Astronomy x103 Lab 5
Purpose: In this lab we will learn how to determine a stars luminosity and temperature enabling us to plot the star on a Hertzsprung-Russel (H-R) diagram.
Introduction: The beauty of an H-R diagram lies in the fact that we can organize all the stars we find in the universe in a simple way allowing us to better understand how stars form, live and eventually die. To plot stars on an H-R we need to know a stars temperature and luminosity. Temperature can be determined by studying a stars spectrum and luminosity can be calculated from knowledge of a stars distance and apparent brightness.
Activity: As an example, we will study the star Altair to better understand the process of determining a stars temperature and luminosity. Before we start looking closely at Altair perhaps it would be nice to remind us where this star is located in the night sky. Start the Starry Night program and advance the time forward until about 9:00 p.m. Set the date for October 31st. Facing west you will see two bright stars above the horizon. The bright one (the 12th brightest in the night sky) on the left is Altair. What constellation is Altair in? _______________. The bright star (the 5th brightest) on the right is Vega soon to be our north star in another 11,000 years. There is a third bright star (18th brightest) named Deneb a little higher above the western horizon. What constellation is Deneb in? ___________. These three bright stars, Deneb, Vega, and Altair form a prominent triangle (“the summer triangle”) in the night sky.
Now if we were to take a closer look at the light coming to us from Altair, we would see something like this. In this case, the light has been separated into the relative flux (or intensity of light) at each wavelength to form a spectrum. We are actually looking at the spectrum of four different stars of the same spectral class. To determine the temperature of this spectral class find the wavelength with the largest flux of light and use the formula, T=0.0029/lmax. Remember that the wavelength must be measured in meters and temperature will be in Kelvins. The fact that one angstrom equals 10-10m will be useful. What do you find the temperature of Altair to be (show your work)? ___________.
To determine the luminosity of Altair we need to know the distance and apparent brightness. The apparent brightness is the flux of light reaching our telescope (or eye) at all the wavelengths added together. Such a measurement is made with a photometer that can be connected to the telescope. If we made such a measurement with Altair, we would find the apparent brightness (b) to be 7.5x10-9 W/m2. The distance to Altair can be found by measuring the parallax angle since it is a relatively close star. In the space below draw a picture of the earth, sun and Altair including the observed parallax angle of 0.194 arcsec (not to scale of course).
The distance to Altair can be found using the parallax-distance formula, d=1/p, where the distance is in parsec and the parallax angle, p, is measured in arcsec. What is the distance to Altair? ___________________ Convert your answer to meters (1 pc = 3.09x1016 m) and calculate the luminosity of Altair using L = 4pd2 b, where b is the brightness given above. What is the luminosity of Altair (show your work)? ______________________
Altair is how many more times luminous than the sun, with a luminosity of 3.9x1026W?
Knowing the luminosity and temperature (or spectral class) of Altair we can now plot it on the H-R diagram provided for you. What is the spectral class of Altair? __________ What is the luminosity class of Altair?_____ The temperature and luminosity of the other stars on this diagram were determined using the same method we used for Altair. On your diagram identify the main-sequence stars. What exactly does it mean to be a main-sequence star? ________________________________________________________
Now let’s take a look at some prominent stars that are not main-sequence stars. Advance the Starry Night program forward in time until about midnight. The date should still be set close to October 31st. Above the southeast horizon is the bright star Sirius. Above Sirius is a prominent constellation. Do you recognize it? What constellation am I referring to? ___________ Betelgeuse is an extremely luminous (100,000 times more than the sun’s luminosity of 3.9 x 1026 W) slightly reddish colored star in this constellation. Betelgeuse is a cooler star (hence the reddish color) with a temperature of about 3500 K. Plot Betelgeuse on your H-R diagram. Because of its large luminosity and enormous size, Betelgeuse is referred to a supergiant. To see how big Betelgeuse is we can use the equation L = (4pR2)sT4, where R is the stars radius, T the temperature and s = 5.67 x 10-8 W m-2 K-4. What is the radius of Betelgeuse (show your work)?
Convert your answer to AU using 1 AU = 1.5 x 1011 m and you should get about 4 AU!! Above Orion is another prominent constellation. What is this constellation? __________ There is a reddish colored star named Aldebaran (the red eye of the bull) with a temperature of about 4500 K and a luminosity 100 times greater than the sun. Aldebaran is what we call a red giant star. Add Aldebaran to your H-R diagram. Now return to a slightly earlier time in the evening when the star Vega is in the sky. Using the find option under selection in the menu bar, look for the ring nebula (M57) but make sure “magnify for best viewing” is not selected so that you can see where M57 is in the constellation Lyra. Draw a picture of the constellation Lyra and the location of the ring nebula in this constellation in the space at the bottom of the page. Now take a close up look at the ring nebula by selecting the “magnify for best viewing” this time. The central star in the planetary nebula is a white dwarf star and we expect this to be the fate of our sun in about 5 billion years. Locate the white dwarf stars on your H-R diagram. What are the temperature, size, and luminosity characteristics of white dwarfs?___________________