HAO 2011 Profiles In Science: Dr. Mark Miesch

Contact:

303-497-1582
miesch@ucar.edu

Area of expertise: Sun and Stars

Specialties: Astrophysical fluid dynamics and magnetohydrodynamics, solar and stellar interiors, convection, dynamo theory, differential rotation, and high-performance computing.

Dr. Mark Miesch is a Scientist II in the Long-Term Solar Variability section of NCAR's High Altitude Observatory. He received a B.Sc. degree in Applied Physics at Michigan Technological University in 1991 and a Ph.D. in Astrophysical, Planetary, and Atmospheric Sciences at the University of Colorado in 1998. Miesch came to HAO as a postdoctoral fellow in 2001 as part of NCAR's Advanced Study Program, after previous postdoctoral appointments at NASA Goddard Space Flight Center in Greenbelt, Maryland (1998) and the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge in the UK (1999–2000). Miesch's research interests lie in astrophysical and geophysical fluid dynamics and magnetohydrodynamics (MHD), with particular emphasis on solar and stellar convection, dynamo theory, and high-performance computing.

Summary of Achievements

In the past year, Miesch has continued to investigate the fundamental mechanisms by which stars like the Sun build magnetic fields. An ongoing challenge is to understand how ordered patterns of magnetic activity such as the sunspot cycle emerge from the highly turbulent conditions in the solar convection zone. The answer must lie in complex self-organization processes linking multiple spatial and temporal scales, and involving helical flows and fields, rotational shear, global circulations, magnetic buoyancy, flux emergence, and subtle boundary layers.

Recent research by Miesch and his colleagues continue to be at the leading edge of the field. They have demonstrated that magnetic cycles can occur in convective dynamos even without three elements that play a crucial role in most current dynamo models of the solar activity cycle, namely magnetic flux emergence, a tacholine of rotational shear, and significant flux transport by the mean meridional circulation. Agents of self-organization include helicity and shear, forming persistent toroidal flux structures in the midst of turbulent convection zones, defying previous theoretical expectations [Brown et al. 2011]. Recent ground-breaking simulations demonstrate that these toroidal flux structures can become buoyantly unstable, rising toward the surface [Nelson et al 2011]. These are the first convection simulations to exhibit the self-consistent generation of buoyant magnetic flux tubes by rotational shear that is maintained by the convection itself. Further work has investigated how idealized flux tubes interact with rotating convection as they emerge [Weber et al 2011].

A prerequisite to understanding the ultimate origins of the solar cycle is to understand the mean flows that are responsible for amplifying and organizing large-scale magnetic fields, namely differential rotation and meridional circulation. The most pressing current challenge in this regard is to understand the role of the complex boundary layers that straddle the solar convection zone, namely the near-surface shear layer (NSSL) above and the solar tachocline below. Miesch & Hindman [2011] have recently formulated a unified model of mean flows in the NSSL and have estimated the efficiency of turbulent transport from helioseismic inversions. Meanwhile, ambitious deep-shell simulations spanning most of the solar interior from 0.07 R to 0.96R are providing new insights into the structure of the tachocline and the dynamical coupling between the convection and radiation zones [Brun et al 2011].

Publications

(1) Brown, B.P, Miesch, M.S., Browning, M.K., Brun, A.S. & Toomre, J. 2011: Magnetic Cycles in a Convective Dynamo Simulation of a Young Solar-Type Star, Astrophysical Journal, 731:69 (19pp).

Abstract: Young solar-type stars rotate rapidly and many are quite magnetically active. Many also appear to undergo magnetic cycles similar to the 22-year solar activity cycle. We conduct simulations of dynamo action in rapidly rotating suns with the three-dimensional magnetohydrodynamic anelastic spherical harmonic (ASH) code to explore dynamo action achieved in the convection zone of a solar-type star rotating at five times the current solar rotation rate. We find that dynamo action builds substantial organized global-scale fields in the midst of the turbulent convection zone. Striking magnetic wreaths span the convection zone and coexist with the turbulent convection. A surprising feature of this wreath-building dynamo is its time-dependence. The dynamo exhibits cyclic activity and undergoes quasi-periodic polarity reversals where both the global-scale poloidal and toroidal fields change in sense on a roughly 1500~day time scale. These magnetic activity patterns emerge spontaneously from the turbulent flow and are substantially more organized temporally and spatially than those realized in our previous simulations of the solar dynamo. As the magnetic fields wax and wane in strength and flip in polarity, the primary response in the convective flows involves the axisymmetric differential rotation which varies on similar time scales. Bands of relatively fast and slow fluid propagate towards the poles on time scales of roughly 500~days and are associated with magnetic structures that propagate in the same fashion. In the Sun, similar patterns are observed in the poleward branch of the torsional oscillations, and these may represent to poleward propagating magnetic fields deep below the solar surface.

