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The Sun as a Dynamo

kolinski — Wed, 15 Dec 2021 20:52:01 +0000

The Sun as a Dynamo kolinski Wed, 12/15/2021 - 13:52

The ultimate origins of solar variability lie below the visible surface, where turbulent convection, differential rotation, and meridional flows work together to produce magnetic fields through the operation of a stellar dynamo, giving rise to the 22-year solar magnetic cycle.

Figure 1: Schematic of solar flux-transport dynamo processes. Red inner sphere represents the Sun's radiative core and blue mesh the solar surface. In between is solar convection zone where dynamo resides. (a) Shearing of poloidal field by the Sun's differential rotation near convection zone bottom. The Sun rotates faster at the equator than the pole. (b) Toroidal field produced due to this shearing by differential rotation. (c) When toroidal field is strong enough, buoyant loops rise to the surface, twisting as they rise due to rotational influence. Sunspots (two black dots) are formed from these loops. (d,e,f) Additional flux emerges (d,e) and spreads (f) in latitude and longitude from decaying spots. (g) Meridional flow (yellow circulation with arrows) carries surface magnetic flux poleward, causing polar fields to reverse. (h) Some of this flux is then transported downward to the bottom and towards the equator. These poloidal fields have sign opposite to those at the beginning of the sequence, in frame (a). (i) This reversed poloidal flux is then sheared again near the bottom by the differential rotation to produce the new toroidal field opposite in sign to that shown in (b).

To seek the theoretical explanation of the cyclic evolution of the solar magnetic features, in the past an oscillatory dynamo in the Sun was postulated. Nowadays it is widely accepted that a magnetohydrodynamic dynamo is indeed responsible for generating and maintaining the magnetic fields of the Sun in the solar convection zone and neighboring layers. This means that the fluid flow of highly conducting plasma there maintains electric currents and (by Amperes law) associated magnetic fields against ohmic dissipation. The history of dynamo theory applied to the sun goes back more than 50 years, to pioneering papers of Eugene Parker.

Solar dynamo research at the High Altitude Observatory started in the 1970s with the work of two visiting scientists, Michael Stix and Hirokazu Yoshimura, using large-scale, kinematic, mean-field models, whereas the more detailed full 3D MHD models were built in the 1980s (Gilman 1983). Almost nothing was known about the solar interior properties at that time. With the advent of helioseismology in late 1980s, the solar dynamo theory has significantly evolved. In the 1990s, two streams of dynamo research developed at HAO. One was the 'interface' dynamos (MacGregor & Charbonneau 1997) and the other was the “flux transport” dynamos (Dikpati & Charbonneau 1999). To date flux-transport dynamos have been the most successful at reproducing and explaining the main features of a solar magnetic cycle. Over the past decade, HAO has been one of the leaders in research on this class of dynamo. The basic workings of a flux-transport dynamo applied to the sun are demonstrated in the schematic diagram (Figure 1).

2D Flux-transport dynamos for the sun

Over the past decade, in the course of developing and exploring the details of 2D flux-transport dynamo, recently a flux-transport dynamo-based predictive tool has also been developed at HAO (Dikpati, de Toma & Gilman 2006) to simulate and predict solar cycle properties.

Observations indicate the existence of time-variations in differential rotation, in the form of torsional oscillations, which correlate well with with the butterfly diagram. Therefore in dynamo models it is necessary to include feedbacks of magnetic fields on the flow fields that produce the magnetic induction. So modeling a dynamical dynamo has been another area of HAO's dynamo research (Rempel 2006).

So far, flux-transport dynamos have been built to be axisymmetric about the solar rotation axis, and can explain well the longitude-averaged solar cycle features. However, observations indicate the existence of longitude-dependent solar cycle features also. So currently a major research effort at HAO is to generalize dynamos to 3D, using two different approaches with similar goals: one includes large-scale non-axisymmetry through low longitudinal wavenumbers in the flow and magnetic fields; the other is a full 3D MHD approach (Miesch et al. 2008).

While solar cycle research is an intriguing and actively ongoing effort, one scientist observes only one or two full magnetic cycle their entire research career. Therefore to understand solar cycle, it is necessary to study stellar dynamos including particularly stellar magnetic activity, another active research area at HAO (Metcalfe et al. 2007).

In axisymmetric flux-transport dynamo models the magnetic fields simulated include the longitudinal or toroidal field, and the field in meridional planes, or poloidal field. A typical evolution of large-scale toroidal and poloidal fields in the Sun are displayed in the animation movie.

The line-contours represent the poloidal fields in the plane of the screen and the color-shades the toroidal field perpendicular to the screen. Poloidal fields are generated by the Babcock-Leighton effect at the surface; then they migrate poleward by the surface meridional flow and cause polar field reversal. A remnant component of these poloidal fields is transported down to the bottom of the convection zone by the downward flow at high-latitudes, and starts getting sheared by the Sun's differential rotation to induce the spot-producing toroidal fields. The emergence of 'tilted' patterns of magnetic flux at the surface that originates from toroidal fields near the bottom of the convection zone, creates the source for new cycle's poloidal fields. However, the flux emergence process has so far been captured in a parameterized form for simplicity. The turbulent diffusion of magnetic flux works everywhere at all times.

Flux-transport models have now provided plausible explanations for the following:

The cycle period, which is determined in such models primarily by the speed of the meridional flow at the bottom of the convection zone (Dikpati & Charbonneau 1999). The equatorward flow speed there is not known directly from observations; it is determined from the observed surface flow-speed and applying the constraint of mass conservation.
The near-coincidence in time between the epoch of sunspots' peak and the epoch of polar field reversals, which is governed by the poleward surface meridional flow and the supergranular type diffusion there.
The dominant symmetry of the solar magnetic field about the equator (radial field antisymmetric or 'dipole' like) (Dikpati & Gilman 2001). The inclusion of tachocline alpha-effect in the model, a process of lifting and twisting of toroidal fields at the base of the convection zone, arising from MHD instabilities very likely occurring there, favors the correct symmetry.
Differences in polar field reversal characteristics between North and South poles in a particular cycle (such as relative timing), namely cycle 23 (Dikpati et al. 2004). These are caused by a combination of differences in surface poloidal sources and differences in meridional flow speeds and patterns in North and South hemispheres.

The robustness of flux-transport dynamo models has been demonstrated with a set of 'benchmark' tests on eight different dynamo codes, including two from HAO, that use widely differing numerical schemes but get virtually the same results for the simulation of an alpha-omega convection zone dynamo and a Babcock-Leighton dynamo. (Jouve et al. 2008).

Application to solar cycle prediction

Attempts have been made for at least the past 40 years to predict the strength of the next solar cycle. Accurate predictions of the peak amplitude and its timing have great practical as well as scientific value. Strong solar cycles can negatively impact many industries, such as power transmission and satellite communications. Strong cycles expand the upper atmosphere, increasing the drag on all orbiting satellites.

Historically, solar cycle predictions have been based on statistical methods, extrapolating from past behavior of the sun. Different methods have produced widely varying forecasts for the same cycle. By contrast, enormous progress has been made in the past 60 years in skillfully predicting future weather and climate by use of numerical models that integrate forward in time the governing laws of physics. Predictive research of this type for the solar cycle started only in the past five years, first in HAO, in the form of integrating forward in time the flux-transport dynamo equations assimilating data of the Sun's past magnetic field.

Necessary conditions for building a predictive solar cycle model that can assimilate date and show good skill in such predictions are that (i) the model must be as constrained as possible by observations, (ii) the model must be calibrated to an average solar cycle, (iii) the model runs must start with reliable initial conditions and continuous assimilation of observed data. Just as ENSO predictions for the Earth's coupled ocean-atmosphere system require a memory of past ocean surface temperatures, in order to have predictive skill for future cycles the Sun and the dynamo model both need to have some memory of past solar magnetic fields. Due to meridional circulation, some memory of the past few cycles' magnetic fields is an inherent characteristic of a flux-transport dynamo model. In particular, for the observed poleward meridional flow at the surface, and with an equatorward return-flow at the base of the convection zone, constructed from mass conservation, dynamo simulations indicated that the poloidal magnetic flux at the surface takes 17-22 years to be 'recycled' or transported via the meridional circulation conveyor belt from the high-latitudes at the top to the mid-latitudes at the bottom of the convection zone. Thus in a flux-transport dynamo model, the 'seed' for a future cycle is formed at the base of the convection zone, from the combination of of the recycled poloidal flux of past cycles. This gives the model the potential for predicting the strength of a new cycle. This hypothesis has been explored (Dikpati, de Toma & Gilman 2006) by integrating forward in time the flux transport dynamo equations, driven by continuous input of observed magnetic data at the upper surface. Meridional circulation also contributes to good calibration of a large-scale mean-field dynamo, no matter whether the dynamo is driven by an interface or Babcock-Leighton alpha-effect (Dikpati, Gilman & MacGregor 2005).

The surface poloidal magnetic field source is critical to making predictions with a flux-transport dynamo calibrated to the sun. This source should be derived from the observed poloidal flux estimated from the decay of active regions. Surface magnetic fields have been measured only over the past three solar cycles, but sunspot areas are known reliably for the past twelve. The spot-area correlates strongly with surface magnetic flux (Figure 2). Thus it is possible to use the much longer sunspot area record as a proxy for surface magnetic fields and its time-variation is captured in a simplified way by a migrating Gaussian (Figure 3).

Figure 2: Spot-area correlates strongly with surface magnetic flux.

Figure 3: Migrating Gaussian plot of magnetic flux.

Several forecasts of solar cycle features for the upcoming cycle 24 such as the onset-timing, amplitude, north-south asymmetry have been made as a part of HAO's dynamo research. By now the delayed onset of cycle 24 predicted at HAO has been verified within the error-bar set by the mean-field approximations, while the other predictions about the cycle 24 features are yet to be verified. Currently HAO's on-going effort on solar cycle prediction research is to develop a more sophisticated 'sequential' data-assimilation scheme, in collaboration with IMAGe scientists.

Figure 4: Yellow circles show scatter plot of correlations between observed peak spot area and cycle rise time; green squares show that between Zurich sunspot number peak and cycle rise time.

