Name / 65 pts HR Diagram Lab Introduction Some of the greatest advances concerning the nature of stars have come about by comparing their properties using graphs. In the early 1900 s, while studying the spectral classification work of the Harvard Observatory, Danish astronomer Ejnar Hertzsprung noticed some systematic differences among the spectra of reddish and orange stars that were related to their proper motions. A star s proper motion is how far it seems to move through the sky each year, relative to extremely distant background stars which don t appear to move. Be careful not to confuse proper motion (a star s actual movement through space) with parallax (due to the earth s orbit around the sun.) What Hertzsprung noticed is that distant stars with small proper motions had one type of spectrum, while nearby stars with large proper motions had a different type of spectrum, even though both sets of stars had the same overall color and surface temperature. Hertzsprung reasoned that the distant stars must be much brighter than the nearby stars. How could this be, if both sets of stars had the same surface temperature? The only explanation was that the distant stars must be much larger than the nearby stars. Hertzsprung had established a relationship between distance, brightness, and the radius or size of a star. Shortly after this breakthrough, Hertzsprung and American astronomer Henry N. Russell developed a graph comparing the absolute magnitude and spectral class (temperature) of stars. This diagram has been named the Hertzsprung-Russell (or HR) Diagram in their honor. The modern theory of stellar evolution is based on this diagram. On the HR diagram, the vertical axis represents stellar brightness in terms of either absolute magnitudes or luminosity (with the sun = 1 Luminosity unit, L). The horizontal axis represents stellar temperature in terms of either actual temperature in Kelvins or spectral class (OBAFGKM). Notice that the temperatures are plotted backwards from normal, with the highest temperatures on the left, coolest on the right. The following diagram shows four of the most interesting regions in which stars are found. Stellar properties tend to cluster in certain regions, rather than being random. This tells us that a relationship between brightness, temperature, and the stage of a star s life exists. The roughly diagonal strip running across the diagram is called the main sequence and contains most (about 90%) of the stars. Area 1 Area 4 Area 5 Area 2 Area 6 Area 3
Use the HR diagram sketch on the first page of the lab to answer the following questions: (1 pt each) 1. In which numbered area of the diagram are hot bright stars found? 2. In which numbered area are cool faint stars found? 3. Which area represents the red giants (not supergiants)? 4. Which area represents blue main-sequence stars? 5. Which area represents the approximate location of the sun, a G2 main sequence star? 6. Which area ( area 3 or area 6 ) represents hotter stars? 7. Which area ( area 3 or area 6 ) represents larger diameter stars? Both areas have the same luminosities. 8. Which area ( area 1 or area 4 ) represents hotter stars? 9. Which area ( area 1 or area 4 ) represents larger diameter stars? Both areas have the same luminosities. Procedure do the following on the attached HR diagram at the end of the lab, not the sketch on the previous page. The data in Table 1 represents the absolute magnitude (M) and the spectral class of 57 of the brightest stars in our sky. Table 2 represents the same data for 55 of the nearest stars. At the end of this lab is a copy of the HR diagram where you will plot the absolute magnitudes (M) vs. the spectral classes of these stars. Follow these directions (20 pts). A. Plot spectral class vs. M for both sets of data. It s not necessary to write down the names of the stars besides their dots. Use different colors or marks for the two different sets of data. B. Run a smooth diagonal band around the strip of stars that runs from top left to bottom right of the diagram. The band should contain the largest number of stars. Label this band Main Sequence. C. Circle the stars that cluster in the upper right corner, and label this region Red Giants and Supergiants. D. Along the bottom of the diagram, in the line just above the spectral class, use colored pencils or markers to shade in the appropriate color for each spectral class, or write in the name of the color. E. Be neat and accurate, because you will need to refer to this graph to answer some of the following questions.
