Stellar Magnitudes

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University of Missouri, Columbia *

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1010

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Astronomy

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Oct 30, 2023

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S TELLAR M AGNITUDES I. S TAR M AGNITUDES & D ISTANCES Millions of stars are scattered across the sky. Astronomers want to study these stars as carefully as possible. This means measuring everything we can about them. All we have is the light that reaches us from the stars and astronomers can really only directly measure three properties of stars: 1) Position 2) Brightness 3) Spectrum (more on this in a future lab) They then use these measurements to deduce many other properties of the stars. We have already had practice measuring a star's position using the Altitude/Azimuth method. Now it is time to look at the second stellar property: brightness . Everyone agrees that stars come in different brightnesses – some are bright, and some are faint. As discussed in the lecture slides, the brightness of a star as it appears in the sky is quantified as a magnitude , where smaller numbers mean brighter stars. Magnitudes can even be negative for very bright stars. Now let us try to figure out what the brightness of a star can tell us. Remember, there are two kinds of magnitudes – Apparent Magnitude (m) , which is how bright the star appears from Earth, and Absolute Magnitude (M) , which is how bright the star would be if it were 10 parsecs away. Let us examine more closely Luminosity and Distance . Luminosity is a measure of how much total light a star gives off every second. A star that looks dim to our eyes could be dim because it has a low luminosity, or because it is far away. Which one is it? If we could measure the star's distance, then we could answer that question. II. A PPARENT AND A BSOLUTE M AGNITUDE 1. What TWO factors determine a star's apparent magnitude (how bright the star will appear to be in our night sky)? Surface temp, size 2. Which value, apparent or absolute magnitude: a. Tells us how bright an object will appear from Earth? Apparent b. Tells us which star is giving off more light? Absolute /35

3. You observe two stars: Canopus has an apparent magnitude of -0.65 and Bellatrix has an apparent magnitude of +1.60. a. Which star looks brighter? Canopus b. You also observed a third, dimmer star. Make up a value for its apparent magnitude. Third Star (+4.5) 4. The star Deneb has an apparent magnitude of +1.25 and is located 433 parsecs away. Which of the following values is likely the absolute magnitude for Deneb? (No calculation needed) a. -6.93 b. 1.25 c. 7.31 Explain your reasoning: I know this will be negative because of the magnitude is less than 5 and parsces number will not be large enough to make it positive Refer to the following table for questions 5-7: Apparent Magnitude Absolute Magnitude Star A 1 1 Star B 1 2 Star C 5 4 Star D 4 4 5. Which object appears brighter from Earth? Star C or D? Explain reasoning. Star D because the apparent magnitude is smaller 6. Which object is more luminous: Star A or Star D? Explain reasoning. Star A because the absolute magnitude is smaller 7. For each star (A-D), state whether the star is closer than, farther than, or exactly 10pc away from Earth. Explain reasoning. A- exactly because the apparent and absolute are equal B- closer than 10 pc because the absolute is greater than the apparent C- farther than 10 pc because the absolute is less than the apparent D- exactly because the apparent and absolute are equal

8. In general, which will be a larger number in the following situations: (Apparent Magnitude, Absolute Magnitude, Neither) a. If a star is further than 10pc away: apparent b. If a star is closer than 10pc away: absolute c. If a star is exactly 10pc away: equal 9. Would the apparent magnitude number of Star A increase, decrease or stay the same if it were located at a distance of 40pc? Increase What about the absolute magnitude number? Stay the same Explain your reasoning. Absolute magnitude is a measure of a star's intrinsic brightness, which means it represents how bright the star would appear if it were located at a standard distance of 10 pc from Earth. So, changing the distance of the star does not affect its absolute magnitude. III. O RION Start Stellarium . Turn off the Atmosphere (A) and Ground (G) . Click on a few stars randomly. For each selected star, its information will appear, as usual, in the upper left-hand corner of the screen. The star's magnitude will be listed in the 2 nd line of information below the star's name. This is the star's Apparent Magnitude . Let's use the constellation Orion as our subject of study. Using Stellarium , determine the properties of the 7 brightest stars in Orion and fill out their corresponding data tables on the next page. You can use the Search window (F3) to type in the name of the star. The distances must be in parsecs (not light years)! See Appendix A to determine how to calculate the distance from parallax (p). Since this version of Stellarium gives these star distances in “mas” or “milli-arc-seconds” you will take 1000 divided by the parallax to get the distance (instead of 1/parallax when it is given in arcseconds). m: apparent magnitude – from 2 nd line

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M: absolute magnitude – from 3 rd line p: parallax – near the bottom of the info pane. Record only the number before the +/- sign. d: distance – need to calculate by taking 1000/parallax. Distance will be in parsecs. Do not copy distance from the info pane; it will be in light years and will not work in our equations! (If doing this in Word, you may need to delete excess rows to see this diagram display correctly) Bellatrix m =1.6 M =-2.84 p =12.920 d =77.399 Betelgeuse m =.45 M =-5.27 p =6.550 d = 152.672 Mintaka m =2.40 M =-4.84 p =3.560 d = 280.899 Rigel m =.15 M =-6.96 p =3.780 d = 264.550 Saiph m =2.05 M =-4.44 p =5.040 d = 198.413 Alnitak m =1.85 M =-5.15 p =3.990 d = 250.627 Alnilam m =1.65 M =-7.26 p =1.650 d = 606.061

1. Which star in Orion is the brightest? Rigel (smallest apparent) 2. Which of these 7 stars is the most luminous? Rigel 3. Betelgeuse is a red supergiant star near the end of its life. Any time in the next 1000 years, Betelgeuse will go supernova and its luminosity will increase by a factor of 10 5 for a few weeks. At its peak, the absolute magnitude will reach M = -18.3. What will its apparent magnitude be? Use the distance modulus equation from Appendix B. The apparent magnitude will be 13.44 4. Imagine that 1 billion years from now, Saiph is now twice as far away from us than it is today. Besides its distance, assume (unrealistically) that the star, Saiph did not change in any way. a. By what fraction does the brightness change? (no calculation needed) ____1/4_____________ b. Will its absolute magnitude change? _________no_____________ c. Calculate its new apparent magnitude : ______1.32________________ 4. The Sun's absolute magnitude is +4.74. How does its luminosity compare to these 7 stars? (no calculation needed, just describe it) The absolute magnitude is larger than all the absolute magnitudes of the 7 stars making the stars more luminous 5. a. What is the closest star in Orion? Bellatrix b. What would the Sun's apparent magnitude be if it were at this distance? 8.68 c. Would we be able to see it naked eye? no d. The naked eye limit is m = 6 magnitudes. Determine how close a star like the sun has to be in order to be visible with the naked eye. Use the equation for distance from Appendix B. 3.47pc e. The star distances on the previous page were calculated from parallax. Choose two stars and calculate their distance from the rearranged distance modulus equation (Appendix B). Compare this distance to the distance you get from parallax. Give the values. Are they the same? salph- 198.61 , rigel- 264.24 yes about the same