GLIMPSES INTO THE STRUCTURE OF THE SUN
PART II- THE SOLAR INTERIOR AND THE SUNSPOT

In Part I of this paper, we have endeavored to develp some important properties of matter at very high temperatures–those that prevail in the stellar interiors. Utilizing the principles developed there, we will now attempt to deduce the internal structure of the sun. For ease of reference, the section numbers, the figure numbers, and the reference numbers are all continued from Part I.

6. Morphology of the Solar Core

We have noted that the energy generation in the stars is by the thermal destruction process, and that preliminary calculations [5] establish that the thermal destructive limits of the elements are in the ultra high temperature range. So the central region of the sun is composed of matter at the intermediate and the ultra high temperatures. The matter in the ultra high temperature core manifests as an ensemble of thredules, which we have seen to be thin, straight, continuous filaments (Section 3.3). We now note that both these thredules, and the embedded co-magnetic field lines that run along the length of these filaments are expanding in the longitudinal direction (Section 4.1).

The directions of the thredules have to be randomly oriented in the three-dimensional space of the reference system when no factor providing for a preferred direction exists. But since the sun is rotating, the axis of rotation does provide such a preferential direction. As such, the great majority of the thredules form in a direction parallel to the axis of rotation.

Once the general direction of the thredules is fixed, we can deduce that, by the operation of probability, half of these will have north magnetic flux lines threading through their length, while the remaining half will have south magnetic lines (the qualifications “north” and “south” being merely chosen for the sake of convenience of reference, and do not mean to point to any external magnetic field).

6.1 Formation of the Two Sheaves of Thredules

For reasons explained in Section 4.2, the south and north thredules segregate into two principal domains of opposite magnetic polarity. Given no other factors, therefore, one would expect the ultra high temperature core to assume a configuration in which two co-axial, cylindrical sheaves of north and south thredules respectively occur.

Since we have seen (Section 4.2) that two parallel co-magnetic lines of the same magnetic field direction attract each other, the minimum energy configuration for either of the sheaves mentioned in the preceding paragraph would be one in which all the thredules are mutually parallel. However, at the interface between the two sheaves we find thredules of opposite magnetic field direction occuring adjacent to each other. Since parallel co-magnetic lines of opposite field directions tend to repel (Section 4.2), we see that the above arrangement of the two sheaves does not yield the least energy configuration for the interface.

Therefore, the above configuration would give way to another in which the interficial energy is also reduced. This could be readily achieved by tilting the adjacent thredules of the two sheaves in opposite directions, while, at the same time, keeping the adjacent thredules of any one sheaf mutually parallel. This would render the cylindrical shape of each sheaf into a hyperboloid. The final configuration of the two sheaves of thredules at the beginning of a solar cycle will be that of two co-axial hyperboloids, as shown in Figure 5. For the sake of clarity, only a few of the thredules of each sheaf are shown in the figure.

Formation of Thredules Image

Figure 5 - Formation of Thredules in the Solar Core
(schematic diagram only–not to scale)

Let us denote the angles of inclination of the thredules of the inner and outer sheaves with respect to the direction of the axis of rotation of the sun by i and o respectively. Remembering that the thredules tend to maximize their length (Section 3.3) and so do the co-magnetic lines (Section 4.1), one can easily compute that the optimal values of i and o would be 45. (More involved calculations point out that i would be around 50, and o around -40.) In Figure 5, the inner thredules are shown inclined such that i = +45, while the outer thredules with o = -45.

6.2 Effect of the Progress of the Solar Cycle

The thredule structure does not extend beyond the ultra high temperature core. The co-magnetic field lines running along the thredules, however, jut out into the outer layers. When they emerge out into the low temperature regions where the magnetic effects are in the space of the reference system, instead of in equivalent space, lines of opposite field directions join in U-loops and start exerting attractive force. This tends to effectively anchor the tips of the thredules of opposite field directions. We might imagine the circular edges of the inner and the outer hyperboloidal sheaves respectively to be jointed at each end.

