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Measuring the Properties of Stars Warm Up 1. 2. 3. 4. 5. 6. 7. 8. Where are bright, cool stars located on the HR Diagram? Where are bright, hot stars located on the H-R Diagram? Where are dim, cool stars located on the H-R Diagram? Where are dim, hot stars located on the H-R Diagram? What is the H-R Diagram? What is the H-R Diagram used for? What are the seven spectral classes of stars? What is luminosity? Warm Up 1. 2. 3. 4. 5. What is parallax? What is an arc second? What is a parsec? How long is a parsec? One degree of arc equals the thickness on a penny on its side from how far away? Warm Up-11/04/12 1. 2. 3. The angular shift from January to June of the star Rigel is 0.25 arc seconds. How far away is Rigel in parsecs? How far away is Rigel in light years? The angular shift from January to June of the star Alhambra is 0.345 arc seconds. How far away is Alhambra l in parsecs? How far away is Alhambra in light years? What is a standard candle? Comet ISON Site http://blogs.discovermagazine.com/outthere/ 2013/10/25/novice-observers-guidecomet-ison/ Warm Up 1. 2. 3. 4. 5. 6. Name two ways to determine the distance to a star. Wein’s Law equates temperature with what? What is luminosity? What is apparent brightness? What is magnitude? List the 7 spectral classes and tell which direction stars are getting hotter? Wondering as You Look at the Stars It’s impossible not to wonder as you look at the stars. What would that star look like if you were close to it? How hot is that star? What is that star made of? Yet, scientists have developed ways to answer many of these questions. Kepler gives us star’s masses, Wein’s Law gives us their temperature and Newton gives us spectra which is their chemical composition. How far away is that star? But, one of the most fundamental questions about a star is…how far away is that star? Measuring Distance Astronomers have several methods for estimating a stars distance. Parallax Triangulation Method on standard candles Triangulation Using simple geometry, the distance of stars can be determined given that you know the Parallax Parallax is the change in an object apparent position caused by a change in the observers position. Parallax The shift in stars closer to us is greater than for those far away. Regardless, the amount of shift is very small. Because of this, these shifts are measured in arc seconds which 1/3600th of a degree. Parallax By definition: Dpc = 1/parc seconds Where: D = distance in parsecs P = measure of angular shift in arc seconds One parsec equals 3.26 light-years or 3.09 X 1013 kilometers Parallax A shift of one degree of arc is what you’d see of a penny’s edge from 4 kilometers (2.5 miles) How Far is Sirius? Using the formula: R = p where R = 1 AU 2pd 360 p = in arc seconds P for Sirius is 0.377 arc seconds, so…. How Far is Sirius? d = 360 / 2pp yields d = 360 AU/2p(.377) = Express p in arc seconds and d in parsecs and both cancel, leaving d = 1/p, therefore Sirius is 1/.377 or 2.65 parsecs away. Multiply times 3.26 to convert into light-years. The answer is 8.6 light-years away. Method of Standard Candles Imagine having two 100-watt light bulbs in front of you. One is close and one is far away. You can learn to tell about how far away the distant light is. Indeed, driving at night, you use this to tell how far another car or a traffic light is away. Standard Candle Astronomers use the concept of the standard candle to estimate distance. They assign a given luminosity (or brightness) as a reference. This reference is called a “standard candle”. Measuring Properties of Stars from Their Light: Temperature The temperature of a star is often indicated by its color. Just like you look are a stove eye to determine how hot it is. Measuring Properties of Stars from Their Light: Temperature Wein’s Law states that: T = 3 x 106/lm where T = temperature and lm is the frequency the star radiates at most strongly (in nanometers). Measuring Properties of Stars from Their Light: Temperature So, how hot is Sirius? T = 3 x 106 / lm Given that Sirius radiates most strongly at 300 nanometers (lm) T = 3 x 106 / 300 nm, therefore T = 10,000 K Measuring Properties of Stars from Their Light: Luminosity Luminosity is the amount of energy a star radiates each second. Our Sun has a luminosity of about 4 X 1026 watts. This a star’s luminosity is an indicator of how quickly it is consuming fuel. Astronomers use stars luminosity to determine their distance and radius. The Inverse Square Law and a Star’s Luminosity The inverse square law relates an object’s luminosity to its distance and apparent