The Beginnings
As part of an attempt to determine the surface temperature of the Sun, Lane (1869), wrote down, for the first time, the set of equations describing a gas sphere in hydrostatic equilibrium. We, therefore, credit Lane with constructing the first physical model of the solar interior. Interestingly, although his model predicted the central temperature of the Sun reasonably well, his predicted surface temperature of 30,000K was well off the mark. This is because Lane's work was done without the aid of Stefan's radiation law (which was published later, in 1879).
Lord Kelvin
Instead he relied on the earlier work of Dulong and Petit and of Hopkins on the rate of radiant energy from heated surfaces [see the excellent historical notes by Chandrasekhar (1939)]. Other solar models with convective interiors were constructed by Ritter (1878), and by Kelvin (see his Collected Works, 1897). In 1861, Kelvin introduced the concept of "convective equilibrium" in geophysics, which was later codified in the stellar context by Emden in his monograph Gaskugeln (1907). Following the development of atomic physics and the first calculations of absorption coefficients, Eddington (1926) improved Lane's stellar models by including a description of the transport of energy by radiation. Cecilia Payne discovered that the Sun and stars are primarily composed of hydrogen.
Payne
Later, Eddington showed that the only way he could produce a solar model with the correct luminosity was to assume that the Sun and presumably all stars were composed primarily of ionized hydrogen.
Sir Eddington
Nuclear Power
The power source for the Sun and stars remained a mystery until the discovery of thermonuclear reactions. Kelvin (1897) recognized the time scale problems associated with the gravitational contraction hypothesis proposed by Helmholtz (1854)-the Sun would complete its contraction in significantly less time than the then current estimates of the age of the Sun. After the discovery of radioactivity, several authors, notably W.D. Harkins, J. Perrin and A.S. Eddington (Chandrasekhar 1939), suggested that subatomic energy might provide enough energy to power the Sun over its lifetime. During the development of nuclear physics, the fusion of hydrogen into helium was discussed by several, in particular Atkinson (1931), von Weizsäcker (1937) and Gamow (1938). Bethe (1939) originally proposed that the Sun derived its power from the CN cycle. Later, with improved interior opacity calculations, it was recognized that the proton-proton chain is responsible for most of the luminosity of the Sun (Oke 1950).
Bethe
Convection
Biermann (1932) and Cowling (1935) were the first to use the mixing length theory to describe the transport of energy by convection in the outer layers of the solar model. Beirmann set the mixing length equal to the size of granules observed on the surface of the Sun. Vitense (1953; see also Böhm-Vitense 1958) refined the mixing length theory by adopting a mixing length proportional to the pressure scale height, which decreases as the surface is approached. In addition, she accounted for radiative losses as the convective bubbles rise and sink. Demarque and Percy (1964) were the first to use the Böhm-Vitense mixing length theory in the construction of solar models.Evolution
In 1955, Hoyle and Schwarzschild used a sequence of static models to explain the evolution of a star. Shortly thereafter, Haselgrove and Hoyle (1956) carried out the first true evolutionary calculations, which were performed with an digital computer. Schwarzschild, Howard, and Härm (1957) then calculated the first evolutionary models of the Sun. The sequences followed the structural evolution of the models as the nuclear burning core converted hydrogen into helium. Calibrated solar models, equivalent to what we now call standard solar models, were introduced Demarque and Percy (1964). In these models, the mixing length parameter and the helium abundance of the solar model are adjusted to produce a model that has the Sun's observed radius and luminosity. These values were then used in model calculations of other stars (Demarque and Larson 1964). Since then many authors have constructed solar models that are increasingly more realistic physically.
Schwarzschild
Present Day
Today, the very precise observations of the Sun's five minute oscillations place severe demands on the standard solar model. Significant improvements have been made to the opacities and the equation of state (Mihalas, Däppen, & Hummer 1988; Rogers and Iglesias 1994; Rogers et al. 1995). Gravitational settling of helium (Proffitt and Michaud 1991; Guenther et al. 1993; Guzik and Cox 1993; Christensen-Dalsgaard, Proffitt, & Thompson, 1993), the effects of slow rotation (Endal and Sofia 1981; Pinsonneault et al. 1989; Chaboyer et al. 1995a, b) have been included in the model calculation, and, most recently, attempts have been made to replace the mixing length theory of convection with a model based on sophisticated numerical simulations of stellar convection (Chan and Sofia 1989; Canuto and Mazzitelli 1991, 1992; Lydon et al. 1992, 1993; Paterno et al. 1993; Kim et al. 1995; Demarque et al. 1996).References
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