 Greetings and welcome to the Introduction to Astronomy. In this video, we are going to be discussing two things, and that will be how we weigh the galaxy, how do we determine what the mass of the galaxy is, and we're going to take a look at the center of our galaxy and see what's going on there. So, let's go ahead and get started and look at how we can determine the mass of our galaxy. Now, big question would be, how do you possibly weigh a galaxy? That does not seem like an easy thing to do. There's not going to be a way to put a galaxy on a scale as we would weigh something here on Earth. And in reality, what we really want to determine is the mass of the galaxy. So, weight really is only the mass in a gravitational field. The mass is the amount of matter in the galaxy, and that's what we're trying to look at. And one way to do this is to consider how the stars are orbiting. If we look at a star at the visible edge of a galaxy, that can tell you how much matter is within the galaxy based on Kepler's third law. So, if we find a star way off here at the edge and observe how it orbits what its orbital period is, we can use Kepler's law, which told us that the mass was equal to A cubed over P squared. So, the mass of the galaxy in solar masses inside that orbit would then be the semi-major axis in astronomical units to the third power divided by the period in years squared. And we can do this, and this will work as long as there is very little matter outside beyond the star. So, if there's little matter out here, this works just fine and allows us to determine the mass of our galaxy. However, what we're finding is that there are significant amounts of dark matter out beyond the visible edge of the galaxy. So, while it looks like our galaxy ends some place here, in reality it goes way off beyond that many times this distance, and there is a lot more material out there. And this is what we call dark matter. Now, dark matter can be determined by looking at the rotation curve of a galaxy instead of looking at just a single star. We look at the velocities of stars at different distances. So, as we start towards the center here and then as we go further out from the center of the galaxy, we can then determine what the rotation curve of the galaxy is. Once you get beyond most of the mass of the galaxy, the curve will decrease. So, what we're looking for is the point where it reaches this blue curve and things start to decline. That is how orbits will occur when most of the mass is inside your object. So, this works very well for our solar system, shows something very similar to this, in that all of the mass in the solar system is essentially in the sun. So, by the time we get to the planets they show a very decreasing velocity as you go further out. However, what we find instead of decreasing is that the further out we go the rotation curve actually increases with distance. So, it is getting large. They're going faster and faster. And since objects are moving faster and faster, that means that there must be far more matter at greater distances than any visible matter that we see. And it can represent 20 times the amount of the luminous matter that we see within our galaxy. So, there's matter out there, but it is simply something that we cannot see. Now, what does this mean? What could this dark matter be? Well, first of all, we know that it could not be ordinary matter. It could not be atoms and dust and gas because we would detect it. We could detect gases by radio emissions. We could detect absorption lines from starlight traveling through them. So, we would not be able to figure that out. Could it be black holes? Black holes would be hard to see. However, if black holes collect matter, they do give off x-rays, which we could find. And if there were that many more black holes, calculations show we would have far higher abundances of the heavy elements, anything heavier than hydrogen or helium, that we do not have. How about things like brown dwarfs or planets, something very small, hard to see, almost impossible to see, but because of their low mass, we would need a tremendous number of these in order to account for the mass that we are that is hiding. And it would also, these would still be detected by gravitational lensing as they passed in front of distant stars. How about exotic subatomic particles? Well, nothing that has yet been detected, but this is something that we are still searching for. So this is an ongoing process searching for these types of objects. Now what does this mean, if there is all of this dark matter out there? And what it means is that really we are studying what we've been looking at so far is only tiny fraction of the mass of our galaxy. And by implication, because we see this in other galaxies, it applies to other galaxies as well. 96% of the mass of the universe is something that is undetectable to us through traditional methods, meaning telescopes. All we're detecting is its gravitational effects. And essentially every galaxy we look at has some kind of dark matter halo around it. So it is not just our galaxy that we see, but within galaxy clusters, we can get large amounts of dark matter that are visible, that extends well beyond the actual galaxies themselves. So it has some very important implications for understanding as we'll look at later as to how galaxies form in the first place, that dark matter may be a part of what helps form the structure in our universe that we see today. So let's go ahead and take a look at our