# Are sunspots vertically displaced from the surrounding photospheric plasma?

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While reading a paper on the helioseismology of sunspots (Cameron, et al.), very brief reference is made to the "vertical displacement of a blob of plasma." This caused me to wonder if the emissive surface of the sunspot itself were perhaps depressed from the remainder of the photosphere. If this does occur, is there any literature on mechanisms? I would be very interested to learn more. There was one paper I came across around formation of sunspots from a toroidal field (Parker); but, it seemed to focus more on the vertical displacement of magnetic field lines rather than the plasma itself.

Thanks.

# Yes.

The idea that sunspots are depressed slightly came as a possible explanation for the Wilson effect. The Wilson effect was discovered as the shape of sunspots as viewed from Earth changed as the Sun rotates, in a way consistent with the change in perspective looking onto a slightly depressed region. While this isn't the only explanation for the effect, it's certainly the most prevalent.

More specifically, as Solanki (2003) writes, the depressions indicate a lowering of the layer where the optical depth $$au=1$$ (keep in mind that the bottom of the photosphere is the layer where $$au=2/3$$). There are two causes mentioned: lower temperature and magnetic effects.

Sunspots are cooler than the surrounding areas, as is well known, and thus appear darker. We see the same thing apparent at the boundaries of solar granules: Cooler, darker gas sinks and lets the hotter gas (which is less dense) move upward. Additionally, the opacity $$kappa$$ is temperature-dependent, which may impact how far one can see into the star.

Not only is temperature a factor, but so is the magnetic field. Sunspots are, at heart, a magnetic phenomenon, and thus the radial force equation is substantially different. Normally, in a star, the equation of hydrostatic equilibrium is $$frac{mathrm{d}P}{mathrm{d}r}=- ho g$$ for pressure $$P$$, density $$ho$$ and gravitational acceleration $$g$$. However, when the magnetic field becomes important in a sunspot on the solar surface, the force balance is $$frac{mathrm{d}P}{mathrm{d}r}=frac{B_z}{4pi}left(frac{mathrm{d}B_r}{mathrm{d}z}-frac{mathrm{d}B_z}{mathrm{d}r} ight)$$ where $$r$$ and $$z$$ are the radial and vertical coordinates (note the change of coordinate system - $$r$$ is along the surface, and $$z$$ is perpendicular to it!). The force from the magnetic field implies a lower gas pressure and a greater depression.

## Spatial pattern of photospheric granules in a sunspot neighborhood

Based on high-resolution (∼0.3 arcsec) observations, we studied the behavior of solar granulation in the neighborhood of a sunspot. The bright granules’ spatial distribution and the granules’ surface density as a function of distance from the center of the sunspot umbra were determined.

Bright granules distribute delimiting cells of dimensions in the mesogranular scale. The mean diameter of these cells does not show significant variation with the variation of the magnetic field of the sunspot. The granules’ surface density does not show significant variation with distance to the sunspot umbra. Both results point to a very weak, if any, influence of the sunspot magnetic field at distances greater than 20 arcsec.

## Abstract

The Alfvén speed and plasma beta in photospheric bright points (BPs) observed by the Broadband Filter Imager (BFI) of the Solar Optical Telescope on board the Hinode satellite are estimated seismologically. The diagnostics is based on the theory of slow magnetoacoustic waves in a non-isothermally stratified photosphere with a uniform vertical magnetic field. We identify and track BPs in a G-band movie by using the 3D region growing method, and align them with blue continuum images to derive their brightness temperatures. From the Fourier power spectra of 118 continuum light curves made in the BPs, we find that light curves of 91 BPs have oscillations with properties that are significantly different from oscillation in quiet regions, with the periods ranging 2.2–16.2 minutes. We find that the model gives a moderate value of the plasma beta when γ lies at around 5/3. The calculated Alfvén speed is 9.68 ± 2.02 km s −1 , ranging in 6.3–17.4 km s −1 . The plasma beta is estimated to be of 0.93 ± 0.36, ranging in 0.2–1.9.

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## 1. Introduction

A sunspot is a localized region of the density depletion relative to the surrounding plasma due to the magnetic pressure (Low 1992), which leads to the increased transparency in the optical band (Jensen et al. 1969). Thus the emission associated with a certain spectral line in the sunspot may be mostly contributed from below the line forming height in the quiet region. Depending on the sunspot magnetic field strength, the line forming height could be depressed up to several hundred kilometers (Solanki et al. 1993 Moon et al. 1998 Mathew et al. 2004). This is the so-called Wilson effect (Wilson & Maskelyne 1774). As the density of the umbra increases as the height decreases (Maltby et al. 1986), similarly to the quiet Sun (Fontenla et al. 2007), the density measured from a certain spectral line may be positively dependent on the magnetic field strength.

Physical parameters of the umbra are important for our understanding of the formation and evolution of a sunspot. Photospheric temperatures inside an umbra can be measured directly from the continuum ratio relative to the quiet Sun (Solanki et al. 1993 Jaeggli et al. 2012). Observations of other important parameters, such as the density and gas pressure in the umbra, is more difficult, as it requires a careful consideration of the line forming and reference heights (Khomenko & Collados 2015).

The combination of the theory of magnetohydrodynamic (MHD) waves with observations of solar atmospheric waves and oscillations gives information on the physical parameters of medium (e.g., Nakariakov et al. 2016), including sunspots (e.g., see Snow et al. 2015 Sych 2016 for recent results). Moreels & van Doorsselaere (2013) designed a method for deriving the temperature of plasma confined in photospheric magnetic flux tubes by using the intensity, velocity, and magnetic field strength fluctuation amplitudes. Reznikova et al. (2012) estimated the inclination angle of umbral magnetic field, based on the interpretation of umbral oscillation as a slow magnetoacoustic gravity (MAG) wave in an inclined magnetic field. Yuan et al. (2014) established that the magnetic inclination angle derived seismologically was 30%–40% larger than that given by the magnetic field extrapolation. Roberts (2004) reviewed the analytical expressions for the cutoff frequency as a function of observable parameters for different solar atmospheric models.

Roberts (2006) provided an analytical form of angular cutoff frequency of a slow magnetoacoustic wave in a non-isothermally stratified atmosphere with a uniform vertical magnetic field. The cutoff frequency not only prescribes the lowest frequency of a propagating wave, but also acts as a natural frequency of a medium (e.g., Roberts 2004). It suggests that the atmosphere should be observed to oscillate at the frequency equal or higher than the cutoff frequency in response to an external broadband excitation (Botha et al. 2011 Chae & Goode 2015 Kwak et al. 2016). Thus, the cutoff frequency is always below the detected frequency (e.g., Tziotziou et al. 2006 Yuan et al. 2014). Thus, the cutoff frequency involves the physical parameter of the medium, independently of the specific excitation mechanism of atmospheric oscillations.

In this work, we determine the cutoff frequency of umbral oscillations by using the weighted frequency, , where P(f) is the power spectrum (Takahashi et al. 2015), for 478 sunspots observed in the continuum with the Heliospheric Magnetic Imager (HMI Scherrer et al. 2012 Schou et al. 2012) on board the Solar Dynamics Observatory (SDO Pesnell et al. 2012). Using the theory given by Roberts (2006), we determine the Alfvén speed, plasma-beta (β), and mass density inside umbrae. In Section 2, we describe the method used to obtain the weighted frequency and its link with the Alfvén speed, plasma-β, and mass density. In Section 3, we provide maps of those quantities as well as their average behavior for the 478 analyzed sunspots. Finally, we summarize and discuss our results.