In order to determine whether the origin of the high skill in amplitude prediction is due to an inherent Waldmeier effect introduced into the model through the migrating Gaussian surface poloidal source derived from spot-area data, the (non)existence of this effect in sunspot-area data was established. The Waldmeier effect is the anti-correlation between the rise-time of a cycle and the peak number of sunspots in that cycle. Surprisingly the Waldmeier effect is an artifact of the Wolf sunspot number (Dikpati, Gilman & de Toma 2008), but is not present in any other proxy for the solar cycle, such as spot area, group spot number, f10.7 flux (Figure 4).

2D Dynamical dynamo

In a 2D kinematic regime, the mean-field induction equation is solved, subject to the constraint that the magnetic field is divergence-free. The velocity fields used in the induction equation are prescribed. However, in reality magnetic fields can react back on the fluid motions. For flux-transport dynamos, therefore, both the differential rotation and the meridional circulation may be dynamically modified. Such back-reactions have been studied (Rempel 2006) using a non-kinematic version of a flux-transport dynamo.

There is observational evidence on the sun of such feedbacks, called torsional oscillations. These are observed perturbations on the time-averaged differential rotation of the sun, originally discovered by Robert Howard and Barry LaBonte of the Carnegie Observatories, using solar surface velocity data collected at Mt Wilson. Since their original discovery, more refined observations of surface doppler motions as well as helioseismic measurements have resulted in the current picture. The perturbations of faster and slower than average rotation speeds (full range ~10 m/sec) are linked in phase to the solar cycle. There is an equatorward migrating branch in middle and low latitudes, and an even stronger poleward migrating branch at high latitudes. There appears to be significant amplitude in the torsional oscillations throughout the solar convection zone, as detected helioseismically.

The amplitude of these torsional oscillations compared to the average differential rotation is no more than about 5%. This relatively small amplitude therefore puts an upper limit on the strength of magnetic fields induced. Still stronger fields would cause still larger perturbations in the differential rotation. This puts a constraint on all dynamo models to limit the size of induced fields to a level consistent with the observed velocity variations through a solar cycle.

Even though the meridional circulation is relatively weak compared to differential rotation, it gets modified significantly only where the induced toroidal field is extremely strong, well above equipartition of kinetic and magnetic energy. This is because the meridional circulation results from a slight imbalance of very large forces, so the work that can be done can greatly exceed the kinetic energy of meridional circulation. By contrast, the differential rotation is more easily damped by the feedbacks.

This non-kinematic model has further shown that both the poleward and equatorward branches of the torsional oscillations can be explained by electromagnetic effects. The poleward branch is a consequence of jxB forces altering the differential rotation, while the equatorward branch is produced indirectly, by the electromagnetic forces changing the thermal structure of the convection zone.

Such back-reaction could also extend even to turbulent part of the flow fields 'quenching' the turbulent magnetic diffusivity, because the electromagnetic body force could alter the form of the turbulence. Thus there may be both macroscopic and microscopic effects to consider, however the subject is relatively less explored compared to alpha-quenching. A recent work (Guerrero, Dikpati & Dal Pino 2009 has shown that the diffusivity-quenching helps amplify the toroidal field strength up to a value required by the rising flux tube simulations and lengthen the dynamo cycle.

Full 3D MHD simulations

Three-dimensional MHD simulations provide further insight into how organized magnetic activity patterns can arise through the combined action of turbulent convection, differential rotation, and meridional circulation (read more »). Turbulent dynamos often tend to build turbulent, small-scale magnetic fields but rotation and stratification impart helicity (both kinetic and magnetic) to solar convection that promotes the generation of larger-scale flux structures. Rotational shear also plays an essential role, stretching and amplifying fields into ribbons and sheets of toroidal flux (see figure). This is particularly efficient in the solar tachocline, which is thought to act as a factory and repository for the generation and storage of toroidal magnetic flux. MHD simulations of penetrative solar convection exhibit downward pumping of magnetic flux into the tachocline where it is amplified and organized by rotational shear (Figure 5 & 6).

Figure 5: Volume visualization of the longitudinal magnetic field component in a 3D MHD simulation of solar convection. Blue and red denote eastward and westward flux respectively and the northern hemisphere is removed in order to highlight the structure in the equatorial plane. Rotational shear stretches fields into toroidal ribbons and sheets while vortical convective downflows penetrate through, cleaving and wrapping the ribbons and recycling the flux.

Figure 6: Pumping, amplification, and organization of toroial magnetic fields in a global MHD simulation of solar convection that incorporates a stably-stratified tachocline of rotational shear below the base of the convection zone. Panels a and b illustrate the longitudinal magnetic field component in the mid convection zone and in the tachocline respectively, each in a Molleweide projection. Red and blue represent eastward and westward field as indicated in the color bar. The field in the convection zone is dominated by turbulent fluctuations while the tachocline field is more ordered, with prominent sheets of toroidal flux that are antisymmetric about the equator. This is particularly apparent in the longitudinally averaged toroidal field shown in frame c. [Miesch et al].

Stellar Dynamos

The solar/stellar connection is another active area of HAO's dynamo research. It is very likely that all stars with either convection zones or convective cores have such dynamos, though for different stellar parameters, such as rotation, the form the dynamo takes may be very different. And stars with convective cores are likely to have distinctly different dynamos than stars with convective envelopes. It is well known from observations that many stars with convective envelopes as thick as or thicker than that of the sun are also cyclic, with dynamo periods ranging from a few years to a few tens of years. The differential rotation of some of these stars is known from observations, but the meridional circulation is not. Therefore stellar dynamo research is a vast area with many topics being pursued simultaneously.

In the case of stars with convective cores, such as early-type stars, the top surface of the dynamo can not be observed because it is hidden inside a radiative envelope. But these stars do show substantial surface magnetic fields. The time-dependence these fields show is readily explained by the so-called oblique rotator model, which assumes a dipole-type field is present, whose axis is tilted compared to the rotation axis. But what is the origin of this surface field? A dynamo origin for this field has been extensively examined (MacGregor 2005). Such fields can be produced by dynamo action from the interaction of convection with the core rotation, if there is only small rotation present. Dynamos of the so-called "alpha^2' type produce fields that are not 'symmetrized' about the rotation axis. With much more differential rotation present, they become symmetrized and will produce a surface field of a different type, not in as close agreement with observations.

Another problem is how the dynamo fields in the core get to the surface to be observed. One candidate is meridional circulation. Charbonneau and MacGregor (ApJ 559,1094,2001) showed that a meridional circulation large enough to transport the fields to the surface is also large enough to interfere with the internal workings of the dynamo, effectively quenching dynamo action altogether. A promising alternative mechanism is the formation of buoyant flux tubes in the core, which then are sufficiently magnetically buoyant to rise throught the stably stratified envelope to the surface. (MacGregor & Cassinelli 2003). showed that this hypothesis is theoretically plausible, with tube taking 10^3-10^4 years to reach the surface.

A solar-type flux-transport dynamo model has been used to seek the origin of long-term non-reversing fields in solar/stellar interior (Dikpati, Gilman & MacGregor 2006). While the mechanism of skin-depth limits the penetration of the dynamo-generated oscillatory fields down to only a few kilometers below the base of the convection zone (the domain where the dynamo operates), the penetration of the non-reversing component down through the radiative core is determined by diffusive leaking. There could be preference in the sign of such non-reversing magnetic field in the radiative solar/stellar interior, decided by the overlying dynamo; however the field could exist for a million of years. Such a time-scale is very long compared to a dynamo cycle, and hence the non-reversing fields should be observable during some fraction of the entire life of a star.

Solar-Stellar Connection

Just as helioseismology revolutionized our understanding of the interior structure of the Sun, asteroseismology is now placing this knowledge into a broader context, by providing structural information for other solar-type stars. Scientists at HAO are developing a stellar model-fitting pipeline, using a parallel genetic algorithm, to prepare for the asteroseismic data soon expected from several satellite missions. Meanwhile, the Solar Oscillations Network Group (SONG) is a concept for a global network of small ground-based telescopes dedicated to asteroseismology and extrasolar planet searches, currently being organized though the Danish AsteroSeismology Center (DASC) at the University of Aarhus. The High Altitude Observatory is participating in the design and development phase of the SONG effort, with the intent to build and operate one of the SONG telescopes at HAO's Mauna Loa Observatory (MLSO) in Hawaii.

Figure 7: Periods of stellar activity cycles in years, plotted as a function of rotation periods in days. The data follow two sequences: a relatively young, active A sequence (red dashed line) and an older less active I sequence (blue dash-dotted line). The letter H indicates Hyades group stars, crosses indicate stars on the A sequence, and asterisks indicate stars on the I sequence. Squares around the crosses show stars with B-V

Effects associated with rotation can modify stellar properties, altering the luminosities, surface temperatures, sizes, and shapes of stars in ways that are unaccounted for in nonrotating models. HAO scientists have developed methods for constructing self-consistent models of differentially rotating, chemically homogeneous stars, whereby the equations of stellar structure and Poisson's equation for the gravitational potential are iteratively solved for an assumed conservative internal rotation law. Such models provide the means of interpreting observations of stars that are known to be rapid rotators.

If the Sun is peculiar in some way, or if we have fine-tuned our models to reproduce its unique properties, we will never know without studying other stars and attempting to match the diverse observations with the same models. For this reason, HAO is committed to maintaining a connection to stellar astrophysics. By observing magnetic activity cycles in other stars (Figure 7), we can improve our understanding of the solar cycle. By measuring the interior properties of different stars that result in a variety of stellar dynamos, we can place our knowledge of the solar dynamo into a broader context. By modeling the effects of rapid rotation on stellar structure, we can learn about the forces that shaped our own star in the past. Our models must be able to reproduce the wide array of behaviors observed in stars at every stage of their evolution, or their validation must be considered incomplete.

Asteroseismology and Stellar Interiors

Significant progress in dynamo modeling could only occur after helioseismology provided meaningful constraints on the Sun's interior structure and dynamics (Brown et al. 1989; Schou et al. 1998). Later observations, with the capability of detecting helioseismic signatures of solar cycle effects, established that variations in the mean strength of the solar magnetic field lead to significant shifts (~0.5 μHz) in the frequencies of even the lowest-degree p-modes (Libbrecht & Woodard 1990; Salabert et al. 2004). These shifts can provide independent constraints on the physical mechanisms that drive the solar dynamo, through their influence on the outer boundary condition for the pulsation modes. They are thought to arise either from changes in the near-surface propagation speed due to a direct magnetic perturbation (Goldreich et al. 1991), or from a slight decrease in the radial component of the turbulent velocity in the outer layers and the associated changes in temperature (Dziembowski & Goode 2004, 2005).