Now while retaining these anchorages at the ends, if the inclination of all thredules is altered by some angle, say , then i becomes + 45 and 0 becomes - 45. This means that the inner thredules would be pointing to lower latitudes and the outer ones to higher latitudes. The effect on the shape of the two hyperboloids would be such that the inner one gets more separated from the outer. Consequently, the repulsive interficial energy decreases further. Therefore, this is what happens with thte progress of the solar cycle, as shown in Figure 6: the inner thredules go on tilting toward lower and lower latitudes, and their average length increases, while the outer thredules of opposite magnetic polarity go on tilting toward higher and higher latitudes, and their average length decreases.

Angular orientation of thredule image

Figure 6 - Change of the Thredule Orientation with the Progress of the Solar Cycle

7. Birth of the Sunspots

The sun‘s atmosphere consists of three distinct layers; the lowest is the photosphere with an estimated depth of 200-400 km, followed by increasingly rarefied and transparent layers of the chromosphere and the corona. The bulk of the energy is emitted by the photosphere as continuum radiation. The opacity of the photosphere increases very rapidly with depth, producing the illusion of a sharply defined outline of the sun. The effective temperature of the photosphere, on the basis of blackbody assumption, is estimated to be 5780 K.

7.1 Observational Description

Sakurai gives a graphic account of how sunspots form:

“At first, a localized magnetic field appears... In general, sunspots start out as pores, which are small regions much darker than the surrounding photosphere... the magnetic field strength increases significantly... and a full-fledged sunspot group develops. The sunspots are concentrated in the preceding... and the following... ends of the group...”

“The magnetic field has different polarity in the spots belonging to the preceding and following ends... It is well-established that most sunspot groups appear as bipolar.”

“... a fully developed sunspot consists of the central dark umbra, through which most of the magnetic flux is channeled, and the less dark penumbra.”

The magnetic field strength has a maximum value near the center of the spot, or where the spot is darkest, i.e., the core of the umbra. The strength of the magnetic field is about 1,000-5,000 gauss for well-developed sunspots... The fully developed sunspot may exist for days, weeks, or months...” [16]

7.2 Explanation of the Origin

We will see that the explanation of the structure of the solar core we have delineated earlier logically leads to the explanation of the origin and properties of the sunspots and the associated phenomena. In the beginning of the previous section, we have noted that the thredules (as well as the co-magnetic lines embedded in them), tend to expand in the longitudinal direction. As they do so and penetrate into the lower temperature outer regions, they give up heat to the surrounding material and eventually drop into the intermediate temperature region and cease to exist as thredules. However, at times due to the local variations in the energy generation process, thredules with large enough energy shoot outwards with sufficient violence as to reach the top of the atmosphere before getting dissolved.

As this ultra high temperature matter breaks through the photosphere, it makes its appearance as a sunspot of low temperature (for reasons explained in Section 3.3) and is seen as a sunspot. Thus, the sunspots are hotter and not cooler than the surrounding photosphere. The characteristic of the co-magnetic field lines to bunch together in the transverse direction naturally produces a field intensity sharply increasing toward the center or core of the spot umbra, which is the hottest (though ostensibly the coolest) portion.

Between the two sheaves of thredules oppositely inclined to the rotation axis (Figure 5), the inner one is naturally at a higher temperature. Moreover, as the solar cycle advances, the thredules in the inner sheaf become longer, while those in the outer become shorter (Figure 6). Consequently, the great majority of the sunspots arise out of the shooting of the more energetic inner thredules. In fact, the magnetic polarity of the precursors of an emerging bipolar spot group is that of these inner thredules. Thredules of opposite magnetic polarity, being induced outwards by the action of the precursors, emerge to form the spots of opposite polarity of the sunspot group. As we will see presently, these latter always appear on the "following" end of the group, and a little while later than the precursors.

