Review in “Solar Magnetic Variability and Climate”
C. de Jager, S. Duhau, A.C.T. Nieuwenhuizen, 2020
book contents Stip Media order<EMAIL_ADDRESS>
Small-scale solar surface magnetism
Robert J. Rutten1,2,3
1 Lingezicht Astrophysics, Deil, The Netherlands
2 Institute of Theoretical Astrophysics, University in Oslo, Oslo, Norway
3 Rosseland Centre for Solar Physics, University in Oslo, Oslo, Norway
Abstract.  This contribution to “Solar Magnetic Variability and Climate”
reviews small-scale magnetic features on the solar surface, in particular the
strong-field but tiny magnetic concentrations that constitute network and
plage and represent most magnetism outside sunspots and filaments. Where these
are mostly of the same polarity, as in active-region plage, their occurrence
varies with the activity variations measured by the sunspot number, but when
they appear bipolar-mixed on small scales they can also result from granular-
scale dynamo action that does not vary with the cycle.

Figure 1:  Overview of characteristic solar surface magnetism patterns using
full-disk images from the Solar Dynamics Observatory. The rows are for three
dates: April 29 2014 with much activity midway Cycle 24, April 29 2015 at
declining activity with only one tiny sunspot, and April 29 2019 at low
activity. Each row contains the HMI continuum image, the HMI line-of-sight
magnetogram and the AIA 1700 Å image collected at 03:00 UT. The white boxes
specify cut-outs that are magnified in the corners, in clockwise order for the
four boxes from disk center to the South limb. The HMI magnetograms are
clipped at 100 Gauss apparent field strength to enhance network and plage
fields. The cut-outs are each greyscaled to maximum contrast.

## Magnetic concentrations constituting network, plage, faculae.

Solar surface magnetism exhibits a major discrete component in addition to
sunspots in active regions. It consists of small magnetic concentrations
(henceforth MC) with kilogauss field strength, spread over the Sun in
irregular patterns. They represent a low but long tail in the size hierarchy
of strong-field features that emanate more or less upright (radially, locally
vertically) through the surface (Zwaan 1967). For reviews see de Wijn et al.
(2009) and Borrero et al. (2017).

Sunspot umbrae are the largest vertical flux concentrations. In their
surrounding penumbrae the fields partly fan out to larger height and partly
bend back to below the surface. Next come magnetic pores: mini-umbrae without
penumbra, of granular or slightly larger size, also appearing dark on the
surface. The yet smaller MCs also represent upright field bundles but with
much smaller cross-section at the surface, at most a few hundred km diameter,
usually less. Hence, telescopes need sub-arcsecond or better angular
resolution to observe them (1 arcsec measures about 700 km on the Sun). Even
then their fine structure is often not resolved. They therefore became known
as magnetic “elements” or “points” (magnetic points, facular points, bright
points). The “bright” is because they appear bright in many diagnostics (more
below). They are not limited to active regions as spots and pores usually are.
In these they do appear in denser concentrations but elsewhere they are also
present, including very quiet areas. There are fewer in the polar caps, but
the ones there are important gauges of polar fields.

Near the limb the small MCs are known as faculae. These were observed well
before their small-bright-point signature closer to disk center was recognized
because they appear brighter in slanted viewing. Faculae were already visible
towards the limb in white light images that did not reach the high resolution
of modern telescopes. This fortunate visibility enables using the number of
polar faculae as polar field proxy, using Sheeley’s inventories of their
numbers on historical Mount Wilson full-disk photographs.

In principle the best way to observe MCs is through their strong-field
signature in Zeeman line splitting or broadening. However, this fails towards
the limb where the radial MC fields become less aligned with the line of sight
as required for circular-polarization Zeeman signature.

However, also on the disk magnetograms sampling Zeeman diagnostics generally
show them incompletely. The Helioseismic and Magnetic Imager (HMI) onboard the
Solar Dynamics Observatory (SDO) collects full-disk magnetograms every 45
seconds since the spring of 2010, but while these monitor the distribution of
the stronger concentrations over the visible disk continuously, their angular
resolution and magnetic sensitivity are low so that they detect only larger
ones and do not resolve these.