Space-based asteroseismology missions, such as MOST (Walker et al. 2003), COROT (Baglin et al. 2006), and Kepler (Borucki et al. 2007) are now providing additional tests of dynamo models using other solar-type stars (see Chaplin et al. 2007). The continuous long-term monitoring from these satellite missions and from future ground-based networks like the Stellar Oscillations Network Group (SONG) are expected to yield the precision necessary for asteroseismic measurements of stellar convection zone depths (Monteiro et al. 2000; Verner, Chaplin & Elsworth 2006). By combining such observations with measurements of stellar differential rotation (see below) and the magnetic activity cycles documented from long-term surveys of the Ca II H and K emission (Figure 8), we can extend the calibration of dynamo models from the solar case to many independent sets of physical conditions.

Figure 8: Turbulent convection near the surface of the Sun and other stars excites acoustic oscillations that can be observed from the resulting surface motions and brightness variations. The characteristics of these oscillations probe both the global properties and the interior conditions of the star.

Scientists at HAO are directly involved in the analysis of asteroseismic data from NASA's Kepler mission, including the development of an innovative stellar model-fitting pipeline using a parallel genetic algorithm. As part of an international collaboration known as the Kepler Asteroseismic Science Consortium (KASC), which is being organized through the University of Aarhus in Denmark, HAO scientists have early access to the Kepler data and are characterizing the properties of thousands of solar-type stars (Figure 9). A small sample of the brightest Kepler targets are also being monitored for Ca II H and K emission throughout the lifetime of the mission from the Nordic Optical Telescope in La Palma, Spain.

Figure 9: An echelle diagram for the Sun observed as a star, where we divide the oscillation spectrum into segments of a fixed length and plot them against the oscillation frequency. Colored symbols show the observations while open points show the best stellar model from the automated pipeline of Metcalfe et al. (2009). Only the points with l=0-2 between the dashed lines were used for the fit, but the model also provides a good match to the data outside this frequency range and the l=3 points.

Sunspots and Photospheric Dynamics

kolinski — Wed, 15 Dec 2021 20:06:20 +0000

Sunspots and Photospheric Dynamics kolinski Wed, 12/15/2021 - 13:06

Sunspots are the most prominent manifestations of magnetic field in the visible layers of the solar atmosphere. Their origin is a dynamo process operating in the solar convection zone. Magnetic field generated there over timescales typical for the solar cycle (~11 years) is transported toward the solar surface through a rapid flux emergence process leading to the formation of active regions. The typical size of sunspots is somewhat larger than the Earth's diameter, their magnetic field is with ~3,000 Gauss strength about 10,000 times stronger than the Earth's magnetic field. Such strong fields modify the convective energy transport leading to a central region (umbra) with predominantly vertical field and a brightness reduced to about 10-20% of that of the undisturbed solar surface. Even though the umbra appears dark compared to the solar surface, the temperature is still 4,000 to 4,500 K. The umbra is surrounded by a filamentary region (penumbra) with a brightness of about 75% (Figure 1). The latter region has strongly inclined field and exhibits large scale outflows of several km/s, the Evershed flow, named after its discoverer (Evershed 1909). At higher resolution the umbra of a sunspot shows fine structure on spacial scales similar to those observed in penumbral filaments. The umbra is not uniformly dark, but shows bright "umbral dots" with a diameter of a few 100 km. At highest possible resolution umbral dots show similar to penumbral filaments a central dark lane (Scharmer et al 2002) (Figure 1).

Figure 1: Sunspot observed with the Swedish Solar Telescope (SST). This image shows the transition from the dark umbra (bottom) toward solar granulation (top). The penumbra in-between shows filaments with central dark lanes. Credit: The SST is operated by the Royal Swedish Academy of Sciences, observation taken 2002 by G. Scharmer.

HAO scientists undertake state-of-the-art computer simulations of sunspots and are working to further enhance sunspot modeling capability by extending the computational domain of a typically observed active region both horizontally and vertically to more realistically simulate flux emergence into the chromospheres.

Radiative MHD simulations of sunspot structure

Performing computer simulations of entire sunspots is a challenging task. Sunspots have a typical size of several 10,000 km and show at the same time details down to the smallest observable scales of the order of a few 100 km. This combination of a large structure with much details requires large virtual computing domains which were out of reach for a long time. First attempts by Schüssler & Vögler (2006) focused on a detailed study of the umbra of a sunspot. Simulations including the transition from umbra toward granulation are more demanding and were first performed in 'slab' geometry, i.e. the simulation domain is a narrow rectangular cut through the center of a sunspot. Recently advances in supercomputing made also simulations of entire sunspots possible.

Simulations in slab geometry

Simulations of the transition from umbra toward granulation in 'slab' geometry were first introduced by Heinemann et al. (2007). In 2008 researches at HAO performed in collaboration with the Max Planck Institute for Solar System Research (MPS) in Germany a numerical simulation of filaments in the inner penumbra using a modified version of the MURaM solar MHD code (Rempel et al. 2009).

Figure 2 shows the formation and evolution of umbral dots in the center and a transition toward filaments with lengths of up to 3,000 km at the periphery. Both, umbral dots and filaments show a substructure with central dark lanes. During their formation phase filaments progress toward the umbra of the spot. Simulations in 'slab' geometry point toward a common magneto-convective origin of umbral dots and filaments in the inner penumbra. While umbral dots as shown by Schüssler & Vögler (2006) consist of instationary almost field free upflow plumes, the presence of more inclined field in the inner penumbra leads to symmetry breaking in the horizontal directions. The result are elongated filaments with reduced field strength and increased inclination angle embedded in a background of more vertical magnetic field. The evidence for an extended outer penumbra hosting a strong Evershed flow is very weak in slab simulations.

Figure 2: Intensity images from numerical simulation of sunspot in 'slab' geometry with about 20,000 km diameter (from Rempel et al. 2009). The computational domain has an extent of 36,000 times 4,600 km and is periodic in the horizontal directions shown, the image is doubled (linked movie is tripled) in the y-direction.

Simulations of full sunspots and spot pairs

Recent advances in supercomputing allowed scientists at HAO and MPS to perform the first comprehensive simulation of a pair of sunspots. The simulation domain encompasses a horizontal size of 98,000 times 49,000 km and a depth extent of 6,100 km. The computation including 1.8 billion grid points was performed on NCAR's new IBM Bluefire supercomputer.

The intensity image (Figure 3, top panel) shows extended outer penumbrae preferentially in-between the two sunspots in the x-direction where the neighboring opposite polarity spots lead to the formation of regions with almost horizontal field. The outer penumbra is somewhat subdued in the y-direction where the periodic boundary imposes same polarity spots. Both spots have different field strengths (left: ~3 kG, right: ~4 kG), leading to the formation of more umbral dots in the weaker spot on the left. The intensity movie shows an inward progression of filaments and peripheral umbral dots during their formation phase.

Figure 3: In black and white: Bolometric intensity. In color: Subsurface magnetic field strength on a vertical cut through the center of the spot pair, values range from 0 G (black) to 8 kG (white).

Evidence for mass flows away from the spots is present in the magnetogram movie (Figure 4, top panel), which shows bipolar magnetic structure diverging from both spots. In the center of the domain the outflows from both spots collide and form a large downflow lane, which is also visible in the evolution of the subsurface magnetic field shown (Figure 4, bottom panel). The umbral and penumbral fine structure is clearly visible in the magnetogram as regions with reduced vertical field strength (gray color).

Figure 4: In black and white: Vertical magnetic field in solar photosphere (magnetogram), values range between -3.5 kG (black) and 3.5 kG (white). In color: Subsurface magnetic field strength on a vertical cut through the center of the spot pair, values range from 0 G (black) to 8 kG (white).

The magnetic field inclination in the photosphere (Figure 5, left image) shows the complex magnetic field structure in the transition from umbra toward penumbra. In the inner penumbra filaments with almost horizontal field (white colors) and rather low filling factor are embedded in a background with more vertical field (dark red). The outer penumbra is dominated with extended patches of horizontal field. In the latter regions we also observe the Evershed flow (Figure 5, right image) with peak velocities of up to 14 km/s.

Figure 5: (left) Inclination angle of the magnetic field in the photosphere (right spot in simulation). Gray indicates regions with field strength < 200 G. (right) Radial flow velocity in photosphere. The color scale is saturated at +/- 8 km/s; red colors show outflows. The ring of red colored patches surrounding the spot shows the Evershed flow.

Structure of magneto convection in umbra and penumbra

Altogether numerical simulations indicate a new level of realism in the theoretical modeling of sunspot structure. The basic properties of the simulated umbral dots and penumbral filaments are consistent with a variety of observational results and provide a basis for a physical understanding of umbral and penumbral structure in terms of a common magneto-convective processes that is modulated by the varying inclination angle of the magnetic background field. Figure 6 displays the connection between magnetic field structure (vertical field strength [top left] and inclination angle [top right]) and flows in the photosphere (radial flow [bottom left] and vertical flow [bottom right]). Convective motions are present everywhere in the penumbra and they are the primary driver for the fine structure we observe. Upflows expand and weaken the magnetic field to a degree that enables overturning motions to take place. The convection affects the vertical field component stronger than the horizontal one, leading to filaments with increased field inclination angle. Horizontal flows are preferentially directed outwards. In the inner penumbra outflows are intermittent with velocities below 1 km/s. The outflows in the outer penumbra largely fill the space and reach several km/s. The presence of horizontal flows is manifest in the field structure (Figure 7): Fieldlines in the inner penumbra show only a small 'dip' close the photosphere, while fieldlines in the outer penumbra are bend over by the strong outflows.

Figure 6: Transition from umbra (at right) to penumbra (at left). Quantities shown are in the photosphere. Top left: Vertical magnetic field component (white: upward, black: downward); Top right: Field inclination (black: vertical, white: horizontal); Bottom left: Radial flow velocity (red: outflows, blue: inflows); Bottom right: Vertical flow velocity (red: downflows, blue: upflows).

Figure 7: Frame from an animation of selected magnetic field lines in the penumbra of a simulated sunspot. Red: Filament in inner penumbra. The fieldlines become more inclined at photospheric levels, but continue upward toward the top boundary of the domain. Green: Filament in outer penumbra. The strong Evershed flow bends over field lines and the magnetic field is returning into the solar interior at the edge of the penumbra. Blue: Background field. The semi-transparent surface indicates the approximate location of the photosphere. The visualization was produced with VAPOR.

