Differential Rotation and Dynamics of the Solar Interior

Dynamics of Large-Scale Solar Flows

The Sun's axisymmetric large-scale flows, differential rotation and meridional circulation, are thought to be maintained by the influence of rotation on the thermal-convective motions in the solar convection zone. These large-scale flows are crucial for maintaining the Sun's global magnetic field. Over the last several decades, our understanding of large-scale motions in the Sun has significantly improved, both through observational and theoretical efforts. Helioseismology has constrained the flow topology in the solar interior, and the growth of supercomputers has enabled simulations that can self-consistently generate large-scale flows in rotating spherical convective shells. In this article, we review our current understanding of solar convection and the large-scale flows present in the Sun, including those associated with the recently discovered inertial modes of oscillation. We discuss some issues still outstanding, and provide an outline of future efforts needed to address these.

Magnetism, dynamo action and the solar-stellar connection

The Sun and other stars are magnetic: magnetism pervades their interiors and affects their evolution in a variety of ways. In the Sun, both the fields themselves and their influence on other phenomena can be uncovered in exquisite detail, but these observations sample only a moment in a single star's life. By turning to observations of other stars, and to theory and simulation, we may infer other aspects of the magnetism-e.g., its dependence on stellar age, mass, or rotation rate-that would be invisible from close study of the Sun alone. Here, we review observations and theory of magnetism in the Sun and other stars, with a partial focus on the "Solar-stellar connection": i.e., ways in which studies of other stars have influenced our understanding of the Sun and vice versa. We briefly review techniques by which magnetic fields can be measured (or their presence otherwise inferred) in stars, and then highlight some key observational findings uncovered by such measurements, focusing (in many cases) on those that offer particularly direct constraints on theories of how the fields are built and maintained. We turn then to a discussion of how the fields arise in different objects: first, we summarize some essential elements of convection and dynamo theory, including a very brief discussion of mean-field theory and related concepts. Next we turn to simulations of convection and magnetism in stellar interiors, highlighting both some peculiarities of field generation in different types of stars and some unifying physical processes that likely influence dynamo action in general. We conclude with a brief summary of what we have learned, and a sampling of issues that remain uncertain or unsolved.

Poynting-Robertson-like Drag at the Sun's Surface

The Sun's internal rotation Ω(r,Θ) has previously been measured using helioseismology techniques and found to be a complex function of colatitude θ and radius r. From helioseismology and observations of apparently "rooted" solar magnetic tracers, we know that the surface rotates more slowly than much of the interior. The cause of this slow-down is not understood, but it is important for understanding stellar rotation generally and any plausible theory of the solar interior. A new analysis using 5-min solar p-mode limb oscillations as a rotation "tracer" finds an even larger velocity gradient in a thin region at the top of the photosphere. This shear occurs where the solar atmosphere radiates energy and angular momentum. We suggest that the net effect of the photospheric angular momentum loss is similar to Poynting-Robertson "photon braking" on, for example, Sun-orbiting dust. The resultant photospheric torque is readily computed and, over the Sun's lifetime, is found to be comparable to the apparent angular momentum deficit in the near-surface shear layer.

Coronal Holes and Open Magnetic Flux over Cycles 23 and 24

As the observational signature of the footprints of solar magnetic field lines open into the heliosphere, coronal holes provide a critical measure of the structure and evolution of these lines. Using a combination of Solar and Heliospheric Observatory/Extreme ultraviolet Imaging Telescope (SOHO/EIT), Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA), and Solar Terrestrial Relations Observatory/Extreme Ultraviolet Imager (STEREO/EUVI A/B) extreme ultraviolet (EUV) observations spanning 1996 - 2015 (nearly two solar cycles), coronal holes are automatically detected and characterized. Coronal hole area distributions show distinct behavior in latitude, defining the domain of polar and low-latitude coronal holes. The northern and southern polar regions show a clear asymmetry, with a lag between hemispheres in the appearance and disappearance of polar coronal holes.

Excitation of inertial modes in an experimental spherical Couette flow

Spherical Couette flow (flow between concentric rotating spheres) is one of flows under consideration for the laboratory magnetic dynamos. Recent experiments have shown that such flows may excite Coriolis restored inertial modes. The present work aims to better understand the properties of the observed modes and the nature of their excitation. Using numerical solutions describing forced inertial modes of a uniformly rotating fluid inside a spherical shell, we first identify the observed oscillations of the Couette flow with nonaxisymmetric, retrograde, equatorially antisymmetric inertial modes, confirming first attempts using a full sphere model. Although the model has no differential rotation, identification is possible because a large fraction of the fluid in a spherical Couette flow rotates rigidly. From the observed sequence of the excited modes appearing when the inner sphere is slowed down by step, we identify a critical Rossby number associated with a given mode, below which it is excited. The matching between this critical number and the one derived from the phase velocity of the numerically computed modes shows that these modes are excited by an instability likely driven by the critical layer that develops in the shear layer, staying along the tangent cylinder of the inner sphere.

