LAB Stellar lifetimes(1)

PURPOSE: This exercise will continue with the techniques used by astronomers to determine the fundamental properties of stars. In this exercise we will use these techniques to study the lifetimes of stars, as well as the characteristics of star clusters. You will also gain experience in  Using models such as a color-magnitude diagram (CMD) for classification of stars.  Identifying the characteristics of main sequence stars, including surface temperature, luminosity, and age.  Determining the age of a star cluster and comparative distances of two star clusters. Rake a look at the following HR diagram [from http://imagine.gsfc.nasa.gov/docs/science/know_l2/stars.html ] What is the spectral type for the main sequence stars that have the largest “fuel tanks”? a. O What is the spectral type for the main sequence stars that have the smallest “fuel tanks”? a. M Which main sequence stars do you think will have the longest lifetimes? M Shortest? O Why? The star burns more fuel the higher its brightness. A star that burns up its fuel more quickly than one that is not as hot will be a 0 type star for the least period of time during its lifetime. As a star converts hydrogen into helium in its core, energy is created. The energy leaving the star is (essentially) equivalent to the energy made in its core. Draw a graph that shows qualitatively how the amount of hydrogen in the core of a star changes over time. The x-axis will be time; the y-axis will be fraction of H nuclei in the core. Assume this starts at 100% Page 1 STELLAR LIFETIMES

What could we observe to find out how quickly the fuel is used up in the core? (remember: The energy LEAVING the star is the same as the energy being created INSIDE the star). a. the star’s size b. the star’s temperature c. the star’s luminosity d. the star’s parallax e. the star’s apparent magnitude Explain your reasoning: a. Luminosity measures the amount of energy that is emitted by a star What is the luminosity of a typical O-type main sequence star in solar luminosity units? a. 10^4 What is the luminosity of a sun-like star? a. 1 What is the luminosity of a typical M-type main sequence star? a. 10^2-10^4 Which statement is true? a. the lowest mass stars use fuel very slowly b. the lowest mass stars use fuel very quickly c. the highest mass stars use fuel very slowly d. high and low-mass stars use fuel at the same rate Explain: Compared to huge mass stars, which burn at temperatures hundreds of times higher than those of lower mass stars, lower mass stars are more "fuel efficient" since they burn at a considerably lower temperature. RELATING LUMINOSITY TO MILEAGE: Stars, like cars, have a given fuel capacity. For a star, this capacity is determined by the laws of physics. There is a certain region in the core of a star where conditions are such that hydrogen fusion can Page 2 STELLAR LIFETIMES

A star that has 10x the mass of the Sun has a luminosity that is about 2000x that of the Sun. Compared to the Sun, its expected LIFETIME would be approximately THE AMOUNT OF FUEL IT HAS divided by THE RATE AT WHICH IT USES UP THAT FUEL. In this example, the lifetime would be (10x the Sun’s fuel)/(2000x the Sun’s luminosity). This gives you a value of approximately 1/200 th the lifetime of the Sun. How much more massive are the highest mass stars than the lowest mass stars? (Hint: determine M highmass /M lowmass ) 720:1 How much more LUMINOUS are the highest mass stars than the lowest mass stars? (Hint: Determine L highmass /L lowmass ) 10^4:10^-4 FILL IN THE BLANKS USING THE NUMBERS YOU COMPUTED ABOVE: High mass stars have 720 times the amount of fuel as low mass stars, and they use up their fuel 10^8 times faster than low-mass stars. Therefore the lifetimes of high-mass stars should be about 720/10^8 times the lifetimes of low-mass stars. THE GORY DETAILS It turns out that a more precise relationship between a star’s mass and its main sequence lifetime is: Lifetime = 10,000,000,000/M 2.5 The Sun’s mass is, by definition, 1 solar mass, so the Sun’s main-sequence life expectancy is 10 billion years (10,000,000,000). It is approximately half way through its life at this point. What would be the main sequence lifetime for a star 10x as massive as the Sun? a. 31,622,776.6 million years What would be the main sequence lifetime for a star 1/2 as massive as the Sun? a. 5.7 x 10^10 years What is the correct order of spectral types based on LONGEST to SHORTEST main sequence lifetime? a. MKGFABO USING MAIN SEQUENCE “TURNOFF” POINTS OF STAR CLUSTERS TO DETERMINE AGES Page 4 STELLAR LIFETIMES

On the HR Diagram below, indicate with an S which main sequence stars will have the shortest lifetimes and with an L which will have the longest. If all the stars on the main sequence were formed at the same time, which spectral type would be the first to leave the main sequence? a. Class O Explain: They lose mass the quickest because they are the most luminous, which means they use more energy than any other star. What could you say about the age of a group of stars that were all formed at the same time, but whose HR diagram had only K and M stars on the main sequence? a. It is very young b. It is very old c. It is very distant d. It is very close PART II – DETERMINING CLUSTER AGES AND COMPARATIVE DISTANCES All HR diagrams have the same information conveyed on their axes, but occasionally astronomers use different methods for measuring this information. Below is an HR diagram that is more accurately called a Page 5 STELLAR LIFETIMES

3.56 3.64 8.05 7.85 3.60 3.71 8.34 8.12 3.81 3.88 8.63 8.27 4.12 4.18 8.67 8.37 4.20 4.31 9.15 8.69 5.01 5.09 9.80 9.25 5.38 5.45 9.97 9.45 5.72 5.76 10.4 2 9.88 6.31 6.29 10.7 5 10.1 3 6.84 6.82 11.12 10.4 8 7.02 6.99 11.63 10.8 3 7.45 7.35 To create a color-magnitude diagram in Excel:  Type the B magnitudes in column A and the V magnitudes in column B. The header for each column should be placed in row 1, and the data should begin with row 2.  In column C, type the header in row 1. In cell C2, type the formula “=A2-B2”. Repeat for each other cell in column C, using the appropriate cell references to calculate B-V for each star.  Copy column B into column D so you have a second copy of the V magnitudes to the right of the B-V values.  Highlight the data in columns C & D.  Click on the “Insert” tab and click on the “Charts” button near the top. Select “Scatter.” A graph of your data will appear.  Right click on the y-axis and choose “Format Axis”. Check the box next to “Values in reverse order” to plot the V magnitudes from highest to lowest. QUESTION: Why do we want to plot the largest V magnitudes at the bottom of the graph and the smallest V magnitudes at the top? Page 7 STELLAR LIFETIMES

QUESTION: How many of the 25 brightest Pleiades stars are apparently HOTTER than 10,000 degrees C? (Hint: What B-V value does this correspond to?) QUESTION: The approximate absolute magnitude of a standard main sequence star with a temperature of 10,000K is +1.4. What is the APPARENT magnitude of a main sequence star in the Pleiades with the same temperature? Insert your Pleiades CMD under or next to the CMD for M67. QUESTION: Which cluster is OLDER? Explain. QUESTION: Which cluster is MORE DISTANT? [hint: compare the apparent magnitudes of main sequence stars with the same temperature in the 2 clusters] Explain. Table 2 below gives the main sequence lifetimes for a number of stars based on spectral type (and B-V value). Page 8 STELLAR LIFETIMES

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