Studying Atmosphere Coupling Using Mesoscale-resolving WACCM

kolinski — Wed, 15 Dec 2021 19:06:24 +0000

Studying Atmosphere Coupling Using Mesoscale-resolving WACCM kolinski Wed, 12/15/2021 - 12:06

An important pathway for the terrestrial weather to affect the space weather is through atmosphere waves, such as atmospheric tides, planetary waves and gravity waves. The impacts of the planetary-scale waves have been extensively studied observationally and numerically. The gravity waves, in spite of their increasing significance at high altitudes in causing large disturbances in the thermosphere and ionosphere, are poorly quantified in the global context. This is mainly due to the very broad scales of these waves and the wave impacts, and it is a major challenge to capture such broad scales in observations and numerical models. To address this challenge, a mesoscale-resolving whole atmosphere general circulation model has been developed for the first time. This was accomplished using the National Center for Atmospheric Research Whole Atmosphere Community Climate Model (WACCM) with ∼0.25° horizontal resolution and 0.1 scale height vertical resolution above the middle stratosphere (higher resolution below). This was made possible by the high accuracy and high scalability of the spectral element dynamical core from the High-Order Method Modeling Environment (HOMME). The latitude-height structure and the magnitudes of the temperature variance, reflecting the gravity wave potential energy density, compare well with those deduced from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) observations.

Figure 1: WACCM simulation results on 4 February at 21:00 UT. (a–d) Vertical winds at 208 hPa (∼11 km), 10 hPa (∼30 km), 2.4 ×10⁻³ hPa (∼87 km), and 2.6 ×10⁻⁴ hPa (∼100 km), respectively. (e-f) Zonal and meridional winds at 2.6 ×10⁻⁴ hPa. The contour range is smaller than the actual range of the winds to better visualize the wave structures. In Figure 1a the maximum upward wind over the tropical cyclone is 4 m s⁻¹; in Figures 1b-d the maximum values of the vertical winds are 0.6 m s⁻¹, 9 m s⁻¹, and 7.5 m s⁻¹, respectively; in Figures 1e and 1f the maximum values of the horizontal winds are 162 m s⁻¹ and 114 m s⁻¹.

The simulation reveals the increasing dominance of gravity waves (GWs) at higher altitudes through both the height dependence of the kinetic energy spectra, which display a steeper slope (∼−3) in the stratosphere and shallower slopes above, and the increasing magnitude and spatial extent of GWs (including a planetary-scale extent of a concentric GW excited by a tropical cyclone) at higher altitudes (Figure 1). GW impacts on the large-scale flow are evaluated in terms of zonal mean zonal wind and tides: with no GW drag parameterized in the simulations, forcing by resolved GWs does reverse the summer mesospheric wind, albeit at an altitude higher than climatology, and only slows down the winter mesospheric wind without closing it. The hemispheric structures and magnitudes of diurnal and semidiurnal migrating tides compare favorably with observations.

In addition to NSF base funding on Award #M0856145, this work was supported by NSF AGS-1138784, NASA LWS NNX09AJ83G, NNX13AE20G, and base fund.

Source: Liu, H.-L., J. M. McInerney, S. Santos, P. H. Lauritzen, M. A. Taylor, and N. M. Pedatella (2014), Gravity waves simulated by high-resolution Whole Atmosphere Community Climate Model, Geophys. Res. Lett., 41, 9106–9112, doi:10.1002/2014GL062468.

Solar Convection and Mean Flows

kolinski — Wed, 15 Dec 2021 17:46:09 +0000

Solar Convection and Mean Flows kolinski Wed, 12/15/2021 - 10:46

Any inquiry into the ultimate origins of solar magnetic activity must soon confront turbulent thermal convection. Convection is a means by which the Sun shines. Energy liberated by nuclear fusion deep in the core of the Sun filters outward by the diffusion of photons. In the outer approximately 30% of the Sun by radius, the solar plasma is cooler and more opaque, making radiative diffusion less efficient. Convection takes over as the primary mechanism by which energy is transported from 0.7 R to the solar photosphere, where it is radiated into space.

Convection in a rotating star not only transports energy, it also transports momentum, establishing global circulations and shearing flows. Such mean flows work together with turbulent convection to amplify, organize, and transport magnetic fields, converting kinetic energy to magnetic energy. This is the solar dynamo, where the chain of events that gives rise to space weather begins.

Turbulent Solar Convection

The surface of the Sun is blanketed by a patchwork of bright and dark patterns which changes continually, renewing itself every five minutes. Each bright patch is about 1000km across and is surrounded by an sinuous network of darker lanes. These are the telltale signs of thermal convection; hot plasma rises to the surface from below while cooler, denser plasma sinks. This surface convection is known as granulation and is readily observed with a moderate-sized optical telescope. Although they cannot be observed directly, researchers have long believed that larger scale convection cells lie deeper down—churning masses of plasma that are as much as 100,000km across—each ten times larger than the diameter of the Earth. These have become known under the evocative name of giant cells

Figure 1: Convective patterns in a computer simulation of solar convection. Shown is a horizontal surface near the top of the convection zone in a Molleweide projection. Bright colors denote plasma flowing upward and dark colors denote plasma flowing downward.

The supercomputing resources required to numerically simulate solar convection are formidable. In order to exploit the latest generation of massively parallel computing architectures, HAO researchers and international collaborators have developed the ASH (Anelastic Spherical Harmonic) computer code, which solves the three-dimensional equations of magnetohydrodynamics (MHD) in rotating spherical shells with high spatial and temporal resolution. ASH simulations provide an unprecedented look into what giant cell convection in the deep interior of a star might be like (Figure 1). Radiative cooling near the solar surface produces relatively cool, dense plumes of plasma that are pulled down by gravity, creating an intricate, interconnected pattern of convection cells. The pattern is reminiscent of granulation but magnified 100 times. Closer scrutiny reveals further structure. At low solar latitudes, the downflow lanes exhibit a preferential north-south orientation, moving eastward relative to the surrounding plasma. Where lanes meet at higher latitudes, solar cyclones appear with a counter-clockwise swirl in the northern hemisphere (clockwise in the southern), only to disappear a few days later as they become subsumed into the global maelstrom.

Helioseismology and the Solar Internal Rotation

Although the interior of the Sun cannot be observed directly, solar internal dynamics may be probed by studying the behavior of sound waves in a research endeavor known as helioseismology. The Sun rings like a bell in millions of distinct tones, referred to as acoustic oscillation modes. Scrutinizing the frequencies of these oscillation modes provides information about the structure and dynamics below the surface. For example, as sound waves propagate through moving plasma, their frequency is shifted as a consequence of the Doppler effect. By carefully measuring such frequency shifts at the surface of the Sun, the flow below the surface may be mapped out. Computer models help to interpret such solar subsurface weather maps and inspire new helioseismic investigations. Similar techniques applied to other stars are referred to as asteroseismology.

Figure 2: Internal rotation profile of the Sun inferred from helioseismology. Blue, green, and red represent progressively faster rotation as indicated in the legend. A rotation rate of 450 nHz corresponds to a rotation period of 26 days and 325 nHz corresponds to 36 days. The image extends from the solar equator on the lower right to the pole on the upper left (averaged over the northern and southern hemispheres).

Among the most remarkable triumphs of helioseismology is the inferred rotation profile of the solar interior (Figure 2). We have known for nearly two centuries that the surface of the Sun rotates differentially, with the rotation period increasing steadily from 25 days at the equator to about 36 days near the poles. Helioseismology now reveals that this rotation profile persists throughout the convection zone, with a sharp transition to nearly uniform rotation in the relatively quiescent radiative interior. The narrow transition layer is known as the solar tachocline (see below).

Shear, Magnetism and Global Circulations

The solar internal rotation profile inferred from helioseismology suggests that convection is be responsible for the differential rotation of the solar envelope. The convection zone rotates differentially whereas the radiative interior does not. Understanding how this rotation profile is established and maintained is one of the most compelling challenges of solar and stellar physics. HAO researchers face this challenge armed with several complementary numerical models, including 3D convection simulations and non-kinematic mean-field models that solve for mean flows as well as mean magnetic fields.

Figure 3: Mean flows versus latitude and radius in a representative selection of ASH solar convection simulations. Panels a and b show internal rotation profiles, panel c shows the latitudinal variation of the specific entropy per unit mass, and panels d and e show meridional circulation patterns, with lines indicating the direction of the mass flux and colors indicating its sense (red for clockwise, blue for counter-clockwise).

Such computer models indicate that the solar differential rotation comes about by means of a subtle nonlinear interplay between convective energy and momentum transport, rotational shear, axisymmetric circulations in the meridionial (radius-latitude) plane, and thermal gradients, meaning variations of temperature, density, pressure, and entropy with radius and latitude. The mean flows thus generated play an important role in the solar dynamo; rotational shear produces strong horizonal sheets and tubes of magnetic flux that ultimately emerge through the solar surface to form sunspots and active regions while the meridional circulation transports magnetic flux, thereby regulating the solar activity cycle (Figure 3).

Figure 4: Non-kinematic mean-field solar dynamo model showing torsional oscillations in the solar convection zone. Red and blue represent plasma flowing eastward and westward respectively. Panel a illustrates how the alternating bands of eastward and westward flow vary with latitude and time while Panel b>shows their variation with latitude and radius at one instant in time.

Magnetism generated by convection, rotational shear, and meridional circulations can feed back on these flows in subtle and interesting ways, providing further clues into the origins and manifestations of solar magnetic activity. A notable example are the torsional oscillations; alternating bands of faster and slower rotation that drift toward the solar equator through the course of the solar activity cycle. HAO's non-kinematic mean-field dynamo models suggest that these originate by means of the combined influence of magnetic stresses and enhanced radiation in photospheric active regions (Figure 4).

The Solar Tachocline

One of the most striking features of the solar internal profile inferred from helioseismology is the solar tachocline; the sharp transition region between the differentially rotating convective envelope and the uniformly rotating radiative interior. The significance of the solar tachocline far outweighs its relatively small spatial extent. Although it only spans a few percent of the solar interior by radius, this is where sunspots and related active regions in the solar photosphere are thought to originate. Furthermore, the tachocline regulates the interaction between the convection zone and the deeper solar interior, with important implications for the rotational and compositional history of the Sun over its five billion year lifetime.

