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Download Lecture Ten - The Sun Amongst the Stars Part II
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Last time we talked about telescopes, and the advantages to be gained by making them very large: 1. More light-collecting area, which lets us see fainter objects. Chandra X-ray Observatory 2. Greater angular resolution, which lets us see objects in greater detail. Hubble Space Telescope We finished noted the benefits of being above the atmosphere: the availability of light which doesn’t reach the Earth’s surface, the freedom from weather and light pollution, and the complete lack of distortive effects from the Earth’s turbulent atmosphere. 1 But the costs, we noted, are quite high. The 6.5m James Webb Space Telescope, scheduled for launch in 2018, will have cost almost 9 billion dollars – far more than the 1-2 billion dollars it would cost to build a 100m telescope on the ground! We also discussed what we can observe from stars – Apparent Brightness, Position and Motion, Colors (in all kinds of light), and Absorption and Emission Lines – and how to use that information to learn other things we want to know about stars like their Luminosity, Distance, Temperature, Radius, Mass, and Age. 2 How do we go from that first list to the second? Distance by measuring the star’s parallax; by knowing the luminosity and measuring apparent brightness (standard candle method). Luminosity by knowing the distance and measuring apparent brightness. Apparent Brightness = L / 4d2 Temperature, we noted, could be estimated in a relative way by the visual colors of stars. Redder stars have colder atmospheres while bluer stars have hotter atmospheres. 3 But a far better approach is to use the spectral type of a star – what patterns of absorption lines appear in light coming from the star. Those patterns do tell us something about the elements in a star’s atmosphere, but that’s not as important as you might think. As it turns out, all stars are made primarily of Hydrogen & Helium, with only very minor differences (<1%) in the amounts of other elements they possess. 4 The differences in spectral types are actually caused by differences in the temperature of the atmospheres of different types of stars – spectral type tells you temperature. O B A F G K M (L,T) 50,000 K 3,000 K Temperature Sirius Spectral Type A Alpha Centauri Spectral Type G (so is our Sun!) Proxima Centauri Spectral Type M A star’s temperature sets which types of ions or molecules can exist in its atmosphere, and the energy states of the electrons and atoms in those ions and molecules. These energy states dictate how the ions and molecules interact with light, and the number and the relative ‘darkness’ of the absorption lines in the star’s spectrum. 5 O-type stars have very few lines because they are so hot that most of their elements have been stripped of electrons – while in cooler, M-type stars, far more atoms retain their electrons. Patterns of absorption lines can reveal the temperatures of the stars to a precision within 50 degrees K – a factor of 10 better than what can be done by looking at “colors” alone. Ok, that’s distance, luminosity, and temperature – what about mass? That can only be measured directly by observing the effect that gravity has on the star. This is most easily done in binary star systems, in which two stars orbit each other. Newton’s version of Kepler’s laws can then tell you the masses of each. 6 Sample of multiple star systems from Stassun, 2012. Fortunately such systems tend to be quite common – almost half of all stars like the Sun are in multiple star systems! Putting It All Together – the Hertzsprung-Russell Diagram This plot, first developed in 1910, turns out to be very useful for understanding stars. It shows two major physical properties: Temperature (x) and Luminosity (y) -- or to put it another way -- Spectral Type (x) and “Absolute Brightness” (y) bright MV faint hot Spectral type cool 7 BRIGHT H-R Diagrams – and the many patterns of stars seen it – reveal a great deal about how stars work. HOT COOL FAINT O B A F G K M Perhaps the most obvious feature in an H-R diagram is the Main Sequence (MS). Over 90% of all stars lie on the MS, which suggests that most stars spend most of their lives generating their luminosity in a similar, temperature dependent manner. O B A F G K M 8 The importance of the Main Sequence is hard to overstate, and we’ll be back to it soon – but there’s something else going on here too. Notice that many stars have the same temperature, but vastly different luminosities. How can that be? O B A F G K M Well, the luminosity of a star depends primarily on its surface temperature – at a fixed size, hotter is brighter. 9 But a star’s luminosity also depends on its surface area (and therefore its radius) – at a fixed temperature, a bigger star is brighter than a smaller star. So if the temperature of two stars is the same, but they have different luminosities, then those stars must have different sizes. L = 4πR2σT4 If we know the luminosity and the temperature of a star (which we must if we can put it on an H-R diagram!), we can estimate its radius by assuming that luminosity is based on the star’s temperature and using well-known laws of thermal radiation. Mind you – the uncertainties can be high, especially if the temperature is poorly constrained! 