The 21cm Signature of Early Relic \HII Regions
  We calculate the spin temperature and 21 cm brightness of early \HII regions
around the first stars. We use outputs from cosmological
radiation-hydrodynamics simulations of the formation and evolution of early
\HII regions. In the pre-reionization era, \HII regions around massive
primordial stars have diameters of a few kpc. The gas within the \HII regions
is almost fully ionized, but begins recombining after the central stars die
off. The relic \HII regions are then seen as bright {\it emission} sources in
hydrogen 21 cm. We make brightness temperature maps of the \HII regions,
accounting for radiative coupling with Lyman-$\alpha$ photons in a simplified
manner. The spin temperature in the relic \HII region is close to the gas
kinetic temperature, generally several hundred to several thousand degrees. We
show that the relic \HII region can be as bright as $\delta T_{\rm b} \sim 100$
mK in differential temperature against the cosmic microwave background for an
angular resolution of sub-arcseconds. While individual early \HII patches will
not be identified by currently planned radio telescopes, the collective
fluctuations from early \HII regions might imprint signatures in the 21 cm
background.
