Dark Matter: MACHOs or WIMPs?

In the hunt for dark matter, there are several candidates that could make up this mysterious substance. One of the more popular candidates are MACHOs, or Massively Compact Halo Objects. But can such objects really comprise 27% of the mass and energy in the observable universe?

Artist interpretation of a black hole, one of the candidates for Dark Matter

Since we are convinced that dark matter really does exist, we should begin thinking carefully about what it might be. We have good evidence from our investigations into big bang nucleosynthesis and the microwave background that dark matter is not ordinary matter, so we will find ourselves driven to more exotic possibilities. But, first, we must consider the possibility 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 are just too small but are still made of ordinary stuff. Some of the ordinary matter in the universe is, in fact, dark. We don’t see the air in this room; we don’t see different forms of gas and dust in the universe.

Image of a galaxy cluster, a possible candidate for Dark Matter
Galaxy cluster MOO J1142+1527. In a typical cluster of galaxies, most of the ordinary matter is not in the galaxies themselves.

Let’s look at a cluster of galaxies. Why? Because clusters of galaxies are fair samples of the universe by which to determine the ratio of matter in between the galaxies to matter in the galaxies. In a typical cluster of galaxies we know that most of the ordinary matter is not in the galaxies themselves; two-thirds of it is in between. Therefore, it should be the case that around two-thirds of the ordinary matter in the universe is not in galaxies. It’s not shining brightly in the form of stars; it’s in very dilute gas in between. Even taking that into account, there is not enough stuff to make up the dark matter in the universe.

Hiding in Plain Sight

image of the Eagle Nebula
The famous “Pillars of Creation” in the Eagle Nebula are actually an example of a stellar nursery—a region in space where matter has contracted under its own gravitational pull to the point where it is beginning to ignite nuclear burning.

What are the different ways in which you can take ordinary matter and hide it? These are called dark baryons, stuff that started life as protons and neutrons but has come into a form where it’s not shining and as easy to see but is hidden from us somehow. The simplest way 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, but it’s a little bit more dense than its neighboring regions. So just as 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.

What kinds of stars are in the universe? The stars like the sun are easy to see because they are shining; they are giving off radiation. These stars are so massive that, at the center, the hydrogen from which they are formed is being fused. When hydrogen is turned into deuterium and then into helium, it gives off energy.

Gravity and Nuclear Fuel

The question is: Are there things like stars, things that are collapsed collections of ordinary matter of gas and dust and so forth, yet are not shining?

The question is: Are there things like stars, things that are collapsed collections of ordinary matter of gas and dust and so forth, yet are not shining? Yes, there are things like that. How many of them are there? What forms do they take? How do you get that? The simplest way is to start with an ordinary star. Start with a star that is burning its fuel. Stars do not have an infinite amount of fuel to burn. A star will burn; the sun has been burning for about 4.5 billion years. It has about another 5 billion years worth of fuel left, but it eventually will give up. All of its fuel will be turned into heavier elements.

Hubble telescope photo of Mira—a red giant star estimated to be 200–400 light years from the Sun in the constellation of Cetus
Hubble telescope photo of Mira—a red giant star

If your star is low mass to begin with, the death of that star is fairly straightforward and calm. It just gives up. It doesn’t have enough nuclear fuel left. In the latter stages, it becomes a big red giant, and it gives off mass slowly into the outer reaches of space. The core just slowly settles down into what we would call a white dwarf star—a collection of gas that has been pulled together by its mutual gravity but has used up its nuclear fuel.

Image of a normal star and a tiny white dwarf appearing next to it as a small dot
Image of Sirius A and Sirius B. Sirius B, a white dwarf, is pointed out by the arrow to the lower left of the much brighter Sirius A.

When it uses up its nuclear fuel, there is pressure created by the temperature of the burning fuel. When all the fuel is used up, the pressure keeping the star big disappears and the star contracts. What is it that stops it from contracting? If a star uses up its fuel and collapses, eventually the electrons and protons and neutrons will become packed into a very, very, very dense substance. That substance is called a white dwarf. Electrons are the particles that take up the most space and define how big the 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 there is just nowhere to go. You can’t put those electrons on top of each other.

A slightly heavier star will not end up as a white dwarf. Larger stars can burn heavier elements into yet heavier elements in a way that a medium- or a low-mass star cannot. In that case, eventually, after the star puffs up and becomes a red giant, the core violently collapses. Their cores collapse very, very quickly to a small state and the outer layers are blown off in a supernova explosion.