## Magnetoconvective Modulation of the Solar Luminosity

Understanding global solar irradiance variations requires measurements of the full solar disk because of the differing center-to-limb contributions of magnetic structures. However, there are significant differences in the magnetic morphology underlying pixels classified as the same structure at full-disk resolution. These differences influence the solar spectral irradiance and its variability with solar cycle. Image on left from the Precision Solar Photometric Telescope (courtesy M.P. Rast, https://lasp.colorado.edu/pspt_access/). Image on right from Rempel 2014, ApJ (reproduced with permission copyright 2014 American Astronomical Society).

##### How do small scale magnetic flux elements contribute to global solar irradiance variations? How well do observed temperature and pressure stratifications within flux elements agree with atmosphere models employed for irradiance reconstruction?

Observational evidence suggests that the solar irradiance is modulated by changes of solar surface magnetism. Based on this, empirical techniques have been developed to reproduce total and spectral solar irradiance variations from observed changes in the coverage of magnetic features over the solar disk. Depending on their size and field strength, different magnetic features show different center-to-limb variation in different spectral regions. Thus both the disk location and disk coverage of the features are needed to model irradiance changes, and full-disk medium resolution (one to two arcsecond) observations are typically employed (e.g., Chapman et al. 1996, Krivova et al. 2003, Yeo et al. 2017).

Unresolved magnetic elements are particularly important to the spectral output of the quiet Sun (Schnerr and Spruit 2011) and its center-to-limb profile (Peck and Rast 2015), against which the contrasts and contributions of magnetic structures is often measured. The quiet Sun covers the majority of the solar photosphere and typically its integrated irradiance contribution is taken to be constant in time, but due to the presence of possibly time varying unresolved magnetic structures this may not be the case. Measuring how the magnetic substructure of the quiet Sun actually changes with the solar cycle is a key DKIST capability. Beyond this, the radiative contributions of magnetic structures such as plage and faculae depend on the fact that they are composite (Okunev and Kneer 2005, Criscuoli and Rast 2009, Uitenbroek and Criscuoli 2011). Some facular pixels show negative continuum contrast in full-disk images even close to the limb, which may reflect their underlying substructure (e.g., Topka et al. 1997, Harder et al. 2019). Measuring the radiative properties of composite features and understanding the physical mechanisms that determine their spectral output is an important next step in the development of irradiance reconstruction techniques. These must be capable of statistically accounting for the contributions from a distribution of small-scale magnetic features unresolved in full-disk images.

Finally, the astrophysical implications of small-scale fields extend beyond the Sun. The spectral energy distribution of stars is a key fundamental input in the modeling of planetary atmospheres (e.g., Hu et al. 2012, Miguel and Kaltenegger 2014). In particular, UV radiation is responsible for the production and destruction of molecular species that are the anticipated biomarkers to be used in future NASA exoplanet atmospheric characterization missions. More critically, UV variability is important in determining the climate and habitability of (e.g., Scalo et al. 2007, France et al. 2013, Linsky et al. 2013, O’Malley-James and Kaltenegger 2019) and biogenic processes on (Buccino et al. 2007) extrasolar planets. While not sensitive to UV radiation directly, DKIST observations can be used to develop and test models of stellar chromospheres and/or proxies that reliably reconstruct stellar UV spectra from measurements obtained at longer wavelengths.

## Are sunspots vertically displaced from the surrounding photospheric plasma? - Astronomy

(Left) A solar flare showing the twisting motion characteristic of a Birkeland current.
(Right) An X-ray image of the sun showing the active lower corona.

In this day and age there is no longer any doubt that electrical effects in plasmas play an important role in the phenomena we observe on the Sun.

The major properties of the "Electric Sun (ES) model" are as follows:

• Most of the space within our galaxy is occupied by plasma (rarefied ionized gas) containing electrons (negative charges) and ionized atoms (positive charges). Every charged particle in the plasma has an electric potential energy (voltage) just as every pebble on a mountain has a mechanical potential energy with respect to sea level. The Sun is surrounded by a plasma cell that stretches far out - many times the radius of Pluto. These are facts not hypotheses.

• The Sun is at a more positive electrical potential (voltage) than is the space plasma surrounding it - probably in the order of 10 billion volts.

• Positive ions leave the Sun and electrons enter the Sun. Both of these flows add to form a net positive current leaving the Sun. This constitutes a plasma discharge analogous in every way (except size) to those that have been observed in electrical plasma laboratories for decades. Because of the Sun's positive charge (voltage), it acts as the anode in a plasma discharge. As such, it exhibits many of the phenomena observed in earthbound plasma experiments, such as anode tufting. The granules observed on the surface of the photosphere are anode tufts (plasma in the arc mode).

• The Sun may be powered, not from within itself, but from outside, by the electric (Birkeland) currents that flow in our arm of our galaxy as they do in all galaxies. This possibility that the Sun may be externally powered by its galactic environment is the most speculative idea in the ES hypothesis and is always attacked by critics while they ignore all the other explanatory properties of the ES model. In the Plasma Universe model, these cosmic sized, low-density currents create the galaxies and the stars within those galaxies by the electromagnetic z-pinch effect.

It is only a small extrapolation to ask whether these currents remain to power those stars. Galactic currents are of low current density, but, because the sizes of the stars are large, the total current (Amperage) is high. The Sun's radiated power at any instant is due to the energy imparted by that amperage. As the Sun moves around the galactic center it may come into regions of higher or lower current density and so its output may vary both periodically and randomly.

The Sun's corona is visible only during solar eclipses (or via sophisticated instruments developed for that specific purpose). It is a vast luminous plasma glow that changes shape with time - always remaining fairly smooth and distributed in its inner regions, and showing filamentary spikes and points in its outer fringes. It is a "normal glow" mode plasma discharge.

If the Sun were not electrical in nature this corona would not exist. If the Sun is simply a (non-electrical) nuclear furnace, the corona has no business being there at all. So one of the most basic questions that ought to arise in any discussion of the Sun is:

Why does our Sun have a corona? Why is it there?

It serves no purpose in a fusion-only model nor can such models explain its existence.

Positive ions stream outward from the Sun's surface and accelerate away, through the corona, for as far as we have been able to measure. It is thought that these particles eventually make up a portion of the cosmic ray flux that permeates the cosmos.

The 'wind' varies with time and has even been observed to stop completely for a period of a day or two. What causes this fluctuation? The ES model proposes a simple explanation and suggests a mechanism that creates fluctuations in this flow.

The standard model provides no such explanation or mechanism.

Electrical Properties of the Photosphere and Chromosphere

The essence of the Electric Sun hypothesis is an analysis of the electrical properties of its photosphere and the chromosphere and the resulting effects on the charged particles that move across them.

A radial cross-section taken through a photospheric 'granule' is shown in the three plots shown, below. The horizontal axis of each of the three plots is distance, measured radially outward, starting at a point near the bottom of the photosphere (the true surface of the Sun - which we can only observe in the umbra of sunspots). Almost every observed property of the Sun can be explained through reference to these three plots for this reason, much of the discussion that follows makes reference to them.

The first plot shows the energy per unit (positive) charge of an ion as a function of its radial distance out from the solar surface. The units of Energy per Unit Charge are Volts, V. The second plot, the E-field, shows the outward radial force (toward the right) experienced by such a positive ion. The third plot shows the locations of the charge densities that will produce the first two plots.

