HAO 2012 Profiles In Science: Dr. Mark Miesch

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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 ultimate origins of solar magnetism, seeking synergies between solar and stellar observations, numerical models, and theoretical insights. All dynamos models of the solar activity cycle rely heavily on global-scale mean flows, namely differential rotation and meridional circulation, that help to amplify and organize magnetic fields, establishing order in an otherwise chaotic convection zone. The origin of these mean flows lies in the dynamics of convection, which most dynamo models take for granted. Although a thorough understanding of deep convection requires sophisticated numerical models, much can be learned from a careful scrutiny of helioseismic observations. In particular, Miesch et al (2012) have shown that the structure and amplitude of the differential rotation and meridional circulation inferred from helioseismology provides fundamental constrains on the deep convection that maintains them. Together with recent complementary helioseismic inversions published by other authors, these constraints place tight limits on the structure and amplitude of deep convection that could promote substantial progress in the coming years. Meanwhile, the leading-edge numerical models of solar and stellar convection by Miesch and colleaguescontinue to improve. The abundant observational data on differential rotation in other stars can be exploited to help validate the model and to help elucidate the underlying physics. This is the motivation behind the recent study of F-type stars (1.2–1.3 times more massive than the Sun) by Augustson et al (2012). The modeled scaling laws for the differential rotation are consistent with stellar observations and the meridional circulation is found to decrease with increasing rotation, posing serious challenges for flux-transport dynamo models. These are also the first stellar convection simulations to exhibit a non-axisymmetric shearing instability, exciting Rossby wave modes that could also exist in stars like the Sun.

Another process that is of fundamental importance in solar dynamo theory but which is generally taken for granted is that of flux emergence. Sunspots and related active regions are thought to originate from the buoyant rise and emergence through the photosphere of subsurface toroidal fields. Understanding this process is necessary in order to link dynamo models to observations of solar and stellar activity and it may play an essential role in the operation of the dynamo, as postulated in so-called Babcock-Leighton dynamo models. In 2011, Miesch and colleagues published the first ever convection simulation to exhibit the self-consistent generation and rise of buoyant toroidal flux structures. In the past year, they have built upon this research to further investigate the nature of the dynamo that produces them (Nelson et al 2012a) and the statistical characteristics of the buoyant flux structures themselves (Nelson et al 2012b). These models are reshaping our paradigm of how buoyant flux tubes are generated in the Sun and stars and are providing new insights into such phenomena as tube helicity and active longitudes.

Although a major step forward, these simulations cannot yet capture all the intricacies involved in flux emergence and dispersal. For this reason, other complementary models are necessary to explore the multifaceted dynamics and consequences of flux emergence. To this end, Weber, Fan & Miesch (2012) have investigated the interaction between rising flux tubes and convection in more detail using the thin flux tube approximation, which eliminates artificial diffusion present in magnetohydrodynamic (MHD) simulations. Meanwhile, Miesch & Brown have studied the role of flux emergence on the operation of a convective dynamo, showing that it can promote cyclic magnetic activity.

Publications

Figure 1: High resolution.

(1) Miesch, M.S., Featherstone, N.A., Rempel, M. & Trampedach, R. 2012: On the Amplitude of Convective Velocities in the Deep Solar Interior, ApJ, 753:128 (14pp).

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: We obtain lower limits on the amplitude of convective velocities in the deep solar convection zone based only on the observed properties of the differential rotation and meridional circulation together with simple and robust dynamical balances obtained from the fundamental MHD equations. The linchpin of the approach is the concept of gyroscopic pumping whereby the meridional circulation across isosurfaces of specific angular momentum is linked to the angular momentum transport by the convective Reynolds stress. We find that the amplitude of the convective velocity must be at least 30 m/s in the upper CZ (r ~ 0.95 R) and at least 8 m/s in the lower CZ (r ~ 0.75 R) in order to be consistent with the observed mean flows. Using the base of the near-surface shear layer as a probe of the rotational influence, we are further able to show that the characteristic length scale of deep convective motions must be no smaller than 5.5–30 Mm. These results are compatible with convection models but suggest that the efficiency of the turbulent transport assumed in advection-dominated flux-transport dynamo models is generally not consistent with the mean flows they employ.

