Unit Five: Investigating Stars
Doing Science

3. How Hot Are They? Black Bodies and the Temperatures of Stars

Introduction:
Temperature is one of the fundamental properties of stars. The determination of the temperatures of stars led to making sense out of the originally arbitrary classification of stellar spectra and the construction of the HR diagram, a fundamental tool of modern astrophysics. But how do you measure the temperature of an object into which you can never stick a thermometer? Although stars are not perfect black bodies, they are close enough that the properties of theoretical black body radiation curves can be used to get good estimates of a star's temperature. In this Going Further, you will compare the spectra of a selection of stars along the OBAFGKM sequence with black body curves to establish the temperature scale of the HR diagram.

Directions:
First, obtain the spectra of a set of stars distributed fairly evenly along the spectral sequence. Go to the Web site of the Spectroscopy of Variable Stars project at the National Optical Astronomy Observatories: http://www.noao.edu/education/arbse/arpd/gvs.

Download the following sample of spectra from the Jacoby Atlas:

The file names all have the same form: spectrum #0001 is jhc0001.txt, spectrum #0011 is jhc0011.txt, etc. Open each spectrum text file in a spreadsheet like Excel and display the data as a chart with wavelength on the horizontal axis, and flux on the vertical axis. You now have a graphical representation of the spectrum of the star. You can also download a color jpeg of the same spectrum in non-graphical format like the spectra in Figure 2-5 for comparison.

Second, bring up a black body curve for comparison. An excellent set of comparison curves can be obtained at the Quantum Science Across Disciplines site at Boston University: http://qsad.bu.edu/applets/index.html.

Click on Spectrum Explorer: Blackbody. A pop-up window with a graph and a thermometer will appear. Arrange your windows so that the floating window is in top of, but not obscuring the Excel chart of the spectrum. Now adjust the temperature until you get a "best visual fit" for the black body curve to the star's spectrum. You should pay attention to the general shape, the slope, and the location of the peak (if within the spectrum range). Note that the applet has put additional menus in the toolbar of your browser that you can use to change the temperature and wavelength range. Since the star spectra are from about 3400 Å to 7400 Å, the default setting of 380 to 780 nm (1 nm = 10 Å) is best. Use a screen capture to get a copy of your best-fit black body curve for your report.

Use this method to estimate the temperature of all the stars in the sample. Once you have practiced a bit getting the temperature for one spectrum, the rest will go fairly quickly.

For those stars that have distinct peaks in their spectra, compute the temperature using Wien's Law for comparison: T = 0.29 cm/ peak wavelength.

Collect your estimated and calculated temperatures in a table with the spectral types to construct a temperature scale for the HR Diagram.

Your Report:

1. Prepare a poster or PowerPoint presenting your spectra and matching black body graphs either side-by-side or superposed on each other. Present your temperature calibration table and discuss uncertainties or problems you found in making the comparisons. Compare your results with the temperatures on the HR Diagram in Figure 2-9. (Don't simply assume that the temperatures in the figure are correct.) You should realize by now that the determination of a star's temperature is not trivial and always involves some approximations. Discuss the difficulties of getting accurate temperature determinations for stars.
2. Try a more accurate method of fitting star spectra with black body curves. Go to a site with the theoretical equations for black body curves such as: http://en.wikipedia.org/wiki/Planck%27s_law_of_black-body_radiation

Use the wavelength data in the spectra to calculate theoretical black body curves in your Excel spread sheet, and then superpose the theoretical curve with the spectra in the same chart. Adjust the temperature until you get a "best fit." Since you are superposing the model directly on the data, you should be able to get a more accurate fit, and thus a more accurate temperature. This approach approximates what professional astronomers do to determine temperatures. Note: This method is not for the mathematically faint hearted!