Figure 5: When a longitudinal band of magnetic flux is embedded in a region where the rotation rate varies with latitude, the band will tend to tip under certain conditions. The images above show a computer simulation of such a tipping instability. The left image shows the magnetic field after an initially east-west oriented band has tipped, with orange and blue denoting eastward and westward magnetic flux. The center and right panels show the velocity in the longitudinal direction and the vorticity variation associated with the tipping of the bands.

The solar tachocline is a rotating, stratified, magnetized shear layer and it exhibits a complex array of physical phenomena including turbulent penetrative convection, internal gravity waves, and a variety of MHD instabilities. HAO researchers investigate the diverse and enigmatic intricacies of the tachocline by means of multiple theoretical and computational modeling approaches, some designed to exploit the tachocline's thin radial extent. An example is shown in (Figure 5) which shows a 3D MHD simulation of the so-called tipping instability that arises when a horizontal loop of magnetic flux is embedded in a rotational shear flow. Such instabilities have also been studied both analytically and numerically using an MHD generalition of the shallow-water approximation originally developed for oceanic applications.

Stellar Differential Rotation

Figure 6: Top, middle and bottom frames in right represent observational synoptic maps of Kitt Peak magnetic field data at Carrington rotations 1921, 1927 and 1936; three theoretical synoptic maps on left are derived from superposition of m=1,S,A and m=2,A modes for a 20 kG toroidal band at times equivalent to 0, 6 and 15 Carrington rotations. Yellow arrows in the frames at right column denote new cycle spots; the spot inside the dotted circle in the top right frame is an old-cycle spot. White arrows in the frames at left column show the longitudes at which the spots errupted at the surface. The only spot that does not fall in a bulge (red area) is circled in the lower right frame.

Even without the short cadence data that is obtained for asteroseismology, the Kepler mission will yield high precision time-series photometry for many stars that will be sufficient to characterize the surface differential rotation through detailed spot modeling (Figure 6). The photometry will be precise enough to reveal the signature of individual star-spots rotating into view, and the continuous monitoring will show spots at different stellar latitudes lapping each other so their locations and rotation rates can be derived without ambiguity. The Kepler data will allow surface differential rotation measurements for up to 100,000 solar-type stars, and over the lifetime of the mission this may even allow the construction of rudimentary "butterfly diagrams" showing the migration of activity belts through some fraction of the stellar magnetic cycles.

Figure 7: The rotation period of spots at various latitudes on the young solar-type star κ1 Ceti from observations by the MOST satellite in 2003 (green), 2004 (blue), and 2005 (pink), showing the same pattern of surface differential rotation as the Sun (red lines). The rotation period from ground-based observations of Ca II H and K emission is in the range shown by vertical dashed lines (adapted from Walker et al. 2007).

For the brighter asteroseismic targets where the individual oscillation frequencies are detectable, the time series should be long enough to resolve rotational splitting of the modes into multiplets for stars with rotation rates between about 2 and 10 times the solar rate (Ballot et al. 2008). Slower rotation makes it difficult to resolve the individual components of each multiplet from their strongly overlapping Lorentzian profiles, while faster rotation produces a splitting that is comparable to the small separation, creating some ambiguity in the mode identification. Measurements of the rotational splitting as a function of radial overtone can indirectly probe radial differential rotation, since the various modes sample slightly different (but overlapping) regions of the star (Figure 7). More directly, even with the limited set of low-degree oscillation frequencies that are available for distant stars, it is possible to construct inversion kernels that might detect a rapidly rotating core (Gough & Kosovichev 1993), although more recent work suggests that a significant detection may require unrealistically strong differential rotation (Chaplin et al. 1999).

Figure 8: A theoretical H-R diagram showing the positions of various models of rotating stars with the same mass as the Sun. Some of the rapidly rotating models appear near the locations of zero age main sequence models for non-rotating stars (dotted line) creating a potential source of confusion. The inset shows the surface topology and convection zones for a rotating model with observable properties similar to the Sun (adapted from MacGregor et al. 2007).

The effects of rotation can modify many stellar properties, altering the luminosities, surface temperatures, sizes, and shapes of stars in ways that are unaccounted for in non-rotating models of stars. HAO scientists have developed methods for constructing self-consistent models of differentially rotating, chemically homogeneous stars, whereby the equations of stellar structure and Poisson's equation for the gravitational potential are iteratively solved for an assumed conservative internal rotation law. Such models provide a means of interpreting observations of stars that are known to be rapid rotators (Figure 8).

Satellite Drag Physical Modeling for Transition to Operations

kolinski — Wed, 15 Dec 2021 17:37:13 +0000

Satellite Drag Physical Modeling for Transition to Operations kolinski Wed, 12/15/2021 - 10:37

The ionosphere and upper atmosphere play a major role in space operations, including communications, navigation, and satellite drag. Satellite drag, the drag force exerted by the tenuous upper atmosphere on orbiting bodies, is the leading cause of error in predicting the locations of objects in low-Earth orbit. As the population of satellites and space debris grows with time, higher orbital prediction accuracy is required for tracking, collision avoidance, reentry prediction, and satellite lifetime calculations. Satellite drag is constantly changing because thermospheric density is highly variable with geographic location and time, due to atmospheric dynamics and waves, solar ultraviolet flux changes, and geomagnetic disturbances, i.e., space weather.

Neutral densities at 400 km during 2007 modeled by the TIME-GCM using a constant eddy diffusion and tides from the Global Scale Wave Model (GSWM) (black), constant eddy diffusion without tides (purple), variable eddy diffusion with GSWM tides (green), and CHAMP accelerometer density measurements (red).

The goal of the Atmospheric Density Assimilation Model (ADAM) development is to accurately predict current and future satellite drag with a suite of thermosphere-ionosphere “full physics” models, using real-time space weather data. This Small Business Technology Transfer (STTR) project for the US Air Force is led by a small business, Atmospheric & Space Technology Research Associates (ASTRA), and has participation from the NCAR High Altitude Observatory, the University of Colorado, and the NOAA Space Weather Prediction Center (SWPC). Recent work by this group has resulted in significant progress understanding the seasonal variation in thermospheric density by Pilinski and Crowley [2015] using the NCAR Thermosphere-Ionosphere-Mesosphere-Electrodynamics General Circulation Model (TIME-GCM), following on from the work of Qian and Solomon at HAO [Qian et al., 2009]. The figure below shows a comparison of TIME-GCM density predictions, using various lower boundary conditions, with measurements from the CHAMP satellite.

Global distribution of helium number densities at 250 km altitude during each season for solar minimum conditions (2008), as calculated by TIE-GCM. (left) Equinox plots share a common color scale, as do (right) solstice plots.

Other advances related to the satellite drag problem include the addition of helium to the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM). At very high altitude (~500 km) it is not enough to calculate the major constituents of the upper atmosphere (molecular nitrogen and atomic oxygen), because helium becomes a significant fraction of the density. Due to its small molecular mass, it diffuses to the top of the atmosphere and tends to collect over the winter polar region. This was successfully simulated by Sutton et al. [2015], working with researchers and programmers at HAO, is now a standard part of both the TIE-GCM and TIME-GCM, and is being added to the WACCM-X model.

Pilinski, M. D., and G. Crowley (2015), Seasonal variability in global eddy diffusion and the effect on neutral density, J. Geophys. Res. Space Physics, 120, 3097, doi:10.1002/2015JA021084.

Sutton, E. K., J. P. Thayer, W. Wang, S. C. Solomon, X. Liu, and B. T. Foster (2015), A self-consistent model of helium in the thermosphere, J. Geophys. Res. Space Physics, 120, 6884, doi:10.1002/2015JA021223.

Modeling high-speed flows in the Earth’s Magnetotail

kolinski — Wed, 15 Dec 2021 17:05:18 +0000

Modeling high-speed flows in the Earth’s Magnetotail kolinski Wed, 12/15/2021 - 10:05

The magnetosphere is created by the interaction between the solar wind and the Earth’s magnetic field. On the dayside of the Earth pressure from the solar wind compresses the Earth’s dipole magnetic field and on the night side this interaction stretches it out forming a region of space commonly referred to as the magnetotail. Depending on the direction of the magnetic field in the solar wind, mass, momentum, and energy can be transferred into the magnetotail making it a highly dynamic region full of high-speed plasma flows. HAO scientist Michael Wiltberger, working with colleagues at Dartmouth College and John’s Hopkin’s University, used the Lyon-Fedder-Mobarry global magnetosphere model in its highest resolution mode to simulate these dynamic flows.

Figure 1: Wiltberger, M., V. Merkin, J. G. Lyon, and S. Ohtani (2015), High-resolution global magnetohydrodynamic simulation of bursty bulk flows, J. Geophys. Res., 120(6), 4555–4566, doi:10.1002/2015JA021080.

Figure 1 shows a scientific visualization of the magnetotail as the interplanetary magnetic field (IMF) goes from northward to southward. Southward IMF allows for the most energy transfer from the solar wind into the magnetosphere. The visualization shows the magnetotail with a colored plane cut through the center of the Earth. On this plane the difference between dipole magnetic field and the current value is illustrated with the green/purple color scheme. You can see the compression of the Earth’s dipole field on the dayside at the beginning of the movie. As the movie progresses, the magnetotail becomes dominated by numerous high-speed flows that propagate from the further down the tail towards the Earth. The colored arrows in the visualization illustrate the strength and direction of these flows. A larger redder arrow represents stronger flows. The green concave feature at the leading of these flows represents a compression of the magnetic field. This compression returns the field to a more dipolar magnetic field configuration and is the origin of the name dipolarization fronts that scientists use for these features.

These dipolarization fronts are often observed in the magnetotail by various NASA spacecraft. A challenge in comparing these observations with the simulation results is that because the flow is nearly turbulent it is difficult if not impossible to have the spacecraft exactly the same spot in the real magnetotail and the simulation. The investigators overcome this challenge by making a statistical comparison between the observed flows and the simulation results. Figure 2 illustrates the results of using the same selection criteria to observe high-speed flows in the simulation and real magnetotail. On the left hand side of Figure are results for the flow speed, magnetic field, and density observed by the Geotail mission while it was in the magnetotail. On the right hand side are results from the high-resolution LFM simulation. The flows show a slightly broader profile than the observations with similar peak value. The magnetic field shows the compression of the BZ field in both the simulation and observations. There is a density drop in both sets of data, but the magnitude is much larger in the simulated results. This is likely due to the preconditioning of the magnetosphere in the simulation. In general, these results are in good agreement and provide verification that the high-resolution simulations are doing a good job of capturing the dynamics of the magnetotail.

