COLOR AND STELLAR TEMPERATURE

COLOR AND STELLAR TEMPERATURE

Two windows should be open. This one in which the instructions are given and a smaller one which contains the actual applet that we will be using.

Tutorial:

The pattern of radiation given off by a perfect radiator is called Blackbody radiation (because the radiation pattern is independent of what the material is made of). This pattern is characterized by a particular function, called the Planck function, which mathematically is expressed as:

The key parameter in this equation is the temperature. Each temperature corresponds to a unique spectrum of emission. In this applet we will explore these patterns as a function of temparture, measure color indices as a function of temperature and then compare the ideal blackbody spectra with that of real stars.

Stars have an overall spectrum a radiation pattern which is governed largely by this formula, but clearly this formula is too complex and scary for the introductory student. In using this applet they never have to deal directly with the formula as the applet is directly coupled to it. The applet allows the student to perform photometry on the curve to get them to understand, empirically the relation between color and temperature. As a visual aid, the optical part of the spectrum from violet to red is part of the background.

The applet should have come up in its default state of temperature 8000 degrees with none of the boxes checked. The intensity is plotted from 1,000 to 10,000 angstroms (this can be changed via parameter tag).

The Y-axis Intensity Scale is in relative units. The X-axis is in units of Angstroms and is labelled at the top. Clicking on the mouse anywhere on the applet will retun the value of the X-axis (wavelength) at that point. This is useful if you want to use this applet for a Wien's Law demonstration.

Suggested Activities:

  • Students can empirically determine Wein's Law just by changing the temperature ( Slider Bar on the left ) and having them measure the approximate peak with the cursor. For the moment, don't worry about the energy scaling with T4. That is dealt with later.

  • Click the box that says Draw Limits of Integration . You will see filter bandpasses that correspond to the Johnson UBV system plotted as dashed curves underneath the spectrum. In addition to Johnson UBV, an R and I band pass is given. Color indices in B-V, U-B and V-I are measured. Since color indices use the correct zero points and hence are very nearly the correct colors for blackbodies of a given temperature. A useful exercise is to have the students record, and later plot, the U-B vs B-V values for a given temperature. In this way they can see how color index is responding to a changing temperature. Try selecting a temperature of 12,000 degrees and notice visually that most of the flux is in the UV and Blue filters. Now select a temperature of 3000 to see the flux at UV and B greatly diminished and the flux in the R and I filters to be larger. Note also the correspondingly large changes in the color index.

    Total Energy Emitted and Temperature

  • Now we compare two stars of identical radius and different temperatures to understand the T4 dependence on the total energy emitted. To do this exercise we use the applet that is on this page immediately below this text. The area under the curve is the total energy emitted. Set the black thermometer to 6,000 degrees and count the number of boxes underneath the black curve. Now set the brown thermometer to 4,000 degrees and count the number of boxes under the brown curve. You can measure and see that the area under the black curve is much larger than the area under the brown curve. Try the same experiment at settings of 4000 and 3000 degrees. Now set the black thermometer at 5000 degrees and have the students try to determine the temperature of the brown thermometer in which the area under the brown curve is 1/2 that under the black curve.

    The intent here is to get the students to realize there their is a strong non-linear relationship between the temperature and the area under the curve (e.g. total energy emitted).


  • Spectrum is plotted from 1000 angstroms to 2 microns



    Advanced Usage:

    Now refer back to the main applet (the one in the other window).

    Set the temperature to 7500 degrees.

    Uncheck the box labelled Draw Limits of Integration

    From the pulldown menu of stars select the spectral type F6-7V.

    Check the box labelled Star Data .

    You should now see a spectrum (plotted in yellow) that is just underneath the blackbody curve. The normalization pion is shown by the grayed out slider on the bottom X-axis. The default normalization is done in the red but this can be changed by parameter tag.

    If you now click on the Draw Limits of Integration button you will get the B-V and V-R color indices as measured on the star. Unchecking the star box will show those color indices as measured on the blackbody curve so that you can determine deviations.

    You should definitely see less flux in the UV in most of the stellar spectra than the blackbody temperature would predict due to line blanketing. This is a straightforward way to show this using real data.

    You can repeat this exercise for any of stars in the stellar library. Because the actual data stars at 3450 angstroms. U-B is not determined for the stars.

    A very good exercise is to have the students plot the B-V, V-R colors of the stars and the blackbody on the same plot to see the deviations as a function of temperature. Please note, however, that the R-filter bandpass used here is not the Johnson R filter of photoelectric photometry. It is closer to the Kron-Cousins R filter. None of this really matters however for the purposes of this exercise. The star data also doesn't extend completely to the red end of this filter anway.

    Parameter Tags in the Applet

    Parameter Tag Functionality
    amin Left most wavelength point; units are meters; so 1000 angstroms would be 10E-7 meters.
    amax Right most wavelength point
    tmin minimum temperature on slider bar
    tmax maximum temperature on slider bar
    norm this is a value entered in meters. It determines the normalization point when comparing stellar spectra to a blackbody curve. The default is 6580 angstroms (chosen because things work well there)
    change_norm this value is either true or false . The default state is false. If its true, that means the user can move this slider around to adjust the normalization. That is, suppose you have an A star spectrum - while you should normalize this on the red curve, you could normalize at the peak if you wanted. You will get slightly different temperaturs of course depending on how you choose to normalize - but your supposed to!