Solar Surface Magneto-Convection
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We review the properties of solar magneto-convection in the top half of the convection zones scale heights (from 20 Mm below the visible surface to the surface, and then through the photosphere to the temperature minimum). Convection is a highly non-linear and nonlocal process, so it is best studied by numerical simulations. We focus on simulations that include sufficient detailed physics so that their results can be quantitatively compared with observations.
The solar surface is covered with magnetic features with spatial sizes ranging from unobservably small to hundreds of megameters. Three orders of magnitude more magnetic flux emerges in the quiet Sun than emerges in active regions. In this review we focus mainly on the properties of the quiet Sun magnetic field.
The Sun's magnetic field is produced by dynamo action throughout the convection zone, primarily by stretching and twisting in the turbulent downflows. Diverging convective upflows and magnetic buoyancy carry magnetic flux toward the surface and sweep the field into the surrounding downflow lanes where the field is dragged downward. The result is a hierarchy of undulating magnetic Ω- and U-loops of different sizes. New magnetic flux first appears at the surface in a mixed polarity random pattern and then collects into isolated unipolar regions due to underlying larger scale magnetic structures. Rising magnetic structures are not coherent, but develop a filamentary structure. Emerging magnetic flux alters the convection properties, producing larger, darker granules.
Strong field concentrations inhibit transverse plasma motions and, as a result, reduce convective heat transport toward the surface which cools. Being cooler, these magnetic field concentrations have a shorter scale height and become evacuated. The field becomes further compressed and can reach strengths in balance with the surrounding gas pressure. Because of their small internal density, photons escape from deeper in the atmosphere. Narrow evacuated field concentrations get heated from their hot sidewalls and become brighter than their surroundings. Wider magnetic concentrations are not heated so they become darker, forming pores and sunspots.
KeywordsMagnetic Flux Flux Tube Convection Zone Convective Motion Dynamo Action
The solar convection zone is the ultimate driver of activity in the solar chromosphere and corona. It is the only available source of mechanical energy. Upper atmosphere activity and heating is empirically intimately connected with the presence of magnetic fields. Hence the need to understand the behavior of magnetic fields at the solar surface. The solar magnetic field is produced by dynamo action within the convection zone. Thus, to understand the energy source of the chromosphere and corona we need to understand the solar dynamo, magneto-convection, and the transport of magnetic flux through the convection zone. For recent reviews see Fan (2009) and Charbonneau (2010). For probing the subsurface layers of the Sun, our best tools are the various techniques of local helioseismology (Gizon and Birch, 2005). Accurate modeling of the rise through the convection zone and emergence of magnetic flux, of sunspots and active regions is needed for improving helioseismic probing of solar subsurface structure.
Convection is the transport of energy by bulk mass motions. In a convection zone, energy is transported as thermal energy, except in layers where hydrogen is only partially ionized, in which case most of the energy is transported as ionization energy. Typically, the motions are slow compared to the sound speed so that approximate horizontal pressure balance is maintained. As a result, warmer fluid is less dense and buoyant while cooler fluid is denser and gets pulled down by gravity. For a detailed review of solar surface convection see Nordlund et al. (2009).
The topology of convection is controlled by mass conservation (Stein and Nordlund, 1989). Convection has a horizontal cellular pattern, with the warm fluid ascending in separate fountainlike cells surrounded by lanes of cool descending fluid. In a stratified atmosphere, with density decreasing outward, most of the ascending fluid must turn over and be entrained in the downflows within a density scale height (ignoring gradients in velocity and filling factor). Fluid moving a distance Δr in an atmosphere with a density gradient dln ρ/dr would, if its density remained constant, be overdense compared to its surroundings by a factor Δρ/ρ = -(dlnρ/dr)Δr. This is unstable and produces a pressure excess in the upflow cell interiors that pushes the fluid to turn over into the surrounding downflow lanes. Since the fluid velocity decreases inward from the top of the convection zone, its derivative has opposite sign to that of the density, so the length scale for entrainment is increased. Warm upflows diverge and tend to be laminar, while cool downflows converge and tend to be turbulent. Temperature in stellar convection zones increases inward, so the scale height and, as a result, the size of the horizontal convective cellular pattern also increase inward. Think of the rising fluid as a cylinder. As described above, most of the fluid entering at the bottom of the cylinder must leave through its sides within a scale height. If the ratio of vertical to horizontal velocities does not change much with depth, then the radius of the cylinder can increase in proportion to the scale height and still maintain mass conservation (Stein and Nordlund, 1998).
