Greetings and welcome to the Introduction to Astronomy. In this video we are going to talk about the deaths of low mass stars. And by low mass we mean to start off with stars similar to our Sun. So we will look at what the deaths of those stars are like and then later on we will look at what other stars are actually like. Now we started looking at this previously and in fact some of the things that happened, one of the stages that we see is the planetary nebula phase of a star. And this is something that will happen to stars like our Sun in which the outer layers were ejected out into space. But what we really want to look at now is what happens to the core. Last time we really concentrated on what was happening to the outer layers. Those layers here being expelled out into space as they could no longer be held on by the gravity of the star. However there is also this section at the center that we want to look at. And this is also important in that it is what is left behind. It is essentially the core of the star left behind and we want to see what that is going to be like. So that is what we are going to look at first. And the first thing we want to consider is cores that are less than 1.4 times the mass of the Sun. This is a very important limit that we will see that has to do with the stability of the remnant left behind. Anything more than 1.4 solar masses, something different is going to happen. And we will look at that later on. Now what we find is that this concludes the vast majority of stars in the universe. Meaning that stars with 10 solar masses or less will be able to lose enough material that the remnant left behind will be under this 1.4 solar mass limit. So that includes the vast majority of all of the stars in the universe. So let's look a little bit at what happens here. And first we need to look at what we mean by a degenerate star. And what happens in these cases is that the core contracts until it becomes degenerate. What does this mean? This means that the electrons in the atoms are pushed as close together as is possible. We are getting down to quantum mechanical limits that two electrons simply cannot be in the same place at the same time. And this is often known as what we call the Pauli Exclusion principle, which simply says that two electrons can't be in the same place at the same time. So they have to be in different places so you can only get them so close together. And what we have to realize is that in normal matter, even though we think it seems solid, there is a lot of empty space there. The electrons are nowhere near as close together as they could possibly get. Essentially you can take something the size of the sun and it will compress down to about the size of the earth. Now there's a tremendous difference between those two. So you can really compress out all of that empty space between the atoms. So what we think of as solid material here on earth is really almost all empty space between all the space between the electrons. It is just when you push against something solid that the electrons will then push back because they are both negatively charged and will repel each other. So unless you start to compress things more and more then you won't notice this. And this is what we call degenerate. The density becomes incredibly high a million times the density of water. The density of some of the denser metals is 10, 20 times the density of water. We're up to a million times the density of water. So far denser than anything we can imagine. And what we notice is that once a white dwarf forms, without any external influences, and if it's just there all by itself this white dwarf will remain stable forever.  That is the only change that can occur. So let's look at this limit that we mentioned, and this is called the Chandra Shekhar limit, which tells us how massive that final core can be. The electron pressure, remember those electrons pushing against each other as close as they can possibly be, do have a limit and can support a core up to 1.4 times the mass of the star. So when we look at that how big is what is going to happen here is this is the limit, is this line here, is right at 1.4 times the mass of the sun. Anything larger than that with more mass is going to be able to crush itself in. Crush in upon itself will overcome that electron degeneracy, pushing those electrons in to the nuclei. Now the other thing that we note, this is plotted here, is the radius of the white dwarf versus its mass. And note how the radius, follow the green line here, the radius gets smaller and smaller and smaller as you get more and more mass. So even though a white dwarf can become more massive, it also becomes smaller. So typical solar mass ones might be about the size of the earth, but as you add more and more mass it crushes down close, smaller and smaller. Now if we have a more massive core what is going to happen? Well those ones become unstable, they've exceeded this 1.4 solar mass limit and they will continue to collapse down further