Supernovas and Neutron Stars

multi color telescope image of the Crab Nebula
The Crab Nebula is a nebula associated with a core collapse supernova.

There are different ways that stars can explode to become a supernova. A core collapse supernova, which is known as a Type II supernova, happens when a massive star has burned up its fuel, the core shrinks, and the outer layers are exploded off. What happens inside? Because there is a lot of energy in these particles, a proton and an electron can come together to form a neutron. A star that has an equal number of protons and electrons is electrically neutral. Those protons can come together with electrons and form neutrons, which take up less space. If all of the electrons and protons form neutrons, it results in a much more densely packed object: a neutron star.

image of a rotating neutron star
Artist’s conception of a neutron star

A neutron star is just a collection of particles that have all been turned into neutrons. A several solar mass star can turn into a neutron star that is only tens of kilometers across, the size of a city here on earth—a very, very dense high-gravity situation. So there are two different possible end states for big stars. If the star is big, but not too big, it will end up as a white dwarf. It’s white because the surface of the white dwarf is still pretty hot, so it gives off some light, but not very much. If white dwarfs are far away, we might not be able to see them. They could be candidates for some dark matter. Neutron stars are also very dim and they would also be candidates for dark matter.

Brown Dwarfs and Gas Giants

Full image of the planet Jupiter showing the red spot and banding taken by Hubble Telescope
Image of Jupiter, a gas giant

Finally, what about very low-mass stars—stars that are so small that they are almost closer to being planets than to being 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 a hundred 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. It is an object, which is collapsed gas and dust. It’s star-like in its initial stages, but never hot enough to begin burning, never hot enough to begin shining. What that means is there are a whole collection of possibilities for ways to take matter, 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, and a neutron star.

Massive Compact Halo Objects

People invented a clever nickname for these compact objects. They call them MAssive Compact Halo Objects, or MACHOs, for short.

Together, these are all candidates for a certain kind of dark matter. It’s baryonic dark matter because all of these come from ordinary protons and neutrons. They are just ordinary matter hidden in a way that it’s hard to find them. People invented a clever nickname for these compact objects. They call them MAssive Compact Halo Objects, or MACHOs, for short.

MACHOs are a candidate for a way to take ordinary matter and hide it, to put it in a form where it would be hard to see. It would look kind of like dark matter. I want to give you arguments that have nothing to do with big bang nucleosynthesis or the microwave background as to why MACHOs are not a huge part of that 25% of the universe that we really think is not ordinary matter. Even if we didn’t know from nucleosynthesis or the microwave background that the dark matter was not ordinary, could it be possible to rule out that possibility by looking at all the candidates one by one? I would like to argue, yes.

First, let’s consider white dwarfs and neutron stars. White dwarfs and neutron stars are dim. If, let’s say, our galaxy was filled with many, many white dwarfs and neutron stars, 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 are very dense. A lot of mass can be packed into these kinds of objects. The problem is that we only have very specific ways to create white dwarfs and neutron stars. First, you have to make a big star. That star that shines has to eventually give off its nuclear fuel and condense into a white dwarf or a neutron star.

To imagine that the universe is full of white dwarfs and neutron stars, then it would have to be filled with all the matter that has been ejected into interstellar space during the process of forming the white dwarfs and neutron stars. That ejected mass isn’t there.

In the process of condensation, these stars give off a lot of mass. In fact, it’s a minority of the original mass of the star that ends up in the form of the white dwarf or the neutron star. Most of the original mass of that star gets ejected into interstellar space. To imagine that the universe is full of white dwarfs and neutron stars, then it would have to be filled with all the matter that has been ejected into interstellar space during the process of forming the white dwarfs and neutron stars. That ejected mass isn’t there. There is no way that we know of to efficiently take ordinary matter and convert any substantial fraction of it into white dwarfs and neutron stars.

How do we know there are not a lot of brown dwarfs in the universe? There could be, but our most reasonable extrapolations say that there are not.

For brown dwarfs, it’s a little bit more complicated. The brown dwarf is not something that you get by the end of a star; it’s something you create at the beginning as a very, very low-mass star. How do we know there are not a lot of brown dwarfs in the universe? There could be, but our most reasonable extrapolations say that there are not. We can figure out how many stars are made as a function of their mass. How many very massive stars are there? How many medium-mass stars are there? How many not-so-massive stars are there? From that, we can extrapolate to how many brown dwarfs there probably are. It turns out that the most reasonable extrapolations say there shouldn’t be that many brown dwarfs out there. This is not an airtight argument. We could certainly very well be surprised. After all, if the alternative is new laws of physics, we should be thinking very hard.