The mid-ultraviolet images (1600 Å and 1700 Å) of the Atmospheric Imaging
Assembly (AIA) onboard SDO chart these small magnetic concentrations more
completely in the form of bright grains, but without polarity distinction as
magnetograms do. The resolution is as bad as for HMI but the MC inventory is
more complete through higher contrast, especially towards the solar limb.

Figure 1 shows simultaneous images from HMI and AIA at high, medium, and low
levels of activity. Each image contains magnified cut-outs to show detail.
Only the top continuum image in the first column contains sizable spots,
primarily in the southern activity belt. Elsewhere it shows granulation. The
corresponding magnetogram in the second column show extended groupings of
small black or white (opposite polarity) grains marking MCs. They are densest
where there is most activity and there display the Hale polarity laws. The
dense groups around spots constitute active-region plage, but away from spots
there are also extended clusters with a preferred polarity, also called plage
or “active network”. They display tilts according to Joy’s law. Similar ones
appear in the second magnetogram but in the bottom magnetogram there are no
extended groupings. The insets show that the plages have roughly cellular
ordering constituting magnetic network. The top-right inset in the second
magnetogram shows this network as mostly unipolar (white) but with a few
opposite-polarity (black) “internetwork” grains in the cell interiors.

Towards the poles the magnetograms show less network patterning and more
bipolar salt-and-pepper MC sprinkling, but still with some preference for
small-scale polarity sharing.

The ultraviolet 1700 Å images from AIA in the third column illustrate that all
magnetic elements appear as bright grains at this wavelength. The weaker 1700
Å grains between these mark acoustic waves fed by the solar surface
oscillations. Comparing the various insets with the corresponding magnetogram
insets shows nearly 1:1 pattern equality (apart from the polarity sign)
between bright ultraviolet grains and kilogauss MCs.

## Formation and brightness of small magnetic concentrations.

Much higher resolution than in Fig. 1 is obtained at the best ground-based
telescopes, in images in which these small magnetic concentrations appear
bright with respect to their surroundings. Most reside in intergranular lanes
so they become invisible at low resolution because their local brightness
cancels against the surrounding darkness. Figure 2 shows the state of the art
with observations from the Swedish 1-m Solar Telescope (SST), currently the
best ground-based solar telescope by combining an outstanding site, superb
optics, vacuum technology, advanced adaptive wavefront correction, further
numerical image restoration, and fast high-quality Fabry-Pérot imaging
spectrometers operating at red and at violet wavelengths (Scharmer et al.
2019).

The top panel shows surface granulation. Within some intergranular lanes there
are numerous small bright features, clearly not “points” but with varying
shape, often elongated, that generally follow the morphology of the
intergranular lane in which they reside (and follow with time in image
sequences). The SST magnetic map in the second panel shows that this small
scene contains mostly negative-polarity network, including a somewhat larger
“enhanced network” patch with larger bright point density. There is some
positive-polarity network at right. There are very few magnetic concentrations
above the sensitivity threshold in the internetwork areas; also these have
corresponding bright features in the top panel.

The two magnetograms are both clipped at 1500 Gauss absolute field strength.
The magnetic features appear much weaker in the HMI magnetogram because they
are much smaller than the pixels over which their averaged magnetic signature
is measured, as demonstrated by the smallness of the bright points in the top
panel. This comparison shows the poor rendering of small-scale magnetism in
HMI magnetograms. Only the larger field patches remain diffusely visible.
Thus, the magnetograms in Fig. 1 show tips of MC icebergs only. These were
clipped at only 100 Gauss in order to display their location and polarity more
completely, not their actual field strength. The SST field map comes closer to
resolving them, with many pixels showing apparent field strengths above 1000
Gauss.