As those of the thredules belonging to the inner sheaf, and which will be emerging at the photospheric level as the leader spots travel through the matter of the intermediate temperature shell surrounding the core, that matter in the immediate vicinity of these passing thredules gets heated up. Some of this matter in the line of travel rises to the ultra high temperature level and transforms into the thredule state (see Figure 7). The co-magnetic lines in these induced thredules will, of course, be of opposite polarity. These induced thredules, therefore, appear as the spots of the opposite polarity when they emerge at the photospheric level. The general finding that the preceding spot appears first, develops first, and disappears last, is exactly what is to be expected from our above theoretical account if we remember that the induced thredules are less energetic, as well as time-lagged, compared to the inducing thredules.

Diagram of sunspot thredules

Figure 7 - Preceding and Following Spots in the two Hemispheres

The reason why the induced spots always form behind, with reference to the direction of rotation of the solar surface may not, however, be readily understood. We have already noted in Section 3.3 that the motion at the ultra high speed pertains to a scalar dimension altogether different from the scalar dimension that is coincident with the conventional reference system. [11] Even though such motion does not produce direct effects in the reference system, being itself a motion in space it always acts to oppose the motion represented in the reference system. Inasmuch as the motion in the dimension of the reference system did produce changes of position in that system, the overcoming of that motion (by the ultra high speed motion in the second scalar dimension) reverses those changes of position. The position of the induced thredule, thus, would be located at a little angular distance backwards compared to the position of the inducing thredule relative to the direction of rotation of the sun. This produces the separation between the preceding and the following members of a spot group.

8. Sunspot Properties

8.1 Characteristics of the Spot Groups

Figure 7 illustrates one of Hale‘s polarity laws of sunspot groups: namely, that the polarity of the preceding (following) spots in each hemisphere is opposite. We have just now explained its origin.

Currently, the formation of spot groups is being attributed to the buoying up of toroidal magnetic flux tubes supposed to be subsisting below the photosphere. If this were to be true, all spot groups have to be bipolar. The occurrence of unipolar and those classified as complex groups cannot be accounted for.

Large-scale, low intensity magnetic regions of the photosphere within which sunspots rarely appear are referred to as the bipolar magnetic regions (BMR), and the unipolar magnetic regions (UMR). Like the bipolar sunspot groups, the BM regions also are found to obey Hale‘s polarity laws. It is not difficult to see that these regions arise as the thredules and the embedded co-magnetic lines shoot outwards, but the thredules give up heat and completely dissolve prior to reaching the visible layers of the photosphere, whereas the co-magnetic lines emerge out. Since they are no longer in equivalent space when they so emerge, these lines no longer bunch together, but tend to diverge and their intensity falls to a low value. This is the origin of the magnetic regions. Once again, in the conventional theory it is difficult to account for existence of the UM regions.

“The belts where sunspots most frequently appear migrate from high latitudes around 35 - 40 at the start of the new solar activity cycle, to the low latitude region around 5 - 10 at the end of the solar activity cycle. This migration of the sunspot producing areas occurs at almost the same time in both the northern and southern hemispheres.” [17] We have already arrived exactly at this finding by theoretical deductions toward the end of Section 6 above. Bray and Loughheed, who have done extensive work on sunspot studies, comment, “The cause of the latitude drift is very obscure.” [18]

Solar prominences are arch-like structures, which appear as dark filaments against the solar disk, but appear luminous at the limb. There are two types of prominences: one type appears in the region of 45 latitude where sunspot groups are born and migrates with them toward the equator, as shown in Figure 8. The other type is not associated with sunspots, and appears around 45 latitude and tends to migrate polewards, reaching the pole toward the maximum of the solar activity cycle. Both types of prominences are known to form along the borders between magnetic regions of opposite polarity. The magnetic polarity distribution around the polar prominences is opposite to that around the spot prominences, as indicated in Figure 8. Sakurai states, “... as yet we do not know the cause of this relationship... This subject is not yet fully understood in spite of extensive efforts to discover the cause of the formation of solar magnetic fields, both sunspot and ‘general’.” [20]