Measuring with Microlensing

image of the Einstein's Cross gravitational lens - four white dots in a diamond shape with a white dot in the center.
A gravitational lens is matter, between a distant light source and an observer, that is capable of bending the light from the source as the light travels towards the observer. In this example, known as Einstein’s Cross, a single quasar is imaged 4 times around a foreground galaxy.

The amount of lensing due to one tiny little white dwarf or one tiny little brown dwarf or neutron star is very, very little. It would be difficult to notice a big deflection of a background object. However, if a white dwarf is aligned perfectly in between us and a background star, the background star will appear a little bit brighter than it would have without the lens. The problem there, of course, is how would we know if something were right in the middle? The good news is that MACHOs move around.

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. In events where the MACHO goes in front of the background star, the brightness of the background star will be seen to go up and then go down in very specific ways. It will go up and down in a perfectly symmetric way. Every wavelength of light coming from that star will be amplified and then go back down again in precisely the same way. Scientists searching for these microlensing events have found them. They observe literally millions of stars while waiting for a coincident brown dwarf or white dwarf to go by.

What they’ve found is that there are not enough of these events to account for the dark matter of the universe. If there were enough brown dwarfs, white dwarfs, or neutron stars to be a substantial fraction of the dark matter, scientists would have seen them using microlensing and they don’t.

How to Detect a Black Hole

image of matter spinning around a black hole and forming an accretion disk
Matter spinning around a black hole will form an accretion disk and heat up, giving off X-rays.

There is, of course, one other way to make very, very dense stuff in the universe. If you have white dwarfs as the end points of medium-mass stars, neutron stars as the end points of more massive stars, what happens if we squeeze those neutrons even more? According to general relativity, something will happen if we keep adding mass to a neutron star; it can’t last forever. What we think happens is that it just collapses into a singularity with a gravitational field that’s so strong that light itself cannot escape. A black hole is the end point of gravitational collapse where gravity is as strong as it can possibly be. You might think black holes would be hard to detect in the universe; after all, they are black. But there are ways to detect gravitational fields in the universe, even if the thing creating the gravitational field is not visible.

Ordinary matter spinning around the black hole can either be directly visible or it can give off light as it’s spinning. If you have a small black hole at the end of the lifecycle of a massive star, the stuff that is spiraling into the black hole will heat up and give off X-rays.

Inside Supermassive Black Holes

NASA image of a spiral galaxy
Spiral galaxies are thought to be rotating around supermassive black holes.

There is another class of black holes called supermassive black holes that are a million or 10 million times the mass of the sun. Supermassive black holes live at the center of galaxies and we can detect them because stars orbit them. We can see the stars going in an ellipse around nothing, around a region of space where there isn’t anything there.

The only way to have that much mass—over a million times the mass of the sun—into a tiny region is for it to be a black hole. There are stellar-sized black holes that exist; there are supermassive black holes that exist. Could either one of these be an important part of the dark matter? The answer, again, is probably not. For stellar-sized black holes, all of the arguments that we used for MACHOs still apply.

We don’t see enough microlensing events from black holes or from anything else to be a substantial part of the dark matter.

Number one, we have no way of knowing how to make them. You could make them from stars, but that would eject a lot of mass. Number two, they would be MACHOs; they would lead to microlensing events. We don’t see enough microlensing events from black holes or from anything else to be a substantial part of the dark matter. But then, we have supermassive black holes. Could the dark matter be a million solar mass black holes? A million solar mass black holes are hard to hide. It’s true that we couldn’t see any one of them, but as one moves through a collection of stars, it would cause a lot of disruption to the total dynamics of that system of stars.

10 Million Solar Masses

It sounds like 10 million solar masses is a lot of mass, but remember that the mass of a galaxy is something like a trillion solar masses. Even though supermassive black holes exist, they are a tiny, tiny fraction of the total mass of a galaxy. They are not an important part of the dark matter. The remaining possibility for black holes is that, in fact, there are primordial black holes; some process in the very, very early universe created black holes that are very tiny. Unfortunately, we have no way of ruling out the possibility that the dark matter is tiny black holes.

So we’re back once again to the possibility that the dark matter is particles.

If these black holes formed before big bang nucleosynthesis, they would not count toward the counting of ordinary matter in the universe. However, once you make the dark matter of tiny little black holes, it’s practically indistinguishable for making the dark matter out of particles. They are individual little objects; they are 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.

From the lecture series Dark Matter, Dark Energy: The Dark Side of the Universe
Taught by Professor Sean Carroll, California Institute of Technology

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