Nicholas J. Nelson

MAGNETIC WREATHS AND CYCLES IN CONVECTIVE DYNAMOS

Solar-type stars exhibit a rich variety of magnetic activity. Seeking to explore the convective origins of this activity, we have carried out a series of global three-dimensional magnetohydrodynamic simulations with the anelastic spherical harmonic code. Here we report on the dynamo mechanisms achieved as the effects of artificial diffusion are systematically decreased. The simulations are carried out at a nominal rotation rate of three times the solar value (3 Ω☉), but similar dynamics may also apply to the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreaths) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreaths. Here we demonstrate that magnetic cycles can also be achieved by reducing the diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these more turbulent models, diffusive processes no longer play a significant role in the key dynamical balances that establish and maintain the differential rotation and magnetic wreaths. Magnetic reversals are attributed to an imbalance in the poloidal magnetic induction by convective motions that is stabilized at higher diffusion levels. Additionally, the enhanced levels of turbulence lead to greater intermittency in the toroidal magnetic wreaths, promoting the generation of buoyant magnetic loops that rise from the deep interior to the upper regions of our simulated domain. The implications of such turbulence-induced magnetic buoyancy for solar and stellar flux emergence are also discussed.

BUOYANT MAGNETIC LOOPS IN A GLOBAL DYNAMO SIMULATION OF A YOUNG SUN

The current dynamo paradigm for the Sun and Sun-like stars places the generation site for strong toroidal magnetic structures deep in the solar interior. Sunspots and starspots on Sun-like stars are believed to arise when sections of these magnetic structures become buoyantly unstable and rise from the deep interior to the photosphere. Here, we present the first three-dimensional global magnetohydrodynamic (MHD) simulation in which turbulent convection, stratification, and rotation combine to yield a dynamo that self-consistently generates buoyant magnetic loops. We simulate stellar convection and dynamo action in a spherical shell with solar stratification, but rotating three times faster than the current solar rate. Strong wreaths of toroidal magnetic field are realized by dynamo action in the convection zone. By turning to a dynamic Smagorinsky model for subgrid-scale turbulence, we here attain considerably reduced diffusion in our simulation. This permits the regions of strongest magnetic field in these wreaths to rise toward the top of the convection zone via a combination of magnetic buoyancy instabilities and advection by convective giant cells. Such a global simulation yielding buoyant loops represents a significant step forward in combining numerical models of dynamo action and flux emergence.

Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much higher values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength of the axisymmetric toroidal field is not a good predictor of the production rate for buoyant loops or the amount of magnetic flux in the loops that are produced.

Strong Dynamo Action in Rapidly Rotating Suns

Stellar dynamos are driven by complex couplings between rotation and turbulent convection, which drive global‐scale flows and build and rebuild stellar magnetic fields. When stars like our sun are young, they rotate much more rapidly than the current solar rate. Observations generally indicate that more rapid rotation is correlated with stronger magnetic activity and perhaps more effective dynamo action. Here we examine the effects of more rapid rotation on dynamo action in a star like our sun. We find that vigorous dynamo action is realized, with magnetic field generated throughout the bulk of the convection zone. These simulations do not possess a penetrative tachocline of shear where global‐scale fields are thought to be organized in our sun, but despite this we find strikingly ordered fields, much like sea‐snakes of toroidal field, which are organized on global scales. We believe this to be a novel finding.

Generating buoyant magnetic flux ropes in solar-like convective dynamos

Our Sun exhibits strong convective dynamo action which results in magnetic flux bundles emerging through the stellar surface as magnetic spots. Global-scale dynamo action is believed to generate large-scale magnetic structures in the deep solar interior through the interplay of convection, rotation and shear. Portions of these large-scale magnetic structures are then believed to rise through the convective layer, forming magnetic loops which then pierce the photosphere as sunspot pairs. Previous global simulations of three-dimensional magnetohydrodynamic convection in rotating spherical shells have demonstrated mechanisms whereby large-scale magnetic wreaths can be generated in the bulk of the convection zone. Our recent simulations have achieved sufficiently high levels of turbulence to permit portions of these wreaths to become magnetically buoyant and rise through the simulated convective layer through a combination of magnetic buoyancy and advection by convective giant cells. These buoyant magnetic loops are created in the bulk of the convective layer as strong Lorentz force feedback in the cores of the magnetic wreaths dampen small-scale convective motions, permitting the amplification of local magnetic energies to over 100 times the local kinetic energy. While the magnetic wreaths are largely generated the shearing of axisymmetric poloidal magnetic fields by axisymmetric rotational shear (the Ω-effect), the loops are amplified to their peak field strengths before beginning to rise by non-axisymmetric processes. This further extends and enhances a new paradigm for the generation of emergent magnetic flux bundles, which we term turbulence-enabled magnetic buoyancy.