The chromosphere is the location of a plasma double layer (DL) of electrical charge. Recall that one of the properties of electric plasma is its excellent (although not perfect) conductivity. Such an excellent conductor will support only a weak electric field.

Notice in the second plot that the almost ideal plasmas of the photosphere (region b to c) and the corona (from point e outward) are regions of almost zero electric field strength.

Energy, Electric field strength, and Charge density
as a function of radial distance from the Sun's surface.

All three of these plots are related mathematically. By the laws of electrophysics: E = - dV/dr, and Charge density = dE/dr.

In words: The value of the E-field, at every point r, is the (negative of) the slope of the energy plot at that point. (The reason for the negative sign in the first equation is that the force on a positively charged particle is down the potential hill, not up.)

The value of the charge density at each point, r, is the slope of the E-field plot at that point. The two layers of opposite charge density necessary to produce the compound shaped energy curve between points c and e used to be called a 'double sheath'. Modern nomenclature calls it a 'double layer' (DL). It is a well known phenomenon in plasma discharges.

Because of the DL positioned between points c and e, a +ion to the right of point e sees no electrostatic force from +ions to the left of point c. The 'primary plasma' of the corona and the 'secondary plasma' of the photosphere are separated by the DL - a well known, and often observed property of plasmas.

The energy plot shown above is valid for positively charged particles. Because a positive E-field represents an outward radial force (toward the right) per unit charge on any such particle, the region wherein the E-field is negative (a to b) constitutes an inward force. This region of the lower photosphere is, thus, an energy barrier that positive ions must surmount in order to escape the body of the Sun. Any +ions attempting to escape outward from within the Sun must have enough energy to get over this energy barrier.

So the presence of the single positive charge layer at the bottom of the tuft plasma serves as a constraint on unlimited escape of +ions from the surface of the Sun.

Tuft Shrinkage and Movement

In order to visualize the effect this energy diagram has on electrons (negative charges) coming in toward the Sun from cosmic space (from the right), we can turn the energy plot upside down.

Doing this enables us to visualize the 'trap' that these photospheric tufts are for incoming electrons. As the trap fills, the energy gap between b and c decreases in height, and so the tuft weakens, shrinks, and eventually disappears.

This is the cause of the observed shrinkage and disappearance of photospheric granules.

Charged particles do not experience external electrostatic forces when they are in the range b to c - within the photosphere.

Only random thermal movement occurs due to diffusion. (Temperature is simply the measurement of the violence of such random movement.) This is where the 6,000 K temperature is measured. Positive ions have their maximum electrical potential energy when they are in this photospheric plasma.

But their mechanical kinetic energy is relatively low. At a point just to the left of point c, any random movement toward the right (radially outward) that carries a + ion even slightly to the right of point c will result in it being swept away, down the energy hill, toward the right. Such movement of charged particles due to an E-field is called a 'drift current'.

This drift current of accelerating positive ions is a constituent of the solar 'wind' (which is a serious misnomer). As positive ions begin to accelerate down the potential energy drop from point c through e, they convert the high (electrical) potential energy they had in the photosphere into kinetic energy - they gain extremely high outward radial velocity and lose side-to-side random motion.

Thus, they become 'dethermalized'. In this region, in the upper photosphere and lower chromosphere, the movement of these ions becomes extremely organized (parallel).

When these rapidly moving + ions pass point e (leave the chromosphere) they move beyond the radially directed E-field force that has been accelerating them. Because of their high kinetic energy (velocity), any collisions they have at this point (with other ions or with neutral atoms) are violent and create high amplitude random motions, thereby re-thermalizing the plasma to a much greater degree than it was in the photospheric tufts (in the range b to c).

This is what is responsible for the high temperature we observe in the lower corona. Ions just to the right of point e are reported to be at temperatures of 1 to 2 million K. Nothing else but exactly this kind of mechanism could be expected from the electric sun (anode tuft - double layer) model.

The re-thermalization takes place in a region analogous to the turbulent 'white water' boiling at the bottom of a smooth laminar water slide. In the fusion model no such (water slide) phenomenon exists - and so neither does a simple explanation of the temperature discontinuity.

Acceleration of the Solar 'Wind'

The energy plot (to the right of point e) actually trails off, with slightly negative slope, toward the negative voltage of deep space (our arm of the Milky Way galaxy). A relatively low density plasma can support a weak E-field. Consistent with this, a low amplitude (positive) E-field extends indefinitely to the right from point e. This is the effect of the Sun being at a higher voltage level than is distant space beyond the heliopause.

The outward force on positive ions due to this E-field causes the observed acceleration of +ions in the solar wind.

The particles in our solar wind eventually join with the spent solar winds of all the other stars in our galaxy to make up the total cosmic ray flux in our arm of our galaxy.

Juergens points out that the Sun is a rather mediocre star as far as radiating energy goes. If it is electrically powered, perhaps its mediocrity is attributable to a relatively unimpressive driving potential. This would mean that hotter, more luminous stars should have driving potentials greater than that of the Sun and should consequently expel cosmic rays of greater energies than solar cosmic rays.

A star with a driving potential of 20 billion volts would expel protons energetic enough to reach the Sun's surface, arriving with 10 billion electron volts of energy to spare. Such cosmic ions, when they collide with Earth's upper atmosphere release the muon neutrinos that have been much in the news recently.

Hannes Alfven in his book, The New Astronomy, Chapter 2, Section III, pp 74-79, said about cosmic rays:

"How these particles are driven to their fantastic energies, sometimes as high as a million billion electron volts, is one of the prime puzzles of astronomy. No known (or even unknown) nuclear reaction could account for the firing of particles with such energies even the complete annihilation of a proton would not yield more than a billion electron volts."

Fluctuations in the Solar "Wind"

It is interesting to note in passing that the three plots presented above are identically the plots of energy, E-field, and charge distribution found in a pnp transistor.

Of course in that solid-state device there are different processes going on at different energy levels (valence band and conduction band) within a solid crystal. In the solar plasma there are no fixed atomic centers and so there is only one energy band.

In a transistor, the amplitude of the collector current (analogous to the drift of +ions in the solar wind toward the right) is easily controlled by raising and lowering the difference between the base and emitter voltages.

Is the same mechanism (a voltage fluctuation between the anode-Sun and its photosphere) at work in the Sun? e.g., If the Sun's voltage were to decrease slightly - say, because of an excessive flow of outgoing +ions - the voltage rise from point a to b in the energy diagram would increase in height and so reduce the solar wind (both the inward electron flow and the outward +ion flow) in a negative feedback effect.

In May of 1999 the solar wind completely stopped for about two days. There are also periodic variations in the solar wind. The transistor-like mechanism described above is certainly capable of causing these phenomena. The fusion model is at a complete loss to explain them.

Transistor 'cutoff' is a process that is used in all digital circuits.

Characteristic Modes of a Plasma

In the page on Electric Plasma the three characteristic static modes in which a plasma can operate are discussed. Here is a more detailed description. The volt-ampere characteristic of a typical plasma discharge has the general shape shown below.

The volt-ampere plot of a plasma discharge.

This plot is easily measured for a laboratory plasma contained in a column - a cylindrical glass tube with the anode at one end and the cathode at the other.

These two terminals are connected into an electrical circuit whereby the current through the tube can be controlled. In such an experiment, the plasma has a constant cross-sectional area from one end of the tube to the other. The vertical axis of the volt-ampere plot is the voltage rise from the cathode up to the anode (across the entire plasma) as a function of the current passing through the plasma. The horizontal axis shows the Current Density.