brightness. Like a shotgun pattern, the farther away from an object the fewer number of photons hit in a particular area. The Inverse Square Law and a Star’s Luminosity Astronomers have determined that the relationship between brightness and distance is an inverse square law: B = L / 4pd2 where B is the apparent brightness, L is luminosity and d is the object’s distance. Measuring Properties of Stars from Their Light: Radius If two stars have the same temperature, but one is more luminous than the other, then the brighter star must have a larger radius. The Stephen-Boltzmann Law The Stephen-Boltzmann Law states that a star’s luminosity equals its surface area times sT4: L = 4pR2sT4 where L=luminosity, R = radius and sT4 is the relationship between temperature and surface area. You increase the temperature or radius and you increase the star’s luminosity. s = 5.6686 x 10- 6 (Watts/meters2Kelvins4). The Stephen-Boltzmann Law So, what is the radius of Sirius? LSun = 4pRs2sTs4 where R and T are LSirius 4pRSr2sTSr4 the Sun and Sirius values respectively. Solved for RSirius (25/1)1/2/(6,000k/10,000k)2 RSirius = 5(0.6)2 RSirius = 1.8 Solar radii Page 359 text What is a Parsec Anyway? By definition, one arc second spans 1 AU at the distance of one parsec. Aah, but I digress… So, back to Hipparcus. He wants to classify stars. The characteristic he decides to use is apparent brightness (or how bright a star looks to you and me). It’s All About Magnitude Hipparcus calls this apparent (or how bright a star appears) brightness, magnitude. It is, with a few changes, the same classification system used today. Magnitude The system does have some problems. First, it’s backwards, meaning that the more positive the number, the fainter the star. So, bright stars are like -1 or -2 and really dim stars are magnitude 10. Our Sun is something whacked like -27 (I think). Magnitude Hipparcus didn’t start out with negative numbers on his scale. He did, however, seriously misjudge how bright the brightest stars actually are. This pushed the scale negative or brighter. Magnitude Here’s the part you’re going to hate. Magnitude differences correspond to brightness ratios. Now, this whole system is based on the first magnitude 1. This is half a ratio. The other half of the ratio is 2.512 (or the fifth root of 100). Magnitude Now naturally your first thought is, hell, why didn’t I think of that. The idea is that a magnitude 1 star is 100 times brighter than a magnitude 6 star, so the 5th root of 100, see? Magnitude So, a magnitude 1 star’s ratio is: 2.5121 = 2.512 : 1 A magnitude 2 star’s is 2.5122 = 6.31 : 1 A magnitude 3 star’s ratio is 2.5123 = 15.85:1 A magnitude 4 star’s ratio is 2.5124 = 39.8:1 Yada, yada, yada… Absolute Magnitude Still, given all this, we’re still comparing apples to oranges. The magnitude of a star is related to its distance away from us. Astronomers needed a better system to level the playing field where stars could be compared directly. Absolute Magnitude A new scale was invented that places stars at a standard distance from us. That distance is 10 parsecs (pc). Absolute magnitude is a true measure of a star’s luminosity. The Dumbing it Down Slide or it Gets Way Too Boring! Now, very quickly. Stars give off light that can be divided into spectra. The spectra indicate a star’s temperature. People have studied these spectra since the early 1800’s. One man, Henry Draper (1870’s) studied the classification of spectra. He died and his wife gave a fortune to Harvard to compile a book of these spectra called the Henry Draper catalog. Remember the HD catalog numbers from the constellations. This is a way to reference the spectra of stars in a constellation. Cool, eh? Oh Boy, A Fine Girl Kissed Me! Star’s fit into one of seven distinct spectral classes. Spectral classes convey information on a star’s composition and temperature. The seven spectral classes are: O, B, A, F, G, K and M. From O to M temperatures decline. Spectral Classes Other mnemonics include: Only Brilliant Artistic Females Generate Killer Mnemonics and my personal favorite: Oh Big And Furry Gorilla, Kill My Roommate. Four other very rare spectral classes exist called R, N, S and W. Can you include them in a mnemonic? Summary of Stellar Properties Quantity Distance Temperature Luminosity Composition Radius Mass Radial Velocity Method Parallax (up to about 250 parsecs Wien’s Law Spectral class (O- M) B = L / 4pd2 Spectral lines Stephen-Boltzmann law Interferometer Eclipsing binaries Kepler’s third law Doppler shift of spectral lines Warm Up 1. 2. 3. 4. 5. 6. 7. 