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Hello,
Luminosity is determined by the equation L = 4*pi*R^2*a*T^4, where the
important parts are the R (radius) and T (temperature). So, if I raise
the temperature and don't change the radius, the luminosity goes up.
Likewise, if I make the star bigger without changing the temperature,
then the luminosity goes up. So, if I raise the temperature, and the
luminosity doesn't go up, then something happened to bring the luminosity
back down. The only thing left to change is the size of the star, which
must shrink. Whited dwarfs are about the size of the Earth; much smaller
than the sun.
Sirius B is a white dwarf (you should know where that fits in in size
now). Betelgeuse is a star cooler than the sun but many times more
luminous, so you should be able to figure that one out, too. Procyon is
hotter than the sun and brighter than the sun, so this you can't reason
out too well, but it turns out to be a little bit larger than the sun.
Sincerely,
Kurtis Williams
"A man is like a fraction whose numerator is what he is and
whose denominator is what he thinks of himself. The larger the
denominator the smaller the fraction. " -- Lev Tolstoy
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