Magnetic Flux Emergence

kolinski — Wed, 15 Dec 2021 14:56:03 +0000

Magnetic Flux Emergence kolinski Wed, 12/15/2021 - 07:56

Understanding the process of magnetic flux emergence through the solar convection zone is crucial for understanding the link between the observed magnetic activities at the surface and the dynamo-generated magnetic fields in the interior.

The current prevailing picture is that magnetic active regions on the solar surface originate from strong, predominantly toroidal magnetic fields generated by the solar dynamo mechanism at the thin tachocline layer at the base of the solar convection zone. Thus the magnetic fields need to traverse the entire convection zone (the outer 30% of the solar interior) before they reach the photosphere to form the observed sunspots and solar active regions, which are centers of solar eruptions. Understanding the process of magnetic flux emergence through the solar convection zone is therefore crucial for understanding the link between the observed magnetic activities at the surface and the dynamo-generated magnetic fields in the interior.

Using MHD numerical simulations, HAO scientists have modeled the formation and rise of buoyant of magnetic flux tubes in the solar convection zone and their emergence through the photosphere into the solar atmosphere.

Figure 1: A full disk magnetogram from the Kitt Peak Solar Observatory showing the line of sight magnetic flux density on the photosphere of the Sun on May 11, 2000. White (Black) color indicates a field of positive (negative) polarity.

If the magnetic field seen in sunspots and active regions on the solar surface originates from a large-scale, predominantly toroidal magneticfield generated at the base of the solar convection zone, then the process of how active region flux is transported through the convection zone and emerge into the solar atmosphere becomes a crucial link in the solar cycle dynamo puzzle. It is generally thought that magnetic flux rises buoyantly through the convection zone in the form of discrete flux tubes, and that the tubes should maintain reasonable cohesion in order that the emerging flux be organized as active regions, which display a well-defined order as described by Hale's polarity rule and Joy's law of active region tilts (Figure 1). Theoretical, numerical, and observational studies in the past 3 decades have greatly improved our understanding of the process, but have also raised many new questions. A review article on this subject can be found in Living Reviews in Solar Physics.

Buoyant rise of active region flux tubes in the solar interior

Figure 2: (a) 3D volume rendering of the magnetic field strength of a weakly twisted, rising Omega-shaped, whose apex is approaching the top boundary, resulting from a simulation described in (Fan 2008); (b) A cross section of |B| near the top boundary at r=0.937 R; (c) selected field lines threading through the coherent apex cross-section of the Omega-shaped tube.

Fan (2008) has carried out a set of 3D anelastic MHD simulations of the buoyant rise of active region scale flux tubes in a "quiescent" model solar convective envelope in a rotating spherical shell geometry. These simulations have considered twisted, buoyant toroidal flux tubes at the base of the solar convection zone with an initial field strength of 100 KG, being highly super-equipartition compared to the kinetic energy density of the convective motions, and thus have neglected the effect of convection. The main finding from these simulations is that the twist of the tube induces a tilt at the apex of the rising Omega-shaped tube that is opposite to the direction of the observed mean tilt of solar active regions, if the sign of the twist follows the observed hemispheric preference. It is found that in order for the tilt driven by the Coriolis force to dominate, such that the emerging Omega-shaped tube shows a tilt consistent with Joy's law of active region mean tilt, the initial twist rate of the flux tube needs to be smaller than about a half of that required for the tube to rise cohesively. Under such conditions, the buoyant flux tube is found to undergo severe flux loss during its rise, with less than 50% of the initial flux remaining in the final Omega-shaped tube that rises to the surface (Figure 2a).

It is also found that the Coriolis force drives a retrograde flow along the apex portion, resulting in a relatively greater stretching of the field lines and hence stronger field strength in the leading leg of the tube. With a greater field strength, the leading leg is more buoyant and remains more cohesive compared to the following leg (Figure 2a). Figure 2c shows selected field lines threading through the coherent apex cross-section of the final Omega-shaped tube, resulting from a simulation of a weakly twisted buoyant tube. It can be seen that the field lines in the leading side are winding about each other smoothly in a coherent fashion, while the field lines in the following side are significantly more frayed. The emergence of such an asymmetric tube may explain the observed more coherent leading polarity compared to the following polarity in an active region. Furthermore, the greater buoyancy and hence higher rise velocity of the leading leg in conjunction with its more coherent twist may give rise to a greater upward helicity flux in the leading polarity comparing to the following as a result of the emergence of the Omega-shaped tube. Such an asymmetry in helicity injection between the leading and following polarities of emerging active regions has been observed (Tian & Alexander 2009).

Flux emergence into the atmosphere, sunspot rotations, and the formation of a coronal flux rope

Figure 3: The left panel shows the 3D coronal magnetic field resulting from flux emergence. The black field line is the line going through the O-point of the transverse magnetic field in the central cross-section (at x=0), representing the new axis of the coronal flux rope structure. The right image shows the z-component of the vorticity on the photosphere overlaid with contours of Bz with solid (dotted) contours representing positive (negative) Bz. The image show counter-clockwise vortical motion (i.e. positive z-vorticity) centered on the peaks of the vertical flux concentrations of the two polarities.

Understanding how twisted magnetic fields emerge from the dense, convectively unstable solar convection zone into the stably stratified, rarefied solar atmosphere and corona is fundamentally important for understanding the formation of solar active regions and the development of precursor structures for solar eruptions such as flares and coronal mass ejections (Figure 3).

Fan (2009) has carried out 3D MHD simulations of the dynamic emergence of a twisted flux tube from the top layer of the convection zone into the solar atmosphere and corona. It is found that after an initial stage of flux emergence, during which the two polarity flux concentrations on the photosphere undergo a shearing motion and become separated, a prominent rotational/vortical motion develops within each polarity, reminiscent of sunspot rotations. This rotational motion persists throughout the subsequent evolution and steadily transports magnetic energy and twist into the atmosphere. It is shown that the initial shearing and the subsequent rotational motions of the two polarity flux concentrations twist up the inner field lines of the emerged field (near and include the original tube axis), causing them to rotate in the atmosphere from an initial normal configuration (i.e. arching over the polarity inversion line from the positive to the negative polarity), into an inverse configuration (i.e. directed from the negative polarity to the positive polarity over the neutral line). As a result, a flux rope with sigmoid-shaped, dipped core fields form in the corona, and the center of the flux rope rises in the corona with increasing velocity as the twisting of the flux rope footpoints continues.

Figure 4: The left panel shows the electric current density in a horizontal plane at height z=10 in the chromosphere. The middle and right panels show two perspective views of a set of 3D field lines traced from a few points along the current concentration shown in the left panel.

A current sheet forms in the lower atmosphere, extending up to the base of the corona, with field lines going through it all showing sigmoid shapes. Heating in the current sheet may therefore cause these field lines to brighten up in X-ray as the observed sigmoid loops in active regions. Field lines going through the center portion of the current sheet undergo sharp dips. Reconnection in the current sheet allows for removal of the heavy plasma trapped in the dips and hence enhance the upward acceleration of the coronal flux rope (Figure 4).

It is shown that the rotational motions of two polarity flux concentrations on the photosphere are a manifestation of nonlinear torsional Alfven waves propagating along the flux tube, consistent with what has been predicted by an idealized analytical model (Longcope and Welsch2000). Due to the rapid stretching of the emerged magnetic field in the atmosphere and corona, the rate of twist per unit length along the coronal field lines drastically decreases. As a result, a gradient of the rate of twist is established along the flux tube from the interior into the atmosphere with the interior portion of the flux tube having a much higher rate of twist.

Figure 5: The variation of the rate of twist per unit length as a function of z along three field lines (distinguished by three different colors) in the neighborhood of the original tube axial field line, at a time near the end of the simulation when a coronal flux rope has formed.

This gradient in the rate of twist drives torsional waves along the flux tube, transporting twist from the interior highly twisted portion into the expanded coronal portion (Longcope and Welsch 2000}. Thus the rotational motion will continue until the coronal twist rate equilibrates with the interior twist rate along the field lines. The time scale for establishing the equilibrium is on the order of the Alfven transient time along the interior flux tube, which means that the rotational motion can persists for a few days after the initial emergence. Sunspot rotations have been observed in many events preceding X-ray sigmoid brightening and the onset of eruptive flares (e.g. Brown et al. 2003, zhang et al. 2008). Our simulations suggest that these rotational motions are due to non-linear torsional Alfven waves naturally occurring during the emergence of a twisted flux tube, and is an important means whereby twist is transported from the interior into the corona, driving the development of a coronal flux rope as a precursor structure for solar eruptions (Figure 5).

Long-Term Solar Variability

kolinski — Tue, 14 Dec 2021 22:57:43 +0000

Long-Term Solar Variability kolinski Tue, 12/14/2021 - 15:57

HAO scientists pursue an interdisciplinary, system-wide view on the origins and impacts of solar and stellar cycle variation, with a particular focus on magnetic minima as times of low activity and relatively simple heliospheric structure.

The solar activity cycle, as manifested by repeated increase and then decrease in the number of sunspots visible on the Sun, has been observed and analyzed for centuries. However, only for the past two to three ~11-year activity cycles have new capabilities in satellite and ground-based observations allowed us to consider how a broad range of solar, heliospheric, and geospace observables vary within and between cycles. These observations, in conjunction with theoretical and numerical modeling advances, enable an interdisciplinary, system-wide view on the origins and impacts of solar cycle variation.

SOLAR CYCLE OBSERVATIONS

While sunspots were first observed by Chinese astronomers in 800 B.C., systematic observations of sunspots through the telescope started around 1600. In 1843, a German astronomer, Samuel Schawbe, first discovered that the number of sunspots wax and wane in a cyclic fashion with an 11-year periodicity. This is called the sunspot cycle or the solar cycle, which is also compactly characterized by a butterfly diagram (Courtesy: G. de Toma). This diagram represents a latitude-time plot of the positions of all observed sunspots. Such a latitude-time diagram is generally derived from the longitude-averaged magnetograms of the National Solar Observatory.

