In Post 3, we recalled that we should be able to add up the density parameter for everything in the universe and get 1 (because we set it up this way: everything is in relation to the critical density at which the universe appears spatially flat, which we confirm observationally).
Then we asked ourselves, "okay, so what is the density parameter for stars, gas, and everything baryonic: "normal" matter?" We found that the density parameter for baryonic matter is only 0.048, or ~4.8% of the energy density necessary to have a flat universe! That's not a lot, there has to be something else in the universe to make it flat!
What about radiation? Nope: the density parameter for all radiation (and, while it is not technically correct, we are including neutrinos here) is on the order of 10^-5, completely negligible!
There's something "else" out there, there has to be, otherwise we wouldn't observe a spatially flat universe like we do.
This is a good place to have an aside on galactic rotation curves. Gravity is very well understood, and probably an undergraduate could write up a simple gravitation simulation of a low body number system if they really wanted to. We should be able to take Newtonian physics (and in some cases, like Mercury, some relativistic corrections) and predict the way orbiting bodies "should" be orbiting.
However, there was a problem when we started doing this for galaxies: at certain points further away from the center, galaxies weren't rotating the way they were supposed to:
[GALLERY=media, 9503]Rotcurve by Meow Mix posted Jun 24, 2021 at 9:23 PM[/GALLERY]
When plotted, the "curve" differed from what would be expected if we count up all the baryonic/visible mass in the galaxy. Why?
A good explanation is that there's something else there that we're not counting! (This is how Neptune was discovered as well, by the way: the orbits of the known planets were "off" from what they should be, which could be explained by a massive object orbiting at a certain location. When astronomers turned their telescopes to that location, there it was: Neptune).
Here is our first indication that the "missing" matter of the universe is "dark," meaning it either weakly interacts or doesn't interact with light: if there was something massive causing the rotation curves to look the way that they look, we couldn't see it. But more than that, if whatever it is doesn't interact with light, it would also explain its location and shape (so, the key point here is not just that scientists said, "well I don't see anything, so there must just be something invisible there." That is not the reasoning.)
Consider this: when hot, orbiting baryonic matter cools, it emits radiation (think back to basic science classes and remember blackbody-like radiation). Due to conservation laws, that means the orbiting baryonic matter loses a little bit of energy with that radiation: the radius of its orbit shrinks a little bit. So we would expect a glob of hot, spinning baryonic matter to condense into a tighter spinning radius as it cools. This is just basic Newtonian physics so far.
What happens if you have matter that, because of its properties, doesn't interact with light? Matter that can't emit radiation? Its orbit will never condense, it remains puffy and diffuse.
Consider: if a galaxy were to form with both baryonic matter and a hypothetical dark matter (matter that doesn't radiate), the baryonic matter would condense into a central spinning disk while the dark matter would remain diffuse: towards the edge of the baryonic matter's disk (where its mass starts falling off), the dark matter's mass is not falling off because it never became centrally concentrated. This scenario would look an awful lot like the rotation curves that we observe!
Now, let's consider the motion of galactic clusters. The dispersion of radial velocity in galactic clusters can be very high (1000 km/s, if you recall in Post 1 where I talked about peculiar velocities) because of the amount of mass in the clusters. Counting up the baryonic matter isn't enough: again, if we only consider the matter that interacts with light, we don't end up with enough.
Furthermore, we can use something called the Virial Theorem to relate time derivatives of the moment of inertia to the potential and kinetic energies of the cluster (I don't know how to write that less physics-y, sorry). The short version of this story is that there are ways to obtain the mass of the cluster that isn't just inferred from its motion: and again, when we measure the mass, the baryonic matter is not enough. There is mass that can't be seen (at the very least), and that makes it "dark."
So we have two independent ways to mass the cluster, and both agree that the baryonic matter is not sufficient to account for its mass. Why not add a third independent way? We can use its x-ray spectrum to derive the temperature and density of the gas in the cluster, and infer that the gas is supported against its own gravity by its pressure. We measure the gradient of the density and temperature profiles to measure the enclosed mass (if you have questions, ask them; I can show how we do this).
