Three evidences of Dark Matter – the second and the third evidence

We talked about the 24 percent of the energy budget of the universe is occupied by the dark matter, so-called dark matter. Last time we saw the first evidence of dark matter, which is from very fast rotation velocity of spiral galaxies. And today, we’re gonna see the second and third evidence of the dark matter. The second evidence comes from galaxy clusters. So this is a typical galaxy cluster. Uh there’s a two big galaxies at the center, and then there are numerous, thousands of smaller galaxies are in one group. And they are bounded by the gravity. This is a galaxy cluster. And then this particular picture is Coma cluster, it’s one of the nearby very massive galaxy cluster.

Ah then this guy, Fritz Zwicky, he’s actually the one who named dark matter, and he was observing these galaxy clusters and then velocity of individual galaxies. In galaxy cluster, in gala-, galaxies in galaxy clusters are flying at very high speed. See, this is uh, a typical cartoon, and then Fritz Zwicky, was he was measuring the speed of these, uh, galaxy clus-, galaxies in galaxy clusters. And if you make a histogram of this velocity, then if galaxies are flying fast, and then you get a very large velocity dispersion, very large dispersion. But if galaxies are moving slowly, then you get a very thin velocity dispersion.

And then, again, this velocity is governed by the gravity of galaxy cluster, unless you can, galaxies can fly along very fast, because it’s a huge gravity, if there’s a huge gravity. If gravity is weak, the speed velocity of the galaxies are also slow. So by this measuring this speed of galaxies in galaxy clusters, you can measure how strong the gravity in the galaxy clusters are, okay? Then, um, let me explain this, on how to measure this. 00:02:24.000 –> 00:02:33.000 Galaxies in galaxy clusters are so-called in virial equilibrium.

This is bounded by gravity in, in, then already in equilibrium. And in this virial situation, uh, kinematic energy is going to be equal to minus one half of potential energy. And then by modifying the equation here, you can measure the mass is equal to radius times velocity dispersion square, R divided by gravitational constant. And here, we can measure the velocity dispersion, like Zwicky did, and also we can measure the radius, and then gravitational constant we know, so that’s how we can measure the total mass in a cluster. Let’s put the numbers in, the, this Coma cluster is at redshift of 0.023, or the distance is 100 megaparsec.

And then velocity dispersion we can measure, and then galaxies in average, are flying at the velocity of 900 kilometers per second, that’s very, very fast velocity. And the radius of Coma cluster is about 1.5 megaparsec so we can put these numbers in this equation, and then we get mass, total mass, is two times a 10 to the 15 solar mass, solar mass is the mass of the sun, so 10 to the 15 times more massive than the sun. So that’s the total mass in galaxy cluster. What’s surprising here is we can again calculate the mass in stars in cluster.

So we get we take picture, and then we, there are galaxies, right, and then stars are inside galaxies, so, we measure how much stars are here, and then measure the massing cluster, a, stars in galaxy cluster. Then, if you do that calculation, total stellar mass in a cluster, in Coma cluster, is 3 times 10 to the 13 solar mass. You see, there’s a hundred times less than the total mass, only one percent of the mass of the cluster is in stars. And then galaxy clusters are also filled in the hot X-ray plasma gas.

It doesn’t show up in this pic, optical picture, but if you take a picture of a galaxy cluster in x-lay, you see hot plasma gas, about tens of thousands of Kelvin. Then if you make, take x-lay picture, and then measure the mass in x-lay plasma, you get something like two times 10 to the 14th solar mass, so ten times more mass in gas than stars, but still this number is 14, is 15, so this is only ten percent of the mass of the cluster. Then, again, where is 90 percent of the mass? It’s not in star, it’s not in x-lay gas, it’s soaked in dark matter. So, again in galaxy cluster, 90 percent of the mass is in dark matter.

And then because of the gravity from this dark matter, galaxies can fly around at the very high velocity of 900 kilometers per second. So that’s the second evidence of the dark matter. The third evidence of the dark matter comes from gravitational lensing. This picture is a so-called gravitational lensing. Here’s a, in foreground here, there’s a very massive galaxy cluster, it’s something like similar to Coma cluster, this is another Coma cluster, but it looks like a lot of elliptical galaxies, there are hundreds of them, and then you might notice there are very thin galaxies here, here, here, here, here.

These galaxies are not in a cluster, but these galaxies are far behind, um, but the, because when the light from these faraway galaxies are coming to us, because of a huge gravity of galaxy cluster here, the galaxies are bended by the gravity. And then it, the shape becomes this thin arc-like shape. This is the so-called gravitational lensing phenomenon, this is predicted by Einstein’s general relativity. This schematic view graph is explaining it, far away galaxy’s light is bended by the huge gravity from the foreground galaxy cluster, and then it looks like an arc-like shape from the earth. This is galaxy (gravitational) lensing.

And what’s nice about this gravitational lensing is by using this phenomenon we can again calculate the total mass in a foreground cluster. In a very short explanation, um, this arc, if this is far away from center of galaxy cluster, there’s a more mass. If arc is closer then there’s less mass in galaxy cluster. And again, gravity expected from stars in this foreground galaxy cluster, it can only put the this arc here, the image should appear here without dark matter. But in galaxy cluster in this galaxy cluster this arc are far away, it’s a very large distance from the center. That’s because of the huge mass of the galaxy cluster here.

And again, the mass is 10 to the 15, if you measure its solar mass, that’s 100 times more than stellar mass, or ten times X-ray gas mass, and again, 90 percent of the mass in galaxy cluster is in dark matter. So that’s the third evidence of the dark matter. Let’s summarize, and this is how we know that 24 percent of the total energy budget of the universe it’s in the so-called dark matter. 00:08:46.000 –> 00:08:50.000 And this is very, very mysterious.

We know dark matter is out there because of its gravity. It causes gravitational lensing and a very fast rotation speed, or very fast speed of galaxy in cluster. And then dark matter doesn’t emit light, that’s why it’s called dark matter. Um, and it doesn’t show up in our picture. (But) and then it occupies 24 percent of the energy budget of the universe. Um, yet we do not know what is dark matter. It’s not the regular substances like atoms, hydrogen, um, it’s something else. So there’s a big mystery here. The mystery of the universe here to be solved by ourselves in the future. Okay I stop here, uh, see you next time.