Dependence of the Magnetic Energy of Solar Active Regions on the Twist   Intensity of the Initial Flux Tubes
  We present a series of numerical experiments that model the evolution of magnetic flux tubes with a different amount of initial twist. As a result of calculations, tightly twisted tubes reveal a rapid two-step emergence to the atmosphere with a slight slowdown at the surface, while weakly twisted tubes show a slow two-step emergence waiting longer the secondary instability to be triggered. This picture of the two-step emergence is highly consistent with recent observations. These tubes show multiple magnetic domes above the surface, indicating that the secondary emergence is caused by interchange mode of magnetic buoyancy instability. As for the weakest twist case, the tube exhibits an elongated photospheric structure and never rises into the corona. The formation of the photospheric structure is due to inward magnetic tension force of the azimuthal field component of the rising flux tube (i.e., tube's twist). When the twist is weak, azimuthal field cannot hold the tube's coherency, and the tube extends laterally at the subadiabatic surface. In addition, we newly find that the total magnetic energy measured above the surface depends on the initial twist. Strong twist tubes follow the initial relation between the twist and the magnetic energy, while weak twist tubes deviates from this relation, because these tubes store their magnetic energy in the photospheric structures. 
Shin Toriumi, Takehiro Miyagoshi, Takaaki Yokoyama, Hiroaki Isobe, and   Kazunari Shibata
astro-ph.SR