Introduction

In part I of this duology, we have covered the most basic phenomena of Solar Physics like the source of the Sun's energy, its composition, the photosphere, the faculae, the chromosphere, the Solar Corona, and the Solar Prominences. This part entails a brief account of notions like the 11-year Solar Cycle, the Theory of Sunspots, the Solar Neutrino Puzzle, and the Standard Solar Model.

The Solar Cycle

Long years of investigation the German amateur astronomer, Heinrich Schwabe, concluded in 1851 that the number of visible spots on the Sun’s disk varied with time. He also discovered a periodicity associated with such variations. The period proposed by Schwabe was 10 years. Later observations, however, established that the period is in fact 11.2 years (but commonly described as an 11-year cycle). The cycle of activity of the Sun is repeated nearly over this period, which is therefore known as the solar cycle. Within a solar cycle which is defined by the period between one minimum to the next, the number of sunspots and the intensity of other transient phenomena change appreciably. The maximum solar activity is characterized by the maximum number of spots which maybe 100 or so or about 10 groups of spots. This is the time of sunspot maximum. The activity of the Sun and so the sunspot number decreases subsequently until it reaches a minimum. This is the time of sunspot minimum when scarcely any spot is visible on the solar disk.

The period between two successive maxima or two successive minima is not always the same. The average value between a maximum to the next minimum is about 6.7 years while that between a minimum and the next maximum is about 4.6 years. Two successive maxima may occur in an interval of as short as 8 years (1830 to 1838), and as long as 16 years (1888 to 1904). Thus quite a large variation to the commonly described 11-year cycle may occur in any particular cycle.

The Standard Solar Model

In the standard solar model, the sun is considered as a spherically symmetric body of hydrogen gas whose most of its luminosity originates from nuclear reactions. The different features like luminosity, radius, age, and composition (hydrogen-to-heavy elements ratio) are calculated using helium abundance and mixing length parameter as free parameters and are matched with their observed values though, both the sun’s neutrino flux and the ‘p’ mode oscillation spectrum, predicted by standard model do not match with the observed values (Super KamioKande experiment in Japan and the experiment held by Davis in 1978 in South Dakota) but the free parameters are adjusted so that the derived solar mass and radius match with the observed values. So the purpose of the standard solar model is to provide an estimate of the solar model-free parameters, as well as to put a benchmark to compare “improved” solar models which have merely complicated physics, like, rotation, magnetic field, diffusion, overshooting, and metal-rich cores.

The fundamental equations consisting of the standard model are conservation of mass, momentum, energy equations, energy transport equations, and nuclear reaction network. It is assumed that the system is in hydrostatic equilibrium, i.e. the weight of any volume element is supported by the sum of all pressure forces acting on the element.

The nuclear reactions have two results: (i) they determine the energy output per unit time of a given shell which is used in the energy balance equation and (ii) they determine the abundances of elements involved in the nuclear reactions. The former is used in the energy balance equation and the latter is used to find the evolution of mean molecular weight. The standard model is constructed through an iterative method. First, an initial guess of mixing length parameter and helium abundance are considered and their evolution is found at the current age of the sun. Then these are compared to the observed values, and the discrepancy is adjusted by adjusting the mixing length and abundance.

Solutions and Contradictions

In 2001, the results from Sudbury Neutrino Observatory (SNO) in Canada, confirmed that electron neutrinos produced by nuclear reactions inside the sun, ‘oscillate’ or change flavor on their journey to earth, i.e. they have been transformed into muon and tau neutrinos and this is possible only if neutrinos have mass. Although the Super Kamiokande experiment in Japan has seen a strong discrepancy in the observed and predicted neutrinos, the SNO results when combined with solar neutrino data from Super Kamiokande, showed that the disappearance of one neutrino flavor is accompanied by the appearance of another. But there are contradictions too to SNU results. First of all, there can be no confirmation of oscillation of neutrino flavor between sun and earth without simultaneous measurements being made near the sun. 

On the other hand, an electrical model for stars has been proposed by Ralph Jurgens. According to this model, the sun is not a sphere of neutral gas. Due to a large difference in mass between the electrons and the protons, the hydrogen atoms act like a dipole with positive aimed at the Sun’s center. Since the electric force outguns gravity by 1039, its omission from the standard model makes it unrealistic. The electric sun model expects heavy element synthesis so that various neutrino flavors are all generated in sun and do not need to oscillate on their way to earth. Here fluctuations in neutrino counts are expected to be correlated with various solar activities, e.g. sunspot numbers, solar wind activity, etc. It has been observed that the standard solar model has no such correlation as there is a lag of million years between nuclear reactions in the core and its final expression at the surface of the sun.

With this, we have covered most of the basic Solar Physics. There are still some theories in development and existent ones are being criticized. Solar Physics has been expanding far and wide for decades with several unknown phenomena about our nearest star.

I hope this article proved instrumental in imparting some knowledge.

Bon Reading!

Note: Several results from spectroscopic studies which gave justification of some of the above-mentioned phenomena and some mathematical explanations also were skipped to make this article suitable for a general audience and for science communication. If you wish to get further and detailed insight into the concepts, please check out the books and links mentioned in the references section.

References -

[1] Sagan, Carl, The New Solar System, Cambridge University Press, Cambridge, 1990.

[2] Phillips, Kenneth, J.H., Guide to the Sun, Cambridge University Press, Cambridge, 1992.

[3] NASA -  Marshall Space Flight Center

[4] Image Credits - NASA, European Space Agency