Figure 2:  Granulation and magnetic concentrations in a small quiet-Sun area
near disk center. Image sizes: $48\times 22$ arcsec or $35,400\times 16,100$
km. The upper two panels are cut-outs of larger images taken by V.M.J.
Henriques with the Swedish 1-m Solar Telescope (SST) and described and
analyzed by Bose et al. (2019). Top panel: intensity at 3950 Å with bandwith
13.2 Å. Middle panel: corresponding map of the line-of-sight magnetic field
derived with an inversion technique from simultaneous polarimetry in the Fe I
6301.5 and 6302.5 Å lines. Bottom panel: corresponding cut-out from a
simultaneous SDO/HMI full-disk magnetogram. Its pixels are 16 times larger
linearly. The greyscale of both magnetograms is clipped at 1500 Gauss absolute
strength. SST data courtesy of L.H.M. Rouppe van der Voort.

The nature of these small MCs and why they appear bright are well understood.
Just as in umbrae the strong magnetic field suppresses turbulent convection
locally, so that outward convective energy transport from below is inhibited
which makes them cooler than their surroundings. The strong field also
contributes high magnetic pressure. Persistent presence of such strong-field
features (they often last hours) requires correspondingly low gas pressure
inside so that the sum of both pressures balances the outside field-free gas
pressure (“magnetostatic equilibrium”, Spruit 1976).

In contrast to sunspot umbrae and pores, the small MCs do not appear darker
but brighter than their surroundings. Naturally this was initially attributed
to unidentified heating, but from their magnetostatic modeling Spruit (1976)
and Spruit & Zwaan (1981) suggested that the apparent brightening comes from
the hot walls of the tube-like MCs below the surface. Their insides are
relatively cool from the magnetic suppression of outward convective energy
flow, but the hot-wall radiation scatters out to produce a bright feature if
the MC is small enough, whereas this contribution becomes negligible for
larger pores and umbrae. Towards the limb the viewing along the slanted line
of sight passes further through the relatively empty fluxtube than besides
that, and so samples the hot granule behind causing the enhanced contrast of
limbward faculae with stalk-like appearance.

Subsequently, the kilogauss strength of MC fields was established with dual-
line spectropolarimetry by Frazier & Stenflo (1978), verified in a number of
studies (reviewed by Solanki 1993), and then followed by detailed numerical
MHD simulations (e.g., Keller et al. 2004; Carlsson et al. 2004) in which
magnetic concentrations appear and brighten very similar to those in the best
observations, also as limb faculae in slanted viewing. These simulations
insert uniform magnetic field of a few hundred Gauss, horizontal or vertical,
throughout or at the bottom of a well-developed purely hydrodynamic simulation
and then follow its reconfiguration and shredding by the continuing turbulent
convection. Below the surface the gas pressure generally dominates over the
magnetic pressure so that the fields are forced to follow the gas motions (in
the low-density corona this is reversed so that gas in coronal loops is
frozen-in to the field). The uniform initial field is so quickly transformed
into more or less vertical threads that are expelled by the convective flows
from granules to their surrounding lanes, and then swept to mesogranular
boundaries.

The simulations are yet too small in volume to harbor larger supergranulation,
but the observed network patterning which outlines boundaries between
supergranulation flow cells implies that subsequent sweeping to and collection
in supergranular boundaries follows (more below). In summary, the simulations
show that any field moving from somewhere into the turbulent convection just
below the surface is transformed into kilogauss concentrations that are swept
along by the local granular, mesogranular and supergranular flows.

