hello and welcome to general astronomy lecture 23 stellar classification and the HR diagram now if you recall from our last lecture we discussed how color and temperature are related here we're going to shift our focus to how spectral types and temperature are related now keep in mind that we discussed spectrum of light in our light lectures so make sure you have covered that before you get into the stuff because we'll be talking a lot about Spectras coming from stars now so just keep that mind as we move forward we see an absorption line spectrum when a cool gas lies between us and a hot glowing object as we've discussed in our light lectures the light from the hot glowing object itself has a continuous spectrum in the case of a star light with a continuous spectrum is produced at low lying levels of the star's atmosphere where the gases are hot and dense the absorption lines are created when this light flows outward through the upper layers of the stars atmosphere atoms and these cooler less dense layers absorb radiation at specific wavelengths which depends on the specific kinds of atoms present that being may be hydrogen helium or other elements and on whether or not the atoms are ionized a star's spectral line lines provide a second way to measure a star's surface temperature in fact because interstellar dust can often affect the apparent colors of stars temperatures determined from spectral lines are generally more accurate than temperatures determined from colors alone stars displaying spectral lines of highly ionized elements must be fairly hot because takes a high temperature to ionize atoms stars displaying spectral lines of molecules must be relatively cool because molecules break apart into Vitt into individual atoms unless they are at relatively cool temperatures the types of spectral lines present in the star spectrum therefore provide a direct measurement of the Stars surface temperature astronomers classify stars according to surface temperature by assigning a spectral type determined from the spectrum lines present in the star spectrum the hottest stars with the bluest colors are called spectral type Type O followed an order of declining surface temperature by BA FG K and M each spectral type is subdivided into numbered subcategories such as B 0 B 1 and so on through B 9 the larger the number the cooler the star for example the Sun is designated as a spectral type G 2 which means it is slightly hotter than a G 3 star but cooler than a G 1 the traditional mnemonic for remembering this sequence Oba FG km is o be a fine girl or guy kiss me so just a way to memorize it now this is very important you're going to see this classification showing up a lot through the rest of our class so again make sure you try to understand this classification we're o-type stars are the hottest and the more blue and you know down the spectrum M is typically the reddest and B coolest and the numbers in between don't matter a lot but you will see them coming up again and again so keep in mind that each category of these letters has its own number associated with it too so this table here summarizes a lot of different properties based on these spectral types so here you see the spectral types again OB a FG km on the left it gives you an example star of such a star let's in that classification category and then it shows you the ranges of temperatures what kind of features you might see in the spectrum and then its brightest wavelength and hence what its color would likely be and you can actually see an actual spectrum of stars of these types so notice when it's a cool star remember we said that cool stars probably show lots of molecules because it's cool enough that they don't break apart and that's what you're seeing here you see lots of these darker bands on the right showing molecules so this is just a useful table to come back to for reference again like with every table I'm not going to sit here and go through everything but it's a great reference for you if you ever need to find some general information about these different spectral types and again just notice the main trend here that as you go from m2 oh you're going from cooler to hotter stars and also from red to blue stars now recall that this figure here shows representative spectra of cell of several spectral types so we have the spectral types again on the right now OB AF g/km with the numbers to the strengths of the spectral lines change gradually from one spectral type to the next stars displaying spectral lines of highly ionized elements must be fairly hot because it takes a high temperature to ionize them and again we've mentioned this already but stars displaying spectral lines molecules must be relatively cool because molecules break apart into it into individual atoms so I'm saying this again because it's important now that we have this image up the range of surface temperature temperatures for stars is much narrower than the range of luminosities the coolest stars of spectral type M have temperatures as low as 3,000 degrees Kelvin or as the hottest of spectral type o have temperatures of about 40,000 degrees Kelvin cool red stars by the way as we learned again last time are much more common than hot blue stars so this is just another great reference it shows you a graphical representation of these different spectral types their temperatures and what kind of elements or molecules you might find in such a spectrum and notice that it gradually changes from one to the next so again I'm not going to spend a lot of time going through this just know that it's really important and if you want to learn more about it you can do that outside of the class just look up about spectral types it's a huge branch of astronomy and again notice that for the hottest stars you see really strong bands of different types of hydrogen so these are ionized gases and again you need really hot temperatures for these gases to show up whereas again for the cool temperatures you have lots of molecules like titanium oxide and things like that so just some important properties to keep in mind now I'm going to take this pretty much the same exact graph or table that you see here and we're going to put it into