Chart of spot and prominence zones

Figure 8 - Migration of Prominences
(adopted from Reference 19)

But our theoretical derivation correctly predicts this state of affairs: in Section 6 we have shown that the thredules of the outer sheaf assume higher latitude positions with the advance of the solar cycle. These thredules are shorter and less energetic and succeed in producing only the bipolar magnetic regions in the photosphere, and not the sunspots. It is evident that the polar prominences are associated with these regions. Since the inner and the outer thredules are of opposite polarity, the preceding and following members of the BMR associated with spot prominences (arising from the inner thredules) are of opposite polarity compared to the corresponding members of the BMR associated with polar prominences (arising from the outer thredules). The migration of the two classes of BMRs, one poleward, and the other toward the equator, is similarly explained (see the end of Section 7.2).

Before leaving the subject of prominences, we should mention that scientists find it hard to explain why the gaseous material arching out in space sustains the filamental shape, when there is nothing to prevent its lateral expansion. Sakurai remarks, “Even now we do not have a definite explanation of how the cool gas constituting the prominences is supported by the magnetic lines of force of the sunspots, because this gas may easily diffuse out without resistance from the magnetic lines of force.” [21] But we have already seen why the matter in the very high temperature range retains the thread-like structure and how expansion in the context of such temperatures is observed as contraction.

We will now move on to the explanation of another observational fact–a fact which the conventional theories find most difficult to explain–namely, the reversal of the polarity scheme of the bipolar spot groups in both the hemispheres with each new cycle of solar activity. This is expressed as another of Hale‘s polarity laws: “The entire system of polarities remains unchanged during any one 11-year cycle of sunspot activity, but reverses with the beginning of the next cycle...”

“The reversal... begins with the appearance of spots of the new cycle in high latitudes before the spots of the old cycle have completely disappeared.” [22] (See Figure 8.)

The beginning of the next cycle of the energy generation process takes place at the center of the sun as the temperature there once again reaches the thermal destructive level of the element present there. This creates a fresh pair of inner and outer sheaves of thredules lying inside the pair of sheaves belonging to the old cycle. The thredules of either sheaf of the new cycle also will be inclined at nearly 45 on either side of the axis, respectively. In view of the fact that the co-magnetic lines of like polarity have an affinity to each other, two things happen. Firstly, the thredules of the outer sheaf of the new cycle will form inclined to the axis on the same side in which the thredules of the inner sheaf of the previous cycle happened to be inclined. Secondly, the magnetic polarities of the thredules of these two sheaves will be identical. Since the polarity of the thredules of the inner sheaf is opposite to that of the thredules of the outer sheaf, we have the final result that the polarity of the thredules of the inner sheaf (and hence of the preceding spots) of the new cycle is opposite to the polarity of the thredules of the inner sheaf (and that of the preceding spots) of the old cycle.

8.2 The Sunspot Penumbrae

Soon after the appearance of a sunspot, the surrounding material of the photosphere in its immediate neighborhood starts becoming darker and at some subsequent stage, thin filaments directed more or less radially outwards from the spot umbra form. These annular regions around the umbrae are referred to as the penumbrae. The lengths of these radial filaments are known to vary according to the spot size and complexity. The radiation intensity in the penumbra gradually decreases inwards from the photosphere to the penumbra-umbra border, where it falls very steeply. The filaments end abruptly such that this border is sharply outlined.

Bray and Loughhead state: “It must be admitted that neither the mode of origin of the penumbra nor the role it plays in the sunspot phenomenon as a whole is yet properly understood.” [23] However, we can readily see that the penumbra must comprise of the photospheric material heated up to the intermediate temperature by the thredules that form the spot unbra. Both its filamental configuration, and sharply demarcated interface with the umbra suggestive of the phase change that occurs on crossing the boundary between the ultra high speed region and the intermediate speed region, clearly point to this.

