  We investigate the rising flux tube and the formation of sunspots in an
unprecedentedly deep computational domain that covers the whole convection zone
with a radiative magnetohydrodynamics simulation. Previous calculations had
shallow computational boxes (< 30 Mm) and convection zones at a depth of 200
Mm. By using our new numerical code R2D2, we succeed in covering the whole
convection zone and reproduce the formation of the sunspot from a simple
horizontal flux tube because of the turbulent thermal convection. The main
findings are (1) The rising speed of the flux tube is larger than the upward
convection velocity because of the low density caused by the magnetic pressure
and the suppression of the mixing. (2) The rising speed of the flux tube
exceeds 250 m/s at a depth of 18 Mm, while we do not see any clear evidence of
the divergent flow 3 hr before the emergence at the solar surface. (3)
Initially, the root of the flux tube is filled with the downflows and then the
upflow fills the center of the flux tube during the formation of the sunspot.
(4) The essential mechanisms for the formation of the sunspot are the coherent
inflow and the turbulent transport. (5) The low-temperature region is extended
to a depth of at least 40 Mm in the matured sunspot, with the high-temperature
region in the center of the flux tube. Some of the findings indicate the
importance of the deep computational domain for the flux emergence simulations.
