Differential Rotation and Emerging Flux in Solar Convective Dynamo Simulations

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1 Differential Rotation and Emerging Flux in Solar Convective Dynamo Simulations Yuhong Fan (HAO/NCAR), Fang Fang (LASP/CU) GTP workshop August 17, 2016 The High Altitude Observatory (HAO) at the National Center for Atmospheric Research (NCAR). The National Center for Atmospheric Research is sponsored by the National Science Foundation. Any opinions, findings and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

2 Finite-difference Spherical Anelastic MHD (FSAM) code solves the following anelastic MHD equations in a partial spherical shell domain: where D is the viscous stress tensor, and F rad is the radiative diffusive heat flux :

3 Simulation setup Simulation domain r Î ( 0.722R s, 0.971R s ), q Î ( p / 2 - p / 3, p / 2 + p / 3), f Î ( 0,2p ) Grid: 96(r) 512(q) 768(f), horizontal res. at top boundary 2.8 Mm to 5.5 Mm, vertical res. 1.8 Mm K = cm 2 s -1, n =10 12 cm 2 s -1, h =10 12 cm 2 s -1, at top and decrease with depth as 1/ r (Fan and Fang 2014) K is the same as above but n=0, h=0 (Fan and Fang 2016) Convection is driven by the radiative diffusive heat flux as a source term Ñ F rad in the entropy equation: The boundary condition for s 1 : The velocity boundary condition is non-penetrating and stress free at the and the top, bottom and q- bondaries For the magnetic field: perfect conducting walls for the bottom and the q-boundaries; radial field at the top boundary Angular rotation rate for the reference frame reference frame is zero., net angular momentum relative to the

4 Fan and Fang (2014) at r = 0.73 Rs

5 minimum maximum

6 RS = r 0 r^ v r^ v f MS = - 1 4p r^ B r^b f Ro = u rms / (WH p ) = 0.74 dynamo B=0 Ro = u rms / (WH p ) = 0.96 HD increase viscosity Ro = u rms / (WH p ) = 0.71 HVHD

7 Angular momentum flux density due to meridional circulation: F mc = r 0 L v m, where L = r^ 2 W If L» L(r^), then the net angular momentum flux across a constant r^ cylinder (e.g. Miesch 2005, Rempel 2005): f (r^) = ò r 0 L(r^) v m ds» L(r^) ò r 0 v m ds = 0 s(r^ ) Meridional circulation does not transport net angular momentum across the cylinders, but only redistributes it along the cylinders A net angular momentum flux across the cylinders by the Reynolds stress cannot be balanced by meridional circulation differential rotation s(r^ )

8 RS = r 0 r^ v r^ v f MS = - 1 4p r^ B r^b f Ro = u rms / (WH p ) = 0.74 dynamo B=0 Ro = u rms / (WH p ) = 0.96 HD increase viscosity Ro = u rms / (WH p ) = 0.71 HVHD

9 dynamo HVHD HD

10 Less diffusive dynamo dynamo Less diffusive dynamo dynamo

11 m=0 modes excluded Solid lines: less diffusive dynamo Dashed lines: dynamo Dotted line: hydro Solid lines: less diffusive dynamo Dashed lines: dynamo Dotted line: hydro Less diffusive dynamo dynamo W buoyancy L sol L sol W lorentz L sol L sol Solid lines: less diffusive dynamo Dashed lines: dynamo

12 with latitudinal gradient of s at base of CZ without latitudinal gradient of s at base of CZ

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14 Tilt angles of super-equipartition flux emergence areas at R s : Conform to Hale s rule by 2.4 to 1 in area Statistically significant mean tilt angle: 7.5 ± 1.6 Weak Joy s law trend

15 Strong emerging flux bundles sheared by giant cell convection Emerging fields are not isolated flux tubes rising from the bottom of the CZ, but are continually formed in the bulk of the CZ through sheared amplification by the giant-cell convection The emerging flux bundle is sheared into a hairpin shape with the leading end up against the down flow lane of the giant cell.

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17 Inserting strong, buoyant toroidal flux tubes at the base of the CZ with the background convective dynamo: Untwisted toroidal flux tubes: B = 100 kg, a = 0.16 H p, F = Mx For magnetic buoyancy to dominate convection: æ B > H ö p ç è a ø 1/2 B eq B eq for rms speed ~ 5-10 kg B eq for peak downflow ~ 60 kg

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19 Tilt angles of super-equipartition flux emergence areas at R s : Less diffusive dynamo case: Conform to Hale s rule by 2.7 to 1 in area Statistically significant mean tilt angle: 4.5 ± 1.6 Weak Joy s law trend Less diffusive dynamo + 2 strong toroidal tubes: Conform to Hale s rule by 2.7 to 1 in area Statistically significant mean tilt angle: 7.4 ± 2.2 Weak Joy s law trend

20 Inserting strong toroidal flux tubes at the base of the CZ with the background convective dynamo: Untwisted toroidal flux tubes: B = 100 kg, a = 0.24 H p, F = Mx

21 Summary Simulations of 3D convective dynamo in the rotating solar convective envelope driven by the radiative heat flux: o produce a large-scale mean magnetic field that exhibits irregular cyclic behavior with polarity reversals. o Produce emergence of coherent super-equipartition toroidal flux bundles with properties similar to solar active regions: following Hale s rule by 2.7:1, a weak Joy s law trend. o The presence of the magnetic fields are necessary for the self-consistent maintenance of the solar-like differential rotation. In several ways it acts like an enhanced viscosity. o With further reduced magnetic diffusivity and viscosity, we find an enhanced magnetic energy, and a reduced kinetic energy in the large scales. This results in a further enhanced outward transport (away from the rotation axis) of angular momentum by the Reynolds stress, balanced by an increased inward transport by the magnetic stress, with the transport by the viscous stress reduced to a negligible level Simulations of buoyant rise of highly super-equipartition toroidal flux tubes from the bottom of the CZ in the background convective dynamo: o For B 100 kg, the rise of active region scale flux tubes are strongly influenced by the giant-cell convection and become in-distinguishable from the background dynamo fields after rising to about the middle of the CZ o The rise of larger flux tubes (significantly greater than active region flux) from the bottom of CZ may result in changes to the differential rotation that are incompatible with observations.