Lab4 Magnitudes (Complete)

Magnitudes L AB 4 THE M AGNITUDE S CALE P URPOSE The purpose of this lab is to learn more about an alternate measurement astronomers use to designate the luminosity and apparent brightness of stars. After doing this lab, you should be able to explain the concept of apparent and absolute magnitudes, how they relate to the brightness of a star, and how this system of measurement works. You will also gain experience in ● relating apparent versus absolute magnitude to the distances of celestial objects. ● demonstrating the use of units of measurement in astronomy, including Astronomical Units, light years and parsecs. ● using essential vocabulary of the discipline being studied. B ACKGROUND I NFORMATION W HAT ARE M AGNITUDES ? When the Greek scientist Hipparcos determined first studied the brightnesses of stars, he did it "by eye." The first stars that "came out" at night were of first importance or first "rank", and today we call those stars "first magnitude stars". The dimmest stars that he could observe were called “sixth magnitude stars” with other stars of varying brightness being classified somewhere in between. Today, with measuring instruments, we know that what the Greeks called a difference of 5 magnitudes (from 1st magnitude to 6th magnitude) is close to a 100 times difference in apparent brightness. This difference now defines the magnitude scale. With this new definition, the magnitude scale was broadened to the very brightest stars the Greeks saw, and some magnitudes became negative. With light-meter instruments capable of discerning small differences in brightness, some magnitudes became fractional, much like earthquake magnitudes. And some objects that could be seen only with telescopes could now have magnitudes attached to them, and those magnitudes were numbers larger than 6, the naked eye (unaided) limit for most people.

Magnitudes Magnitudes and brightnesses are related to each other, but the magnitude scale is a DIFFERENCE (subtractive) scale and the apparent brightnesses (how bright the objects appear) make up a MULTIPLICATIVE scale. Thus if two stars have NO difference in their apparent magnitudes (i.e. they look exactly the same brightness), you multiply the brightness of one star by 1.0 to get the brightness of the second. On the other hand, if two stars have a difference of 1.0 in their apparent magnitudes, the brighter one (lower magnitude) will appear 2.512 times brighter than the dimmer one. Table 1 shows how the differences in magnitude correspond to changes in apparent brightness: T ABLE 1: T HE R ELATIONSHIP B ETWEEN M AGNITUDE C HANGES AND B RIGHTNESS C HANGES Apparent Magnitude Difference Brightness Multiplier 0.0 1.0 1.0 2.512 2.0 6.310 3.0 15.85 4.0 39.81 5.0 100.0 6.0 251.2 7.0 631.0 8.0 1585 9.0 3981 10.0 10,000 Each magnitude difference corresponds to 100^(0.2) or 100^(1/5) times in brightness. A magnitude difference of "m" corresponds to a change of 100^(0.2m) times in brightness. A little algebra will show that this is the same as 10^(0.4m). If we wanted to know what a 20 magnitude difference would be, we could calculate it as: 10^(0.4*20) = 10^8, or 100,000,000 times! Between the brightest object we see from Earth (the Sun, magnitude -26.8) and the faintest stars we see from Earth (with the Hubble Space telescope & the Keck Foundation telescope on Mauna Kea in Hawaii, magnitude = +30), there is a difference of 30-(-26.8)= 56.8 magnitudes or 10^(0.4*56.8)= 10^(22.72)= 5.25x10 22 times difference in brightness! B RIGHTNESS & M AGNITUDES : You may recall from the previous lab that for two objects of the same luminosity, if one is 10 times farther away then it will appear 100 times dimmer (due to the inverse square law of light). A factor of 100 in brightness is ALSO the same as making an object 5 magnitudes fainter! So there is a way of relating the apparent brightness to changes in magnitude and distance. 2

Magnitudes M V = 5.19 – 6.705 + 5 M V = 3.48 The absolute magnitude of HD 14802 is 3.48. Remember that the SMALLER the number, the greater the wattage. HD 14802 therefore has a smaller wattage than Sirius – it would be dimmer if you placed these two stars side by side. 4

Magnitudes P RE -L AB Q UESTIONS These questions must be answered before you show up to your lab class. You will not be able to start the lab exercise without the answers to these questions. A quiz based on these questions will be given at the beginning of the lab session. You should use your textbook (or any other reference source) to help answer these questions. 1. Star A has an apparent magnitude of 1.0. Star B has an apparent magnitude of 6.0. Which star appears brighter? By what factor? Star A. 2. At what distance from Earth is the absolute magnitude of a star equal to its apparent magnitude? 10 parsecs. 3. What is the apparent magnitude of our Sun? the absolute magnitude? The apparent magnitude of our Sun is -26.8. The absolute magnitude is 4.7. 4. If we could fly in a spaceship towards another star, as we traveled toward the star, how would its apparent and absolute magnitudes change? The star would seem brighter and the value of the apparent magnitude would change. The absolute magnitude would stay the same. 5. What is the absolute magnitude of Sirius, the brightest star in the night sky? -1.5 5