Estimate the size of the white dwarf stars near
        a color of (BP - RP) = 1.

         The white dwarfs are about 10 magnitudes fainter than
         the normal, main-sequence stars at this color.
         A difference of (m1 - m2) = 10 mag corresponds
         to a ratio of (m2/m1) = 10,000 in luminosity.

         If they have the same temperature, then

                               2                4
                Lum  =  (4 pi R  ) *  (sigma * T  )


         they must have an area only 1/10,000 of a main-sequence star.
         Since area goes as radius R squared, this means that
         the white dwarfs must have a radius of about 1/100 of a
         main-sequence star.

         The Sun doesn't have exactly a color of (BP - RP) = 1,
         but we can use it as a generic main-sequence star.
         It has a radius of about 7 x 10^(8) meters, so a white
         dwarf must have a radius about 7 x 10^(6) meters,

              Radius ~  7000 km     similar to that of the Earth
         
         
         

 


   Are all main sequence stars exactly the same size?

        If all stars had exactly the same radius R, then
        their luminosities would rise as temperature to the 
        fourth power:
 
                               2                4
                Lum  =  (4 pi R  ) *  (sigma * T  )


        On a log-log graph, we see that luminosity increases
        with a slope of GREATER than 4; that means that
        hot stars must be LARGER than cool ones, in order
        to increase in luminosity faster than T^4.





    If not, are bluer main-sequence stars larger or smaller
         than red main-sequence stars?


        Very hot, but low in luminosity.  The only way that 
        a hot object can emit very little light is if it has
        a small surface area.  We could call these "white dwarfs."