. However, it is nevertheless the case, that according to General Relativity, something will happen if you keep adding mass to neutron stars. It can't last forever.

We think that if just collapses into a singularity, with a gravitational field so strong that light itself cannot escape. This is what we call a black hole, the end point of gravitational collapse, where gravity is as strong as it can possibly be. There's nothing left after that. Now you'd think black holes would be hard to detect in the universe, since after all, they are black. Yet we've stressed again and again that there are ways to detect gravitational fields in the universe, even if the thing you are looking at that creates the field, is not directly visible.

So ordinary matter, spinning around a black hole, can either be directly visible, or it can give off light as it's spinning. If you have a small black hole, the endpoint of a massive star, stuff that is spiraling into the black hole will heat up, and give off x-rays. This is one of the primary targets for x-ray astronomy, to look at accretion disks, as they are called. These are disks of gas and dust, swirling around, into a black hole, giving off x-rays as they go.

There's another class of black holes called supermassive black holes, that are a million or ten million times the mass of the sun. They live at the center of galaxies and we can detect them because what happens is stars orbit them. So what you see are stars moving in an orbit, which we can actually detect and make movies of in their elliptical orbits, around nothing. They orbit around a region of space where there isn't anything. We know how far away these stars are, so we know how big their orbits are. We can then measure the mass, confined to a really tiny region. The only way you can put that much mass, over a million times the mass of the sun, into such a tiny region, is for it to be a black hole.

So there are stellar-sized black holes that exist, there are supermassive black holes that exist, so could either one of these be an important part of the dark matter? Well the answer again is probably not. For stellar-sized black holes, all of the arguments that we used for MACHOs, still apply. First we have no way of knowing how to make them. You could make them from stars, yet that would eject a lot of mass. Second, they would be MACHOs and thus lead to microlensing events. Yet we don't see enough of these microlensing events, from black holes or anything else, to be a substantial part of the dark matter.

Yet then we have supermassive black holes. Could the dark matter be "million solar mass" black holes? So almost as we say this, we realize no, probably not! Such "million solar mass" black holes are hard to hide. It's true that you couldn't see any one of them, but if one is moving through a collection of stars and it's not all by itself, it would cause a lot of disruption of the total dynamics of that system of stars.

So supermassive black holes sit at the centers of galaxies, yet they don't play a significant role in the overall mass of the galaxy. It may sound like ten million solar masses is indeed a lot of mass, but remember that the mass of a galaxy is something like a trillion solar masses. So even though supermassive black holes exist, they're a tiny fraction of the total mass of a galaxy. They're not an important part of the dark matter.

The remaining possibility for black holes, is that in fact we could have primordial black holes. We could make black holes not from stars collapsing, or from things collapsing at the centers of galaxies, yet some process in the very early universe, creates black holes that are very tiny. That is something that is actually completely plausible in terms of dark matter candidates. We have no way of ruling out the possibility that the dark matter is such tiny black holes. If they formed before Big Bang nucleosynthesis, they would not count towards their counting of ordinary matter in the universe.

However, once you make the dark matter these tiny black holes, it's practically indistinguishable from making the dark matter out of particles. They're individual little objects, not big stellar-sized things. We can't look for them using microlensing. So we're back once again to the possibility that the dark matter is particles. What we'll do in subsequent lectures is go through all the different possibilities of ways to make particles that would count as dark matter. So black holes are one possible candidate for such dark matter candidates that are basically particles. They are very tiny, little black holes.

It turns out that they are not among the most promising candidates. The reason is that we don't know how to make them. We have no theory of black hole production in the early universe that would predict a large density of tiny black holes today. The best candidate theories we have for the origin of the dark matter, are those where we have a natural way of making them. So it turns out that the absolutely best candidate that we have for making dark matter, is something called supersymmetry, a new particle physics theory that naturally gives rise to a set of particles that are stable, massive, and weakly interacting, which is exactly what we want the dark matter to be.

There are other candidates, like the black holes we mentioned, there is a particle called the axion, there's even neutrinos that are in the standard model. For neutrinos there's a good idea why we don't like them, they're hot dark matter. The other particles are cold dark matter, but they seem to be less plausible from a particle physics point of view than supersymmetry. However, we are keeping an open mind. We don't yet know what the dark matter is, and that's part of the excitement of the next ten years of cosmology. We'll be trying to point our fingers very specifically on where the dark matter comes from.