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We investigate the rising flux tube and the formation of sunspots in anunprecedentedly deep computational domain that covers the whole convection zonewith a radiative magnetohydrodynamics simulation. Previous calculations hadshallow computational boxes (< 30 Mm) and convection zones at a depth of 200Mm. By using our new numerical code R2D2, we succeed in covering the wholeconvection zone and reproduce the formation of the sunspot from a simplehorizontal flux tube because of the turbulent thermal convection. The mainfindings are (1) The rising speed of the flux tube is larger than the upwardconvection velocity because of the low density caused by the magnetic pressureand the suppression of the mixing. (2) The rising speed of the flux tubeexceeds 250 m/s at a depth of 18 Mm, while we do not see any clear evidence ofthe 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 theupflow 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 coherentinflow and the turbulent transport. (5) The low-temperature region is extendedto a depth of at least 40 Mm in the matured sunspot, with the high-temperatureregion in the center of the flux tube. Some of the findings indicate theimportance of the deep computational domain for the flux emergence simulations.

On rising magnetic flux tube and formation of sunspots in a deep domain