The solar surface is covered with magnetic features with spatial sizes ranging from unobservably small to hundreds of megameters. Their distribution is featureless (Parnell et al., 2009; Thornton and Parnell, 2011). Large-scale magnetic structures, sunspots and active regions, possess some well defined global properties (Hathaway, 2010). The main observed properties of small scale magnetic structures are (de Wijn et al., 2009): Strong fields tend to be vertical and weaker fields horizontal. The strongest vertical fields are in pressure equilibrium with their surroundings and tend to occur in the magnetic network and the intergranular lanes. Horizontal fields are found predominantly inside granules and near the edges of granules. Horizontal field properties are similar in the quiet Sun, plage, and polar regions (Ishikawa and Tsuneta, 2009). Three orders of magnitude more magnetic flux emerges in the quiet Sun than emerges in active regions (Thornton and Parnell, 2011). This new flux is first seen as horizontal field inside granules followed by the appearance of vertical field at the ends of the horizontal field (Centeno et al., 2007; Martínez González and Bellot Rubio, 2009; Ishikawa et al., 2010; Guglielmino et al., 2012).
In the presence of magnetic fields, convection is altered by the Lorentz force, while convection influences the magnetic field via the curl (v × B) term in the induction equation.
Where the conductivity high, the magnetic field is frozen into the ionized plasma. Where the magnetic field is weak (magnetic energy small compared to kinetic energy), convective motions drag it around. To maintain force balance, locations of higher field strength (higher magnetic pressure) tend to have smaller plasma density and lower gas pressure. Diverging, overturning motions quickly sweep the field (on granular times of minutes) from the granules into the intergranular lanes (Tao et al., 1998a; Emonet and Cattaneo, 2001; Weiss et al., 2002; Stein and Nordlund, 2004; Vögler et al., 2005; Stein and Nordlund, 2006). In hours (mesogranular times), the field tends to collect on a mesogranule scale. In days (supergranule times), the slower, large scale supergranule motions collect the field in the magnetic network at the supergranule boundaries. Convective flows produce a hierarchy of loop structures in rising magnetic flux. Slow upflows and buoyancy raise the flux, while fast downflows pin it down, which produces Ω- and U-loops (Cheung et al., 2007). The different scales of convective motion produce loops on these different scales, with smaller loops riding piggy-back in a serpentine fashion on the larger loops (Cheung et al., 2007; Stein et al., 2010b). Dynamo action occurs in the turbulent downflows where the magnetic field lines are stretched, twisted, and reconnected, increasing the field strength (Nordlund et al., 1992; Cattaneo, 1999; Vögler and Schüssler, 2007; Schüssler and Vögler, 2008; Pietarila Graham et al., 2010).
Magnetic fields influence convection via the Lorentz force, which inhibits motion perpendicular to the field. As a result, the overturning motions that are essential for convection are suppressed and convective energy transport from the interior to the surface is reduced. Radiative energy loss to space continues, so regions of strong field cool relative to their surroundings. Being cooler, these locations have a smaller scale height. Plasma drains out of the magnetic field concentrations in a process called “convective intensification” or “convective collapse” (Parker, 1978; Spruit, 1979; Unno and Ando, 1979; Nordlund, 1986; Bercik et al., 1998; Grossmann-Doerth et al., 1998; Bushby et al., 2008). This process can continue until the magnetic pressure (plus a small gas pressure) inside the flux concentration equals the gas pressure outside, giving rise to a field strength much greater than the equipartition value with the dynamic pressure of the convective motions. These magnetic flux concentrations are cooler than their surroundings at the same geometric layer. However, because they are evacuated, their opacity is reduced so photons escape from deeper in the atmosphere (Wilson depression, Maltby, 2000). Where the magnetic concentrations are narrow, there is heating from their hotter side walls and they appear as bright points (Spruit, 1976). Where the concentrations are wide, the side wall heating is not significant and the flux concentrations appear darker than the surroundings as pores or sunspots.
Magnetic fields alter granules’ properties - producing smaller, elongated, lower intensity contrast, “abnormal” granules (Muller et al., 1989; Title et al., 1992; Bercik et al., 1998; Vögler, 2005; Cheung et al., 2007). Strong magnetic flux concentrations typically form in convective downflow lanes, especially at the vertices of several such lanes, due to the sweeping of flux by the diverging convective upflows (Vögler et al., 2005; Stein and Nordlund, 2006). They are surrounded by downflows which sometimes become supersonic.
