THE EVOLUTION AND DYNAMICS OF THE SUN The Sun's bright surface, the photosphere, is an opaque layer of incan descent gas at a temperature of about 5800°K* and with a density of about The properties of the deeper layers can only be theoretically calculated, on the basis of conditions of hydrostatic equilibrium, thermal equilibrium (constancy of temperature at any given point), and local thermo dynamic equilibrium. These conditions, expressed in the form of a set of differential equations, make it possible to compute the distribution of the properties of the gas with depth, given the chemical composition of the gas (the relative content of hydrogen, helium, and heavy elements), the condi tions on the outer boundary, and some additional parameters. The calcula tion also includes the energy released in the nuclear reactions taking place at the high temperature and density prevailing in the Sun's inner core. The first reaction involves the fusion of two hydrogen nuclei, which form deuterium and a positron. In the process gamma rays are given off. The deuterium nucleus quickly captures a proton, turning into the isotope, and then two nuclei fuse, transforming into and two protons. In the course of these reactions a large amount of energy is released, which gradually diffuses outward in the form of radiation quanta. The mean wavelength of the radiation depends on the temperature; in the interior it falls within the X-ray range, while at the surface visible light emerges.
The rate at which energy is released depends on the temperature and density at the center, and in a star of normal constitution it is ultimately determined by the mass. Under the conditions existing inside the Sun, it will take about 7 billion years for the hydrogen in the central region to transform almost completely into helium. At present more than half of the hydrogen originally contained in this region has been transformed into helium. The composition of the middle and surface layers has apparently remained the same as it was when the Sun was formed. The increasing helium content in the core makes the mean molecular weight of the gas higher, and that causes the temperature at the center to rise. At present the temperature there is about 13 million degrees. The rate of the reactions strongly depends on the temperature, and thus the Sun's radiation is growing stronger, even though the relative content of hydrogen is decreasing. Cal
culations show that during its existence (about 5 billion years) the brightness of the Sun has risen by about 60%. Accordingly, in the course of the last billion years the radiant energy received by the Earth has increased by about 10% and there has been a rise in the Earth's mean temperature.
It is a fact, though, that the temperature of the Earth depends to a large extent on factors such as the atmospheric composition and circulation, and it is therefore difficult to obtain a precise value for the net rise in temperature.
As the hydrogen in the center of the Sun becomes depleted, a core of high molecular weight is formed. This core, deprived of energy sources, will start contracting until it goes into a state of degeneracy in which the contraction will almost cease. There will be no energy release either in the core Jr in the outer portion of the Sun, but only at the boundary of the core, where some hydrogen will have remained and the temperature will be sufficiently high. The size of the outer portion of the Sun will slowly increase, and the Sun will eventually turn into a red giant. At that time the temperature of the Earth will have reached about 1000'K. The Sun's envelope will gradually expand and transform into a planetary nebula (Figure I), while the core will become a small dense hot star, i. e. , a white dwarf.
At an early stage of its development the Sun was apparently a contracting gas sphere. It might have possibly been formed from the central part of the same cloud of gas and dust from which the planets were produced. The main argument against the nebular hypothesis of the formation of the Sun and planets has been the fact that the specific angular momentum of the Sun is too small, only 1/50,000 of that of the planets, per unit mass. It has been found, however, that in the presence of a magnetic field momentum could be transferred from the central part of the cloud to the disk. The lines of force are twisted by the rapidly rotating central condensation and slow it down, and at the same time they speed up the rotation of the disk. This effect is apparently associated with the fact that, beginning with the F class, stars have a slow rotation, much slower than should be the rotation of a body condensed from a relatively rarefied medium which possesses even a very small momentum. This suggests that most stars of the main sequence may have planetary systems or gas-dust disks.