5. SOLAR EVOLUTION


 

    The general evolution scheme of the Sun postulates a progressive contraction of gas by self-gravitation which is periodically interrupted by thermonuclear burning. After particular types of nuclear fuel (hydrogen, helium) are exhausted, the contraction-burning cycle will be repeated, but at higher temperatures. The stages of the Sun's evolution from primitive solar nebula contraction to the black-dwarf stage can be followed in the Hertzsprung-Russell (H-R) diagram. There is a rapid movement of the Sun toward the main-sequence, where the Sun spends the major part of its life, and then an eventual movement toward the black-dwarf evolution stage, which is the final stage in its evolution (Schwarzschild 1958; Gibson 1973).

 


 

Figure 1-8. The path of a 1Msun star in the Hertzsprung-Russel diagram.

 


  5.1 Presolar evolution stages.

5.1.1 Cloud

    Over 4.5 billion years ago, the gas cloud which would become the Sun had a diameter of over 480 trillion kilometers, which is approximately 50 light years. This cloud was not dense, containing only a few thousand atoms per cubic centimeters of space. The total mass of the cloud would have been sufficient for building up several solar systems. Its temperature was that of the interstellar space, of the order of 3 K, not radiating any light into the surrounding space. The fragile equilibrium state of the cloud, having only the choice of dissipating further into outer space or contracting into a denser configuration, eventually became disturbed either by an impact from outside or by random condensation of a large number of cloud particles, and finally began to condense.

5.1.2 Globule

    After a time of the order of several thousand years, random concentrations of matter called globules formed at various places in the giant condensing matter cloud. The cloud collapses almost in free fall, however, due to the influence of pressure, the motion is non homologous. The free fall time of the cloud is

t_sub_(ff cloud) = [(3 * Pi) / (32 * G * rho_sub_0)]^(1/2) , (17)

where rho0 denotes the initial mean matter density of the cloud. The temperature in the cloud was rising very slowly, still not able to radiate light. Later, one of those globules, now having a dimension of several hundred solar systems, would become the Sun. The globule continued condensing with the effect of increasing its temperature.

5.1.3 Protostar

    Within 400,000 years the globule had condensed to a millionth of its original size, but still over four times the size of the present solar system. At the centre of the globule a core had developed, heated by the concentration of its matter, already able to radiate a substantial amount of energy into the less dense outer regions of the former globule. The emission of radiation by the core began to slow the condensation of its matter. The matter becomes opaque and the free fall is stopped by the pressure. This core had now developed into a stable and well-defined configuration called protostar or protosun. With the birth of the protosun the evolution of this matter configuration advanced more rapidly. After the formation of a core, its free fall time is

t_sub_(ff_core) = {[Pi^2 / (8G)] * [R^3 / M]}^(1/2) , (18)

where M is the mass and R the radius of the core, respectively. Within a few thousand years it collapsed to a size of the diameter of the orbit of planet Mars. The interior temperature reached values of 56,000K leading to an ionization of atoms. The red light emitted at the surface of the protosun was not produced by fusion of atomic nuclei but by gravitational contraction of matter. Gravitation released the potential energy of the globule, 7 x 1048 erg, during the condensation of the protosun. According to the Virial theorem (2Tk + OMEGA = 0) one half of the released gravitational energy OMEGA of the system was radiated from the protosun while the other half had been transformed into heat of the central core; Tk denotes the total kinetic energy of the particles.

5.1.4 Sun

    Finally the protosun contracted further until its temperature was high enough for burning deuterium to form helium-3. The Sun was fully convective in the contraction phase and the chemical composition was always uniform. Through deuterium burning the contraction was momentarily slowed down. As the Sun continued to contract, the central temperature increased and the radiative temperature gradient decreased relative to the convective gradient. Convection ceased and a radiative core grew outward. With the ignition of hydrogen the protosun became a star, characterized by the gravitationally stabilized fusion reactor located at its center. Its binding gravitational energy |OMEGA| round CMsun2 / Rsun was initially stored in the extended globule, called the primitive solar nebula. If the sun would shine by its store of thermal energy |Tk| = |OMEGA| / 2 (Virial theorem), then its lifetime is given by the Kelvin-Helmholtz time scale, that is

t_sub_(kw) = (T_sub_k / L_sub_sun) round G * {[(M_sub_sun)^2] / [R_sub_sun * L_sub_sun]} . (19)