Current density is the measurement of how many Amps per square meter are flowing through a cross-section of the tube. In a cylindrical tube the cross-section is the same size at all points along the tube and so, the current density at every cross-section is just proportional to the total current passing through the plasma.

When we consider the Sun, however, a spherical geometry exists - with the sun at the center. The cross-section becomes an imaginary sphere. Assume a constant total electron drift moving from all directions toward the Sun and a constant total radial flow of +ions outward. Imagine a spherical surface of large radius through which this total current passes. As we approach the Sun from deep space, this spherical surface has an ever decreasing area. Therefore, for a fixed total current, the current density (A/m 2 ) increases as we move inward toward the Sun.

In deep space the current density there is extremely low even though the total current may be huge we are in the dark current region there are no glowing gases, nothing to tell us we are in a plasma discharge - except possibly some radio frequency emissions.

As we get closer to the Sun, the spherical boundary has a smaller surface area the current density increases we enter the normal glow region this is what we call the Sun's "corona". The intensity of the radiated light is much like a neon sign.

As we approach still closer to the Sun, the spherical boundary gets to be only slightly larger than the Sun itself the current density becomes extremely large we enter the arc region of the discharge. This is the anode tuft. This is the photosphere. The intensity of the radiated light is much like an arc welding machine or continuous lightning. A high intensity ultraviolet light is emitted.

Some early plasma researchers and most modern astronomers believe that the only "true" plasma is one that is perfectly conductive (and so will "freeze" magnetic fields into itself). The volt-ampere plot shown above indicates that this does not happen. Every point on the plot (except the origin) has a non-zero voltage coordinate.

The static resistivity of a plasma operating at any point on the above volt-ampere plot is proportional to the slope of a straight line drawn from the origin to the point. This means that, at every possible mode in which a plasma can operate, it has a non-zero static resistivity it takes a non-zero E-field to produce the current density. Obviously the static resistivity of a plasma in the high end of the dark mode can be quite large. (The arc region and the left half of the glow region exhibit negative dynamic resistance - and the E-field can be quite small - but that is not what is in question.)

No real plasma can "freeze-in" a magnetic field. The highest conductivity plasmas are those in the arc mode.

But, even in that mode, it takes a finite, non-zero valued electric field to produce a current density. No plasma is an "ideal conductor".

Fusion in the Double Layer

The z-pinch effect of high intensity, parallel current filaments in an arc plasma is very strong.

Whatever nuclear fusion is taking place on the Sun is occurring here in the double layer (DL) at the top of the photosphere (not deep within the core). The result of this fusion process are the "metals" that give rise to absorption lines in the Sun's spectrum. Traces of sixty eight of the ninety two natural elements are found in the Sun's atmosphere. Most of the radio frequency noise emitted by the Sun emanates from this region.

Radio noise is a well known property of DLs.

The electrical power available to be delivered to the plasma at any point is the product of the E-field (Volts per meter) times current density (Amps per square meter). This multiplication operation yields Watts per cubic meter. The current density is relatively constant over the height of the photospheric / chromospheric layers. However, the E-field is by far the strongest at the center of the DL. Nuclear fusion takes a great deal of power - and that power is available in the DL.

It is also observed that the neutrino flux from the Sun varies inversely with sunspot number.

This is expected in the ES hypothesis because the source of those neutrinos is z-pinch produced fusion which is occurring in the double layer - and sunspots are locations where there is no DL in which this process can occur.

Sunspots and Coronal Holes

In a plasma, both the dimensions and the voltages of the anode tufts depend on the current density at that location (near the anode).

The tufts appear and/or disappear, as needed, to maintain a certain required relationship between +ion and electron numbers in the total current. This property of anode tuft plasmas was discovered, quantified, and reported by Irving Langmuir over fifty years ago.

In the Electric Sun model, as with any plasma discharge, tufting disappears wherever the flux of incoming electrons impinging onto a given area of the Sun's surface is not sufficiently strong to require the shielding produced by the plasma double layer. At any such location, the anode tufting collapses and we can see down to the actual anode surface of the Sun.

Since there is no arc discharge occurring in these locations, they appear darker than the surrounding area and are termed "sunspots". Of course, if a tremendous amount of energy were being produced in the Sun's interior, the spot should be brighter and hotter than the surrounding photosphere. The fact that sunspots are dark and cool strongly supports the contention that very little, if anything, is going on in the Sun's interior.

The center of the spot is called its umbra.

A sunspot showing the umbra, penumbra, and surrounding anode tufts (DLs).

Because there is no anode tufting where a spot is located, the voltage rise (region a to b in the energy plot above), which normally limits the local flow of positive ions leaving the anode surface, does not exist there.

In sunspots, then, a large number of ions will flood outward toward the lower corona.

Such a flow constitutes a large electrical current - and, as such, will produce a strong localized magnetic field near the sunspot.

The Sun's corona is difficult to see except in solar eclipses and in X ray images. This is because the corona is a "normal glow" discharge compared to the tufts which are in "arc mode". In some X ray images of the Sun (such as the one shown in the first figure at the very top of this page) we can see "coronal holes" - large dark regions in the brighter image of the solar corona.

The bright regions in X-ray images of the corona indicate hotter, more energetic areas these are mainly above the sunspot regions.

In the three images of a sunspot group, shown below:

1. The top one is the photosphere - taken in visible light - where, in the umbrae, we can see down to the dark (cool) surface of the Sun. Ions are pouring upward out of the Sun at these locations.

2. The middle image is taken in ultraviolet light and shows the chromosphere / transition region.

3. The lower panel is an X-ray image showing the violent activity in the lower corona. This activity is due to the flood of accelerating positive ions escaping the Sun and colliding with atoms higher in the atmosphere (lower corona).

The effects of +ions flowing out of a sunspot.

Strong electric currents also flow in and above the Sun's surface at the edge of sunspot umbrae due to the voltage difference between nearby anode tufts and the central umbrae of the spots (where there are no tufts).

This region is called a sunspot's penumbra.

These currents of course produce magnetic fields. Since, in plasmas, twisting electrical (Birkeland) currents follow the direction of magnetic fields, the glowing plasma in these regions often shows the complicated shapes of these spot related looping magnetic fields.

Remember. Brikeland currents TWIST!

(Left) The Penumbra - Birkeland currents following the voltage drop from the photosphere down to the umbra.
(Right) The twisting Birkeland currents evident in a detailed image of the penumbral streamers.

Prominences, Flares, and CME's

All of the above discussion applies to the steady-state (or almost steady-state) operation of the Electric Sun.

But there are several dynamic phenomena such as flares, prominences, and coronal mass ejections (CME's) that we observe. How are they produced? Nobel laureate Hannes Alfven, although not aware of the Juergens Electric Sun model, advanced his own theory (3) of how prominences and solar flares are formed electrically. It is completely consistent with the Juergens model. It too is electrical.

Any electric current, i, creates a magnetic field (the stronger the current - the stronger the magnetic field, and the more energy it contains). Curved magnetic fields cannot exist without either electrical currents or time varying electric fields. Energy, Wm, stored in any magnetic field, is given by the expression
Wm = 1/2 Li 2 . If the current, i, is interrupted, the field collapses and its energy must be delivered somewhere.