Observations of sunspots near the solar limb show a marked asymmetry in the penumbral width (the Wilson effect) that seemed to suggest that the sunspots are saucer-like depressions in the photosphere. But recent observations with improved resolution never revealed such depressions when seen right up to the limb. The Wilson effect results if the umbra is much more transparent, rather than the penumbra, as compared to the photospheric material. This, of course, is what is to be expected. Opacity is a result of the absorption of radiation by the processes of photoionization and photoexcitation. With increasing temperature, more and more atoms are completely ionized, and the scope for the above absorption processes decreases. Therefore the matter in the penumbra is more transparent than the low temperature photospheric matter and that in the umbra more transparent than both of these.

8.3 The Evershed Effect

Radially outward motions in the sunspot penumbrae (parallel to the photospheric surface), named as the “Evershed velocities” (after their discoverer) are known to exist. No vertical or tangential velocities were ever observed in the penumbrae. The radial velocity–radial to the spot–increases from about 1.0 km/sec at the boundary between umbra and penumbra, reaches a maximum of about 2.0 km/sec near the center of the penumbra and comes to zero at the outer edge of the penumbra. It is also known that the Evershed velocity increases with the depth.

According to Bray and Loughhead:

“... The simplest interpretation of the Evershed effect is that it consists of a laminar flow of matter outwards from the umbra along the filaments...

“One piece of evidence against the hypothesis is the observed variation of the Evershed velocity with height: this would seem to be of sufficient magnitude to prevent the occurrence of a purely laminar flow... the shearing effect of the vertical velocity gradient would quickly lead to the disintegration of the filaments. Yet individual filaments are observed to persist...

“No trustworthy mechanism for the origin of the driving force of the Evershed flow has yet been proposed. It is rather interesting to note that at the photospheric level the direction of the motion is opposed to the pressure gradient, the pressure in the umbra being less than that in the photosphere.” [24]

All the above description of the Evershed effect exactly fits our theoretical conclusion that the penumbral matter is in the intermediate temperature range. The commencement of the radial velocity with a finite value (instead of a zero value) at the boundary of the umbra, the sustained laminar-like flow, despite the existence of a steep velocity gradient in the vertical direction, the apparent motion against the pressure gradient, all of these point to the same thing, namely, that the motions in the penumbra pertain to the region of equivalent space.

In Section 3.2.4 we have shown that thermal motion beyond the unit level tends to contract a material aggregate. Therefore the decrease in the intermediate temperature with the increase in the penumbral radius involves a re-expansion that extends all along the radius. Although this manifests as a flow in the penumbral filaments, in reality, its true nature is altogether different.

We shall let Larson explain it:

“At this time we will take a look at another of the observable effects of motion in time... its effect in distorting the scale of the spatial reference system.

“... in the physical universe we are able to use the spatial reference system only on the basis of an assumption that the rate of change of time remains constant ... the scale of spatial co-ordinate system is related to the rate of change of time ... At speeds in excess of unity, space is the entity that progresses at the fixed normal rate, and time is variable. Consequently, the excess speed above unity distorts the spatial co-ordinate system.”[25]

Thus at higher intermediate temperatures there will be a greater scale distortion (in the manner of contraction) and vice versa.

The Evershed flow is not a genuine change of position of the particles of matter in the space of the reference system: it is, rather, the effect of the occurrence of a scale gradient accompanying the temperature gradient in the intermediate region.

8.4 Evidence Against the Apparent Low Temperature of the Spots

8.4.1 Intensity Measurements

The radiation intensity of the sunspots is measured at several frequency ranges. The current practice of treating this radiation as conforming to the continuum spectrum of the blackbody radiation has lead to conflicting results.

