  Dark Stars are the very first phase of stellar evolution in the history of
the universe: the first stars to form (typically at redshifts $z \sim 10-50$)
are powered by heating from dark matter (DM) annihilation instead of fusion (if
the DM is made of particles which are their own antiparticles). We find
equilibrium polytropic configurations for these stars; we start from the time
DM heating becomes important ($M \sim 1-10 M_\odot$) and build up the star via
accretion up to 1000 M$_\odot$. The dark stars, with an assumed particle mass
of 100 GeV, are found to have luminosities of a few times $10^6$ L$_\odot$,
surface temperatures of 4000--10,000 K, radii $\sim 10^{14}$ cm, lifetimes of
at least $ 0.5$ Myr, and are predicted to show lines of atomic and molecular
hydrogen. Dark stars look quite different from standard metal-free stars
without DM heating: they are far more massive (e.g. $\sim 800 M_\odot$ for 100
GeV WIMPs), cooler, and larger, and can be distinguished in future
observations, possibly even by JWST or TMT.