(2) Augustson, K.C., Brown, B.P., Brun, A.S., Miesch, M.S. & Toomre, J. 2012: Convection and Differential Rotation in F-Type Stars, ApJ, 756:169 (23pp).

Figure 2: High resolution.

Abstract: The Sun is a star, and a complete understanding of its internal dynamics can only come if it is considered within the context of other stars. Thanks to ongoing ground based observations and recent space missions such as Kepler and CoRot, we now have a large sample of observational data on how the differential rotation in stars varies with rotation rate and stellar type. This is particularly true for stars slightly (20-30 percent) more massive than the Sun that fall into the classification of F-type stars. Here we present numerical simulations of convection and differential rotation in F-type stars carried out with the ASH (Anelastic Spherical Harmonic) code. The simulations are carried out in spherical shells that encompass most of the convection zone and a portion of the stably stratified radiative zone below it, allowing us to explore the effects of overshooting convection. We find that the differential rotation Delta Omega increases with mass M and rotation rate Omega approximately as M^3.9 Omega^0.6 while the kinetic energy of the mean meridional flow decreases as M^-1.2 Omega^-0.8. Accompanying the growing differential rotation is a significant latitudinal temperature contrast whereby the poles are warmer than the equator by as much as 1000K in the most rapidly rotating cases. The temperature difference between the equator and poles scales as Delta T ~M^6.4 Omega^1.6. Additionally, three of our simulations exhibit a global-scale shear instability that originates in the stable zone and spreads up to the convection zone. This is the first time such an instability has been achieved in a global convection simulation in which the shear is self-consistently maintained by the convection itself.

Figure 2 caption: Illustration of convective patterns (left column) and differential rotation (right column) in numerical simulations of F type stars with a mass of 1.2 solar masses. Such stars have narrower convection zones than the Sun (evident in the right column), and this is reflected in the convective patterns, which show a clear distinction between rotationally-aligned columns near the equator and an interconnected network near the poles. The top and bottom rows correspond respectively to rotation rates of 5 and 20 times faster than the Sun. The images in the left column are snapshots near the surface of the star in Molleweide projection, with yellow/orange tones in the left column indicating upflowing plasma (positive radial velocity Vr) and blue/black tones denote downflowing plasma (negative Vr). White/red and blue/black tones in the right column denote faster and slower rotation respectively. The coupling between the convection zone and the thin but significant stable zone (below the dashed line) helps shape the form of the Omega contours.

Figure 3: High resolution.

(3) Nelson, N.J., Brown, B.P., Brun, A.S., Miesch, M.S. & Toomre, J. 2012: Magnetic Wreathes and Cycles in Convective Dynamos, ApJ, submitted (22pp).

Abstract: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 3D magnetohydrodynamic (MHD) simulations with the anelastic spherical harmonic (ASH) 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 Omega_sun), but similar dynamics may also be occurring in the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreathes) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreathes. 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 wreathes. 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 wreathes, 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.

Figure 3 caption: Buoyant magnetic loops evolving from small-scale wreath sections generated by rotational shear and convective turbulence. (a) Field line rendering of magnetic wreathes at low latitudes. Field lines are colored by the strength of the longitudinal field component (Bphi; negative in blue, positive in red). (b) Zoom-in on region highlighted in (a) showing field line tracings of the core of the loops, colored by the total magnetic field strength (with purple and yellow denoting weak and strong fields as indicated in the color table). The volume rendering shows Bphi using the same color scheme as in (a). (c ) The same region four days later, showing the rise and expansion of the loops.

Figure 4: High resolution.

(4) Nelson, N.J., Brown, B.P., Brun, A.S., Miesch, M.S. & Toomre, J. 2012b: Buoyant Magnetic Loops Generated by Global Convective Dynamo Action, Solar Physics, submitted (22pp).

Abstract: Our global 3D simulations of convective dynamos in solar-like stars have revealed that coherent, magnetic flux structures can be built and sustained in the midst of a turbulent convection zone. Furthermore, we have shown that if the diffusion is low enough, the coupled action of rotational shear and turbulent intermittency can induce the cores of these wreathes to form buoyant loops that rise through the convection zone. Here we examine the characteristics of these buoyant loops by identifying over 100 realizations produced by a single simulation, rotating at three times the solar rate (3 Omega_sun). We quantify statistical trends in the polarity, twist, and tilt of these loops which are qualitatively consistent with observations. Loops are shown to arise preferentially in longitudinal patches reminiscent of active longitudes in the Sun, though broader in extent. We show that the production of buoyant loops occurs in non axisymmetric structures that are not reliably traced by the mean (axisymmetric) toroidal field.