Part 1 Read this paragraph before answering the questions!! The luminosity of a star is the total amount of energy the star radiates into space each second. The luminosity depends on how much surface area the star has and also on how much energy the star emits from each square meter of its surface. The radius of a star determines its surface area and the temperature determines how much energy it radiates. Therefore, if two stars have the same surface temperatures, but different luminosities, they must have different amounts of surface area, i.e. they differ in radius (size). Questions (1 pt each unless shown otherwise) 1. Compare the red supergiants on your diagram with the same temperature main sequence stars. Which group is brighter? ( red supergiants main sequence ) 2. Why are these stars brighter? 3. Compare the white dwarfs on your diagram with the same temperature main sequence stars. Which group is dimmer? ( white dwarfs main sequence ) 4. Why are these stars dimmer? 5. Which has more main sequence stars: the 100 brightest stars or the 100 closest stars? Circle one. 6. Why aren t there any white dwarfs among the 100 brightest stars? 7. Why don t most of the nearest stars have famous names? Read this paragraph before continuing!! The parallax method of measuring distances is only accurate out to about 1000 light years. For more distant stars, it s possible to estimate their distances by using the HR diagram. If the spectrum of a star can be measured, its spectral class and position on the HR diagram can be determined. This allows astronomers to estimate the star s absolute magnitude (M) and compare it to its apparent magnitude (m). The distance to the star can then be calculated using the distance modulus formula below. [(m M + 5) / 5] distance in parsecs = 10 distance in LY = parsecs x 3.26 8. The distances to 6 stars were left out of Tables 1 & 2. Calculate the distances (in light years) to these 6 stars using the formulas above. Please show your calculations. (12 pts)
9. It s often difficult to accurately estimate the absolute magnitudes of K-class and M-class stars without closely examining their stellar spectra. Explain why. (Hint: Consider what types of K and M-class stars exist!) (2 pts) 10. Estimate the magnitude difference between the brightest K0 supergiant star and the dimmest main sequence K0 star. 11. Would a K0 supergiant or a K0 main sequence star be visible at a greater distance from the earth? 12. In the table below are observations for 3 stars as seen from earth. Use your HR diagram to determine the absolute magnitude (M) for each star. (3 pts) At a distance of 10 parsecs from a star, a star s apparent magnitude (m) would equal its absolute magnitude (M). At a distance closer than 10 pc, a star s apparent magnitude would be smaller (or more negative) than its absolute magnitude. Fill in the last space for each star in the chart. (3 pts) Star Spectral Class m M farther or closer than 10 pc? #1 M0 supergiant 7 #2 A0 white dwarf 7 #3 G0 main sequence 7 13. Which star in question 12 is the farthest from earth? 14. The closest to earth? Part 2 15. Determine the mean average absolute magnitude (M) for the 57 Brightest Stars. 16. Determine the mean average absolute magnitude (M) for the 55 Nearest Stars. 17. How much brighter is the average bright star compared to the average nearby star? Calculate the difference in magnitudes ( M) between question 16 question 15. Now, recall that a difference of each magnitude unit = a change in brightness of 2.512. Take 2.512 to the M power for the answer. 2.512 ^ M =. 18. How much fainter than the sun (M = +4.8) is the average nearby star? Show your calculation (similar to the calculation in question 17.) 19. How much brighter than the sun is the average bright star? Show your calculation (similar to the calculation in question 17.) 20. Take the square root of the answer to question 17. The inverse square law of light tells us that this answer is how many times farther away an average bright star would have to be than an average nearby star in order to appear equally bright. 21. Cube the result (x 3 ) of question 20. This result is an estimate of the volume of space which would contain the brightest stars if the volume of space which contains the nearest stars = 1 cubic unit.
