Solutions -- Homework 2 (Colors of Light and Stars)

Part I

1.  Vega has the hottest surface; I know that because it's bluest.
    Antares has the coolest surface because it's reddest.

    Hotter things emit bluer light than red things; 
    (this is the Wein law  lambda(micron) = 2900 / T(Kelvin)  )

2.  Kaler says that Antares has an apparent magnitude of 0.96 (see page xiii
    on Kaler for explanation), and a luminosity of 90,000 L_sun.

    He says Arcturus is apparently even brighter, at magnitude -0.04,
    and has a luminosity of 215 L_sun.

    He finally says Vega is a bit fainter than Arcturus, at magnitude 0.03
    (they're really about the same, within 7% of each other), and has
    a luminosity of 54 L_sun.

    So Arcturus looks the brightest, antares looks the faintest.

    Antares emits the most light, Vega emits the least light.

3.  Temperature is the easier quantity of stars to measure (since it
    doesn't depend on distance.)

4.  To know luminosity, I also need to know how far away the star is.

PART II

1 a.  Gliese 229B is a brown dwarf, so its interesting because it's...
        [anything right and vaguely relevant, like:]
	* a failed star.
        * some of the missing matter.
        * a link between planets and stars.
 	* full of weird, complicated molecular chemistry.
        * they've only been discovered recently.
        
  b.   Gl 229B is putting out most of its light at 3 micron (see math below). 
         wavelength (micron) = 2900 / T(kelvin)
                             = 2900 / 950 K 
                             = 3.0 micron   (4x redder than you can see)
   c.  The 3 micron camera onboard SIRTF is the closest match.

2  a.  The dist disk around Vega is worth studying because..
      *   it's similar to the debris in our own solar system.
      *   gaps or other disk features may tell you that planets are there.
      *   we'd like to know about the asteroids and comets around other stars.
      *   we'd ike to know what the dust around other stas is made of.
         ...
   b.  wavelength (micron) = 2900 / Temperature (Kelvin)
                           = 2900 / 70 K
                           = 40 micron 
   c.  So no camera onboard SIRTF sees the peak wavelength of this emission.
       The best cameras to use to see this light are the 24 and 70 micron cameras,
       because they come as close as SIRTF can get.

3  a.  Antares is interesting because....
       *  it will soon blow up.
       *  it's a huge supegiant star.
       *  it has a much hotter stellar companion.
          
    b.  wavelength (micron) = 2900 / Temperature (Kelvin)
                            = 2900 / 3100 K
                            = 0.94 micron
    c.  So Antares is putting out most of its light bluer than the SIRTF cameras can see.
        Still, if you're going to observe Antares with SIRTF, you should use the bluest camera,
        which would be the 3 micron one.