As it turns out, we get masses in agreement with the previous two methods discussed: so again, baryonic matter is not enough to explain the mass of the clusters.
Why do I keep harping on independent methods to cross check other results? Because imagine if we were just wrong about gravity for some reason: we wouldn't expect a completely independent method to agree with other methods that depend on gravity. It's evidence that we're correct about gravity when we independently cross-check it.
We can go further: since the velocity dispersion (in the Virial theorem method) and the temperature both trace the underlying gravitational potential in independent ways, we should be able to plot them against each other and they should trace each other. It's another way for us to just make sure we're not chasing phantoms, and that's exactly what we see!
[GALLERY=media, 9480]Disp by Meow Mix posted Jun 22, 2021 at 12:45 AM[/GALLERY]
(This is velocity dispersion on the y-axis vs. temperature on the x-axis of a cluster).
There is a fourth way to measure the mass in a galaxy: gravitational lensing. Lensing is a consequence of General Relativity, and since I'm trying to keep these posts really "light," just take my word on this: mass bends spacetime, and light will "bend" around massive objects (take questions to the comments if you want).
[GALLERY=media, 9504]Gravlensing by Meow Mix posted Jun 24, 2021 at 9:58 PM[/GALLERY]
If we know the distances and angles, this is a very accurate way to mass a galaxy or a cluster: and again, we find both that baryonic matter is not enough to account for it and that we get masses in agreement with the other methods listed above.
Now, gravitational lensing brings us in another direction that we can use: we can use weak lensing and microlensing to make a "map" of where mass is distributed in space (the process is involved, again, take questions on that to the comments if desired).
So what would happen if we were to find some mass via lensing but we couldn't see anything else there? That would be a good indication that there was some kind of "dark" matter, right? Well, we can do exactly that! Behold, the Bullet Cluster:
[GALLERY=media, 9505]Bulletcluster by Meow Mix posted Jun 24, 2021 at 10:06 PM[/GALLERY]
What you're looking at here is four images. In the top left is just a plain optical view of the cluster. In the top right, you're looking at the baryonic matter of the cluster as viewed via x-ray.
The bottom left shows mass as mapped by weak gravitational lensing. The bottom right shows mass detected via weak gravitational lensing on top of baryonic matter observed via x-ray. You're seeing that where a bulk of the mass is for this cluster is not where the baryonic matter is.
So what's the story here? I'll tell you. Two galaxy clusters collided to form the Bullet Cluster. The interesting thing is that while all matter interacts gravitationally, only the gases and such from the baryonic matter would self-interact with other baryonic gases in various ways. Imagine these two "clouds" as passing through each other. The baryonic mass self-interacts, so it gets caught on itself passing through, passing through slowly (in fact, on the right side, you can see a bow shock shape from the baryonic matter passing through the other baryonic matter). The dark matter does not interact with photons (so it doesn't radiate as it gets excited, etc.), so it just passes right through, ending up further away on either side of the collision!
Is the Bullet Cluster unique in terms of cluster mergers, have we maybe just measured the mass wrong in this one instance or something maybe?
No. There are tons of them to observe:
[GALLERY=media, 9506]Clustercollisions by Meow Mix posted Jun 24, 2021 at 10:13 PM[/GALLERY]
So, to wrap this up, there is matter out there that is not baryonic.
Furthermore, as far as we can tell, this matter does not interact with light. It's "dark."
Is it maybe just regular matter that doesn't have light shining on it, or doesn't get excited enough to radiate? No. Remember, we know how much baryonic matter there is total, and it's not enough to get a flat universe. We know how much baryonic matter there is in these galaxies, and it's not enough to account for their mass. We know how much baryonic matter there is in galaxy clusters, and it's not enough to account for their velocity dispersions, temperature, etc.
There aren't enough rogue brown dwarves and so on in the universe that could make up this difference (and remember, there wouldn't be enough baryonic material in the first place to make them).
So there is some other kind of matter than baryonic matter, and it is "dark."
Next post will conclude the dark matter section with dark matter's influence on structure formation in the universe, the cosmic microwave background anisotropies, and baryon acoustic oscillations. These are some of the best evidences for dark matter, probably even better than anything presented in this post.