The low internal gas pressure enhances apparent MC brightness in spectral
diagnostics that are density-sensitive. Atomic lines such as the optical ones
from Fe I weaken or even vanish in MCs because most or all iron becomes
ionized within them; in the older literature this small-scale vanishing was
called “line gaps”. Molecular bands as the Fraunhofer-named G-band of CH
molecules near 4310 Å and the CN band below 3884 Å weaken from enhanced
dissociation. The first convincing bright-point MC observations were therefore
done (at Pic du Midi) in the G band which permits imaging with relative wide
(10 Å) spectral bandpass, hence high signal-to-noise. In the outer damping
wings of the Balmer lines and the strong Ca II lines the opacity diminishes
from smaller density-sensitive collisional broadening; this is the case in the
top panel of Fig. 2 which samples wavelengths in the overlapping outer damping
wings of Ca II H & K between these lines. In the mid-ultraviolet continua
sampled by AIA the MCs show enhanced brightening from ionization of Fe I and
Mg I which contribute most continuous opacity at these wavelengths; this
brightening is evident in the third column of Fig. 1. For all these
diagnostics the smaller opacity within the MCs implies deeper apparent holes
for outward hot-wall radiation, hence a larger contribution of that, and also
larger transparency in facular viewing along slanted lines of sight close to
the limb that so penetrate further into the hotter granules behind the MCs and
sample more of their brightness.

## Weak internetwork fields.

The kilogauss MCs that constitute network and plage are smaller than the spots
and pores in active regions, but they do not represent the smallest or weakest
in the hierarchy of solar magnetic surface features. In recent years it has
become clear that also within quiet-Sun supergranular cells weak
“internetwork” fields are copiously present in very tangled and dynamic form
on granular scales. The first telltale was measurement of Hanle depolarization
(Trujillo Bueno et al. 2004), followed by detection of abundant primarily
horizontal fields at granular scales in full-Stokes spectropolarimetry with
the Hinode satellite (Lites et al. 2008, 2017) of which the 50-cm aperture
furnishes the highest resolution and sensitivity in magnetogram sequences from
space so far. The absence of fast-varying atmospheric image distortion
(“seeing”) in space permits much longer integration times than for groundbased
telescopes, resulting in much higher sensitivity and hence weaker field
detection than possible with SST and HMI magnetometry as in Fig. 2.

Numerical MHD simulations (see Pietarila Graham et al. 2010) have established
that such weak small-scale quiet-Sun fields likely result mostly from local
convection near the surface operating as a small-scale dynamo, less from
convective shredding of stronger kilogauss network/plage MCs or from shredding
yet larger preceding active regions. These weak internetwork fields are
relatively stronger and more vertical in intergranular lanes. Higher up, but
still within the low photosphere, they close across granules in tiny
horizontal loops. The latter loops cover more area than the lane fields so
that the dominating weak-field signature in Hinode data is horizontal. This
small-scale near-surface dynamo action is inherent in the turbulent convection
producing the granulation and does not vary with latitude or the activity
cycle.

Figure 3:  Companion to Fig. 1 showing the corresponding chromosphere and
corona for the same observing moments sampled in the three rows. The first
column repeats the HMI magnetograms in the center column of Fig. 1. The second
column shows the overlying chromosphere with AIA 304Å̇ images which sample the
He II Lyman-alpha line formed at temperatures around 100,000 K. The third
column shows the overlying corona with AIA 171 Å images which sample Fe IX and
Fe X lines formed at temperatures around one million Kelvin. The brightest
parts of the AIA images are clipped to enhance quieter areas. The full-disk
images are less cropped than in Fig. 1 to admit off-limb features in the 171 Å
images. The fourth cut-out (at bottom left per panel) therefore includes the
limb.

## Network and plage patterns.

Small kilogauss concentrations and weak internetwork fields are the producers
of larger-scale network and plage patterns on the solar surface as seen in the
magnetograms of Fig. 1. Such production was first established for the
kilogauss concentrations called ephemeral regions (Harvey & Martin 1973). They
are small bipolar kilogauss MC pairs that emerge from deeper layers,
presumably as tiny Omega loops in the overall toroidal field system that rise
buoyantly through the surface, similarly to the much larger ones that produce
active regions with bipolar spot pairs. They seem to emerge randomly in the
activity belts but not near the poles. The emerging pairs are most easily
detected in internetwork regions where they pop up in isolation. They are then
seen to split; the two components are then transported in random-walk fashion
along with the supergranular flows to the cell boundaries. Underway they
frequently suffer same-polarity merging and opposite-polarity cancelation, but
enough survive and make it to the network to replenish all its magnetic flux
on a time scale of one to a few days, while a similar amount of flux vanishes
though cancelation (Schrijver et al. 1997).