a graph so what I'm going to show you that this next slide looks very confusing but it's pretty much the exact same thing so let's see if we can draw - this graph shows similar results to that of the previous slide here each curve is in this graph peaks at the surface at the stellar surface temperature for which chemicals absorption lines are the strongest notice how the Balmer lines of hydrogen that is hydrogen alpha or is this o hydrogen alpha hydrogen beta gamma and Delta are strongest for hot stars of spectral Class A so you have hydrogen here and their strongest for spectral type a while absorption lines due to calcium that is C a which is over here is strongest in cooler K and M stars the spectral type M also has broad dark bands caused by molecules of titanium oxide which you see here is T IO which can only exist at relatively low temperatures when the effects of temperature are accounted for astronomers find that all stars have essentially the same chemical composition so we can state the rule the results as a general rule by mass almost all stars are about three-quarters hydrogen one quarter helium and 1% or less metals our Sun is no exception it is about 75 percent hydrogen with the remainder consisting mostly of helium and about 1.7 percent heavier elements while the composition of most stars is similar their size and temperature can be quite different so this again is just a graph showing you you know you'll see hydrogen lines for a-type stars so let's go back and look at that do we see that happening well here's an a-type star and look you have very strong hydrogen lines and if you look for m-type stars you see a strong titanium oxide so you go back use titanium oxide showing up in the m-type stars in fact you see some more down here so it's just another way to view this these spectra so these are basically the same things to show in different ways so we mentioned that okay although compositions are the same well temperature in size varies greatly so let's dig into that a little bit before we put it all together to determine the size of a star astronomers combine information about its luminosity which you can determine from its distance and apparent brightness and its surface temperature using the following formula L is equal to 4 PI R squared Sigma T to the fourth where L is the luminosity in watts R as the Stars radius and meters Sigma is just a number it's a constant you don't have to even memorize it you know anything like that it's just a number that you plug in and T is of course the surface temperature although this equation is a little bit longer than most it's still quite simple it's basically just saying that we can figure out the size of the star say the radius if we just know its luminosity and its temperature that's all so this equation says that a relatively cool star that is a low surface temperature T so if you have a small number for T here well it can nonetheless be very luminous if it has a large enough radius right so just because it's a cold star doesn't mean it's going to have a low luminosity you can have a cool star but have a really big radius here to overcome that and so that means you can still have a considerate luminosity or considerable luminosity and of course the opposite is true so alternatively a relatively hot star which means a large temperature T here can have a very low luminosity if the star happens to be very small so small R here so we can express the idea behind these calculations in terms of the following general rules and these are important first we can determine the radius of a star from its luminosity and surface temperature second for a given luminosity the greater the temperature the smaller the radius must be for a given surface temperature the greater the luminosity the larger the radius so these things are very important so be careful it is a no another equation I know a lot of people don't like to have the mathematics injected into these things but there's some equations that I just can't ignore in our course so just be careful and do your best to understand this and follow along with it so here we have a summary of how astronomers determine the properties of relatively nearby stars purple boxes in the case our measurements that need to be made blue denotes calculations and green shows the inferred properties of the stars so this is just a flow chart showing you how you might determine some property of a star so maybe we want to figure out what the composition of some random stars well if we want to get the chemical composition we just need to look at its spectrum but let's make it more complicated let's say we want to know let's say we want to know the luminosity of the star well here's the luminosity well we get the luminosity from this equation but to do that we need to know both the distance D over here and the apparent brightness so you have to figure out the distance first and the apparent brightness before you can together use them to get the luminosity so this just shows you a nice little flow chart on how to get from one thing to the next I think it's a great way to summarize our results and in fact you'll see this come back at the end of this lecture with a few more parts to it as we learn more now we get to the most important thing in quite some time to me this is the most important diagram that we have in astronomy but that's just because I mean I might have a personal bias because I love stellar astronomy and studying the lives of stars this is what we call the HR diagram or hertzsprung-russell diagram you might get sick of these because we're going to see them a lot and you're going to have lots of questions and problems dealing with these things if you're in my class but it's so important because it basically takes every property of a star and then somehow manages to put it all on the same graph and somehow without it being incredibly confusing as well so we're going to spend most of the rest of this lecture now just discussing these diagrams and seeing how they work and why they're so important we have seen that stars come in a wide variety of luminosities surface temperatures sizes and masses but are these characteristics randomly distributed among the