Then we asked ourselves, "okay, so what is the density parameter for stars, gas, and everything baryonic: "normal" matter?" We found that the density parameter for baryonic matter is only 0.048, or ~4.8% of the energy density necessary to have a flat universe! That's not a lot, there has to be something else in the universe to make it flat!
What about radiation? Nope: the density parameter for all radiation (and, while it is not technically correct, we are including neutrinos here) is on the order of 10^-5, completely negligible!
There's something "else" out there, there has to be, otherwise we wouldn't observe a spatially flat universe like we do.
This is a good place to have an aside on galactic rotation curves. Gravity is very well understood, and probably an undergraduate could write up a simple gravitation simulation of a low body number system if they really wanted to. We should be able to take Newtonian physics (and in some cases, like Mercury, some relativistic corrections) and predict the way orbiting bodies "should" be orbiting.
However, there was a problem when we started doing this for galaxies: at certain points further away from the center, galaxies weren't rotating the way they were supposed to:
[GALLERY=media, 9503]Rotcurve by Meow Mix posted Jun 24, 2021 at 9:23 PM[/GALLERY]
When plotted, the "curve" differed from what would be expected if we count up all the baryonic/visible mass in the galaxy. Why?
A good explanation is that there's something else there that we're not counting! (This is how Neptune was discovered as well, by the way: the orbits of the known planets were "off" from what they should be, which could be explained by a massive object orbiting at a certain location. When astronomers turned their telescopes to that location, there it was: Neptune).
Here is our first indication that the "missing" matter of the universe is "dark," meaning it either weakly interacts or doesn't interact with light: if there was something massive causing the rotation curves to look the way that they look, we couldn't see it. But more than that, if whatever it is doesn't interact with light, it would also explain its location and shape (so, the key point here is not just that scientists said, "well I don't see anything, so there must just be something invisible there." That is not the reasoning.)
Consider this: when hot, orbiting baryonic matter cools, it emits radiation (think back to basic science classes and remember blackbody-like radiation). Due to conservation laws, that means the orbiting baryonic matter loses a little bit of energy with that radiation: the radius of its orbit shrinks a little bit. So we would expect a glob of hot, spinning baryonic matter to condense into a tighter spinning radius as it cools. This is just basic Newtonian physics so far.
What happens if you have matter that, because of its properties, doesn't interact with light? Matter that can't emit radiation? Its orbit will never condense, it remains puffy and diffuse.
Consider: if a galaxy were to form with both baryonic matter and a hypothetical dark matter (matter that doesn't radiate), the baryonic matter would condense into a central spinning disk while the dark matter would remain diffuse: towards the edge of the baryonic matter's disk (where its mass starts falling off), the dark matter's mass is not falling off because it never became centrally concentrated. This scenario would look an awful lot like the rotation curves that we observe!
Now, let's consider the motion of galactic clusters. The dispersion of radial velocity in galactic clusters can be very high (1000 km/s, if you recall in Post 1 where I talked about peculiar velocities) because of the amount of mass in the clusters. Counting up the baryonic matter isn't enough: again, if we only consider the matter that interacts with light, we don't end up with enough.
Furthermore, we can use something called the Virial Theorem to relate time derivatives of the moment of inertia to the potential and kinetic energies of the cluster (I don't know how to write that less physics-y, sorry). The short version of this story is that there are ways to obtain the mass of the cluster that isn't just inferred from its motion: and again, when we measure the mass, the baryonic matter is not enough. There is mass that can't be seen (at the very least), and that makes it "dark."
So we have two independent ways to mass the cluster, and both agree that the baryonic matter is not sufficient to account for its mass. Why not add a third independent way? We can use its x-ray spectrum to derive the temperature and density of the gas in the cluster, and infer that the gas is supported against its own gravity by its pressure. We measure the gradient of the density and temperature profiles to measure the enclosed mass (if you have questions, ask them; I can show how we do this).
As it turns out, we get masses in agreement with the previous two methods discussed: so again, baryonic matter is not enough to explain the mass of the clusters.