Figure 1 caption: Magnetic cycles in a young solar-like star. A) Convective patterns, shown as the radial velocity on a horizontal surface in a Molweide projection near the outer boundary of the computational domain (yellow upflow, blue/black downflow). (B) Differential rotation (pink/red faster, blue/black slower), averaged over time. Mean toroidal field at an illustrative instant (C) and as a function of latitude and time near the base of the convection zone (D). Note the organized large-scale magnetic field in the midst of the turbulentconvection zone and the quasi-periodic polarity reversals.

(2) Miesch, M.S. & Hindman, B.W. 2011: Gyroscopic Pumping in the Solar Near-Surface Shear Layer, Astrophysical Journal, in press.

Abstract: We use global and local helioseismic inversions to explore the prevailing dynamical balances in the solar Near-Surface Shear Layer (NSSL). The differential rotation and meridional circulation are intimately linked, with a common origin in the turbulent stresses of the upper solar convection zone. The existence and structure of the NSSL cannot be attributed solely to the conservation of angular momentum by solar surface convection, as is often supposed. Rather, the turbulent angular momentum transport accounts for the poleward meridional flow while the often overlooked meridional force balance is required to maintain the mid-latitude rotational shear. We suggest that the base of the NSSL is marked by a transition from baroclinic to turbulent stresses in the meridional plane that suppress Coriolis-induced circulations that would otherwise establish a cylindrical rotation profile. The turbulent angular momentum transport must be non-diffusive and directed radially inward. Inferred mean flows are consistent with the idea that turbulent convection tends to mix angular momentum but only if the mixing efficiency is inhomogeneous and/or anisotropic. The latitudinal and longitudinal components of the estimated turbulent transport are comparable in amplitude and about an order of magnitude larger than the vertical component. We estimate that it requires 2–4% of the solar luminosity to maintain the solar NSSL against the inertia of the mean flow. Most of this energy is associated with the turbulent transport of angular momentum out of the layer, with a spin-down time scale of $\sim$ 600 days. We also address implications of these results for numerical modeling of the NSSL.

Figure 2 caption: Turbulent momentum transport in the solar near-surface shear layer estimated from helioseismic inversions of mean flows and proposed force balances. Black, red, and blue lines represent latitudinal, longitudinal, and vertical transport respectively, with the latter multiplied by a factor of ten for clarity of presentation. Results are expressed as an equivalent acceleration in cgs units and plotted verses latitude for several radii (a)-(d), as indicated. It is notable that the horizonal components are comparable in amplitude even though the means used to estimate them are very different.

(3) Nelson, N.J., Brown, B.P., Brun, A.S., Miesch, M.S. & Toomre, J. 2011: Buoyant Magnetic Loops in a Global Dynamo Simulation of a Young Sun, Astrophysical Journal Letters, 739:L38 (5pp).

Abstract: 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.

Figure 3 caption: Buoyant magnetic loop in a convective dynamo simulation of a young solar-like star. (a) Time sequence of Meridional (latitude-radius) cuts showing the rise of two buoyant flux loops, A and B. Colors represent the strength of the longitudinal magnetic field, as indicated. (b) Three-dimensional visualization of magnetic field lines in one of the rising tubes. (c) Radial location of the apex of loops A and B as a funciton of time, with projected motions attributed to magnetic buoyancy (blue lines) and and advection by convective upflows (red lines) indicated.

(4) Weber, M.A., Fan, Y. & Miesch, M.S. 2011: The Rise of Active Region Flux Tubes in the Turbulent Solar Convective Envelope, Astrophysical Journal, 741:11 (14pp).

Abstract: We use a thin flux tube model in a rotating spherical shell of turbulent convective flows to study how active region scale flux tubes rise buoyantly from the bottom of the convection zone to near the solar surface. We investigate toroidal flux tubes at the base of the convection zone with field strengths ranging from 15 kG to 100 kG at initial latitudes ranging from 1¬∞ to 40¬∞ with a total flux of 1022 Mx. We find that the dynamic evolution of the flux tube changes from convection dominated to magnetic buoyancy dominated as the initial field strength increases from 15 kG to 100 kG. At 100 kG, the development of Omega-shaped rising loops is mainly controlled by the growth of the magnetic buoyancy instability. However, at low field strengths of 15 kG, the development of rising Ω-shaped loops is largely controlled by convective flows, and properties of the emerging loops are significantly changed compared to previous results in the absence of convection. With convection, rise times are drastically reduced (from years to a few months), loops are able to emerge at low latitudes, and tilt angles of emerging loops are consistent with Joy's law for initial field strengths of ≥40 kG. We also examine other asymmetries that develop between the leading and following legs of the emerging loops. Taking all the results together, we find that mid-range field strengths of ~40–50 kG produce emerging loops that best match the observed properties of solar active regions.

Figure 4 caption: Simulation of a thin magnetic flux tube rising through a turbulent convection zone. Each frame shows a snapshot of tubes with initial field strengths of 15kG (left column), 40 kG (center column), and 100 kG (right column) as each approaches the surface of the computational domain. The top and bottom rows show polar and equatorial views respectively. All simulations shown were initiated with the tube located near the base of the convection zone at a latitude of 6 degrees. Rise times are indicated and are generally shorter than values in the absence of convection.

