Stellar Homework #2

Remember to show all your work and to put your final answer for each question in the form of a complete English sentence!

1.   a.   A white dwarf becomes a "black dwarf" when its surface temperature decreases to the point where its wavelength of maximum emission is in the infrared region (say, 10000 Angstroms). Use Wien's Law to compute the temperature at which that occurs.

HINT: This is an application of Wien's Law, except that we are looking for temperature instead of lambda-max.

       b.   From the time the white dwarf "starts out" (ie, its star dies) at an initial temperature of 50,000K, how long does it take to "vanish" if we assume that they cool down at a rate of 2 X 10^-5 K per year?

HINT: There is no equation for this problem. Just figure out how far the temperature must drop from the original value, then use the information in the problem to compute how many years required for the temperature to drop that far! Should be a LOT of years!

• 3931.9 Angstroms 
• 3940.0 Angstroms 
• 3963.0 Angstroms 

HINT: This problem asks you to utilize the Doppler Effect. The first step is always to calculate the Doppler Shift, the difference between the observed wavelength and the "rest" wavelength. By looking at the sign of that difference (- is a blueshift, + is a redshift), you can immediately tell whether the object is coming towards us or moving away from us. Divide the shift by the rest wavelength, and then multiply by c, the speed of light, to get the speed of the star. The units for the velocity of the star will be the same as the ones you chose for the speed of light.

3.    Below are two tables of star data, one for the nearest stars, the other for the brightest stars.  The tables contain information on the stars' temperatures as well as information on their absolute magnitudes.  Absolute magnitude is a measure of how truly bright a star is.  The absolute magnitude system is a "backward" system:  the smaller the value of absolute magnitude, the brighter the star is.

a.  Make a large, whole-page graph with temperature on the x-axis and absolute magnitude on the y-axis.  In one color (say, pencil) put the nearest stars on this graph.  Then, in a different color (say, blue ink) put the brightest stars on the graph.  There is no need to label the points.

b.  Are the stars evenly distributed on the graph?  Are there any obvious patterns?  Describe these patterns, if any.

c.  Of the nearest stars, are the majority dimmer than the Sun, or brighter?

d.  Of the nearest stars, are the majority hotter than the Sun, or cooler?

e.  Most of the brightest stars are more luminous than the Sun.  Are most of these stars hotter than the Sun, or cooler?  Explain how this makes sense, in view of the relationship between luminosity and temperature.

f.  There are a some very luminous stars that are cooler than the Sun, yet more luminous than the Sun.  Looking at the formula for luminosity, explain how this can be so.

The Nearest Stars

The Brightest Stars in the Sky
(Based on apparent brightness, not luminosity)

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