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Download Distances to the Stars in Leo
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Summary The student determines the distances to seven of the brightest stars in the constellation Leo using the method of spectroscopic parallax and compares the results to the more accurate distances derived from measured trigonometric parallaxes. Background and Theory If the distance to the star is known via its measured parallax (as it was discussed in class), it is a somewhat easyl matter for astronomers, or anyone else for that matter, to determine the absolute magnitude of the star using the distance-magnitude relation. However, most stars are too far away to have a measurable parallax. In these cases, the distance to the star must be determined by some other method. We can use our knowledge of the Hertsprung-Russell (or H-R) Diagram and our analysis of a star's spectrum to determine stellar distances. The H-R Diagram is a graph measuring a star's absolute magnitude or brightness against its temperature and colour. Below is an example of the diagram: L stands for luminosity (or brightness) and T stands for temperature (in Kelvins or K, a different unit like Celsius). The light from a star can be analysed using a spectrum diagram on the next page: From the strength of the lines in a star's spectrum, we can give it a spectral type (O, B, A, F, G, K & M) and luminosity class. We can use the luminosity to find its absolute magnitude and thus its distance. Finding the distances to stars based upon their spectral type and luminosity is known as spectroscopic parallax (even though no parallax determination or trigonometry is involved). This method is neither easy nor exact; however, it has proved to be one of the best ways to learn about the more distant stars. The first part of this method involves determining the star's spectral type and luminosity class. Procedure Table 1 lists the 14 stars Leo in order of their apparent magnitude. Seven of the stars have already been classified, and their absolute magnitudes and distances calculated. Your mission is to fill in the details for the other seven stars. 1. Use the Internet to find the spectral type (O, B, A, F, G, K & M) of the seven stars (Wikipedia contains this information; see Mr. Jennings if you have difficulty finding the information). Fill in column 3. 2. Use the Internet to find the absolute magnitude of each star. Fill in column 6. 3. Solving for the distance in the distance-magnitude relation, we get: d 10 ( m M 5)5 Solve for the exponent of 10 first, then use either the inv log; keys or the 10x key on your calculator. Calculate the distance to each of the seven stars based upon the absolute magnitude (M) from spectroscopic parallax. 4. For the seven unclassified stars, fill in column 9 in Table 1 for the distances determined from the parallax values, where d = 1/parallax (d is in parsecs for parallax measured in seconds of arc). Table 1 - Distances to Stars in Leo Worksheet Fourteen Stars in the Constellation Leo Star ID Star Name Leo Regulus Leo Denebola Leo Al Geiba A* Leo Zozma Leo Spectral Luminosity Type Class Apparent Magnitude M from d from Spec. Spectroscopic Parallax Parallax Measured Parallax (arc sec) d from Parallax V 1.36 V 2.14 III 2.14 V 2.55 Ras Elased Australis II 2.98 0.009 Leo Chort V 3.34 0.036 Leo Al Geiba B* III 3.39 0.036 Leo Aldhafera F0 III 3.44 ~1 32 0.025 40 Leo 30 Leonis A0 I 3.48 ~ -5 500 N/A ** Leo Subra V 3.52 B1 I 3.85 ~ -6 900 N/A ** K2 III 3.88 ~2 25 0.025 40 B9 V 4.05 ~2 25 0.017 59 III 5 - 10 -1 to +4 160 N/A ** 1 2 Leo Leo Ras Elased Borealis Leo R Leo A3 A5 *** 0.038 ~2 10 0.076 13 0.036 ~1 20 0.040 25 0.034 * Visual Binary ** Distance is too far for a measurable parallax ***Variable Star M = absolute magnitude of the star Luminosity class symbols: V = dwarf, IV = subgiant, III = giant, II = luminous giant, I = supergiant. 1. As part of this exercise, you determined the distances to these stars based on the method of spectroscopic parallax. In your own words, summarize why the method is an important tool for astronomers. 2. Compare the two values for the distance to each of the seven stars. Do certain spectral types or luminosity classes lead to larger differences between the two values? 3. Comment on the accuracy of the spectroscopic parallax method vs. the trigonometric parallax measurements (i.e. the difference in columns 7 & 9). © 2000 University of Washington Revised: 11 July, 2000