Global magnetic cycles in rapidly rotating younger suns

Observations of sun-like stars rotating faster than our current sun tend to exhibit increased magnetic activity as well as magnetic cycles spanning multiple years. Using global simulations in spherical shells to study the coupling of large-scale convection, rotation, and magnetism in a younger sun, we have probed effects of rotation on stellar dynamos and the nature of magnetic cycles. Major 3D MHD simulations carried out at three times the current solar rotation rate reveal hydromagnetic dynamo action that yields wreaths of strong toroidal magnetic field at low latitudes, often with opposite polarity in the two hemispheres. Our recent simulations have explored behavior in systems with considerably lower diffusivities, achieved with sub-grid scale models including a dynamic Smagorinsky treatment of unresolved turbulence. The lower diffusion promotes the generation of magnetic wreaths that undergo prominent temporal variations in field strength, exhibiting global magnetic cycles that involve polarity reversals. In our least diffusive simulation, we find that magnetic buoyancy coupled with advection by convective giant cells can lead to the rise of coherent loops of magnetic field toward the top of the simulated domain. 1. Coupling rotation, convection, and magnetism in younger suns Global-scale magnetic fields and cycles of magnetic activity in sun-like stars are generated by the interplay of rotation and convection. At rotation rates greater than that of the current sun, such as when our sun was younger, observations tend to show increased magnetic activity indicating a strong global dynamo may be operating (Pizzolato et al. 2003). Here we explore large-scale dynamo action in sun-like stars rotating at three times the current solar rate, or 3Ω⊙, with a rotational period of 9.32 days. As shown by helioseismology, the solar interior is in a state of prominent differential rotation in the convection zone (roughly the outer 30% by radius) whereas the radiative interior is in uniform rotation. A prominent shear layer, or tachocline, is evident at the interface between the convective and radiative regions. Motivated by these observations, a number of theoretical models have been proposed for the solar Global magnetic cycles in rapidly rotating younger suns 2 Figure 1. (A) Radial velocity in global Mollweide projection at 0.94R⊙ with fast, narrow downflows in dark tones and broad, slow upflows in light tones. (B) Differential rotation profile, with lines of constant angular velocity Ω largely along cylinders, as expected for rapidly rotating systems. Some deviation toward conical contours is seen at low latitudes. Magnetic wreaths tend to form in the regions of strong shear near the equator. dynamo. The current paradigms for large-scale solar dynamo action favor a scenario in which the generation sites of toroidal and poloidal fields are spatially separated (e.g., Charbonneau 2005). Poloidal fields generated by cyclonic turbulence within the bulk of the convection zone, or by breakup of active regions, are pumped downward to the tachocline of rotational shear at its base. The differential rotation there stretches such poloidal fields into strong toroidal structures, which may succumb to magnetic buoyancy instabilities and rise upward to pierce the photosphere as curved structures that form the observed active regions. Similiar dynamo processes are believed to be active in sun-like stars rotating several times faster than the current sun. Here we explore a variation to this paradigm by excluding the tachocline and the photosphere from our simulated domain, which extends from 0.72R⊙ to 0.96R⊙, in order to see if magnetic cycles can be realized in the bulk of the convection zone itself. Using massively-parallel supercomputers, we solve the nonlinear anelastic MHD equations in rotating 3-D spherical shells using the anelastic spherical harmonic (ASH) code (Brun et al. 2004). The anelastic approximation filters out fast-moving sound and magneto-acoustic waves, allowing us to follow the decidedly subsonic flows in the solar convection zone with overturning times of days to months. In large-eddy simulation (LES) such as those using ASH, the effects of small, unresolved scales on larger scales must be parameterized using a turbulence closure model. Previous ASH simulations of convective dynamos in sun-like stars rotating at 3Ω⊙ have yielded large-scale wreaths of strong toroidal magnetic field in the bulk of their convection zones (Brown et al 2010). These wreaths persist for decades of simulation time, remarkably coexisting with the strongly turbulent flows. Here we explore the effects of decreased levels of diffusion on these wreaths in two simulations, labeled case B and case S. Case B uses an eddy viscosity that varies with depth as the square root of the mean density. Case S uses the dynamic Smagorinsky model of Germano et al. (1991), which is based on the assumption of self-similarity in the inertial range of the velocity spectra. Case S has 50 times less diffusion on average than case B. Figure 1a shows the radial velocity field for case S near the top of the convection zone with columnar cells at low latitudes and smaller-scale helical convection at higher latitudes. Figure 1b shows the differential rotation profile for case S with roughly 20% (250 nHz) Global magnetic cycles in rapidly rotating younger suns 3 Figure 2. (A) Longitudinal magnetic field Bφ for case B at 0.84R⊙ in Mollweide projection, showing two strong but patchy magnetic wreaths of opposite polarity with peak field strengths of 38 kG. (B) Time-latitude plot of Bφ averaged over longitude 〈

Driving Solar Giant Cells through the Self-organization of Near-surface Plumes

Global 3D simulations of solar giant-cell convection have provided significant insight into the processes which yield the Suns observed differential rotation and cyclic dynamo action. However, as we move to higher resolution simulations a variety of codes have encountered what has been termed the convection conundrum. As these simulations increase in resolution and hence the level of turbulence achieved, they tend to produce weak or even anti-solar differential rotation patterns associated with a weak rotational influence (high Rossby number) due to large convective velocities. One potential culprit for this convection conundrum is the upper boundary condition applied in most simulations which is generally impenetrable. Here we present an alternative stochastic plume boundary condition which imposes small-scale convective plumes designed to mimic near-surface convective downflows, thus allowing convection to carry the majority of the outward solar energy flux up to and through our simulated upper boundary. The use of a plume boundary condition leads to significant changes in the convective driving realized in the simulated domain and thus to the convective energy transport, the dominant scale of the convective enthalpy flux, and the relative strength of the strongest downflows, the downflow network, and the convective upflows. These changes are present even far from the upper boundary layer. Additionally, we demonstrate that in spite of significant changes, giant cell morphology in the convective patterns is still achieved with self-organization of the imposed boundary plumes into downflow lanes, cellular patterns, and even rotationally-aligned banana cells in equatorial regions. This plume boundary presents an alternative pathway for 3D global convection simulations where driving is non-local and may provide a new approach towards addressing the convection conundrum.