and further. No longer can the electrons hold them up if you go just over that 1.4 solar mass limit. So we know of white dwarf stars, how can we actually go about detecting these? How do we know that they exist? Well white dwarf stars, we can actually see many of them visually. And in fact in the image here this is Sirius B, so the bright star Sirius is visible, but also is the white dwarf star right there. So there are some cases where you can actually see them if they're relatively close together. So in this case the brightest star in the sky actually has a companion that has gone through its life and is just a white dwarf star left behind. They've also been detected in binary star systems and binary star systems in some cases we can actually transfer matter from the ordinary star to the white dwarf. So you can have one star, an ordinary star, and you can have the compact white dwarf. If they are close enough together material can be transferred into a disc around the white dwarf and slowly spiral into the white dwarf. And that what we call an accretion disc will actually give off energy. And we will see things like this type of disc in the future as well with even other compact objects. But we can detect the white dwarf even if we cannot see it directly. We can detect its influences gravitationally as the star moves if we can't see the white dwarf. And we can detect emissions from the accretion disc perhaps around the white dwarf. Now what will happen to a white dwarf over time? As I said it's going to remain stable forever. The only thing that can change is that it is slowly going to cool off. And that is because it has no energy source so all it will do is continue to cool. So it'll start off looking a bluish white color and that will slowly fade to a yellowish to an orange to a red and finally to black meaning that it is now emitting most of its light in the infrared portion of the spectrum. Because it is so small it will cool very slowly so this takes a long time. And it will take many billions of years it will now be considered what we call a black dwarf star. It's the same white dwarf star it's just had plenty of time to cool off. This is eventually the fate of almost every star in the universe will become a black dwarf. However because of how long it takes to cool no such stars have ever had time to form in the history of the universe.  However hundreds of billions or a trillion years from now could we come back most of the stars that we see would be these black dwarf stars. So the other question that we might have is can stars really lose enough mass to be able to become white dwarfs? If we think about this for a six solar mass star that means that it needs to lose 4.6 solar masses worth of material in order to become a white dwarf. Otherwise it will be over that 1.4 solar mass limit and it will not be able to become a white dwarf. Electron degeneracy pressure will not be able to hold it up. So it essentially has to lose 75% of its mass. For something like our sun this is no big deal. Our sun is by definition one solar mass so it doesn't have to lose any mass at all. It could keep all of its mass and would still become a white dwarf star. It will lose some as it goes through the planetary nebula phase but here's where we're seeing the issue is when we look at these more massive stars. Is this really possible? Is this something that can happen? And we have evidence from star clusters that says yes this can occur. And that can occur because we have detected white dwarf stars in young clusters. So we can then use the cluster age determination method looking at the turn-off point of those clusters and find out that the only stars that would have had time to evolve were those of six solar masses or more. So while we have not been able to see six solar mass stars become white dwarfs we can infer that because we see white dwarfs in these clusters and the only stars that have been able to evolve have been six solar mass or more that they must be able. There must be methods by which these stars will be able to lose sufficient mass to be able to become a white dwarf. So let's finish up as we do with our summary and what we looked at this time was first of all looking at low mass star as it ages the outer layers are expelled as a planetary nebula and the core contracts to become a white dwarf and that's what we've been looking at a lot of this lecture. The white dwarf is a million times denser than water and is about the size of the earth and it has been compressed down so that the electrons are as close together as they possibly can be. The white dwarf will slowly cool over time to become a black dwarf and this is the eventual fate of essentially almost all stars in the universe anything under 10 solar masses. Now those stars that are over 10 solar masses have some more interesting things that will happen that we will look at later. So that concludes this lecture on the deaths of the low mass stars. 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.