The principal features of solar cycles seen here are:

Appearance of sunspots in a latitude belt within ~±35° latitude
Equatorward migration of this belt with an ~11 year periodicity
Poleward migration of the large-scale radial fields with an ~11 year periodicity
A certain phase relationship between the sunspots and surface radial fields, such that the polar reversal takes place approximately during the epoch of sunspot maxima, and polar field surges to maximum strength occur during sunspot minima
The sign of the magnetic field in each hemisphere for a given cycle is by convention defined to be the follower spots in that hemisphere. With this sign convention, the polar field is seen to change sign from positive (white) to negative (black) when the sunspot cycle (sign of the follower spots) has already been negative
The northern and southern hemispheres of the sun are magnetically coupled by antisymmetric magnetic fields about the equator. We see in the butterfly diagram (Figure 1) that in a particular cycle, all the follower spots in the bipolar spot groups are positive (white) in one hemisphere and negative (dark) in the other hemisphere. In the next and preceding cycles, all the polarities are reversed. In each cycle, the dark features are poleward in one hemisphere, the white features poleward in the other hemisphere. These patterns also reverse with each succeeding cycle.

Figure 1: NSO magnetogram Butterfly diagram.

AN UNUSUAL MINIMUM

Figure 2: Net polar magnetic flux as measured at the Sun's photosphere between 60° and 80° latitude by SOHO/MDI (squares) and at NSO (diamonds) from 1995 to 2010. The polar magnetic flux has been at about the same level since 2004 and is significantly lower than during the previous minimum in 1996. See De Toma (2011).

Solar minimum represents the time of lowest solar activity and simplest heliospheric structure, and as such is a good place to begin putting together a system-wide understanding. However, recent observations imply complexities in the variation within and between solar minima that have implications for analyzing and predicting space weather responses at the Earth during solar quiet intervals, and also for interpreting the Sun's past behavior as preserved in cosmogenic isotopes and historical sunspot and aurorae records. For example, the last solar cycle minimum was very quiet, with the sunspot number dropping to its lowest values in at least 75 years. Additionally, the polar magnetic fields were about 40% weaker than during the previous minimum (Figure 2).

Figure 3: Artist's conception of the sun-heliosphere-Earth system for the last two solar minimum. Compared are solar wind morphology (faster wind streams indicated in yellow emanating from coronal holes), impact for the Earth's radiation belt (large relativistic electron population indicated by red), and cosmic rays (high levels indicated by number of squiggly red arrows). See Gibson et al. (2009) and Gibson et al. (2011).

However, despite this global "weakness", the Sun continued to send out strong solar wind gusts during low-activity months that acted as periodic drivers of the Earth's space environment and upper atmosphere, sustaining the population of relativistic electrons in the Earth's outer radiation belt even in 2008 when sunspots had reached record lows (Figure 3).

Figure 4: White-light images of the solar corona from LASCO/C2 for the previous solar minimum on February 20, 1996 (left panel), and the recent minimum (last three panels) on February 15, 2007, July 25, 2008, and May 22, 2009. All images correspond to very quiet times: the observed sunspot number for the four days was 8, 0, 8, and 0, respectively. During the 1996 minimum, the shape of the corona was dipolar and coronal streamers were confined to a narrow region around the heliographic equator while in 2007, 2008, and 2009 coronal streamers extended to relatively high heliolatitudes. See De Toma et al. (2010).

This was in contrast to the past cycle, in which the radiation belts faded away before solar minimum, and was a direct consequence of a more complex magnetic configuration at the Sun. In particular, the coronal magnetic field this cycle did not simplify to a dipole and the heliospheric current sheet remained substantially warped (Figure 4) even after sunspots and TSI decreased dramatically. It is possible that these seemingly discrepant observations are jointly consequences of the weakened polar magnetic field. In any event, it is clear that the sunspot number does not tell the whole story about how the interaction between the solar wind and the Earth's geospace environment may be substantially altered during times of low solar activity.

Figure 5: (a) An illustration of the motions of the magnetic field on the Sun in the frame corotating with the equatorial rotation rate (Fisk, 1996, 2005; Fisk, Zurbuchen, and Schwadron, 1999b; Fisk and Schwadron 2001). The M-axis is the axis of symmetry for the expansion of the magnetic field from a polar coronal hole. The Ω-axis is the solar rotation axis. P marks one of the open lines (green) that connects to the Pole. The curves with arrows (red) are the trajectories of the open lines. (b)The open lines reconnect and diffuse outside the streamer-stalk region, which is marked in yellow. See Zhao and Fisk (2010).

Analyses of solar-wind composition data also indicate differences between the most recent solar minimum and prior ones, although without necessarily requiring revision of concepts relating the solar wind and interplanetary magnetic field. These studies demonstrate that there are two distinct regions of solar wind: solar wind likely to originate from the stalk of the streamer belt (the highly elongated loops that underlie the heliospheric current sheet), and solar wind from outside this region (Figure 5). The region outside the streamer-stalk region is noticeably larger in the Cycle 23–24 minimum; however, the increased area can account for the reduction in the heliospheric magnetic-field strength in this minimum. Thus, the total magnetic flux contained in this region is the same in the two minima. Various correlations among the solar-wind mass flux and coronal electron temperature inferred from solar-wind charge states were developed for the Cycle 22–23 solar minimum. The data for the Cycle 23–24 minimum suggest that the correlations still hold, and thus the basic acceleration mechanism is unchanged in this minimum.

STELLAR MAGNETIC ACTIVITY CYCLES

Figure 6: Examples of stellar magnetic activity cycles documented from long-term measurements of Ca II H and K emission in several Sun-like stars observed by the Mount Wilson survey (Baliunas et al. 1995) including the Sun measured with stellar techniques. The complete sample includes cycle periods ranging from 2.5 to more than 25 years, as well as some stars that currently appear to be in a Maunder Minimum phase.

Although we cannot observe spots on other solar-type stars directly, these areas of concentrated magnetic field produce strong emission in the Ca II H (396.8nm) and K (393.4nm) spectral lines. The intensity of the emission scales with the amount of non-thermal heating in the chromosphere, making these lines a useful spectroscopic proxy for the strength of, and fractional area covered by, magnetic fields (Leighton 1959). Wilson (1978) was the first to demonstrate that many solar-type stars exhibit long-term cyclic variations in their Ca II H and K emission, analogous to the solar variations (Figure 6). Early analysis of these data revealed an empirical correlation between the mean level of magnetic activity and the rotation period normalized by the convective timescale (Noyes et al. 1984a), as well as a relation between the rotation rate and the period of the observed activity cycle (Noyes et al. 1984b; Saar & Brandenburg 1999), which generally supports a dynamo interpretation.

In 2007, scientists at HAO initiated a survey of the brightest solar-type stars in the southern hemisphere, to complement the existing data from the northern surveys at the Mount Wilson and Lowell Observatories. With collaborators at Yale, Georgia State University, and the Space Telescope Science Institute, more than 50 stars are monitored monthly from the SMARTS 1.5m telescope at Cerro Tololo Interamerican Observatory in Chile, to monitor their Ca II H and K emission. Over the long term, these data will provide important new constraints on the physical mechanisms that drive the solar dynamo.

INTERNATIONAL CAMPAIGNS AND WORKING GROUPS

Event poster: The goal of IAU Symposium 286 was to consider solar and stellar minima.

Determining the solar origins and net impacts at the Earth of solar minimum differences requires coordinated, interdisciplinary modeling efforts to bring the pieces together. The current and last cycle minima were well-studied via international observational and modeling coordinated campaigns known as the Whole Sun Month (WSM) and the Whole Heliosphere Interval (WHI). The observations taken during these campaign periods were analyzed (and continue to be analyzed) via a series of workshops and special sessions at national and international meetings. The goals of these campaigns were to characterize the 3-D solar minimum heliosphere and to trace the effects of solar structures and activity through the solar wind to the Earth and other planetary systems, and beyond. The modus operandi of both WHI and WSM has been to coordinate comprehensive observations of the global heliosphere near solar minimum, including focused, quantitative observations designed to provide constraints on models of the Sun-Earth coupled system. Side-by-side modeling efforts then allow both intra-model and model-data validation and comparison. Results from WSM may be found in a special issue of the Journal of Geophysical Research Space Physics (May 1, 1999), and similarly results from WHI may be found in a topical issue of the journal "Solar Physics" on The Sun-Earth Connection near Solar Minimum.

As a means of extending the WSM and WHI legacy, an International Astronomical Working Group on Comparative Solar Minima was formed. The mission of this working group is to facilitate international and interdisciplinary research that focusses on the coupled Sun-Earth system during solar minimum periods, and to this end the working group organized and sponsored IAU Symposium 286, "Comparative Magnetic Minima: Characterizing Quiet Times in the Sun and Stars", which was held in Mendoza, Argentina from 3 to 7 October 2011. The goal of IAU Symposium 286 was to consider solar and stellar minima, from generative dynamo mechanisms to in-depth analyses from Sun to Earth for recent well-observed and modeled minima, to a range of stellar cyclic activity, to outlier "grand minima". Solar, heliospheric, geospace, atmospheric, stellar, and planetary sciences were included in the meeting's scope.

Impact of Energetic Particles on the upper Atmosphere

kolinski — Tue, 14 Dec 2021 22:44:48 +0000

Impact of Energetic Particles on the upper Atmosphere kolinski Tue, 12/14/2021 - 15:44

Energetic particles, namely electrons and protons, released from the magnetosphere cover a wide range of energies from a few electron volts (eV) to hundreds of milli-electron volts (MeV). Precipitating electrons of several kilo electron volts (keV) are deposited in the 90–150 km altitude range, and they are mostly responsible for producing auroras and creating the E-region ionosphere. Though protons with energies less than 30 keV also produce auroral emission at higher altitudes, they contribute less than 20% of the total energy input in the auroral zone. More energetic electrons of a few hundred keV can penetrate to the lower thermosphere and mesosphere. Modeling studies have demonstrated that these energetic particles can significantly enhance the D-region electron density and also alternate the chemical compositions between 70 and 80 km altitudes. Solar energetic protons (SEPs), particularly those with energies >1 MeV, penetrate even deeper into the atmosphere, and their effects have been seen down to the upper stratosphere. To understand and elucidate the effects of the different energetic particles on the upper atmosphere, the Thermosphere Ionosphere Mesosphere Electrodynamics General Circulation Model (TIMEGCM), together with observations from the NOAA Polar Orbiting Environment Satellites (POES) and the Geostationary Operational Environmental Satellites (GOES), are used to delineate and understand how the various energetic particles affect the upper atmosphere during the well-known Halloween storm of October 2003.