stars or can we find patterns that might tell us something about stellar lives the key that finally unlocked the secrets of stars was the development of an appropriate classification system Danish astronomer Anjar hertzsprung and American astronomer Henry Norris Russell relationships between these properties in the first decade of the 20th century building on the work of any job Canon and others hertzsprung and Russell independently decided to make graphs of stellar properties by plotting their luminosities on one axis and spectral types on the other these graphs revealed previously unsuspected patterns among the properties of stars and ultimately unlocked the secrets of stellar life cycles graphs of the type made by Hertz Fung and Russell are now now called hertzsprung-russell diagram or HR diagrams these diagrams quickly became one of the most important tools in the astronomical research and they remain central to the study of stars today the horizontal axis so take a look at the graph on the right the horizontal axis represents stellar surface temperature and/or spectral type note that the two come hand-in-hand so cool stars are m-type stars hot stars are o-type stars so the x axis here represents temperature and spectral type temperature decreases from left to right because hertz plug and rustle based their diagrams on the spectral sequence obas g/km the vertical axis in this case represents stellar luminosity and/or absolute magnitude stellar luminosities span a wide range so we keep the graph compact by making each tick mark represent the luminosity ten times as large as that of the prior tick mark each location on the diagram represents a unique combination of spectral type and luminosity for example the dot representing the Sun corresponds to the sun's spectral type g2 so if you follow it down it appears as a g2 Staller and this luminosity is 1 times that of the Sun so if we put this dot here we immediately know even if it's not the Sun we know it has the same brightness of the Sun and the same spectral type as the Sun so now we can start to plot other stars on here and see what happens because luminosity increases upward on the diagram and surface temperature increases leftward stars near the upper-left or hot lumen and so on and so forth all right so we're going to start to piece together what a fold hertzsprung-russell diagram looks like this is not the whole thing I'm just showing you it piece by piece in fact you can even see like a little arrow down here because I've cut this into pieces so we're going to slowly put this thing together because I figure that if I give you the whole thing at once it might be a little overbearing so we're going to start just piece by piece so this band here that you see stretching diagonally it happens to include about 90 percent of all of the stars in the night sky this band called the main-sequence extends from the hot luminous blue stars in the upper left corner of the diagram to the cool dim red stars in the lower right corner a star whose properties place it in this region of an HR diagram is therefore known as a main-sequence star something you're going to hear a lot main-sequence stars are defined by gaining their energy through conversion of hydrogen to helium in their cores in other words if there's nuclear Fermo nuclear fusion in the core it is a main-sequence star that is hydrogen to helium in the core so these are our main sequence stars that is the first portion but there's more the upper right side of the HR diagram shows a second major grouping of datapoints stars represented by these points are both luminous and cool right so they're pretty bright and luminous because they're up here toward the top but they're relatively cool ke and m-type stars from the stefan-boltzmann law we know that a cool star radiates much less light per unit surface area than a hot star in order for these stars to be as luminous as they are they must be huge and so we call them Giants Giants are about 10 to 100 times larger than the Sun most giant stars are about 100 to 1000 times more luminous than the Sun and have surface temperatures of about 3000 to 6000 degrees Kelvin cooler members of this class of stars those with temperatures of about 3 to 4 thousand degrees Kelvin are often called red giants because they appear reddish in color so we have Giants as the main category but typically we call them red giants if they happen to be toward the right a little bit more well that's the second category there's still more next are these super Giants a few rare stars in the night sky are considerably brighter and bigger than typical red giants with radii up to a thousand times that of the Sun appropriately enough these super luminous stars are called super Giants together Giants and supergiant's make up only about 1% of stars in the night sky or in the sky in general so it just so happens that these bigger stars happen to be much more rare and we'll get to that more soon we still have one main category to look at and that is the white dwarfs the remaining 9% of stars in the HR diagram form a distinct grouping of data points toward the lower left corner although these stars are very hot their luminosities are quite low and hence they must be very small in fact most of them are roughly earth sized they are appropriately called white dwarfs as we will soon learn no Thuan thermonuclear reactions take place within white dwarf stars rather like embers left over from a fire they are still glowing remnants of what were once giant stars so what I'm showing you here is actually surprisingly important and you might not seem like it right now but where I basically just stepped through the entire life of a star with you stars begin on the main sequence they turn into Giants or super Giants and then they become white dwarfs these are all things we'll see very soon so here is my goodness a full HR diagram with even more information than I've showed you this is to me one of the most beautiful things I've seen and it sounds crazy because it's just a graph and a lot of people don't really care but there's so many things on this graph with so much information that it's really hard to believe so the existence of fundamentally