Why do I keep harping on independent methods to cross check other results? Because imagine if we were just wrong about gravity for some reason: we wouldn't expect a completely independent method to agree with other methods that depend on gravity. It's evidence that we're correct about gravity when we independently cross-check it.
We can go further: since the velocity dispersion (in the Virial theorem method) and the temperature both trace the underlying gravitational potential in independent ways, we should be able to plot them against each other and they should trace each other. It's another way for us to just make sure we're not chasing phantoms, and that's exactly what we see!
[GALLERY=media, 9480]Disp by Meow Mix posted Jun 22, 2021 at 12:45 AM[/GALLERY]
(This is velocity dispersion on the y-axis vs. temperature on the x-axis of a cluster).
There is a fourth way to measure the mass in a galaxy: gravitational lensing. Lensing is a consequence of General Relativity, and since I'm trying to keep these posts really "light," just take my word on this: mass bends spacetime, and light will "bend" around massive objects (take questions to the comments if you want).
[GALLERY=media, 9504]Gravlensing by Meow Mix posted Jun 24, 2021 at 9:58 PM[/GALLERY]
If we know the distances and angles, this is a very accurate way to mass a galaxy or a cluster: and again, we find both that baryonic matter is not enough to account for it and that we get masses in agreement with the other methods listed above.
Now, gravitational lensing brings us in another direction that we can use: we can use weak lensing and microlensing to make a "map" of where mass is distributed in space (the process is involved, again, take questions on that to the comments if desired).
So what would happen if we were to find some mass via lensing but we couldn't see anything else there? That would be a good indication that there was some kind of "dark" matter, right? Well, we can do exactly that! Behold, the Bullet Cluster:
[GALLERY=media, 9505]Bulletcluster by Meow Mix posted Jun 24, 2021 at 10:06 PM[/GALLERY]
What you're looking at here is four images. In the top left is just a plain optical view of the cluster. In the top right, you're looking at the baryonic matter of the cluster as viewed via x-ray.
The bottom left shows mass as mapped by weak gravitational lensing. The bottom right shows mass detected via weak gravitational lensing on top of baryonic matter observed via x-ray. You're seeing that where a bulk of the mass is for this cluster is not where the baryonic matter is.
So what's the story here? I'll tell you. Two galaxy clusters collided to form the Bullet Cluster. The interesting thing is that while all matter interacts gravitationally, only the gases and such from the baryonic matter would self-interact with other baryonic gases in various ways. Imagine these two "clouds" as passing through each other. The baryonic mass self-interacts, so it gets caught on itself passing through, passing through slowly (in fact, on the right side, you can see a bow shock shape from the baryonic matter passing through the other baryonic matter). The dark matter does not interact with photons (so it doesn't radiate as it gets excited, etc.), so it just passes right through, ending up further away on either side of the collision!
Is the Bullet Cluster unique in terms of cluster mergers, have we maybe just measured the mass wrong in this one instance or something maybe?
No. There are tons of them to observe:
[GALLERY=media, 9506]Clustercollisions by Meow Mix posted Jun 24, 2021 at 10:13 PM[/GALLERY]
So, to wrap this up, there is matter out there that is not baryonic.
Furthermore, as far as we can tell, this matter does not interact with light. It's "dark."
Is it maybe just regular matter that doesn't have light shining on it, or doesn't get excited enough to radiate? No. Remember, we know how much baryonic matter there is total, and it's not enough to get a flat universe. We know how much baryonic matter there is in these galaxies, and it's not enough to account for their mass. We know how much baryonic matter there is in galaxy clusters, and it's not enough to account for their velocity dispersions, temperature, etc.
There aren't enough rogue brown dwarves and so on in the universe that could make up this difference (and remember, there wouldn't be enough baryonic material in the first place to make them).
So there is some other kind of matter than baryonic matter, and it is "dark."
Next post will conclude the dark matter section with dark matter's influence on structure formation in the universe, the cosmic microwave background anisotropies, and baryon acoustic oscillations. These are some of the best evidences for dark matter, probably even better than anything presented in this post.