Bray and Loughhead remark, “As a direct consequence of the umbra's low temperature, its spectral class is later than that of the photosphere–dKo as compared to dGo-2 for the photosphere.” Then on making a comparison with the observed intensity values they conclude: “It follows that the spectral class of the umbra is decidedly earlier than the temperature derived from intensity measurements made in the continuous spectrum would lead one to expect. The origin of this discrepancy is unknown.” [26] This must be so, as long as the true status of this radiation is not recognized.

Quoting again from them: “... numerous weak [spectral] bands due to unidentified compounds have so far been seen only in spots, and ... unidentified bands in the sunspot spectrum are more numerous than those now accounted for.” [27]

8.4.2 Sunspot Effects on the Surrounding Granulation

The entire surface of the photosphere appears covered with uniformly bright cells, called the granules, separated by the darker intergranular material. These granules are believed to be convection cells. Observations show that there is an increase in intensity at the Violet and UV wavelengths giving rise to the appearance of bright, ring-like regions around the spots.

Bray and Loughhead report that it is “found that the intensity of the bright ring is greatest immediately outside the penumbra and decreases slowly outwards... the bright rings are unusually intense around spots showing large Evershed velocities.

“No satisfactory explanation of the presence of the bright rings in the photosphere around spots ... has yet been given.” [28] Rightly so. But the moment we realize that the spots are hotter and not cooler than the photosphere, then enhanced brightness can be attributed to the energy transfer from the spot.

Moreover, from heat transfer studies, it is known that an increased heat transfer rate is correlated with smaller size of the convective cells. We see from Bray et al that “the size distribution of the solar granulation is extremely uniform over the solar surface...

... Several authors have observed a reduction in the granule diameter or mean spacing in the close neighborhood of sunspots..., which so far has received no theoretical attention.” [29] In addition, these areas of reduced granule size adjacent to the spots are found to coincide with the regions of enhanced brightness mentioned above. [30]

8.5 Polarization of the Radiation

Polarization measurements on the integrated radiation from the sunspots indicates that it is partially plane polarized. This, of course, is what is to be expected (see the end of Section 3.1).

9. Radiation Associated with Sunspots

We have already discussed some aspects of the magnetic fields, the prominences, and the granulation in association with the spots.

In addition to the continuum and line emission, different other patterns of radiation emission are observed in conjunction with sunspot groups. Non-thermal radio emission in the metric frequency range is often found above spot groups and is known as the Type I continuum storm. Such sunspot groups with Type I emission are also found responsible for the generation of solar flares (sudden, local increases in the surface brightness of the sun).

Emission of micro-waves, soft thermal X-rays, high energy particles (of MeV-BeV range), hard non-thermal X-rays, gamma rays, and non-thermal burst emissions at radio frequencies are all known to occur in the several phases of the solar flares. Some of the radiation is seen to be strongly polarized. The scientists admit that as yet no satisfactory and consistent explanation of the complex nature of these radiation phenomena is available.

Larson discusses at length the processes that generate non-thermal X-rays and radio waves. [2] He explains how stable isotopes become radioactive and emit radiation at radio wavelengths when they are transported from the low temperature region to the intermediate temperature region. In a similar manner, he shows that when matter which has attained isotopic stability in the intermediate temperature region is transported to the low temperature region, it again becomes radioactive and emits X-rays and gamma rays. [31] As such, it is not difficult to account for the origin of the variety of the observed radiations in association with the sunspots, once the presence of the ultra high and the intermediate speed matter in and around them is recognized.

10. Epilog

We have shown that reasoning from the principles embodied in the Reciprocal System it is possible to explore the internal structure of the sun. The theoretical understanding so obtained is in consonance with the observations of sunspot and relevant phenomena.

The main thesis derived is that sunspots are produced by the surfacing of the ultra high temperature matter in the solar core in the form of “thredules” to the photospheric level.

It must be mentioned that the theoretical account of the solar interior herein reported is a simplified one that is meant to serve as the basis for further, more detailed, work.


References