Magneto-convection simulations have been very useful in understanding and interpreting observations. Sánchez Almeida et al. (2003), Khomenko et al. (2005), Shelyag et al. (2007), and Bello González et al. (2009) have used simulations to calibrate the procedures for analyzing and interpreting Stokes spectra in order to determine the solar vector magnetic field. Fabbian et al. (2010) has shown that magnetic fields alter line equivalent widths by altering the temperature stratification and by Zeeman broadening. These two effects act in opposite directions, but still leave a net result and hence alter abundance determinations. Zhao et al. (2007), Braun et al. (2007), Kitiashvili et al. (2009), Birch et al. (2010), and Braun et al. (2012) have used convection and magneto-convection simulation results to analyze local helioseismic inversion methods.
Magneto-convection is highly non-linear and non-local, so it needs to be modeled using numerical simulations. Two complementary approaches are being used to study magneto-convection, which we will call “idealized” and “realistic”. “Idealized” studies ignore complex physics by assuming a fully ionized, ideal plasma and energy transport by thermal conduction. Magneto-convection in the deep, slow moving, adiabatic portion of the convection zone satisfies these idealized assumptions and, in addition, can use the anelastic approximation whereby acoustic waves are eliminated from the calculation, which permits larger time steps. “Idealized” calculations are important for isolating and studying fundamental physical phenomena as well as for exploring parameter space (because they run fast). “Realistic” studies include complex physics - an equation of state for partially ionized gas, non-grey radiation transport and, in some cases, even some non-equilibrium effects. “Realistic” calculations are necessary to make quantitative comparisons with observations in order to understand the observations and to provide artificial data for evaluating data analysis procedures. In this review we focus on the “realistic” numerical modeling of solar surface magneto-convection. It updates and extends the section on magneto-convection from the review by Nordlund et al. (2009) of solar surface convection.
It is organized as follows: Section 2 states the equations that need to be solved. Section 3 describes the solar observations. Section 4 describes the simulation results for: dynamo action (4.1), flux emergence (4.2), flux concentrations (4.3), and pores and sunspots (4.4).
To simulate magneto-convection, the conservation equations for mass, momentum, energy and the induction equation for the magnetic field must be solved, together with Ohm’s law for the electric field and an equation of state relating pressure to the density and energy. For a detailed discussion of the equations governing convection see Nordlund et al. (2009).
Internal energy is changed by transport, by PdV work, by Joule heating, by viscous dissipation, and by radiative heating and cooling. It is the fluid version of the 2nd law of thermodynamics and (together with the density) determines the plasma temperature, pressure, and entropy.
To make “realistic” models of solar surface magneto-convection it is necessary to include all the significant physical processes occurring near the solar surface. In the photosphere and upper convection zone Local Thermodynamic Equilibrium (LTE) is a good approximation. For models that extend into the chromosphere non-local thermodynamic equilibrium (NLTE) effects must also be included, as is being done in the bifrost code (Gudiksen et al., 2011).
Ionization energy accounts for 2/3 of the energy transported near the solar surface and must be included to obtain the observed solar velocities and temperature fluctuations (Stein and Nordlund, 1998). An equation of state (EOS) is used to determine the pressure and temperature for the partially ionized plasma. Typically this is in tabular form and includes LTE ionization of the abundant elements as well as hydrogen molecule formation as a function of log(density) and internal energy per unit mass.
There is an excellent review of small-scale solar magnetic field observations (network and internetwork quiet Sun) by de Wijn et al. (2009). The main observational results are: strong fields tend to be vertical and weaker fields horizontal. Vertical kilogauss fields (in pressure equilibrium with their surroundings) are found in the magnetic network and as isolated, intermittent concentrations in intergranular lanes. Horizontal magnetic fields are found all over the Sun (Trujillo Bueno et al., 2004; Harvey et al., 2007), predominantly inside and near the edges of granules. They are transient, intermittent and have granule-scale sizes and lifetimes and strengths in the hectogauss range (generally less than equipartition with the convective dynamic pressure) (Ishikawa and Tsuneta, 2010). Weaker horizontal fields have no preferred orientation. Stronger ones tend to align with the active regions. The horizontal field properties are similar in the quiet Sun, plage, and polar regions (Ishikawa and Tsuneta, 2009). The spatially averaged horizontal magnetic field strength is 50 – 60 G, while the spatially averaged vertical field strength is only 11 G (Lites et al., 2008). This may be due to the larger area covered by horizontal fields compared to the isolated vertical field concentrations. There is no characteristic size or lifetime for the horizontal fields (they have an exponential distribution both in size and lifetime) (Danilovic et al., 2010). There is some question of the accuracy of Hinode determinations of quiet Sun transverse magnetic fields due to s/n problems (Borrero and Kobel, 2011).