Merging enhances their local field strength. Apparent cancelation can be due
to fields with U-loop shape rising through and out of the surface, with the
observed surface cross-sections of their legs appearing to move together and
vanishing. Similarly, apparent cancelation may result from fields with
inverted U-loop shape sinking below the surface. Other cancelation can occur
in small-scale magnetic reconnection in which only the net surplus of the
polarity with larger flux remains visible. Operating at small scales, these
processes are probably also important in shredding and converting larger-scale
magnetic fields to the small scales where Ohmic dissipation can remove them,
hence in doing away with the flux that surfaces at large activity and is not
spilled into space by CMEs etc. A good discussion of these processes and their
role in flux spreading and removal is given in Chapt. 6 of Schrijver & Zwaan
(2000).

Numerical simulations suggest that the weak granular internetwork fields found
with Hinode are insufficient to play a direct role in the overlying
chromosphere (Martínez-Sykora et al. 2019). However, Gošić et al. (2014) have
used sensitive multi-day Hinode spectropolarimetry to show that also these
weak features tend to drift per random walk to the supergranular cell
boundaries, suffering much merging and cancelation underway. In merging the
combined weak field may become strong enough to suppress internal convection
and “collapse” into kilogauss tube-like MCs which may so contribute to strong-
field network as seen in Fig. 1. Gošić et al. (2014) found that weak-field
merging dominates markedly over cancelation and that the resulting net quiet-
field contribution can replenish all network flux within one day, competitive
with ephemeral regions. The picture so emerges that larger-scale unipolar
network and plage patterns are found where equatorial field in the form of
ephemeral regions or polar field in the form of polar faculae win the
competition with the weak-field granular dynamo producing salt-and-pepper
bipolar network.

The full-disk magnetograms and their cut-out enlargements in the second column
of Fig. 1 demonstrate resulting strong-field plage and network patterns. The
high activity sampled in the first-row magnetogram has extended dominating-
polarity plage areas along the activity belts but fewer MCs with more salt-
and-pepper appearance and less cellular patterning in faculae towards the
poles. The medium activity sampled in the second magnetogram shows similar but
lower amplitude patterns. The low activity sampled in the bottom magnetogram
shows salt-and-pepper sprinkling all over the disk, with only one minor active
region in the North-East.

Quiet bipolar network produced by local dynamo action on granular scales does
not vary with cycle phase or latitude. Ephemeral regions tend to emerge
preferentially in the activity belts and produce bipolar network in addition
to the more active unipolar network and plage found in and near active regions
that resulted from much larger toroidal-system loop emergence. Thus, active
region network and plage as well as quieter network produced by ephemeral
regions occupies the activity belts and is modulated along with the cycle,
with the sunspot number a valid proxy. Similarly, where polar field emergence
dominates over the granular dynamo the number of polar faculae represents a
valid proxy (Muñoz-Jaramillo et al. 2012).

## Small-scale magnetism and the heliosphere.

Figure 3 is a companion to Fig. 1. It shows corresponding heating patterns in
the outer solar atmosphere: the chromosphere in the middle column, the corona
in the third column. For these diagnostics brightness implies the presence of
100 000 K gas (304 Å) and of 1 million K gas (171 Å), respectively.

The top row sampling high activity shows activity belts dominated by active
regions, especially on the Southern hemisphere. These harbor dense clusters of
304 Å emission (here truncated by greyscale clipping). In 171 Å they show much
closed connectivity in the form of coronal loops. Towards the poles the
heating appears more homogeneous, showing grainy patterns in 304 Å that
correspond fairly close to the underlying magnetic network patterns (compare
the 304 Åinsets with the magnetogram insets). Towards the poles the 171 Åimage
shows more diffuse million-K brightness with many polar plumes (bright outward
stalks). The 171 Å cut-outs retain only slight and diffuse underlying network
signature.

