The Dynamic Evolution of Twisted Magnetic Flux Tubes in a Three‐dimensional Convecting Flow. I. Uniformly Buoyant Horizontal Tubes

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Abstract
We present three-dimensional numerical simulations of the dynamic evolution of uniformly buoyant, twisted horizontal magnetic flux tubes in a three-dimensional stratified convective velocity field. Our calculations are relevant to understanding how stratified convection in the deep solar convection zone may affect the rise and the structure of buoyant flux tubes that are responsible for the emergence of solar active regions. We find that in order for the magnetic buoyancy force of the tube to dominate the hydrodynamic force due to the convective downflows, the field strength B of the flux tube needs to be greater than ðHp=aÞ 1=2 Beq � 3Beq ,w hereHp is the pressure scale height, a is the tube radius, and Beq is the field strength in equipartition with the kinetic energy density of the strong downdrafts. For tubes of equipartition field strength (B ¼ Beq), the dynamic evolution depends sensitively on the local condition of the convective flow. Sections of the tube in the paths of strong downdrafts are pinned down to the bottom despite their buoyancy, while the rise speed of sections within upflow regions is significantly boosted; � -shaped emerging tubes can form between downdrafts. Although flux tubes with B ¼ Beq are found to be severely distorted by convection, the degree of distortion obtained from our simulations is not severe enough to clearly rule out the � -tubes that are able to emerge between downdrafts as possible progenitors of solar active regions. As the initial field strength of the tube becomes higher than the critical value of �ð Hp=aÞ 1=2 Beq given above, the dynamic evolution converges toward the results of previous simulations of the buoyant rise of magnetic flux tubes in a static, adiabatically stratified model solar convection zone. Tubes with 10 times the equipartition field strength are found to rise unimpeded by the downdrafts and are not significantly distorted by the three-dimensional convective flow. Subject headings: convection — methods: numerical — MHD — Sun: interior — Sun: magnetic fields