Bright points in the G-band (dominated by CH molecular transitions) have been used as proxies for the magnetic field. At disk center small magnetic concentrations appear as bright points in the intergranular lanes, while larger concentrations are dark. The increased brightness in magnetic concentrations is due to their lower density compared with their surroundings. At a given geometric height, granules are hotter than the intergranular lanes, which are, in turn, hotter than G-band bright points. Although at a given geometric height the magnetic elements are cooler than the surrounding medium, one sees into deeper layers, to where the temperature is higher, due to the reduced opacity and to heating from the hot surrounding granules. Locations of large magnetic concentrations are cooler than even the G-band bright points because both convective heat transport and side wall heating are reduced.
High resolution observations of solar faculae show that they have an asymmetric contrast profile, with some brightness extending up to one arcsecond in the limbward direction from their peak in brightness (Hirzberger and Wiehr, 2005). The wide contrast profile cannot be explained solely by the “hot wall” effect, as was noted by Lites et al. (2004). The works by Keller et al. (2004) and Steiner (2005) address this issues, with somewhat conflicting but broadly consistent explanations. One conclusion is that the limbward extension of brightness comes from seeing the granule behind the facular magnetic field through the rarefied facular magnetic flux concentration; a circumstance that observers suspected decades ago. The explanation is corroborated by the direct comparisons of observations and simulations by De Pontieu et al. (2006).
These Ω-loop footpoints get quickly swept into the intergranular lanes and the horizontal field to the edges of the granules. They do not show a helical structure. Transient horizontal fields also appear briefly where new downflow lanes form (Danilovic et al., 2010). The flux in these emerging bipoles is small, 1016 × few × 1017 Mx, but their rate of appearance is large, around a few × 10-10 km2 s, hence their dominant contribution to the emerging flux of the Sun (Martínez González and Bellot Rubio, 2009; Ishikawa and Tsuneta, 2009; Ishikawa et al., 2010). Most of these small loops are low lying, with only about a quarter reaching up to chromospheric heights.
Two types of numerical studies of magneto-convection are being undertaken: “idealized” and “realistic”. Both approaches give valuable, but different, insights into the properties of magnetoconvection. Idealized simulations were pioneered by Weiss (1966) and extensively used by Tao et al. (1998b), Cattaneo (1999), Abbett et al. (2000), Hurlburt and Rucklidge (2000), Emonet and Cattaneo (2001), Weiss et al. (2002), Cattaneo et al. (2003), and Bushby et al. (2008). See reviews by Weiss (1991) and Schüssler (2001). They are especially useful for gaining physical insights into convective properties. In these calculations an ideal gas equation of state is assumed and energy transport is assumed to be only by convection and thermal conduction. For modeling magneto-convection in the solar interior anelastic or reduced sound speed calculations with an ideal gas equation of state and diffusive radiation transport are appropriate (Miesch, 2005; Miesch et al., 2008; Fan, 2009; Miesch et al., 2011; Hotta et al., 2012). An alternative approach applicable to the deep convective layers is to reduce the sound speed (Hotta et al., 2012). This, as in the anelastice approximation, allows larger time steps. “Realistic” simulations were pioneered by Nordlund (1982) and have been extensively developed by Stein and Nordlund (1998, 2006), Steiner et al. (1998); Vögler et al. (2005), Schaffenberger et al. (2005), Hansteen et al. (2007), Abbett (2007), Jacoutot et al. (2008), Carlsson et al. (2010), and Gudiksen et al. (2011). A tabular equation of state is used, which includes the partial ionization of hydrogen, helium and other abundant elements, because below 40,000 K in the Sun ionization energy dominates over thermal energy in convective energy transport. The radiation transfer equation is solved to determine the radiative heating and cooling, because the optical depth is of order unity near the visible solar surface, so that neither the diffusion nor optically thin approximations are valid. Such detailed physics is necessary to make quantitative comparisons with observations. Here we restrict ourselves to the more “realistic” surface simulations. Magneto-convection and dynamo action in the deeper layers of the convection zone are reviewed by Miesch (2005) and Miesch and Toomre (2009).