The middle row shows similar scenes but with an extra component: coronal holes
that are visible in both the chromospheric and coronal images. They include an
extended polar cap one at the South pole. Comparison with the magnetogram at
left shows that the holes tend to neighbor unipolar plage. The 171 Å insets
show better (but diffuse) correspondence with the 304 Å ones here.

The bottom low-activity row shows more common regular polar-cap holes, in the
chromosphere regular network-size blobs everywhere, roughly representing a map
of the supergranulation. The corona shows much less loop connectivity but yet
there is 1-million K heating everywhere, with isolated grainy patches of extra
heating of which some coincide with bright 304 Å enhanced-heating grains.

The precise mechanisms through which small-scale MCs govern this overlying
heating are not yet identified, but most likely they are a mixture of magnetic
reconnection and Alvenic wave and shock generation and dissipation. In larger-
scale eruptions as flares and surges reconnection plays a key role. On the
smaller scales discussed here it is now well established that small Ellerman
bombs in active regions are due to opposite-polarity MC cancelation marking
strong-field reconnection, both observationally (Watanabe et al. 2011 and with
numerical simulations (Hansteen et al. 2019). In quiet network well away from
active regions similar but smaller “Ellerman-bomb like” reconnective
cancelation events were detected with the SST (Rouppe van der Voort et al.
2016) and then also in simulations (Danilovic 2017).

Much more ubiquitous are so-called “spicules type II” that emanate from all
network including monopolar network and also in coronal holes; the latter are
easier detected as off-limb spicules through less closed-field confusion.
Their tips may reach coronal temperatures (off-limb: De Pontieu et al. 2011,
on-disk: Henriques et al. 2016). Recent simulations including ion-neutral
separation (Martínez-Sykora et al. 2018) suggest that these are not produced
by kilogauss MC cancelation but as shocks from tension release of complex
tangled weaker fields. These spicules are probably a major contributor to
quiet-Sun heating.

Within coronal holes, in particular polar ones, the production of solar plumes
that may also govern the fast solar wind is attributed to opposite-polarity
cancelation against network MCs (Wang & Sheeley 1995).

The largest-scale eruptive effect of network and plage outside active regions
concerns quiet-Sun filament formation and eruption into coronal mass ejections
(CME). Away from activity, filaments form above polarity dividing lines
between extended opposite-polarity regions as those in the magnetograms in the
top and center rows of Fig. 1), in particular dividers where closed fields
arch away on both sides. Filaments may then live for months but suddenly snap
into CME-producing eruptions from tether cutting by pattern changes including
new flux emergence. The CME catalogs compiled and compared in detail by Lamy
et al. (2019) show that from cycle minimum to maximum the overall CME
frequency increases tenfold, while the latitudes where they occur spread from
only near the equator to all latitudes, with polar crown filaments during
cycle maximum. Twice more CMEs result from erupting filaments than from
flares, but the highest source-region correlation is with coronal streamers.
Thus, the large-scale polarity patterns as in the high-activity magnetograms
in Fig. 1 play a pivotal role. Such patterns are absent in the minimum-
activity magnetogram at the bottom. Indeed, the observed daily CME production
rate tracks the sunspot number quite well and without delay, so that both
active-region and quiet-Sun CME production can be handled with this proxy.