22. If 55 stars similar to the nearest stars are contained in every 1 cubic unit of space, divide the number of brightest stars by the answer to question 21 to find out how many bright stars are contained in each 1 cubic unit of space. (Your answer should be very small, well under 0.001 bright star per cubic unit. Show your work.) 23. Divide the number of nearest stars by the answer to question 22. This gives you the number of fainter, nearby-like stars per each one bright star. Show your calculation. 24. Assume that the average surface temperature for a typical bright star is 9000 K and the average surface temperature for a typical nearby star is 3000 K. Multiply each temperature by itself 4 times (temp 4 ). The Stefan- Boltzmann Law says that the luminosity of a star (energy given off per second per square meter of surface area) is proportional to the 4 th power of the star s surface temperature. Show your calculations. Divide the result for the bright star by the result for the nearby star. This is the ratio of how much energy is given off per square meter by a bright star compared to a nearby star. Show your calculation. (3 pts) 25. If you assume that a typical bright star has a radius 100X larger than the sun s radius, and a typical nearby star has a radius 1/10 th of the sun s radius, that means that a typical bright star is 1000X larger than a typical nearby star, and has a surface area 1,000,000 times greater. The total energy output of a star is equal to its luminosity x its surface area. Multiply the final answer to question 24 by 1,000,000. This is how much total energy is produced by a typical bright star compared to a typical nearby star. 26. If each bright star emits the energy in question 25 (compared to a fainter, nearby-like star), compare the relative importance of the bright stars to the fainter, nearby stars in terms of total energy emitted, by dividing the final result of question 25 by the result of question 23.
Table 1: 57 of the Brightest Stars plot these two columns Common Name Constellation m M Spectral Class Distance (LY) 1 Sirius Canis Major -1.44 1.45 A0 9 2 Canopus Carina -0.62-5.53 F0 3 Arcturus Bootes -0.05-0.31 K2 37 4 Rigel Kentaurus Centaurus -0.01 4.34 G2 4 5 Vega Lyra 0.03 0.58 A0 25 6 Capella Auriga 0.08-0.48 G5 42 7 Rigel Orion 0.18-6.69 B8 773 8 Procyon Canis Minor 0.40 2.68 F5 11 9 Betelgeuse Orion 0.45-5.14 M2 552 10 Achernar Eridanus 0.45-2.77 B3 144 11 Hadar (Agena) Centaurus 0.61-5.42 B1 526 12 Altair Aquila 0.76 2.20 A7 17 13 Acrux Crux 0.77-4.19 B0 321 14 Aldebaran Taurus 0.87-0.63 K5 65 15 Spica Virgo 0.98-3.55 B1 262 16 Antares Scorpius 1.06-5.28 B1 604 17 Pollux Gemini 1.16 1.09 K0 34 18 Fomalhaut Piscis Austrinus 1.17 1.74 A3 25 19 Deneb Cygnus 1.25-8.73 A2 20 Mimosa Crux 1.25-3.92 B0 352 21 Regulus Leo 1.36-0.52 B7 77 22 Adhara Canis Major 1.50-4.10 B2 431 23 Castor Gemini 1.58 0.59 A2 52 24 Gacrux Crux 1.59-0.56 M4 88 25 Shaula Scorpius 1.62-5.05 B2 359 26 Bellatrix Orion 1.64-2.72 B2 243 27 Al Nath Taurus 1.65-1.37 B7 131 28 Miaplacidus Carina 1.67-0.99 A2 111 29 Alnilam Orion 1.69-6.38 