The magnetic field of the Sun sometimes, and in some places on its surface, forms an "omega" shaped loop. This loop extends out through the double sheath layer (DL) of the chromosphere. One of the primary properties of Birkeland currents is that they generally follow magnetic field lines. A strong looping current will produce a secondary toroidal magnetic field that will surround and try to expand the loop. If the current following the loop becomes too strong, the DL will be destroyed1.

This interrupts the current (like opening a switch in an inductive circuit) and the energy stored in the primary magnetic field is explosively released into space.

Hannes Alfven's Solar Prominence Circuit TRACE Image of Plasma Loops

It should be well understood (certainly by anyone who has had a basic physics course) that the magnetic field "lines"2 that are drawn to describe a magnetic field, have no beginning nor end.

They are closed paths. In fact one of Maxwell's famous equations is: "div B = 0". Which says precisely that (in the language of vector differential calculus).

So when magnetic fields collapse due to the interruption of the currents that produce them, they do not "break" or "merge" and "recombine" as some uninformed astronomers have claimed (e.g., see the quote regarding the mainstream concerns above - in 4. Acceleration of the Solar "Wind" Ions). The field simply collapses (very quickly!). On the Sun this collapse releases a tremendous amount of energy, and matter is thrown out away from the surface - as with any explosively rapid reaction.

This release is consistent with and predicted by the Electric Sun model as described above. Some astronomers have proposed that heat is routinely transported out to the lower corona by magnetic fields and released there by,

"reconnection of magnetic field lines, whereby oppositely directed lines cancel each other out, converting magnetic energy into heat. The process requires that the field lines be able to diffuse through the plasma."

This idea is inventive but, unfortunately, has no scientific basis whatever.

Note that although astronomers ought to be aware that magnetic fields require electrical currents or time varying E-fields to produce them, currents and E-fields are never mentioned in standard models.

Possibly because they do not seem to be included in astrophysics curricula.

1. Double layers can be destroyed by at least two different mechanisms:

1. Zener Breakdown - The electric field gradient becomes strong enough to rip all charges away from an area, thus breaking the discharge path

2. Avalanche Breakdown - A literal avalanche occurs wherein all charges are swept away and no conducting charges are left - thus the conducting path is opened

A magnetic field is a continuum. It is not a set of discrete 'lines'. Lines are drawn in the classroom to describe the magnetic field (its direction and magnitude). But the lines themselves do not actually exist. They are simply a pedagogical device. Proposing that these lines break, merge, and/or recombine is an error (violation of Maxwell's equations) compounded on another error (the lines do not really exist in the first place).

Magnetic field lines are analogous to lines of latitude and longitude. They are not discrete entities with nothing in between them - you can draw as many of them as close together as you'd like. And they most certainly do not break, merge, or reconnect any more than lines of latitude do.

Oppositely directed magnetic intensity H-fields simply cancel each other - no energy is stored or released in that event.

This has been the briefest of introductions to Juergens' Electric Sun model - the realization that our Sun functions electrically - that it is a huge electrically charged, relatively quiescent, sphere of ionized gas that supports an electric plasma arc discharge on its surface and is powered by subtle currents that move throughout the now well known tenuous plasma that fills our galaxy.

A more detailed description of the ES hypothesis as well as the deficiencies of the standard solar fusion model are presented in The Electric Sky.

Today's orthodox thermonuclear models fail to explain many observed solar phenomena. The Electric Sun model is inherently predictive of all these observed phenomena. It is relatively simple. It is self consistent. And it does not require the existence of mysterious entities such as the unseen solar 'dynamo' genie that lurks somewhere beneath the surface of the fusion model.

The Electric Sun model does not violate Maxwell's equations as the fusion model does.

Ralph Juergens had the genius to develop the Electric Sun model back in the 1970's. His hypothesis has so far passed the harsh tests of observed reality. His seminal work may eventually get the recognition it deserves. Or, of course, others may try to claim it, or parts of it, and hope the world forgets who came up with these ideas first.

There is now enough inescapable evidence that a majority of the phenomena we observe on the Sun are fundamentally electrical in nature. Ralph Juergens was the person with the vision to see it.

## Sunspot seismology

Thomas, Cram and Nye (1982) were the first to suggest that sunspot oscillations could be used to probe the subsurface structure of a sunspot, introducing the concept of 'sunspot seismology' based on the interaction of the solar p-modes with the sunspot and the way in which different p-modes sample different depths below the solar surface. They interpreted a temporal power spectrum of 5-minute umbral oscillations in terms of a naive model of the interaction of these oscillations with the sunspot, producing a seismic measurement of the diameter of the sunspot's flux bundle at a depth of about 10 Mm that was consistent with sunspot models. This crude result was intended only to illustrate what might be achieved with better spatial and temporal resolution of the oscillations and better theoretical models. Alas, in spite of the development of a number of new observational techniques and theoretical ideas, reliable results from sunspot seismology have proved to be remarkably difficult to obtain.

An early approach was to compare space-time power spectra of oscillations inside and outside a sunspot, as in the work of Abdelatif, Lites and Thomas (1986) and Penn and LaBonte (1993) discussed in Section 6.2.1 above. This approach had some success in clarifying the interaction between the p-modes and a sunspot, but failed to produce any firm results on subsurface structure.

A different approach, based on observations of ingoing and outgoing waves in an annular region outside the sunspot, was developed by Braun, Duvall and LaBonte (1987, 1988). They made the remarkable discovery that a sunspot is a net absorber of the power of the incident p-modes, absorbing as much as half of the power at certain frequencies and horizontal wavenumbers. We discuss this phenomenon in some detail in Section 6.4.1 below. More recently, attention has focused on local helioseismology of sunspots, employing time-distance and holographic techniques this work is discussed in Section 6.4.2.

### 6.4.1 Absorption of p-modes by a sunspot

When the p-mode oscillations in a circular annulus surrounding an isolated sunspot are decomposed into waves propagating radially inward and radially outward (in the form of a Fourier-Hankel decomposition), it is found that there is a relative deficit in power in the

0 200 400 600 800 1000 1200 1400

Fig. 6.6. p-mode absorption by a sunspot. Shown here is the absorption coefficient a integrated over frequency from v = 1.5mHz to v = 5.5 mHz and summed over different sets of azimuthal order m. The upper panel is for an isolated sunspot centred within the circular annulus, while the lower panel is for a field of view containing only quiet Sun. (From Bogdan et al. 1993.)

outward-propagating waves (Braun, Duvall and LaBonte 1987, 1988 Bogdan et al. 1993 Chen et al. 1996, 1997). This power deficit is as high as 50% at some horizontal wavenum-bers (see Fig. 6.6). No such power deficit is found for a circular annulus surrounding only quiet Sun.

Figure 6.7 shows the dependence on horizontal wavenumber of the absorption coefficient integrated over a range of frequencies and summed over a range of azimuthal orders, for two different sunspots (Braun, Duvall and LaBonte 1988 Bogdan et al. 1993). The agreement between the two data sets up to wavenumber 0.8 Mm-1 is striking, considering that different techniques of observing and data reduction were used. For higher wavenumbers, the higher-resolution results of Bogdan et al. show the absorption coefficient decreasing with increasing wavenumber k. The absorption coefficient can also be evaluated along individual p-mode ridges for radial orders up to n = 5: it is found that the absorption is greatest for n = 1 and decreases with increasing n, and that the absorption along each ridge peaks at an intermediate value of the spherical harmonic degree l in the range 200 < l < 400 (Bogdan etal. 1993).