As the nuclear reactions began to release vast amounts of subatomic energy, the Sun was a quite variable star, varying in luminosity and surface activity as the result of the development of a radiative core and convective currents in its outer layers of gas. After a period of some 30 million years, its structure stabilized into the structure of a main-sequence star of one solar mass. The newly born Sun possessed enough fuel in the form of hydrogen to keep shining steadily for a time period of the order of

t_sub_(nuc) = [E_sub_(nuc) / L_sub_sun] round 10^(-3) * [(M_sub_sun * c^2) / L_sub_sun] , (20)

where the factor 10-3 is due to the product of the percentage of mass of the Sun available for hydrogen burning (0.1) and the fraction of mass converted into energy in hydrogen burning deltam/4mp round 0.01, where deltam is the mass difference in the net reaction 4p -> alpha + 2e+ + 2v_sub_e.

    That means also that the present Sun is right in the middle of its age as a main-sequence star (4.5 billion years).

5.2 Postsolar evolution stages

5.2.1 Red Giant

    As the Sun ages, helium collects in its center. After a lifetime of 9 billion years as main-sequence star, approximately 10% of the hydrogen in the Sun's core will have been converted into helium and nuclear fusion reactions will cease producing energy. The equilibrium between the total pressure force directed outwards and the gravitational force directed towards the centre of the Sun will be disturbed. The core of the Sun starts slowly collapsing under its own gravitational attraction. Fusion moves outward to a shell surrounding the core, where hydrogen-rich material is still present. The gravitational energy from the collapse will be converted into heat causing the shell to burn vigorously and so the Sun's outer layers to swell immensely. The surface is now far removed from the central energy source, cools and appears to glow red. The Sun now evolves into the stage of a red giant. For a few hundred million years, the expansion of the outer solar layers will continue, and the Sun will engulf the planet Mercury. The temperature on Venus and Earth will rise tremendously. Hydrogen fusion in the shell continues to deposit helium "ash" onto the core, which becomes even hotter and more massive.

    In the Sun's core nuclear fusion of helium into carbon and oxygen will start to trigger even further the expansion of its outer layers. The helium-rich core is unable to lose heat fast enough and becomes unstable. In a very short time of few hours the core gets too hot and is forced to expand explosively. Outer layers of the Sun will absorb the core explosion but the core will no longer be able to produce energy by thermonuclear burning. Helium fusion then continues in a shell and the structure of the Sun would look like an onion: An outer, hydrogen-fusion layer and an inner, helium-fusion layer which surrounds an inert core of carbon and oxygen.

    The old Sun may repeat the cycle of shrinking and swelling several times. In this stage of evolution the Sun is called an asymptotic giant branch star. Finally enough carbon will accumulate in the core to prevent the core explosion. Helium-shell burning will add heat to the outer layers of the Sun, mainly containing hydrogen and helium. The asymptotic giant Sun will generate eventually an intense wind that begins to carry off its outer envelope. The precise mechanism behind this phenomenon is not yet well understood. The Sun will expand a final time and after about 30 million years it will swallow Venus and Earth, outer layers will keep expanding outward and as much as half of the Sun's mass gets lost into space.

5.2.2 White Dwarf

    The solar core keeps shrinking and because it is not able anymore to produce radiation by fusion the further evolution of this configuration is governed by gravitation. All matter will collapse into a small body about the size of the Earth. Thus, the Sun will have become a white dwarf, this is a dense-matter configuration, having radiated away the energy of its collapse. Then the white dwarf rapidly begins to cool.

5.2.3 Black Dwarf

    The final stage of solar evolution will be the black dwarf stage. The white dwarf will emit yellow light and then red light in the course of its evolution, drawing from the star's reservoir of thermal energy. Its nuclei will be packed as tightly as physically possible and no further collapse is possible. The body is progressively cooling down and finally becomes as cold as the interstellar space around it, emitting no light at all. As a carbon-oxygen-rich black dwarf it will continue its journey through the galaxy (milky way) and may eventually encounter another giant gas cloud to become involved in the birth of a new star.