4.1 Turbulent convection and dynamo action
Global dynamos have been simulated by Brun et al. (2004), Miesch (2005), Dobler et al. (2006), Browning et al. (2006), and Brown et al. (2007, 2010). See reviews by Brandenburg and Dobler (2002), Ossendrijver (2003), Miesch and Toomre (2009), and Charbonneau (2010). Note that the fact that both the rate of magnetic flux emergence and the probability distribution of magnetic flux magnitudes are featureless power laws from 1016 – 1023 Mx suggests that the solar dynamo has no preferred scale, that it acts throughout the convection zone with each scale of convective motions generating new flux on that scale (Parnell et al., 2009; Thornton and Parnell, 2011). That is, all the surface magnetic features are produced by a common process (which can not be all dominated by surface effects since the sunspots and active regions clearly are not).
4.2 Subsurface rise and emergence of magnetic flux
Magnetic fields are produced by dynamo action throughout the solar convection zone. Their emergence through the visible surface is driven by two processes: advection by convective upflows and buoyancy (to maintain approximate pressure equilibrium with their surroundings the density inside the concentration is smaller than in its surroundings). Fan (2009) has reviewed the rise of magnetic flux through the deep convection zone. Simulations of magnetic flux emerging from the surface layers of the convection zone have been initiated in three ways: either from coherent twisted flux tubes forced into the computational domain through the bottom boundary or made buoyant by lowering their density (Yelles Chaouche et al., 2005; Cheung et al., 2007, 2008; Martínez-Sykora et al., 2008, 2009; Cheung et al., 2010), or by inflows at the bottom advecting minimally structured, uniform, untwisted, horizontal field advected by inflows into the domain through the bottom boundary (Stein et al., 2010a,b), or produced locally by dynamo action (Abbett, 2007; Abbett and Fisher, 2010). These very different approaches, using several different computer codes, show several, robust, common features.
Magnetic fields alter the granule properties - producing smaller, lower intensity contrast, “abnormal” granules (Bercik et al., 1998; Vögler, 2005). Strong magnetic flux concentrations typically form in convective downflow lanes, especially at the vertices of several such lanes, due to the sweeping of flux by the diverging convective upflows (Vögler et al., 2005; Stein and Nordlund, 2006). They are surrounded by downflows which sometimes become supersonic. The normal convective downflows are enhanced surrounding the flux concentrations by baroclinic driving due to the influx of radiation into the concentration (Deinzer et al., 1984; Knölker et al., 1991; Bercik, 2002; Vögler et al., 2005).
The main differences between these two approaches are that a coherent initial flux tube leads to a more coherent symmetrical structure when it emerges through the surface and field line connections below the surface are more localized. In the minimally structured approach organized magnetic field concentrations develop spontaneously when sufficient flux is present, instead of being imposed as initial and boundary conditions, so the emergent structures are less coherent.
4.3 Small scale flux concentrations
Magnetic concentrations arise from loops emerging into the upper solar atmosphere and leaving their legs behind and from the diverging convective upflows which sweep magnetic field into the intergranular lanes and concentrate the field into sheets and at the vertices of the lanes into “tubes” of magnetic flux (Vögler et al., 2005; Schaffenberger et al., 2005; Stein and Nordlund, 2006). To maintain force balance, locations of higher field strength (higher magnetic pressure) tend to have smaller plasma density and lower gas pressure. Strong magnetic fields, through the Lorentz force, inhibit overturning convective motions and hence the transport of energy toward the surface. Radiative energy loss to space continues, so regions of strong field cool relative to their surroundings at the same geometric layer. Being cooler, these locations have a smaller scale height. Plasma drains out of the magnetic field concentrations in a process called “convective intensification” or “convective collapse” (Parker, 1978; Spruit, 1979; Unno and Ando, 1979; Nordlund, 1986; Bercik et al., 1998; Grossmann-Doerth et al., 1998; Bushby et al., 2008). This process continues until the magnetic pressure (plus a small gas pressure) inside the flux concentration approximately equals the gas pressure outside, giving rise to a field strength much greater than the equipartition value with the dynamic pressure of the convective motions.