120 Oscillations in sunspots 0.6

A'f A ! ' , i A1 i i 1 , 1 A i i , ii.ir

A'f A ! ' , i A1 i i 1 , 1 A i i , ii.ir a

Horizontal wavenumber (Mm 1)

Fig. 6.7. The absorption coefficient a, integrated over frequency from v = 1.5mHz to v = 5.5 mHz and summed over azimuthal orders m = -5, -4, . +4, +5, as a function of the horizontal wavenumber for an annular region surrounding a sunspot. The vertical line segments are the error bars for the original measurements of Braun et al. (1988) for a sunspot observed on 18 January 1983. The triangles (with dashed error bars) are for the later observations of Bogdan et al. (1993) of sunspot SPO 7983 on 19 March 1989. (From Bogdan et al. 1993.)

With sufficient temporal resolution (from data sets spanning longer times), one can determine not only the amplitudes of p-modes absorbed by a sunspot, but also their phase shifts. Braun et al. (1992a) presented the first measurements of these phase shifts using a 68-hour data set obtained at the South Pole. They found that the sunspot causes a phase shift 8 that increases linearly with spherical harmonic degree l from 0° at l = 125 to about 150° at l = 400, while the absorption coefficient a increases nearly linearly from 0% to 40%. (Here a and 8 are averaged over azimuthal orders -5 < m < 5.)

Following the discovery of acoustic absorption by sunspots, a number of different possible mechanisms for the absorption were soon put forward (see the review by Bogdan 1992). Hollweg (1988) proposed the resonant absorption of acoustic waves in a thin surface layer of the sunspot's magnetic flux tube. This suggestion was followed up in several subsequent papers (e.g. Lou 1990 Rosenthal 1990, 1992 Chitre and Davila 1991 Sakurai, Goossens and Hollweg 1991 Goossens and Poedts 1992 Keppens, Bogdan and Goossens 1994) these models are based on equilibrium configurations that do not include density stratification, and so they are not suitable for direct comparison with observations. Ryutova and colleagues (Ryutova, Kaisig and Tajima 1991: LaBonte and Ryutova 1993) proposed the enhanced dissipation due to inhomogeneities in a close-packed bundle of magnetic flux tubes. Another proposed mechanism involves mode mixing, in which incoming acoustic energy gets dispersed into a wide range of magnetic wave modes within the sunspot (e.g. D'Silva 1994).

Perhaps the most convincing model, and certainly the one that has been worked out in the most detail, is based on the suggestion by Spruit (1991) and Spruit and Bogdan (1992) that a purely acoustic oscillation impinging on a sunspot will be partially converted to a slow magneto-acoustic wave that propagates downward along the sunspot's magnetic flux tube and hence causes a leak of energy out of the near-surface acoustic cavity in which the resonant p-mode resides. With this mechanism, p-mode power is not actually absorbed within the surface layers of the sunspot, but instead is carried downward into the convection zone where presumably it is diffused and becomes part of the overall convective energy. The partial conversion of the incoming acoustic wave to the slow MHD wave takes place a little below the surface, at a depth where the sound speed and the Alfven speed are equal (or equivalently, where the plasma beta is near unity).

A detailed normal-mode description of this mechanism has been developed in a series of papers by Cally and collaborators, first assuming a uniform vertical magnetic field (Cally and Bogdan 1993 Cally, Bogdan and Zweibel 1994 see also Rosenthal and Julien 2000) and then allowing the uniform field to be tilted (Crouch and Cally 2003 Crouch et al. 2005 Schunker and Cally 2006), which substantially enhances the process of mode conversion for higher-order modes. Numerical simulations of the process generally confirm the results of the analytical models (Cally and Bogdan 1997 Cally 2000). These results are in fairly good agreement with the measured variations of the absorption coefficient and phase shift with spherical harmonic degree (Cally, Crouch and Braun 2004). The mode conversion of incident p-modes into magneto-acoustic-gravity waves in a sunspot will produce not only downward-propagating waves, which are largely responsible for the absorption of p-mode power, but also upward-propagating waves that might be associated with umbral oscillations and running penumbral waves.

6.4.2 Time-distance and holographic seismology of sunspots

Time-distance helioseismology, introduced by Duvall et al. (1993), provides an effective technique for detecting sound speed variations and flow patterns beneath the solar surface. The technique in its simplest form is based on ray theory, but it can be formulated more generally (Gizon and Birch 2002). It was first applied to sunspots by Duvall et al. (1996), who found downflows beneath the spots extending down to a depth of about 2 Mm, with speeds of about 2 km s-1. Since then, the technique has been applied to active regions and sunspots with several interesting results.

Using the time-distance technique, Gizon, Duvall and Larsen (2000) detected the sunspot moat flow using just the surface gravity mode (the /-mode), which is sensitive to the flow velocity over the first 2 Mm beneath the solar surface. They found a radially directed horizontal outflow with speeds up to 1 km s-1 in an annular region extending out to 30 Mm from the centre of the sunspot. Outside the moat they detected an annular counter-flow, implying a downflow at the moat boundary. Using the time-distance technique with a range of acoustic waves, Zhao, Kosovichev and Duvall (2001 see also Kosovichev 2006) found a horizontal inflow in a sunspot moat at depths of 0-3 Mm, in disagreement with the outflow found by Gizon et al. (and with direct Doppler measurements), as already mentioned in Section 3.6. This conflict is likely to be resolved as the spatial resolution of the time-distance technique improves. Zhao et al. also found downflows beneath the sunspot to depths of about 6 Mm and horizontal outflows away from the sunspot at depths of about 5-10 Mm, a pattern suggestive of the 'collar flow' proposed as a mechanism for stabilizing the sunspot flux tube (see Section 3.5).

Most of the work on time-distance helioseismology of sunspots has ignored the effects of the sunspot's magnetic field on the acoustic waves passing through it. These acoustic waves will be partially converted to magneto-acoustic waves, especially at depths where the local sound speed is comparable to the local Alfven speed, and this mode conversion will depend on frequency and also on the angle of incidence (Cally 2005). More detailed models of this interaction are clearly needed in order to interpret the results of time-distance helioseismology of sunspots and active regions.

Another approach to local helioseismology of sunspots is that known as helioseismic holography (Lindsey and Braun 1990, 1997 Braun and Lindsey 2000), which involves a computational reconstruction of the acoustic wave field in the solar interior based on the disturbances it creates at the surface. This technique has revealed that a sunspot is typically surrounded by an 'acoustic moat', a region with a deficit of acoustic power (of order 10-30%) extending radially outward from the spot over a distance of 30-60 Mm (Braun et al. 1998). The acoustic moat is roughly contiguous with the traditional sunspot moat defined by the surface velocity pattern (see Section 3.6).

### 6.4.3 Acoustic halos

The effect of near-surface magnetic fields, both inside and outside sunspots, on the p-modes is an important consideration in helioseismology. It has been known since their discovery (Leighton, Noyes and Simon 1962) that the amplitude of the 5-minute oscillations is reduced in regions of strong magnetic field (see e.g. Howard, Tanenbaum and Wilcox 1968 Woods and Cram 1981). More recently, however, it was discovered that the amplitude of higher-frequency acoustic waves, with frequencies in the range 5.5-7.7 mHz (just above the acoustic cutoff frequency in the low photosphere), is actually increased in areas surrounding regions of strong magnetic field. In the chromosphere so-called 'halos' of excess high-frequency acoustic power (in Ca II K intensity) surround active regions and often extend well into the surrounding quiet Sun (Braun et al. 1992b Toner and LaBonte 1993), while in the photosphere more compact and fragmented halos of excess acoustic power (in Doppler velocity) surround small patches of strong magnetic field (Brown et al. 1992 Hindman and Brown 1998 Jain and Haber 2002). Both the suppression of p-mode power within a developing pore and the surrounding halo of enhanced higher-frequency acoustic power can be detected even before the pore begins to appear as a dark patch in the photosphere (Thomas and Stanchfield 2000).

