  The first phase of stellar evolution in the history of the Universe may be
Dark Stars, powered by dark matter heating rather than by nuclear fusion.
Weakly Interacting Massive Particles, which may be their own antipartners,
collect inside the first stars and annihilate to produce a heat source that can
power the stars for millions to billions of years. In this paper we show that
these objects can grow to be supermassive dark stars (SMDS) with masses
$\gtrsim (10^5-10^7) \msun$. The growth continues as long as dark matter
heating persists, since dark stars are large and cool (surface temperature
$\lesssim 5\times 10^4$K) and do not emit enough ionizing photons to prevent
further accretion of baryons onto the star. The dark matter may be provided by
two mechanisms: (1) gravitational attraction of dark matter particles on a
variety of orbits not previously considered, and (2) capture of WIMPs due to
elastic scattering. Once the dark matter fuel is exhausted, the SMDS becomes a
heavy main sequence star; these stars eventually collapse to form massive black
holes that may provide seeds for supermassive black holes in the Universe. SMDS
are very bright, with luminosities exceeding $(10^9-10^{11}) L_\odot$. We
demonstrate that for several reasonable parameters, these objects will be
detectable with JWST. Such an observational discovery would confirm the
existence of a new phase of stellar evolution powered by dark matter.