Just about anybody watching this is familiar with Blizzard Entertainment, they're responsible for some of the most memorable games of the past 20 years, from Diablo to StarCraft 2, of course, World of Warcraft, but way back in the early 90s Blizzard Entertainment was just getting started under the name Silicon and Synapse. Under that moniker they developed the thoroughly mediocre R.P.M. racing for Super Nintendo and followed that up with the excellent Rock n' Roll racing. But also in that timeframe came the Lost Vikings, no not those Lost Vikings, don't get me started on those guys. Silicon and Synapse developed two Lost Vikings games for the Super Nintendo and they are the definitive puzzle platformers for the system. They're both two player co-op and a perfect blend of style and substance. Let's start with the first game. The basic premise here is guiding three Vikings to the exit of each level and using each Vikings unique skill to deal with the appropriate enemy and obstacle. The three Vikings are Eric, Baleog, and Olaf. Eric is the fastest and can jump the highest but can't attack.  And Olaf has a shield which can be used for many different things. You only control one Viking at a time, but you flip between them using the L and R buttons and I love the immediacy of that. No cumbersome menu screen or anything, thankfully. There's also items like bombs and health replenishments that each Viking can carry, the latter of which can be pretty important because there's only three hit points here for each character. When one dies, the other two are left to fend for themselves and you won't be able to finish the level. That's kind of a point of frustration, especially since there's jump damage when you fall from certain heights, but there are at least unlimited continues here. You might initially think that it's kind of pointless to continue on with only two characters since you can't complete the level, but it does allow for an opportunity to explore a little bit so you can plan ahead for your next try. But yeah, you have to get all three Vikings to the exit and that's much easier said than done because this game quickly gets pretty challenging and complex, but nothing ever seems impossible. Maybe it's best to just do a walkthrough example of how this game is played. Take this level here, take all three Vikings down the elevator, smash the wall with Eric the speedy guy, that's one of his abilities, then take Baileog and activate the switch behind each barrier with an arrow, then take all three down this elevator and place Olaf in a spot where Eric can use his shield as a platform to go up and grab the key. It's a pretty simple example, but you can see how it can get pretty complex the further you go. Now some of you might think that's kind of tedious, but what really helps spice the game up is the amount of personality they put into this game. From the bizarre locations you explore to the cartoony appearance of the Vikings themselves, to the occasional dialogue you get from the characters and from occasional oddballs you meet here and there. No it's not laugh out loud funny, but it's amusing enough and it helps this game stand out quite a bit from the rest of the Super Nintendo library in terms of presentation. If nothing else the dialogue is a clever way to provide some gameplay exposition without holding your hand. One nitpicky thing I got to point out though, the music in this game is just odd. It's not bad at all, it's just a strange choice, but it at least adds to the game's bizarre cartoony atmosphere. Lost Vikings was originally developed for the Super Nintendo, but later on got ports for everything from the Amiga to Sega Genesis to Game Boy Advance. They're all pretty much the same game, but the Genesis version has 42 levels while the SNES game has 37. Also the Game Boy Advance version has a battery save, if four little passwords bother you for some reason. Now the trouble with most puzzle platformers is that the replay value only extends as far as your memory. Once you know most of the puzzles it makes the game kind of boring to play through again, but thankfully there's a second Lost Vikings game, Lost Vikings 2 that was released late in the SNES life span in February of 1997. The three Vikings are back, but with two new playable characters, Fang the Werewolf who can jump and climb walls and Scorch the Dragon who can fly and use a fireball attack. The Vikings also have updated abilities like how Eric can swim in addition to sprinting and jumping and Bailey Ugg's bionic arm attack, and of course there's 31 all-new puzzles here as well. Lost Vikings 2 does what a sequel to a good game should do. If it ain't broke, don't fix it, and the only real changes here are the additional characters and the fact that a lot of the backgrounds are darker. The user interface hasn't changed and it's still two-player co-op, so there's not much else to add here. If you like the Lost Vikings and just want more levels and more characters with some new abilities then you'll love Lost Vikings 2, and you also have the option to play this one on Sega Saturn, PlayStation, and PC if you'd like, where the game is titled Norse by Norse West. So yeah, the Lost Vikings games are a great time. They're fun and stimulating puzzle platformers that have held up really well over time thanks to the easy to use interface, the quick pace, the puzzle design, and the weird bits of personality you'll find here and there. Both of these games are fantastic.