The origin of the acoustic halos and the connection between the chromospheric and pho-tospheric halos are still not fully understood. The large chromospheric halos might be caused by a general enhancement of acoustic emission from the convection zone in regions adjacent to a strong magnetic field. The more localized photospheric halos might be associated with some sort of magnetic flux-tube wave concentrated around the surface of the flux tube, such as the 'jacket modes' found by Bogdan and Cally (1995) or a surface Alfven wave excited by resonant absorption of incident acoustic waves. Hindman and Brown (1998) found that the photospheric halos show up in Doppler velocity but not in continuum intensity, suggesting either nearly incompressible motions or compressible acoustic motions aligned vertically by the magnetic field, increasing the line-of-sight velocity without increasing the intensity variations. Muglach (2003) found no enhancement of 3-minute chromospheric power around active regions in UV intensity variations measured with broad-band filters on the TRACE satellite, suggesting that the halos in Ca II K intensity observed with narrow-band filters may be more a product of Doppler shifts of the line than of intensity variations within the line.

## 2. OBSERVATIONS AND DATA ANALYSIS

We conducted a survey of all observations in the Huairou Solar Observing Station (HSOS) of the National Observatories of China and selected the events satisfying the following criteria: (1) vector magnetograms before and after a flare are available, (2) ARs are within 35° from the solar disk center to minimize projection effects (no projection correction has been applied to the data in the current study), and (3) WL difference images show evident darkenings at the flaring PIL and brightenings at the peripheral penumbrae as defined by Liu et al. (2005). With these criteria, our sample includes one M-class and three X-class flares as shown in Table 1. In addition, we have also included an interesting B-class flare, which possesses a similar pattern of darkenings and brightenings in the WL difference image.

Table 1. Events of AR Vector Magnetic Field Change After Flare and Downward LF

Date Loc (°) Bz1 (G) a Bt1 (G) a θ1 (°) a Bz1 (G) b Bt1 (G) b θ1 (°) b A (10 19 cm 2 ) c
NOAA GOES Bz2 (G) a Bt2 (G) a θ2 (°) a Bz2 (G) b Bt2 (G) b θ1 (°) b δfz (G 2 ) d
1989 Jan 11 S34E33 150 370 22.2 ± 9.8 70 400 9.2 ± 5.0 0.4
5312 M1.9 150 400 20.6 ± 8.6 90 400 12.5 ± 6.3 −3000
1997 Apr 9 S29W04 180 190 45.0 ± 16.0 120 170 35.0 ± 17.0 0.2
8027 B4.2 90 310 17.0 ± 5.7 130 150 40.0 ± 20.0 −2000
2000 Jul 14 N17W11 460 750 31.8 ± 8.2 500 850 30.0 ± 7.0 1.4
9077 X5.7 420 950 24.8 ± 5.5 330 660 27.0 ± 8.5 −14000
2003 May 29 N34E10 410 520 38.2 ± 9.9 700 580 50.7 ± 9.0 0.7
10365 X1.2 450 710 32.4 ± 6.9 730 530 53.8 ± 9.5 −9000
2006 Dec 13 S06W35 590 1100 28.1 ± 2.6 690 1200 30.0 ± 2.4 3.3
10930 X3.4 540 1390 21.2 ± 1.9 600 1140 27.7 ± 2.5 −17000

Notes. Magnetic field parameters listed above are the mean values over the specified regions. Bz is the unsigned longitudinal field. Inclination and its measurement errors are obtained with Equations (5) and (6), respectively. Subscripts 1 and 2 represent pre-flare and post-flare states, respectively. a Parameters in the darkened areas of WL difference image. b Same as the note a, but in the brightened areas. c Integrated areas of downward LF within the regions of sunspot WL structure change. d Downward LF per unit area. Its measurement error is of the same order of magnitude as the value itself.

To construct a complete picture of the analyzed events, our database consists of HSOS vector magnetograms, Fe i 5324 Å and Hβ filtergrams from HSOS, vector magnetograms obtained by the Spectropolarimeter of the Hinode Solar Optical Telescope (Tsuneta et al. 2008), longitudinal magnetograms of MDI on board the Solar and Heliospheric Observatory (SOHO Scherrer et al. 1995), and UV 1600 Å and WL images from the Transition Region and Coronal Explorer (TRACE Handy et al. 1999). For HSOS data, partial-frame and full-disk vector magnetograms were obtained by the Solar Magnetic Field Telescope (Ai & Hu 1986) and the Solar Magnetism and Activity Telescope (SMAT Zhang et al. 2007), respectively. The original magnetograms had a pixel size of 06, and since a new CCD camera was used in 2001, the resolution has changed to be 035. However, the actual spatial resolution is determined by the seeing condition, which is typically about 2''. The full-disk magnetogram has a pixel size of 2'' and a spatial resolution of 4'' under the typical seeing condition. To increase the polarimetric sensitivity, HSOS vector magnetograms are integrated over 256 pairs of images and spatially smoothed by 2 × 2 pixels. The noise level of the vector magnetograms in this study is determined as 2σ (where σ is the standard deviation) calculated in a relatively quiet region. The magnetic signal is set to be zero, if it is below the noise level. The 1σ errors of HSOS longitudinal and transverse magnetograms are found to be

Comparing magnetic field observations from different instruments on the ground (e.g., HSOS-SMAT) or in space (e.g., SOHO-MDI) is a challenging task (e.g., Demidov et al. 2008 Demidov & Balthasar 2009). We need to confirm that the changes of photospheric magnetic fields are intrinsically related to flares rather than instrumental or observational effects. In fact, we find that the seeing conditions play an important role in impacting the magnetic field measurements on the ground. The top panels in Figure 1 show scatter plots of the HSOS longitudinal magnetogram taken on 2002 July 21 at 01:09 UT versus HSOS longitudinal magnetograms taken on the same day at 03:00 UT, 06:09 UT, and 07:04 UT, respectively. We select this data set because of good sky transparency and the absence of flares on that day. For comparison, the bottom panels show similar scatter plots in which an MDI longitudinal magnetogram taken at 01:35 UT is plotted against magnetograms taken at 03:11 UT, 06:23 UT, and 07:59 UT, respectively. In general, the linear correlations between HSOS longitudinal magnetograms are not as strong as those between MDI magnetograms. Here, a ratio is defined to quantitatively describe the magnetogram variation with time, i.e., , where Bref refers to the reference magnetogram and i = 1, 2, and 3 indicates the other three magnetograms (other than the reference one) of each data set. For the MDI magnetograms, the ri values are close to unity in all three cases, while for the HSOS magnetograms, the ri values decrease from

1 at 03:00 UT to 0.8 at 06:09 UT, and further to 0.5 at 07:04 UT. This variation is caused by the variation of terrestrial stray light during a day.