different types of stars is the first important lesson to come from the HR diagram and later lectures we will find that these different types represent various stages in the lives of stars as I got out of myself and just mentioned for example stars can move through the HR diagram as they leave the main sequence and become red giants we will use the HR diagram as an essential tool for understand how stars evolves and again you're going to see this thing pretty much through the rest of our course now the HR diagram also provides direct information about stellar radii because a star's luminosity depends on both its surface temperature and its radius if two stars have the same surface temperature one can be more luminous than the other only if it is larger in size stellar radii therefore must increase as we go from the high temperature low luminosity corner in the lower left to the low temperature high luminosity corner in the upper right so these diagonal lines are showing you the radius of stars so radius increases you move as you move from bottom left to top right which makes sense you're going from dwarfs up to Giants and supergiant's alright let's do a quick concept check Betelgeuse and Barnard's star which are both pointed to here in the diagram with orange arrows are both in the red portion of the HR diagram what can you deduce about the relative sizes so they're both in the red portion right but one is much more luminous than the other so what can you say about the sizes take a moment to think about it and pause the video and return when you're ready well they are the same color the same spectral type but Betelgeuse is much more luminous so if there's the same temperature but one is far more luminous that means it must be bigger and because of what we saw in the previous slide we know radius increases as they move toward the top right so not only because we know it has to be bigger because of its luminosity but we also know that I mean radius increases as you move up and right so what can we say about their relative sizes well Betelgeuse is much more luminous than Barnard star since they have the same temperature Betelgeuse must be much larger so that it can emit that bigger luminosity speaking of luminosities there is something in addition to spectral types that is important in classifying stars and that is a luminosity class in addition to the four major groups that we've just listed that is the main sequence stars giants super dry and white dwarfs some stars fall into in between categories for more precise work astronomers therefore assign each star to a luminosity class designated with a Roman numeral from I to V the lumen the luminosity class describes the region of the HR diagram in which the star falls thus despite the name a star's luminosity class is more closely related to its size than to its luminosity the basic luminosity classes are one for supergiant's three for giants and five for main-sequence stars luminous luminosity classes two and four are intermediate to the others for example we want to luminosity class four represent stars with radii larger than those of main sequence stars but not quite large enough for them to quantify as giants so we call them some Giants so not only do we have a spectral type now for every single star but we also have a luminosity class so I think I'll get into this in just a second yeah I will so I'll wait for the next slide so now we have a complete way to classify stars we can describe two different ways of categorizing them first a star's spectral type designated by one of the letters OB AF g/km tells us about the surface temperature in color again o type of the hottest and bluest world whereas M types are the coolest and reddest but we also have now the star's luminosity class designated by Roman numerals which is based on luminosity and also tell us about the Stars radius luminosity class one stars have the largest radius with radii decreasing as you go down to luminosity class five we use both spectral type and luminosity class to fully classify a star for example the complete classification of our Sun is G to V G to is the spectral type which means that it's yellowish white in color so here we are here's our Sun it's a spectral type G to its yellowish white in color and the luminosity class here it is is along the V class means that it is a main-sequence star and that fusing hydrogen into helium in its core so it also tells us about that so that is our complete classification not just g2 not just V but g2 V and let's do a couple more examples we can actually go back for a second here Betelgeuse is an M 2 star all right so here's M here's Betelgeuse it's an M 2 star making it a red supergiant Proxima Centauri happens to be a M 5 V Star and similar in color and surface temperature to Betelgeuse but far dimmer because of its much smaller size similarly a description of Aldebaran is that on here yeah here's Aldebaran right here is a k5 3 star so at k5 so here we are in the middle of the k's and it's a 3 star so let's go to our luminosity class that means it's a giant so in this case we have an orange giant star so it tells us that it's a giant with the luminosity of around 370 luminosities of the sun and the surface temperature of about 4000 degrees so you're going to need some practice with those I'm sure it took me a while to learn all these classification schemes and look at these graphs to make any kind of detailed discussion based on them but you know it's really important so your book if you have it will help you explain these things a little bit more but of course if you ever have questions let me know so this can now take us to spectroscopic parallax so I told you will see this flow chart again well here it is a star as spectral type and luminosity class combined with the information on the HR diagram enable astronomers to estimate the stars distance from Earth this method for determining distance in which the luminosity of a star is found using spectroscopy is called spectroscopic parallax spectroscopic parallax is an incredibly powerful technique no matter how remote the star is this technique allows astronomers to determine its distance provided only that it's spectrum and