Figure 4 caption: Molleweide projection of the longitudinal component of the magnetic field (Bphi) between ± 45 degrees latitude in the lower convection zone for a simulation of a rapidly-rotating solar-like star. Red and blue tones denote eastward (positive) and westward (negative) field respectively, averaged over half of a magnetic cycle. Symbols indicate the location of 131 buoyant loops identified in the simulation. The emergence patterns are suggestive of the phenomenon of active longitudes observed in the Sun.

Figure 5: High resolution.

(5) Weber, M.A., Fan, Y. & Miesch, M.S. 2012: Comparing Simulations of Rising Flux Tubes Through the Solar Convection Zone with Observations of Solar Active Regions: Constraining the Dynamo Field Strength, Solar Physics, submitted (30pp).

Abstract: The simulations of convective dynamos by Nelson et al (2011, 2012a,b) are the first to self-consistently produce buoyant toroidal flux structures that rise through the convection zone. However, the artificial diffusion in these and comparable 3D magnetohydrodynamic (MHD) simulations causes the loops to disperse before they reach the stellar surface. This problem can be circumvented through the use of the thin flux tube approximation, which eliminates all artificial diffusion at the expense of imposing an idealized tube structure. Although such simulations cannot be used to address the generation of buoyant flux tubes, they can be used to investigate their interaction with convection in greater detail than is possible with 3D MHD simulations. In this paper we investigate the evolution of thin flux tubes embedded in a simulation of global solar convection, expanding on previous work with improved sample sizes and more extensive diagnostics. The tubes rise through the coordinated action of magnetic buoyancy and advection by and their emergence characteristics are compared with observations. Good agreement is found for flux tubes of initial strength of 40–100kG. All magnetic field strengths show a Joy's Law trend that is insensitive to the amount of magnetic flux.

Figure 5 caption: Distribution of tilt angles in 2.5 degree bins for an ensemble of rising flux tubes with a range of flux values and initial field strengths. The red line shows a non-linear least-squares Gaussian fit to the simulation data. Positive values indicate that the trailing edge of an emergent loop is displaced poleward relative to the leading edge, as seen in solar observations (Joy's Law).

Figure 6: High resolution.

(6) Miesch, M.S. & Brown, B.P. 2012: Convective Babcock-Leighton Dynamo Models, ApJ Let., 746:L26 (5pp).

Abstract: We present the first global, three-dimensional simulations of solar/stellar convection that take into account the influence of magnetic flux emergence by means of the Babcock-Leighton (BL) mechanism. We have shown that the inclusion of a BL poloidal source term in a convection simulation can promote cyclic activity in an otherwise steady dynamo. Some cycle properties are reminiscent of solar observations, such as the equatorward propagation of toroidal flux near the base of the convection zone. However, the cycle period in this young sun (rotating three times faster than the solar rate) is very short (~ 6 months) and it is unclear whether much longer cycles may be achieved within this modeling framework, given the high efficiency of field generation and transport by the convection. Even so, the incorporation of mean-field parameterizations in 3D convection simulations to account for elusive processes such as flux emergence may well prove useful in the future modeling of solar and stellar activity cycles.

Figure 6 caption: Simulated "Butterfly diagram" in a convective dynamo simulation of a star rotating 3 times faster than the Sun that includes Babcock-Leighton (BL) forcing. The top image shows the mean (longitudinally-averaged) toroidal field in the mid convection zone as a function of latitude and time. Red and blue denote positive (eastward) and negative (westward) values respectively, with a saturation level of ±760-8145 4 kG.The amplitude of the BL alpha-effect is 100 m/s. The simulation is initiated from a steady steady dynamo with negative and positive wreathes in the northern and southern hemispheres. After a transient adjustment period, it establishes a quasi-periodic magnetic cycle.The lower frame is a zoomed-in portion of the upper frame, highlighting the magnetic cycles.