10 Low T, High L = BIG High T, Low L = SMALL O B A F G K M But there’s one more point that needs to be made before we press on, because an H-R diagram like this one disguises another key characteristic of the stars in our galaxy… From this figure, what would you guess is the most common type of MS star? O B A F G K M 11 Proper counting reveals that over half of all stars are M dwarfs! A more revealing look at the HR Diagram! 12 Think about what this means – remember this map of the nearby universe? That closest star – Proxima Centauri – is a spectral type M, main sequence star, and you can’t see it with your naked eye! Such dim red stars represent the overwhelming majority of stars in our galaxy, yet even the nearest is completely invisible to you! That dimness is why they do not appear clearly on many HR diagrams. So why are there so many M dwarfs? Does the star formation process strongly favor the production of such stars? Or is there some other process at work ‘removing’ hotter and more luminous stars from the populations we observe? The answer requires us to know how stars change over time, and therefore the ages of different stars – but this is by no means easy. All stars “live” a very long time (billions of years in most cases!), and their observed properties generally do not change significantly on human timescales – so it’s not possible to watch any one star “age” in any meaningful way. 13 To uncover how stars are changing during their ‘lives’, we study large populations of stars and perform ‘demographic’ studies of those populations. With large enough samples, we can be confident we’re seeing both young and old stars – and then work to find a way to determine which is which! Just as in human demographics, this can be simplified by studying unique, isolated populations – which yield insights into both the similarities and differences that can occur in populations. Fortunately, nature provides these specialized groups to astronomers in the form of star clusters. 14 There are two types of these clusters: “Open Clusters”… • Hundreds to thousands of stars • irregular shapes • gas and dust is sometimes seen amongst the stars in the cluster Pleaides 15 … and “Globular Clusters” • 105 stars or more • pronounced spherical shape • very little gas or dust seen between stars M80 16 Omega Centauri 47 Tucanae Both types of cluster are very useful for studying stellar properties! ~ 30,000 light-years ~ 48 light-years Since all the stars in the cluster are at (roughly) the same distance from us, we can compare their apparent brightnesses to each other as though they were true luminosities. This allows us to plot a reliable H-R diagram of the cluster, knowing that the brighter stars in the cluster really are brighter, and not just closer to us! 17 Further, since all the stars in a cluster form within ~ 100 million years of each other, they are very approximately the same age, at least in stellar terms. So our H-R diagram of a cluster is a “snapshot” of what a group of stars – all of very nearly the same age – look like. Open Cluster H-R Diagram – the Pleiades Globular Cluster H-R Diagram – Palomar 3 In general, the H-R Diagrams of globular and open clusters are very different from each other – suggesting very different ages. Where are the bright B and A-type main sequence stars in the Globular Cluster on the right? 18 The key to this agerelated difference is found in another trend seen amongst stars in our H-R diagrams – the mass-luminosity relationship. Brighter main sequence stars are much, much more massive than the less luminous stars on the main sequence. The mass-luminosity relationship for main sequence stars. The reason behind this relationship between mass and luminosity in stars first began to become clear in the early 20 th century, when physicists like Einstein revealed that atoms possess a type of potential energy based only on how massive they are. This mass energy can be changed by altering the atom’s mass, via the processes of fission and fusion. Fission – Heavier element split into multiple lighter elements. 19 Fusion – Lighter elements merge to form a heavier element. Note that the atoms that go into either of these reactions will not have the same overall mass energy as the atoms that come out – depending on which types of atoms go into the process, the new atoms produced can have less mass energy, or more. This means either fusion or fission can require energy to be put in (because you’re adding mass)… …or can possibly give “energy out” (if you’re losing mass). 20 In the early 1920’s, it was suggested that deep in a star’s core, 4 H nuclei could be forced to fuse into 1 He nucleus via a process called the proton-proton chain. This natural process generates energy because the He nucleus has less mass than the 4 H nuclei – that ‘lost’ mass energy is converted primarily into high-energy photons and tiny particles called neutrinos which stream away from the star’s core. The process in a bit more gory detail. There are actually a few more subtleties to this that are far beyond the scope of this course! 21 Fortunately, only a small amount of mass is transformed into energy – and the Sun is crazy huge! Despite ‘losing’ over 4 million tons of mass per second, every second for over 5 billion years, the Sun has still only used up less than 0.1% of its total mass. For a star of the Sun’s mass, this process provides enough energy to keep it stable and shining for a total of 10 billion years. 22