apparent brightness can be measured and both of those are pretty easy to get relatively speaking if a star is too far away its parallax angle is too small to allow a direct determination of its distance this flow chart shows how astronomers deduce the properties of such a distant star note that the HR diagram plays a central role in determining a star's luminosity from its spectral type in luminosity class so here's a new updated flow charts with lots of different properties now so if we did want to find the distance to the star we have to measure two things the apparent brightness and the spectrum from there it's just determining properties to get us there so we plug in our brightness B and we can use our spectrum to get the luminosity class based on the HR diagram to pull out a luminosity and plug in so then we can solve for the distance so there's a lot of things now that are connected and going on and there's lots of things that could be good getting confusion confusing in fact my words are confused because I'm getting excited about this stuff I really love talking about this so this is a great flow chart and a way for you to help reference maybe you know if I work I don't know if it'll happen but if I ever gave you a problem that said find the distance of this star well now you have a way to kind of find it that might be easier than going through the entire lecture again so keep that in mind let's do a concept check so how does a k5v star compared to a k52 star in terms of temperature luminosity and radius so take a few moments to pause the video and think about this and return when you are ready all right well main sequence stars are alumina Khalu Manasi Class V whereas Lumina clock oh my gum luminosity class two stars are giants so right away just because one is a V and one is a two we know that one's a main-sequence and the other is a giant and this is in this instance we know that the two stars have the same temperature because they're both K 5 right K 5 is the same as saying what the temperature is so they do have the same temperatures so that crosses out our temperature question what about luminosity well luminosity class 2 is a star that has a bigger radius because we're moving to the upper right and a greater luminosity than the main-sequence star so the k5 tells us that the temperatures are the same but the V versus the two tells us that the k52 star is both larger and more luminous so these kinds of questions are incredibly important and you'll get them if you're in my class again quite sure of it all right let's look at one more property of the stars before we finish our lecture on the nature of stars and then go into the lives of these stars well we've talked about a lot of different properties of stars but we've been leaving one out for a pretty good reason we now know something about the sizes temperatures and luminosities and stars to complete our picture of the physical properties of stars we need to know their masses mass is generally more difficult to measure than surface temperature or luminosity fortunately for astronomers about half of all of the visible stars in the night sky are not isolated individuals instead they are multiple star systems in which two or more stars orbit each other by carefully observing the motions of these stars astronomers can glean important information about their masses binary stars or binaries are pairs of stars that actually orbit each other they orbit each other because of their mutual gravitational attraction and their orbital motions obey Kepler's third law as formulated by Newton this law can be written as follows the mass of one star plus the mass of the other together equals a cubed over P squared now if you remember way back when we talked about Kepler's law we saw the equation P squared is equal to a cubed these are very much related so m1 and m2 again are the masses of the two stars in solar masses a is the semi-major axis of one of the stars orbits around the other in astronomical units and P is the orbital period in years in other words in order to figure out the masses of the system all we need to know is the orbital period and the distance separating the two stars so that's very important but figure out the masses of each one individually is a bit more tough so for main sequence stars there is a direct correlation between mass and luminosity and this is again very very important the more massive a main-sequence star the more luminous it is the figure here depicts this mass luminosity relationship as a graph the greater the mass of a main-sequence star the greater its luminosity its temperature and its radius so basically mass governs everything so just because we have a bigger mass we have something that's more luminous it has a higher temperature and it has more in size and this is a great relationship so everything is related and it's so important and in fact we're going to get to one more thing and I'm going to go back as several sides to show this mass also determines the age of a star and you're going to hear about this a lot soon but you'll notice in this giant graph it also shows the lifetime in green and notice that as you go toward more massive stars on the main sequence the age is getting lower and lower so the more mass of the star the shorter its lifetime so mass governs all of these properties and we'll start to learn about how this comes to be so I'll leave you then in this lecture with a summary slide here my goodness I'm not going to read all of this but it's a summary of everything we basically just talked about I really do recommend reading through it and referencing it if you need it so this was our lecture on the nature of stars and then how to classify them so there's a lot of important information here again and a lot of it is interconnected so be careful as you work through this stuff and as always ask questions if you need it even if you're not in my class I absolutely welcome you to leave some comments or to message me directly if you have questions or comments about the videos so as always thanks for watching and now we get to talk about the lives of stars and this is my favorite part of the course so I can't wait to show you take care guys