4.4 Pores and sunspots
Recently, “realistic” radiative-convective MHD models of pores and sunspots have become possible. Bercik et al. (2003), Stein et al. (2003), and Vögler et al. (2005) found micropores forming spontaneously in magneto-convection simulations. Cameron et al. (2007a) modeled pores in magneto-convection simulations by imposing them as initial and boundary conditions. Stein et al. (2010b) found that large pores formed spontaneously in deep magneto-convection simulations. Schüssler and Vögler (2006) simulated a sunspot umbra where convection produced umbral dots. Heinemann et al. (2007), Scharmer et al. (2008), and Rempel et al. (2009b) started with flaring, rectangular, slab magnetic concentrations. Rempel et al. (2009a) and Rempel (2011) modeled sunspots in a magneto-convection simulation starting from a pair of axisymmetric, self-similar magnetic funnels. Cheung et al. (2010) modeled sunspots formed from an emerging, twisted half torus magnetic “flux tube”. An excellent review, especially of helioseismic applications, is Moradi et al. (2010). For more details on sunspots see the review by Rempel and Schlichenmaier (2011).
Pores, like micropores, are surrounded by downflows concentrated into a few downdrafts. The ubiquitous occurrence of downflows in the close vicinity but outside magnetic flux concentrations (see, for example, also Steiner et al., 1998) has been explained in terms of baroclinic flows by Deinzer et al. (1984). The effect has been observationally verified by Langangen et al. (2007). Pores are edge brightened (Figure 27). Cameron et al. (2007b) explain this as due to the fact that the surface of unit optical depth occurs at slightly higher temperature at the edges of pores, possibly due to decreased overlying density because of the spreading magnetic field.
In the Cheung et al. (2010) simulation, spots form from an emerging Ω-loop (Figure 14). The field first emerges with mixed polarities. The opposite polarities then counterstream to collect into the opposite polarity sunspots. This counterstreaming of opposite polarities is due to the underlying large-scale structure of the coherent subsurface roots of the emerged “flux tube”, which influence the surface dynamics via the Lorentz force, especially magnetic tension (Cheung et al., 2010).
However, unlike normal convection, it is the pressure force that that is pushing the upflow as well as the overturning horizontal flow. The downflows are in nearly hydrostatic equilibrium. Near the lower pressure photosphere the nearly vertical field lines of the penumbra spread outward (tending toward a potential field structure) and become more horizontal. The mass loading by the overturning, horizontal convective motions bends the magnetic field lines downward even more, when the initial inclination is more than 45°, which produces the nearly horizontal penumbral field (Figure 33). Cooling near τ = 1 increases the plasma density and field line bending. The Lorentz force turns the flow along the magnetic field to produce the Evershed outflow (Figure 34).
5 The Future
Rapid progress is currently occurring in solar magneto-convection simulations. What can we expect in the near future? More physics will be included: more accurate representation of the frequency dependence of the opacity, non-equilibrium ionization, partial ionization and non-LTE radiation. Such work is already begun in the bifrost (Gudiksen et al., 2011; Martínez-Sykora et al., 2012), stagger and MuRAM (Cheung and Cameron, 2012) codes. The next big step for numerical simulations of the upper photosphere and chromosphere is the inclusion of time-dependent and partial ionization effects (generalized Ohm’s Law and ambipolar diffusion) and the extension from single to multifluid equations (neutrals, ions and electrons) (Khomenko and Collados, 2012; Cheung and Cameron, 2012). The most time consuming part of “realistic” convection calculations is the radiative transfer, even with the drastic approximations currently made. Alternative numerical solutions of the transfer equation are possible (Hayek et al., 2010). Observations from larger ground (GREGOR, the Big Bear New Solar Telescope and the Advance Technology Solar Telescope) and new space based observatories (Solar Dynamics Observatory, Interface Region Imaging Spectrograph (IRIS) and Solar Orbiter) will allow more detailed comparisons between observations and simulations, which will assist in clarifying the significant physical processes that determine the solar magneto-dynamics.
The biggest unanswered questions are: exactly how does the solar dynamo work, the details of the process of mass and energy transport through and energy dissipation in the chromosphere and corona, and the origins of eruptive events. We have qualitative models of these processes. We now need a more quantitative understanding. We would like to know: how the large scale regularities of the solar cycle are produced, the relation between global and local surface dynamo action, the origin of supergranulation, the role of weak fields in energizing the chromosphere and corona, the triggers of eruptive events, and the relation between global and local coronal behavior.
The author was supported by NSF grants AST 0605738 and AGS 1141921 and NASA grants NNX07AH79G and NNX08AH44G. The author’s calculations were performed on the Pleiades supercomputer of the NASA Advanced Supercomputing Division at NASA’s Ames Research Center.
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