B0 1342 30 Al Nair Grus 1.73-0.73 B7 101 31 Alnitak Orion 1.74-5.26 O9 817 32 Regor (Al Suhail) Vela 1.75-5.31 O9 840 33 Alioth Ursa Major 1.76-0.21 A0 81 34 Kaus Australis Sagittarius 1.79-1.44 B9 145 35 Mirphak (Al Genib) Perseus 1.79-4.50 F5 592 36 Dubhe Ursa Major 1.81-1.08 K0 37 Wezen Canis Major 1.83-6.87 F8 1791 38 Alkaid Ursa Major 1.85-0.60 B3 101 39 Sargas Scorpius 1.86-2.75 F1 272 40 Avior Carina 1.86-4.58 K3 632 41 Menkalinan Auriga 1.90-0.10 A2 82 42 Atria Trianguli Australis 1.91-3.62 K2 415 43 Delta Velorum Vela 1.93-0.01 A1 80 44 Alhena Gemini 1.93-0.60 A0 105 45 Peacock Pavo 1.94-1.81 B2 183 46 Polaris Ursa Minor 1.97-3.64 F7 431 47 Mirzam Canis Major 1.98-3.95 B1 499 48 Alphard Hydra 1.99-1.69 K3 177 49 Algeiba Leo 2.01-0.92 K0 126 50 Hamal Aries 2.01 0.48 K2 66 51 Deneb Kaitos Cetus 2.04-0.30 K0 96 52 Nunki Sagittarius 2.05-2.14 B2 224 53 Merkent Centaurus 2.06 0.70 K0 61 54 Saiph Orion 2.07-4.65 B0 815 55 Alpheratz Andromeda 2.07-0.30 B9 97 56 Kochab Ursa Minor 2.07-0.87 K4 126 57 Algol Perseus 2.09-0.18 B8 93 Magnitude Info: Hipparchos Catalog Distance Info: Observer's Handbook 2001, by The Royal Astronomical Society of Canada
Table 2: 55 of the Nearest Stars plot these two columns Common Name Hipparchos # m M Spectral Class Distance (LY) 1 Proxima Centauri 70890 11.0 15.4 M5 4.2 2 alpha-centauri B 71681 1.35 5.71 K1 4.4 3 Rigel Kentaurus 71683-0.01 4.34 G2 4.4 4 Barnard s Star 87937 9.54 13.24 M4 5 54035 7.49 10.46 M2 8.3 6 Sirius A 32349-1.44 1.45 A0 9 7 Ross 154 92403 10.37 13.00 M4 9.7 8 alpha-eridani 16537 3.72 6.18 K2 10.5 9 114046 7.35 9.76 M2 10.7 10 57548 11.12 13.50 M5 10.9 11 61 Cygni A 104214 5.2 7.49 K5 11.4 12 Procyon 37279 0.4 2.68 K5 11.4 13 61 Cygni B 104217 6.05 8.33 K7 11.4 14 91772 9.7 11.97 K5 11.5 15 91768 8.94 11.18 K5 11.6 16 1475 8.09 10.33 M1 11.6 17 alpha-indi 108870 4.69 6.89 K5 11.8 18 eta-ceti 8102 3.49 5.68 G8 19 5643 12.1 14.25 M6 12.1 20 36208 9.84 11.94 M5 12.4 21 Kapteyn s Star 24186 8.86 10.89 M0 12.8 22 105090 6.69 8.71 M1 12.9 23 30920 11.12 13.05 M5 13.4 24 72511 11.72 13.58 M5 13.8 25 80824 10.1 11.95 M4 13.9 26 439 8.56 10.36 M2 14.2 27 72509 12.07 13.80 M5 14.7 28 86162 9.15 10.87 M4 14.8 29 85523 9.38 11.10 K5 14.8 30 113020 10.16 11.80 M5 15.3 31 54211 8.82 10.40 M2 15.8 32 49908 6.6 8.16 K8 15.9 33 106440 8.66 10.19 M1 16.1 34 86214 10.94 12.43 M5 16.4 35 Eridani A 19849 4.43 5.93 K1 16.4 36 112460 10.29 11.77 M5 16.5 37 70 Ophiuchi A 88601 4.03 5.50 K0 16.6 38 Altair 97649 0.76 2.20 A7 39 1242 11.49 12.90 M5 17.0 40 57544 10.8 12.14 M4 17.6 41 Wolf 498 67155 8.46 9.79 M3 17.7 42 53020 11.64 12.89 M4 18.4 43 25878 7.97 9.19 M1 18.6 44 82817 9.02 10.23 M3 18.7 45 eta-draconis 96100 4.67 5.87 K0 18.8 46 29295 8.15 9.34 M1 18.8 47 26857 11.56 12.75 M5 18.9 48 86990 10.75 11.93 M5 18.9 49 94761 9.12 10.28 M4 19.1 50 73184 5.72 6.86 K4 19.2 51 37766 11.19 12.32 M5 19.3 52 76074 9.31 10.44 M0 19.3 53 Wolf 24 3821 3.46 4.59 G0 19.4 54 36 Ophiuchi C 84478 6.33 7.45 K5 19.4 55 117473 8.98 10.10 M2 19.5 Information from the website: http://www.astronomynotes.com/tables/tablesc.htm