galactic center. First of all, we say that it is invisible at visible wavelengths. What does this mean? Well, essentially it means that visible light does not penetrate from the center of our galaxy to reach us here on Earth. That is because of large amounts of dust within the galaxy. The dust blocks out the visible light, and even though the center of our galaxy would be located in this part of the sky, we can't see it with visible light. Even the most powerful telescope is not going to be able to show you anything at the center of our galaxy. It would be incredibly bright if it were able to be seen. So if you were able to not have the dust there, this would be one of the brightest objects in the sky. However, it is in the radio part of the spectrum. So in the radio waves, the galactic center is the strongest, brightest object that we see in the sky. Now, we can look in it at radio waves to be able to see a little bit better. And when we do that, when we look at it with radio waves, we can actually see different parts of our galaxy here. And in fact, what we see is one thing we call Sagittarius A star, which is the central portion and the central black hole at the center of the galaxy. We also see a number of other things from supernova remnants scattered around here and various other structures and concentrations at the center. We talk about Sagittarius A, but there are other locations, B and C, as well that are other parts of the galaxy. We also find many stars and clusters within this area. So a lot is going on down there and we're looking at a very small portion of the center of our galaxy at the center here. So we see all sorts of structures. Again, many supernova remnant, meaning that stars must have been here formed recently because stars that go supernova don't live a very long period of time. So the fact that we see this many supernovae means there have been lots of supernovae that have gone off here in the recent past. Now we can also look at this in the infrared. So if we move into the infrared to look at the center of our galaxy, we can actually see stars that are orbiting close to the central black hole. They orbit very quickly around the large mass and we can actually look at their orbit. So central, when we look at the visible light, we can't see this, but when we look at in infrared, we can actually see parts of our center of our galaxy. And if we look at the orbits of these stars, we have actually been able to track some of their orbits, you can see that they're orbiting their orbit very quickly in the large mass and they also change directions very quickly. So if you look at, for example, S14 here, it goes down, comes very close to something in the center, and then turns around and whips right back out. S8 not to quite the same effect, but also has a very, very twisted orbit in that it goes in and it whips around and comes straight back out. We can use Kepler's law as we have before to determine the mass. So the mass equals A cubed over P squared. As long as we can determine the masses of, I mean, the orbits of these objects, we can determine what their semi-major axis A is in astronomical units. We can determine their period in years. We can use that to do a calculation to find out what the mass must be here at this very central portion, and we find that it is consistent with this black hole with a mass of 4 million solar masses. Now, why does it have to be a black hole? Well, that's because the size is so small. There's no other way you could get that much material into such a small space and have it present without it being a black hole. So what do we know about this Sagittarius A star? Well, what we've learned is that it is 4 million solar masses compacted down to an area of less than 0.3 astronomical units. That means 4 million suns within the orbit of Mercury. No way you can possibly put this much mass in such a small space. It's just not possible to get that much material without it being a black hole. We also know that this black hole can grow over time. It absorbs gas at the rate of about one solar mass per year. So it is continually growing and it will consume larger objects, stars and gas clouds. That happens more rarely, maybe once every 10,000 years. When this happens, we can get a significant burst in the activity. So what is going on is that black hole accretes more and more of this matter and that will give us activity from the center and increased x-ray emissions from the center of our galaxy. So let's finish up, as we do with our summary. And what we've looked at is that we can determine the mass of our galaxy and we can also determine the mass of the supermassive black hole at the center using Kepler's third law. So Kepler's third law, which told the cube of the semi-major axis divided by the square of the period, allows us to determine masses within the universe. When we do this for our galaxy, we find that the vast majority of the mass of the galaxy, far more than what we can see, is in a dark matter halo, which is something right now of unknown composition. And then we did talk about the center of our galaxy containing a supermassive of about 4 million solar masses, and actually by galactic standards that's a relatively small one. We can look at other galaxies we'll see far more far larger black holes. So that concludes this lecture on weighing the galaxy and the center of our galaxy. We'll be back again next time for another topic in astronomy. So until then have a great day everyone and I will see you in class.