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radiation both tend to detach electrons and to produce singly ionized calcium atoms. At the same time, these ions can recombine with electrons to produce neutral calcium atoms. At high temperatures or low electron pressures, or both, most of the atoms are ionized. At low temperatures and high densities, the equilibrium favours the neutral state. The concentrations of ions and neutral atoms can be computed from the temperature, the density, and the ionization potential (namely, the energy required to detach an electron from the atom).
    The absorption line of neutral calcium at 4227 Å is thus strong in cool M-type dwarf stars, in which the pressure is high and the temperature is low. In the hotter G-type stars, however, the lines of ionized calcium at 3968 and 3933 Å (the “H” and “K” lines) become much stronger than any other feature in the spectrum.
    In stars of spectral type F, the lines of neutral atoms are weak relative to those of ionized atoms. The hydrogen lines are stronger, attaining their maximum intensities in A-type stars, in which the surface temperature is about 9,000 K. Thereafter, these absorption lines gradually fade as the hydrogen becomes ionized.
    The hot B-type stars, such as Epsilon Orionis, are characterized by lines of helium and of singly ionized oxygen, nitrogen, and neon. In very hot O-type stars, lines of ionized helium appear. Other prominent features include lines of doubly ionized nitrogen, oxygen, and carbon and of trebly ionized silicon, all of which require more energy to produce.
    In the more modern system of spectral classification, called the MK system (after the American astronomers William W. Morgan and Philip C. Keenan, who introduced it), luminosity class is assigned to the star along with the Draper spectral type. For example, the star Alpha Persei is classified as F5 Ib, which means that it falls about halfway between the beginning of type F (i.e., F0) and of type G (i.e., G0). The Ib suffix means that it is a moderately luminous supergiant. The star Pi Cephei, classified as G2 III, is a giant falling between G0 and K0 but much closer to G0. The Sun, a dwarf star of type G2, is classified as G2 V. A star of luminosity class II falls between giants and supergiants; one of class IV is called a subgiant.
B ULK S TELLAR P ROPERTIES
    When a star is considered as a whole, its properties reveal much of interest. From a star’s temperature to how it interacts with a companion star, the considerationof bulk stellar properties has been and will continue to be a major part of astronomical studies.
S TELLAR T EMPERATURES
    Temperatures of stars can be defined in a number of ways. From the character of the spectrum and the various degrees of ionization and excitation found from its analysis, an ionization or excitation temperature can be determined.
    A comparison of the
V
and
B
magnitudes yields a
B
−
V
colour index, which is related to the colour temperature of the star. The colour temperature is therefore a measure of the relative amounts of radiation in two more or less broad wavelength regions, while the ionization and excitation temperatures pertain to the temperatures of strata wherein spectral lines are formed.
    Provided that the angular size of a star can be measured and that the total energy flux received at Earth (corrected for atmospheric extinction) is known, the so-called brightness temperature can be found.
    The effective temperature,
T eff
, of a star is defined in terms of its total energy output and radius. Thus, since σ
T
4
eff
is the rate of radiation per unit area for a perfectly radiating sphere and if
L
is the total radiation (i.e., luminosity) of a star considered to be a sphere of radius
R
, such a sphere (called a blackbody) would emit a total amount of energy equal to its surface area, 4π
R
2 , multiplied by its energy per unit area. In symbols,
    L
= 4π
R
2 σ
T
4 eff .
    This relation defines the star’s equivalent