Figure 1. Difference plots between simulations including and excluding SEPs. –(left column) difference HO_X, NO_X and O₃ over Eureka in northern Canada and (right column) difference HO_X, NO_X and O₃ over McMurdo in Antarctic from 25 October to 31 December 2003. The maximal and minimal values are indicated in the upper right corner of each panel.

The SEP effects on the upper atmosphere are illustrated in Figure 1, which shows the difference plots of HOX, NOX and O3 over Eureka in northern Canada and over McMurdo in Antarctic. The differences are between the TIMEGCM runs with and without the GOES-11 SEP data input while auroral precipitation is kept the same and MEPED data are excluded in the two runs. The increase in HOX by SEPs is short lived due to its short lifetime, and is concentrated between 40~60 km in the northern polar region. The vertical distribution of the SEP-produced HOX in the southern polar cap extends to a broader altitude range from 40 km up to 80 km. This hemispheric difference is largely owing to the seasonal difference between the winter northern polar cap and the summer-like southern polar cap. Though the enhanced SEPs last only a few days in duration, their impact on the upper atmosphere can be seen over several months after the storms. Precipitating SEPs cause significant increase in NOX in the altitude range of 35-70 km initially over both polar regions, which then slowly diminish while being transported downward in the northern hemisphere due to mesospheric circulation. By the end of the year, the remnant of increased NOX can still be seen in the upper stratosphere around 35-40 km in the northern polar cap. The vertical distribution of the difference NOX in the southern polar cap lies about 5 km higher than that in the northern polar cap, and the magnitude of the southern NOX change is also smaller. NOX is one of the most important constituents that catalytically destroy ozone. Indeed, significant O3 reduction is found below 55 km that persists throughout the rest of the year and even into early 2004. The difference O3 by SEPs also displays large hemispheric asymmetry, with the O3 reduction being much larger in the northern polar cap than in the southern polar cap and also the downward transport being more prominent. The hemispheric asymmetry in the NOX and O3 response shown in Figure 1 is a seasonal effect, and has been confirmed by several satellite observations during the same event.

This work was sponsored in part by the Heliophysics Guest Investigators program under NASA grant NNH09AK621, by the Living With a Star program under NASA grant NNX14AE08G, and by the U.S. Participating Investigator (USPI) Program under NASA Grant NNX12AD26G.

Source: Lu, G. (2015), Energetic and Dynamic Coupling of the Magnetosphere-Ionosphere-Thermosphere System, AGU monograph on Magnosphee-Ionosphere Coupling in the Solar System, edited by Rich Chappell, Bob Schunk, Jim Burch, Richard Thorne, and Peter Banks, in press.

Coronal and Heliospheric Evolution

kolinski — Tue, 14 Dec 2021 22:11:19 +0000

Coronal and Heliospheric Evolution kolinski Tue, 12/14/2021 - 15:11

The magnetic field in the Sun's atmosphere continuously evolves through processes of emergence, diffusion, and reconnection, resulting in ongoing reorganizations of the global coronal/heliospheric magnetic morphology, as well as in the slow buildup of magnetic energy in twisted or sheared magnetic fields.

HAO scientists undertake observational and theoretical studies of the build-up of magnetic energy and other slow (month-to-year timescale) changes in coronal and heliospheric magnetic fields. Currently, HAO scientists are conducting observational studies and forward modeling of coronal prominences and cavities to better understand the precursor magnetic structure and triggers of coronal mass ejections.

GLOBAL CORONAL MAGNETIC MORPHOLOGY

HAO archive of solar eclipse images.

The evolution of global magnetic fields, in particular the distribution of structures that are magnetically closed vs. magnetically open to the solar wind, is clearly seen in coronal morphology. Historically, changes in the coronal magnetic morphology have been witnessed via solar eclipses. HAO has built an archive of images of solar eclipses which are deemed to be of sufficient quality for research. The data begin from 1869, extend to the present day and are from a diverse range of sources, but have been converted to a standard format. The data up to 1969 were all compiled by Jack Eddy between 1969 and 1971. Original plates were painstakingly photographed by Eddy and associates at HAO onto plates currently archived at HAO (Judge et al., 2010).

Figure 1: EUV synoptic maps in the Fe XII 19.5 nm line for CR 2048 (September–October 2006) and CR 2055 (April 2007) near the minimum between Cycles 23 and 24 (top)and corresponding coronal hole maps (bottom). The mean sunspot number for the two Carrington Rotations was 10.1 and 2.1, respectively. The maps are in sin(latitude) and the dashed lines in the coronal hole maps correspond to 60° and 50° latitude. De Toma (2011).

Figure 2: Distribution of solar wind speed at the Earth for 1996 (in purple), 2007 and 2008 (in blue), and 2009 (in green). The mean speeds for these years are: 423km/s, 440km/s, 449km/s and 364km/s, respectively. While the yearly averaged solar wind speed in 2007 and 2008 are comparable to the one in 1996, the velocity distribution is quite different. In 2007 and 2008 the distribution is almost a bimodal distribution with a primary peak at slightly lower velocities than in 1996 and a secondary peak near 600km/s. This high velocity tail is due to recurrent, high-speed streams originating in the large, low-latitude coronal holes present at the Sun during these years. In 2009, with the close down of the large low-latitude coronal holes, velocities drop dramatically and speeds above 600km/s become almost completely absent in the solar wind reaching the Earth.

Figure 3: July 22, 2002 observations of a polar crown filament and associated cavity. Clockwise from top left: HAO MLSO Mk4 white-light coronagraph; Big Bear Solar Observatory H-alpha; SOHO/EIT 284 Angstroms; SOHO/EIT 304 Angstroms.Gibson et al. (2006) .

Figure 4: Line-of-sight-integrated Stokes linear polarization P/I for (a) forward-calculated spheromak configuration and (b) Coronal Multi-Channel Polarimeter (CoMP) observations of April 21, 2005 southwest cavity. The range indicated by the color bar for (a) corresponds to 5–28% linear polarization, and for (b) corresponds to 1–11% linear polarization. Red lines indicate direction of P/I vectors. See Dove et al. (2011).

Ongoing evolution of the current coronal magnetic morphology can be seen in daily observations from the Mauna Loa Solar Observatory white light coronagraph, which illustrates the shape and structure of the closed magnetic field. It can also be seen in observations of coronal holes, which represent regions of open coronal magnetic field. They are called coronal holes because they have relatively low electron density and temperature so they appear dark in X-ray and EUV. Coronal holes are not easy to identify in observations because they are not the only dark regions in the corona and bright structures in the optically thin coronal lines can partially obscure their boundaries. In recent years, the availability of observations at multiple wavelengths has made their detection easier, making it possible to follow changes in coronal hole area and location and provide observables to validate against coronal models (Figure 1).

Coronal holes are the source of fast solar wind, and low-latitude coronal holes can result in fast solar wind streams that impact the Earth. When such coronal holes are long-lived, fast wind speeds recur with periods associated with the Sun's ~27 day rotation and contribute significantly to the overall solar wind intersecting the Earth (Figure 2). Such recurring high-speed streams can result in associated periodic signals in the Earth's geospace environment (Gibson et al., 2009; Emery et al, 2011).

CORONAL PROMINENCE CAVITIES

Coronal mass ejections (CMEs) are driven by magnetic energy. In some cases, for example CMEs associated with active regions, rapid flux emergence may drive eruptions over relatively short time periods (e.g., days). However, in other cases the buildup of magnetic energy is slow, occurring over weeks if not months. Polar crown filaments (PCFs) (Figure 3) illustrate such gradual storage of magnetic energy, and may erupt multiple times over the course of their lifetime (months if not years). Dark coronal cavities are fundamental components of CMEs, and are also often seen surrounding PCFs, indicating that they are key components of these magnetohydrodynamic equilibrium states. Their plasma properties as observed in their quiescent phase provide clues to the nature of such equilibria and how they may ultimately be lost during CMEs.

Coronal cavities have long been observed in white light, both during eclipses and in coronagraph data (Read more »). The 2008–2010 International Space Science Institute (ISSI) International Team on Prominence Cavities successfully undertook a broad observational analysis of prominence cavities in multiple wavelengths (from radio to soft Xray to white light), and compared these to physical models (Read more »). This work established for the first time measurements of large-scale line-of-sight flows in cavities, a three-dimensional model of cavity morphology, density and temperature properties of cavities in the low corona, and evidence for twisted magnetic flux rope fields within a cavity (Figure 4), Fuller and Gibson (2009), Schmit et al. (2009), Gibson et al. (2010), Schmit and Gibson (2011), Dove et al. (2011).

science topic content

The Sun as a Dynamo

2D Flux-transport dynamos for the sun

Application to solar cycle prediction

2D Dynamical dynamo

Full 3D MHD simulations

Stellar Dynamos

Solar-Stellar Connection

Asteroseismology and Stellar Interiors

Category

Sunspots and Photospheric Dynamics

Radiative MHD simulations of sunspot structure

Simulations in slab geometry

Simulations of full sunspots and spot pairs

Structure of magneto convection in umbra and penumbra

Category

Studying Atmosphere Coupling Using Mesoscale-resolving WACCM

Category

Solar Convection and Mean Flows

Turbulent Solar Convection

Helioseismology and the Solar Internal Rotation

Shear, Magnetism and Global Circulations

The Solar Tachocline

Stellar Differential Rotation

Category

Satellite Drag Physical Modeling for Transition to Operations

Category

Modeling high-speed flows in the Earth’s Magnetotail

Category

Magnetic Flux Emergence

Buoyant rise of active region flux tubes in the solar interior

Flux emergence into the atmosphere, sunspot rotations, and the formation of a coronal flux rope

Category

Long-Term Solar Variability

SOLAR CYCLE OBSERVATIONS

AN UNUSUAL MINIMUM

STELLAR MAGNETIC ACTIVITY CYCLES

INTERNATIONAL CAMPAIGNS AND WORKING GROUPS

Category

Impact of Energetic Particles on the upper Atmosphere

Category

Coronal and Heliospheric Evolution

GLOBAL CORONAL MAGNETIC MORPHOLOGY

CORONAL PROMINENCE CAVITIES

Category