(5) Brun, A.S., Miesch, M.S. & Toomre, J. 2011: Modeling the Dynamical Coupling of Solar Convection with the Radiative Interior, Astrophysical Journal, in press.

Abstract: The global dynamics of a rotating star like the Sun involves the coupling of a highly turbulent convective envelope overlying a seemingly benign radiative interior. We use the ASH code to develop a new class of 3-D models that nonlinearly couple the convective envelope to a deep stable radiative interior. The numerical simulation assumes a realistic solar stratification from $r=0.07$ up to 0.97 R, thus encompassing part of the nuclear core up through most of the convection zone. We find that a tachocline naturally establishes itself between the differentially rotating convective envelope and the solid body rotation of the interior, with a slow spreading that is here diffusively controlled. The rapid angular momentum redistribution in the convective envelope leads to a fast equator and slow poles, with a conical differential rotation achieved at mid latitudes, much as has been deduced by helioseismology. The convective motions are able to overshoot downward about 0.04 R into the radiative interior. However the convective meridional circulation there is confined to a smaller penetration depth and is directed mostly equatorward at the base of the convection zone. Internal gravity waves are excited by the convective overshooting, yielding a complex wave field throughout the radiative interior.

Figure 5 caption: Maintenance of the differential rotation in a deep simulation of global solar convection that incorporates much of the convection zone and radiative interior. The time-averaged transport of angular momentum by the meridional circulation (a) approximately balances that due to turbulent and viscous stresses (b) in the convection zone. Red indicates a convergence of the angular momentum flux and blue indicates a divergence. In frames, (c), (d), and (e), the net contribution in frame (b) is decomposed into contributions from the radial Reynolds stress, latitudinal Reynolds stress, and the viscous diffusion. The convergence of angular momentum near the equator by the latitudinal Reynolds stress (d) is primarily responsible for both the solar-like differential rotation profile (fast equator, slower poles) and the meridional circulation profile, which is outward at the equator and poleward in the upper convection zone. Although it is not evident from this figure, there is a slight imbalance in the viscous transport in the radiative zone that is causing the tachocline to spread downward on a time scale of about 900 years.

(6) Jones, C.A., Boronski, P., Brun, A.S., Glatzmaier, G.A., Gastine, T., Miesch, M.S. & Wicht, J. 2011: Anelastic Convection-Driven Dynamo Benchmarks, Icarus, in press.

Abstract: Benchmark solutions for fully nonlinear anelastic compressible convection and dynamo action in a rotat-ing spherical shell are proposed. Three benchmarks are specified. The first is a purely hydrodynamic case, which is steady in a uniformly drifting frame. The second is a self-excited saturated dynamo solution, also steady in a drifting frame. The third is again a self-excited dynamo but is unsteady in time, and it has a higher Rayleigh number than the steady dynamo benchmark. Four independent codes have been tested against these benchmarks, and very satisfactory agreement has been found. This provides an accurate reference standard against which new anelastic codes can be tested.

Figure 6 caption: Results from the steady dynamo benchmark. The radial velocity is shown in (a) the equatorial plane and (b) as a three-dimensional cutaway. Similar cut-away perspectives are also shown for (c) the azimuthal velocity and (d) the radial magnetic field. All quantities are dimensionless with amplitudes as shown by the color bars. The solution has an azimuthal symmetry of m=7 and is steady in a frame moving with the convection cells which propagate in a prograde direction, faster than the local rotation rate.

(7) Miesch, M.S. 2011: The Solar Dynamo, Philosophical Transactions of the Royal Society A, Special Issue: Astrophysical Processes on the Sun, guest editor C. Parnell, in press.

Abtract: The origins of solar magnetism lie below the visible surface of the Sun, in the highly turbulent convection zone. Turbulent convection operates in conjunction with rotational shear, global circulations, and intricate boundary layers to produce the rich diversity of magnetic activity we observe. Here we review recent insights into the operation of the solar dynamo obtained from solar and stellar observations and numerical models.

Figure 7 caption: Distribution of vertical magnetic flux in the solar photosphere (from Parnell et al., 2009, ApJ, 698, 75-82). Full-disk (FD) observations from the MDI instrument on SOHO (a)–combined with higher-resolution observations from the SOT instrument on Hinode (b)–reveal a power-law distribution spanning five decades of flux (c). White and black in frames (a) and (b) indicate outward and inward flux with saturation levels of 200 Mx cm-2. The Hinode/SOT field of view is indicated by the smaller of the two squares in (a). Panel (c)–includes SOT and MDI FD measurements at solar minimum (2007) as well as MDI FD measurements at solar maximum (2001), with colors as indicated. The dashed line indicates a power law with an index of -1.85. This serves as a compelling demonstration that the solar dynamo does not just produce the solar cycle. Rather, it produces a continuous spectrum of dynamically significant fields from the global dipole moment to sunspots to the smallest scales we can currently resolve.