Numerical Simulations of Active Region Scale Flux Emergence: From Spot Formation to Decay

Abstract

We present numerical simulations of active region scale flux emergence covering a time span of up to 6 days. Flux emergence is driven by a bottom boundary condition that advects a semi-torus of magnetic field with 1.7 × 10 22 Mx flux into the computational domain. The simulations show that, even in the absense of twist, the magnetic flux is able the rise through the upper 15.5 Mm of the convection zone and emerge into the photosphere to form spots. We find that spot formation is sensitive to the persistence of upflows at the bottom boundary footpoints, i.e. a continuing upflow would prevent spot formation. In addition, the presence of a torus-aligned flow (such flow into the retrograde direction is expected from angular momentum conservation during the rise of flux ropes through the convection zone) leads to a significant asymmetry between the pair of spots, with the spot corresponding to the leading spot on the Sun being more axisymmetric and coherent, but also forming with a delay relative to the following spot. The spot formation phase transitions directly into a decay phase. Subsurface flows fragment the magnetic field and lead to intrusions of almost field free plasma underneath the photosphere. When such intrusions reach photospheric layers, the spot fragments. The time scale for spot decay is comparable to the longest convective time scales present in the simulation domain. We find that the dispersal of flux from a simulated spot in the first two days of the decay phase is consistent with self-similar decay by turbulent diffusion.

Magnetic flux concentrations from dynamo-generated fields

“…Further concentration into thinner tubes would be required if they were to explain sunspots by just letting them pierce the surface. Realistic hydromagnetic simulations of the solar surface are now beginning to demonstrate that ≈10 kG fields at a depth of ≈10 Mm can produce sunspot-like appearances at the surface (Rempel & Cheung 2014). However, we have to ask about the physical process contributing to this phenomenon.…”

“…While global convective dynamo simulations of Nelson et al (2011Nelson et al ( , 2013Nelson et al ( , 2014 show magnetically buoyant magnetic flux tubes of ≈40 kG field strength, they do not yet address bipolar region formation. Indeed, solar surface simulations of Cheung et al (2010) and Rempel & Cheung (2014) A&A 568, A112 (2014) demonstrate that bipolar spots do form once a magnetic flux tube of 10 kG field strength is injected at the bottom of their local domain (7.5 Mm below the surface). On the other hand, the deep solar simulations of Stein & Nordlund (2012) develop a bipolar active region with just 1 kG magnetic field injected at the bottom of their domain.…”

What can large-scale magnetohydrodynamic numerical experiments tell us about coronal heating?

“…However, one can couple a flux emergence model forming an active region [96,97] that covers the solar interior and the near-surface magneto-convection to a coronal model [68]. Some results of this model have already been discussed in §4f.…”

Bipolar Magnetic Spots From Dynamos in Stratified Spherical Shell Turbulence

“…Downdrafts have also been seen in simulations of buoyantly rising flux tubes some time after they reached the surface (Rempel & Cheung 2014). A possible mechanism for producing such downflows might well be the negative effective magnetic pressure instability (NEMPI).…”