## References

  * Borrero et al. (2017) Borrero, J. M., Jafarzadeh, S., Schüssler, M., & Solanki, S. K. 2017, Space Sci. Rev., 210, 275 ADS
  * Bose et al. (2019) Bose, S., Henriques, V. M. J., Joshi, J., & Rouppe van der Voort, L. 2019, A&A, 631, L5 ADS
  * Carlsson et al. (2004) Carlsson, M., Stein, R. F., Nordlund, Å., & Scharmer, G. B. 2004, ApJL, 610, L137 ADS
  * Danilovic (2017) Danilovic, S. 2017, A&A, 601, A122 ADS
  * De Pontieu et al. (2011) De Pontieu, B., McIntosh, S. W., Carlsson, M., et al. 2011, Science, 331, 55 ADS
  * de Wijn et al. (2009) de Wijn, A. G., Stenflo, J. O., Solanki, S. K., & Tsuneta, S. 2009, Space Sci. Rev., 144, 275 ADS
  * Frazier & Stenflo (1978) Frazier, E. N. & Stenflo, J. O. 1978, A&A, 70, 789 ADS
  * Gošić et al. (2014) Gošić, M., Bellot Rubio, L. R., Orozco Suárez, D., Katsukawa, Y., & del Toro Iniesta, J. C. 2014, ApJ, 797, 49 ADS
  * Hansteen et al. (2019) Hansteen, V., Ortiz, A., Archontis, V., et al. 2019, A&A, 626, A33 ADS
  * Harvey & Martin (1973) Harvey, K. L. & Martin, S. F. 1973, SoPh, 32, 389 ADS
  * Henriques et al. (2016) Henriques, V. M. J., Kuridze, D., Mathioudakis, M., & Keenan, F. P. 2016, ApJ, 820, 124 ADS
  * Keller et al. (2004) Keller, C. U., Schüssler, M., Vögler, A., & Zakharov, V. 2004, ApJL, 607, L59 ADS
  * Lamy et al. (2019) Lamy, P. L., Floyd, O., Boclet, B., et al. 2019, Space Sci. Rev., 215, 39 ADS
  * Lites et al. (2008) Lites, B. W., Kubo, M., Socas-Navarro, H., et al. 2008, ApJ, 672, 1237 ADS
  * Lites et al. (2017) Lites, B. W., Rempel, M., Borrero, J. M., & Danilovic, S. 2017, ApJ, 835, 14 ADS
  * Martínez-Sykora et al. (2018) Martínez-Sykora, J., De Pontieu, B., De Moortel, I., Hansteen, V. H., & Carlsson, M. 2018, ApJ, 860, 116 ADS
  * Martínez-Sykora et al. (2019) Martínez-Sykora, J., Hansteen, V. H., Gudiksen, B., et al. 2019, ApJ, 878, 40 ADS
  * Muñoz-Jaramillo et al. (2012) Muñoz-Jaramillo, A., Sheeley, N. R., Zhang, J., & DeLuca, E. E. 2012, ApJ, 753, 146 ADS
  * Pietarila Graham et al. (2010) Pietarila Graham, J., Cameron, R., & Schüssler, M. 2010, ApJ, 714, 1606 ADS
  * Rouppe van der Voort et al. (2016) Rouppe van der Voort, L. H. M., Rutten, R. J., & Vissers, G. J. M. 2016, A&A, 592, A100 ADS
  * Scharmer et al. (2019) Scharmer, G. B., Löfdahl, M. G., Sliepen, G., & de la Cruz Rodríguez, J. 2019, A&A, 626, A55 ADS
  * Schrijver et al. (1997) Schrijver, C. J., Title, A. M., van Ballegooijen, A. A., Hagenaar, H. J., & Shine, R. A. 1997, ApJ, 487, 424 ADS
  * Schrijver & Zwaan (2000) Schrijver, C. J. & Zwaan, C. 2000, Solar and Stellar Magnetic Activity ADS
  * Solanki (1993) Solanki, S. K. 1993, Space Sci. Rev., 63, 1 ADS
  * Spruit (1976) Spruit, H. C. 1976, SoPh, 50, 269 ADS
  * Spruit & Zwaan (1981) Spruit, H. C. & Zwaan, C. 1981, SoPh, 70, 207 ADS
  * Trujillo Bueno et al. (2004) Trujillo Bueno, J., Shchukina, N., & Asensio Ramos, A. 2004, Nat, 430, 326 ADS
  * Wang & Sheeley (1995) Wang, Y. M. & Sheeley, N. R., J. 1995, ApJ, 452, 457 ADS
  * Watanabe et al. (2011) Watanabe, H., Vissers, G., Kitai, R., Rouppe van der Voort, L., & Rutten, R. J. 2011, ApJ, 736, 71 ADS
  * Zwaan (1967) Zwaan, C. 1967, SoPh, 1, 478 ADS