Constitution of the Stars

CONSTITUTION OF THE STARS Density.—When the mass and radius of a star are known, the mean density of the material can be calculated immediately. Direct determinations of the mass are only available for double stars; but for other stars the mass may with some confidence be inferred from the absolute magnitude by means of the mass luminosity relation described later in this section. In any case the range of stellar masses is so restricted that errors are not likely to affect the general order of magnitude of the densities deduced. The radius R may be calculated from the absolute luminosity and the observed surface-temperature. Other things being equal, the luminosity is proportional to the area of the sur face, i.e., to but allowance must be made for the different radiating power of surfaces at different temperatures ; this allow ance can be calculated from the laws of radiation (Planck's law). For a few stars the radii deduced in this way have been con firmed by direct measurement of the apparent angular diameter of the disc with Michelson's interferometer. In this way we find that some of the red giant stars, such as Betelgeuse, Antares, Mira, have densities less than 4- o that of air ; Capella has a mean density nearly equal to air; the sun, we already know, has a density 1.4X water; the faint red dwarfs have density about 10 X water. For the class of stars called white dwarfs, which includes the companion of Sirius (see SiRms), the method gave an enor mous density 6o,000 times that of water ; this result was at first regarded as incredible, but it now appears probable that it is to be accepted literally.

For the more diffuse stars it is evidently legitimate to treat the stellar material as perfect gas. The study of stellar equi librium thus reduces to the study of the equilibrium of a globe of perfect gas held together by its own gravitational attraction. It was thought that the simple theory must break down for stars of higher density (such as the sun) owing to the deviations from the laws of a perfect gas; but in 1924 it was found by Eddington that the dense stars agreed observationally with laws which had been deduced theoretically for gaseous stars. The fact is, that at the temperatures of the order of ten million degrees occurring in the stellar interior, the atoms are stripped of all their outer electrons and reduced to ions of very small dimensions ; conse quently the jamming of atoms against one another, which causes the breakdown of the gas laws, does not occur in the stars until far higher densities are reached. The high density found for

the white dwarfs confirms this conclusion; close packing is possible because the atoms have lost their balloon-like envelopes. In all stars other than white dwarfs the material may be treated as perfect gas, except that in the stars of least mass (red dwarfs) there is a small correction arising from the electrostatic forces between the ions which makes the gas superperfect, i.e., makes it deviate in the opposite direction to the deviations of imperfect terrestrial gases.

Internal Temperature and Pressure.

The distribution of temperature and density in a sphere of gas in equilibrium under its own gravitational attraction is a classical problem studied by Lane, Ritter, Emden and others. The mathematical analysis de veloped in these earlier researches is used in the modern theory, but three new features have been introduced. (I) It used to be supposed that the heat radiated from the star's surface into space was brought up from the interior by convection currents, but it has now become evident that it is transferred by radiation. Accordingly the stars are now assumed to be in radiative equi librium instead of in convective equilibrium. The condition of radiative equilibrium is that each region must have settled down to a temperature at which it radiates an amount of heat equal to that which it absorbs from the radiation passing through it. One simplification resulting from this change is that we no longer need to know the ratio of specific heats of stellar material—a physical constant difficult to estimate. (2) Radiation-pressure is sufficiently great to play an important part in the equilibrium, especially of the massive stars, and it is now taken into account. (3) Formerly the average molecular weight of the stellar gas was taken to be the weight of the atoms likely to preponderate, e.g., iron (at. wt. 56). It is now recognized that the atoms in the interior will be highly ionized; most of the electrons which circulate round the nucleus will have broken loose, and must be counted as independent "molecules." Taking this into account the molecular weight will be slightly over 2, a result nearly inde pendent of the chemical constitution of the star provided only that there is not an excessive proportion of hydrogen. Owing to this decrease in the adopted molecular weight, the internal tem peratures are considerably lower than those calculated on the older theories.