  If the dark matter particles are axions, gravity can cause them to coalesce
into axion stars, which are stable gravitationally bound systems of axions. In
the previously known solutions for axion stars, gravity and the attractive
force between pairs of axions are balanced by the kinetic pressure. The mass of
these dilute axion stars cannot exceed a critical mass, which is about
$10^{-14} M_\odot$ if the axion mass is $10^{-4}$~eV. We study axion stars
using a simple approximation to the effective potential of the nonrelativistic
effective field theory for axions. We find a new branch of dense axion stars in
which gravity is balanced by the mean-field pressure of the axion Bose-Einstein
condensate. The mass on this branch ranges from about $10^{-20} M_\odot$ to
about $M_\odot$. If a dilute axion star with the critical mass accretes
additional axions and collapses, it could produce a bosenova, leaving a dense
axion star as the remnant.