Tracking Solar Gravity Modes: The Dynamics of the Solar Core

Solar gravity modes have been actively sought because they directly probe the solar core (below 0.2 solar radius), but they have not been conclusively detected in the Sun because of their small surface amplitudes. Using data from the Global Oscillation at Low Frequency instrument, we detected a periodic structure in agreement with the period separation predicted by the theory for gravity dipole modes. When studied in relation to simulations including the best physics of the Sun determined through the acoustic modes, such a structure favors a faster rotation rate in the core than in the rest of the radiative zone.

Magnetohelioseismology

The helioseismic investigation of the solar interior to elucidate the behaviour of the Sun's magnetic field and the interior's role in the solar interior is considered. Such study may be called magnetohelioseismology (from the Greek roots magnetis, helios and seismos).

Deeply Penetrating Banded Zonal Flows in the Solar Convection Zone

Helioseismic observations have detected small temporal variations of the rotation rate below the solar surface that correspond to the so-called "torsional oscillations" known from Doppler measurements of the surface. These appear as bands of slower- and faster-than-average rotation moving equatorward. Here we establish, using complementary helioseismic observations over 4 yr from the GONG network and from the MDI instrument on board SOHO, that the banded flows are not merely a near-surface phenomenon: rather, they extend downward at least 60 Mm (some 8% of the total solar radius) and thus are evident over a significant fraction of the nearly 200 Mm depth of the solar convection zone.

Dynamic variations at the base of the solar convection zone

We have detected changes in the rotation of the sun near the base of its convective envelope, including a prominent variation with a period of 1.3 years at low latitudes. Such helioseismic probing of the deep solar interior has been enabled by nearly continuous observation of its oscillation modes with two complementary experiments. Inversion of the global-mode frequency splittings reveals that the largest temporal changes in the angular velocity Omega are of the order of 6 nanohertz and occur above and below the tachocline that separates the sun's differentially rotating convection zone (outer 30% by radius) from the nearly uniformly rotating deeper radiative interior beneath. Such changes are most pronounced near the equator and at high latitudes and are a substantial fraction of the average 30-nanohertz difference in Omega with radius across the tachocline at the equator. The results indicate variations of rotation close to the presumed site of the solar dynamo, which may generate the 22-year cycles of magnetic activity.

The Seismic Structure of the Sun

Global Oscillation Network Group data reveal that the internal structure of the sun can be well represented by a calibrated standard model. However, immediately beneath the convection zone and at the edge of the energy-generating core, the sound-speed variation is somewhat smoother in the sun than it is in the model. This could be a consequence of chemical inhomogeneity that is too severe in the model, perhaps owing to inaccurate modeling of gravitational settling or to neglected macroscopic motion that may be present in the sun. Accurate knowledge of the sun's structure enables inferences to be made about the physics that controls the sun; for example, through the opacity, the equation of state, or wave motion. Those inferences can then be used elsewhere in astrophysics.

GONG Observations of Solar Surface Flows

Doppler velocity observations obtained by the Global Oscillation Network Group (GONG) instruments directly measure the nearly steady flows in the solar photosphere. The sun's differential rotation is accurately determined from single observations. The rotation profile with respect to latitude agrees well with previous measures, but it also shows a slight north-south asymmetry. Rotation profiles averaged over 27-day rotations of the sun reveal the torsional oscillation signal-weak, jetlike features, with amplitudes of 5 meters per second, that are associated with the sunspot latitude activity belts. A meridional circulation with a poleward flow of about 20 meters per second is also evident. Several characteristics of the surface flows suggest the presence of large convection cells.

The Solar Acoustic Spectrum and Eigenmode Parameters

The Global Oscillation Network Group (GONG) project estimates the frequencies, amplitudes, and linewidths of more than 250,000 acoustic resonances of the sun from data sets lasting 36 days. The frequency resolution of a single data set is 0.321 microhertz. For frequencies averaged over the azimuthal order m, the median formal error is 0.044 microhertz, and the associated median fractional error is 1.6 x 10(-5). For a 3-year data set, the fractional error is expected to be 3 x 10(-6). The GONG m-averaged frequency measurements differ from other helioseismic data sets by 0.03 to 0.08 microhertz. The differences arise from a combination of systematic errors, random errors, and possible changes in solar structure.

The Current State of Solar Modeling

Data from the Global Oscillation Network Group (GONG) project and other helioseismic experiments provide a test for models of stellar interiors and for the thermodynamic and radiative properties, on which the models depend, of matter under the extreme conditions found in the sun. Current models are in agreement with the helioseismic inferences, which suggests, for example, that the disagreement between the predicted and observed fluxes of neutrinos from the sun is not caused by errors in the models. However, the GONG data reveal subtle errors in the models, such as an excess in sound speed just beneath the convection zone. These discrepancies indicate effects that have so far not been correctly accounted for; for example, it is plausible that the sound-speed differences reflect weak mixing in stellar interiors, of potential importance to the overall evolution of stars and ultimately to estimates of the age of the galaxy based on stellar evolution calculations.