8. Define a parsec. Who had the idea for apparent brightness? What is another name for apparent brightness? Which is brighter, a magnitude 1 star or a magnitude 6 star. How much brighter is a magnitude 3 star than a magnitude 1 star. What number is the base for the magnitude system? (Hint for number 5) What is absolute magnitude? What are the 7 stellar classifications. What do they mean? The Hertzsprung-Russell Diagram While scientists could calculate the mass, temperature, radius, luminosity and other characteristics of stars, they still understood practically nothing about how they worked. This changed in 1912 with the work of Ejnar Herstzsprung and Henry Norris Russell. The H-R Diagram In a nearly simultaneous discovery, both men found that if you plotted stars’ luminosities against their temperatures (or spectral classes) that the vast majority lay on a single line. The H-R Diagram Traditionally, on the H-R diagram, brighter stars appear at the top and hotter stars appear on the left axes. The H-R Diagram This line that most (90%) stars fall on is called the “main sequence”. A minority of stars appear in the upper right-hand and lower lefthand corners. Looking at the H-R diagram brings several questions to mind. How can stars of different temperature have the same magnitude? Conversely, how can stars with the same temperatures have different magnitudes? The answer lies in the Stephan-Boltzmann law. Analyzing The H-R Diagram When you look at the H-R diagram and see for one temperature that luminosities can range from 10-3 to 106, you get some idea of the great variety is the sizes of stars. The Stephen-Boltzmann Law Stephen-Boltzmann (L = 4pR2sT4) relates luminosity with a star’s temperature and radius. So, if two stars, A and B, have the same luminosity , but the temperature of star A is higher, then the radius of star B must be greater. Conversely, if stars A and B have the same luminosity but star A is larger than star B, then star B must have a higher temperature. It’s all about total luminous output. Analyzing The H-R Diagram To produce the same luminosity as very hot, smaller stars, cooler star must be 1000’s of times larger. These stars are termed “giants” and appear at the top of the H-R diagram. Analyzing The H-R Diagram A similar look at the H-R diagram shows that some stars that lie below the main sequence are very hot, but have very small luminosities. These stars by contrast must be very small. They are called “dwarf” stars. Other Differences in Stars Giants, main sequence stars and dwarfs differ in more ways than just temperature and luminosity. They also differ greatly in density. For a given mass, a larger body must have a lower density, so giants have densities millions of times less than main sequence stars. Smaller stars must therefore have much greater densities than main sequence stars. Other Relationships Revealed by the H-R Diagram The H-R diagram reveals relationships between stars other than just temperature and luminosity. It also reveals the stars’ radii and masses as well. The Luminosity-Radius Relation I relationship can be inferred by the H-R diagram between the luminosity of a star and its radius. The greater the star’s luminosity the greater the star’s radius, The Luminosity-Radius Relation The Mass-Luminosity Relationship Luminosity vs. mass is plotted for the Sun and all Main Sequence stars that have good mass measurements shows that a Main Sequence star's luminosity is very strongly correlated with its mass: The masses are written in terms of solar masses. The relationship is defined as: L = M3, where L= luminosity in solar units and M= solar masses. Summary of the H-R Diagram It offers a simple, pictorial summary of stellar properties. Most stars lie on the main sequence with the hotter stars being more luminous. Blue stars are hottest while red stars are the coolest A star’s mass determines its location along the main sequence with more massive stars located at the top. Stars masses range from about 30 solar masses to about 0.1 solar masses. It shows that stars fall within three main regions of the diagram: main sequence, giants and white dwarves. Variable Stars Not all stars have constant luminosity. Some stars, called variable stars, change brightness over time. The time between the intervals of maximum brightness is called the star’s period. The graph of the star’s brightening and darkening cycle is called its light curve. The Instability Strip Variable stars cluster together in the H-R diagram in a region known as the instability strip. Analyzing The H-R Diagram The H-R diagram shows the evolution of stars. In the next section, we will explore how and why stars evolve.