Figure 1. Scatter plots of the longitudinal fields of AR 10036 on 2002 July 21. Top: HSOS magnetograms vs. the reference one at 01:09 UT. Bottom: MDI magnetograms vs. the reference one at 01:35 UT. The insets are HSOS and MDI longitudinal magnetograms of this AR, respectively.

Therefore, to correct a general decreasing trend of HSOS longitudinal magnetograms with time, we compare all the longitudinal magnetograms of HSOS (except for the data on 1989 January 11) with those of MDI by drawing scatter plots of MDI versus HSOS longitudinal magnetograms, which have been resampled to have the same spatial resolution. However, simply using such scatter plots neglects, for example, different instrumental profiles, seeing effects, formation height of the spectral lines, and how much of the underlying physics can be captured by the sparse spectral sampling of the lines. Thus, this comparison should just be taken as a zero-order approach to the true magnetic field values as measured at HSOS. The HSOS transverse magnetograms are corrected as follows: the corrected longitudinal magnetograms are used as the photospheric boundary to extrapolate potential magnetic fields then, the correction scale is obtained by comparing the measured transverse fields with the extrapolated transverse fields for a section of an isolated sunspot, where the fields are likely potential. The data on 1989 January 11 are only subjected to self-correlation correction because MDI data were not available at that time.

## 6. Active Regions

Active Regions appear in the photosphere as roughly bipolar magnetic regions of intermediate scale (~ 0.2R, or ~ 1.5 × 10 5 km). Sunspots, associated with strong magnetic fields (above � G), are their primary manifestation in the photosphere, bright plage emission, associated with intermediate magnetic fields, prevails in the chromospheric layers together with elongated fibrils (Foukal, 1971 Kianfar et al., 2020), indicating a more organized magnetic field compared to the QS, while impressive loops mark their presence in the corona. They are accompanied by all sorts of dynamic phenomena, most notably flares and Coronal Mass Ejections (CMEs).

Active regions are the result of emergence of large quantities of magnetic flux from the subphotospheric layers, a result of magnetic buoyancy (see, e.g., Parker, 1955 Priest, 1987 Rempel and Schlichenmaier, 2011) and disappear as their magnetic flux is spread out due to convective motions or canceled near polarity inversion lines.

Figure 14 shows images of an active region from the photosphere to the low corona, during its emergence and development phase, as the region crosses the solar disk. Concentrating on the radio emission, we note that in the 17 GHz images of July 30, as well as of August 2 and 4 show the classic two components of sunspot and plage associated emission, identified for the first time by Kundu (1959) with a 2-element interferometer and imaged by Kundu and Alissandrakis (1975) with the Westerbork Synthesis Radio Telescope. Since that time many observations and models have been published (see reviews by Gelfreikh, 1998 and Lee, 2007). It is well-established that the sunspot, or core component of the emission, observed in the microwave range, is due to the gyroresonance process (Kakinuma and Swarup, 1962 Zheleznyakov, 1962 Alissandrakis et al., 1980), whereas the plage, or halo component is due to free-free emission.

Figure 14. Development of Active Region 11260 during its passage on the solar disk. Sunspots and magnetograms from HMI/SDO, Hα images from Big Bear, Nobeyama images at 17 GHz and AIA/SDO images in the 171 Å (FeIX, log T ~ 5.8), and 335 Å (FeXVI, log T ~ 6.4) bands. The region crossed the central meridian on July 30, ߩ UT. The white arc marks the photospheric limb. Figure prepared by the author.

Going back to Figure 14, note that no sunspot component is visible at 17 GHz on the other days, apparently due to the low value of the sunspot field with regard to the observing frequency. Note also that on July 26 and 28, emission as strong as the sunspot emission is observed, probably associated with hot coronal loops seen in the 335 Å, (FeXVI) band. This is reminiscent of the neutral line sources reported by Kundu et al. (1977), see also Uralov et al. (2008) and references therein, and attributed to a quasi-steady, low density population of non-thermal electrons (Alissandrakis et al., 1993).

At longer wavelengths a decimetric halo component of non-thermal nature has been reported (Gelfreikh, 1998), while at even longer decimetric and metric wavelengths no sunspot-associated emission is visible, presumably due to the high opacity of the overlaying plasma and refraction effects we do see, however, non-thermal noise-storm sources in the vicinity of active regions.

The microwave emission of active regions is a powerful diagnostic of the magnetic field in the transition region and the low corona. The magnetic field determines the emissivity of gyroresonance process above sunspots, of the free-free process above plages, as well as the circular polarization inversion higher up. In addition to the magnetic field, sunspot-associated emission can provide information about the temperature and density structure of the sunspot atmosphere (Nindos et al., 1996 Korzhavin et al., 2010 Nita et al., 2018 Stupishin et al., 2018 Alissandrakis et al., 2019). Let us also mention in passing the detection and study of sunspot oscillations (Gelfreikh et al., 1999 Nindos et al., 2002) and refer the reader to the review by Nindos and Aurass (2007) for more details. We also refer the reader to the reviews by Solanki (2003) and by Rempel and Schlichenmaier (2011) for extensive descriptions of sunspots.

## 7. SUMMARY AND DISCUSSION

Our main conclusions can be stated as follows.

As indicated in Figure 1, sunspot activity was systematically greater in the northern (southern) hemisphere during the rising (declining) phase of cycles 20–23. From the rule stated in conclusion (3), it follows that the HCS should have been shifted systematically southward throughout most of this period. Moreover, the displacements should have been more pronounced during the declining phase of cycles 21–23 than during the rising phase of these cycles, when the sunspot number asymmetries were smaller (the opposite being the case for cycle 20). These results are consistent with the southward displacement of the HCS inferred from the Ulysses fast latitude scans of 1994–1995 and 2007 (Erdős & Balogh 2010 Virtanen & Mursula 2010), and with the bias of the IMF polarity at Earth toward that of the north polar field near the 1976, 1986, and 1996 sunspot minima (Mursula & Hiltula 2003 Hiltula & Mursula 2006).

Of particular interest is the reversal in the hemispheric alternation that occurred in cycle 19 (the highest ever recorded), when the southern hemisphere was somewhat more active just before sunspot maximum but the northern hemisphere became heavily dominant thereafter. From our general rule that the neutral line lies in the more active hemisphere during the declining phase (after polar field reversal in that hemisphere) and in the less active hemisphere during the rising phase (before polar field reversal), it follows that the HCS was displaced northward of the equator throughout most of cycle 19. Indeed, Figure 2 of Hiltula & Mursula (2006) shows that the dominant IMF polarity at Earth during the period 1956–1964 corresponded to that of the south polar field, implying an average northward shift of the HCS.

Because 〈b20〉 〈b10〉 throughout most of the sunspot cycle, the north–south displacement of the HCS is a small effect which sometimes shows up only statistically or after annual averages are taken. At sunspot maximum, when the axisymmetric dipole and quadrupole components have comparable strengths, the effect is masked by the much larger nonaxisymmetric components of the field.

Recognizing the uncertainties inherent in the use of in situ measurements to infer north–south displacements of the HCS, we have proposed that these displacements can be determined more reliably from observations of white-light streamer structure in the outer corona. The procedure involves distinguishing between helmet streamers, which separate coronal holes of opposite polarity, and pseudostreamers, which separate coronal holes of the same polarity, and then using the global configuration of helmet streamers to map out the HCS. Further applications of this method to coronagraph observations from SOHO and STEREO will be described in a subsequent study.

We are indebted to N. R. Sheeley Jr. for stimulating discussions. This work was supported by NASA and the Office of Naval Research.