The Milky Way and Beyond (11 page)

The continuous (as distinct from the line) spectrum of the Sun is produced primarily by the photodissociation of negatively charged hydrogen ions (H
^−
)—i.e., atoms of hydrogen to which an extra electron is loosely attached. In the Sun's atmosphere, when H
^−
is subsequently destroyed by photodissociation, it can absorb energy at any of a whole range of wavelengths and thus produce a continuous range of absorption of radiation. The main source of light absorption in the hotter stars is the photoionization of hydrogen atoms, both from ground level and from higher levels.

The physical processes behind the formation of stellar spectra are well enough
understood to permit determinations of temperatures, densities, and chemical compositions of stellar atmospheres. The star studied most extensively is, of course, the Sun, but many others also have been investigated in detail.

The general characteristics of the spectra of stars depend more on temperature variations among the stars than on their chemical differences. Spectral features also depend on the density of the absorbing atmospheric matter, and density in turn is related to a star's surface gravity. Dwarf stars, with great surface gravities, tend to have high atmospheric densities; giants and supergiants, with low surface gravities, have relatively low densities. Hydrogen absorption lines provide a case in point. Normally, an undisturbed atom radiates a very narrow line. If its energy levels are perturbed by charged particles passing nearby, it radiates at a wavelength near its characteristic wavelength. In a hot gas, the range of disturbance of the hydrogen lines is very high, so that the spectral line radiated by the whole mass of gas is spread out considerably; the amount of blurring depends on the density of the gas in a known fashion. Dwarf stars such as Sirius show broad hydrogen features with extensive “wings” where the line fades slowly out into the background, while supergiant stars, with less-dense atmospheres, display relatively narrow hydrogen lines.

Most stars are grouped into a small number of spectral types. The
Henry Draper Catalogue
and the
Bright Star Catalogue
list spectral types from the hottest to the coolest stars. These types are designated, in order of decreasing temperature, by the letters O, B, A, F, G, K, and M. This group is supplemented by R- and N-type stars (today often referred to as carbon, or C-type, stars) and S-type stars. The R-, N-, and S-type stars differ from the others in chemical composition; also, they are invariably giant or supergiant stars. With the discovery of brown dwarfs, objects that form like stars but do not shine through thermonuclear fusion, the system of stellar classification has been expanded to include spectral types L and T.

The spectral sequence O through M represents stars of essentially the same chemical composition but of different temperatures and atmospheric pressures. This simple interpretation, put forward in the 1920s by the Indian astrophysicist Meghnad N. Saha, has provided the physical basis for all subsequent interpretations of stellar spectra. The spectral sequence is also a colour sequence: the O- and B-type stars are intrinsically the bluest and hottest; the M-, R-, N-, and S-type stars are the reddest and coolest.

In the case of cool stars of type M, the spectra indicate the presence of familiar metals, including iron, calcium, magnesium, and also titanium oxide molecules (TiO), particularly in the red and green parts of the spectrum. In the somewhat hotter K-type stars, the TiO features disappear, and the spectrum exhibits a wealth of metallic lines. A few especially stable fragments of molecules such as
cyanogen (CN) and the hydroxyl radical (OH) persist in these stars and even in G-type stars such as the Sun. The spectra of G-type stars are dominated by the characteristic lines of metals, particularly those of iron, calcium, sodium, magnesium, and titanium.

The behaviour of calcium illustrates the phenomenon of thermal ionization. At low temperatures a calcium atom retains all of its electrons and radiates a spectrum characteristic of the neutral, or normal, atom; at higher temperatures collisions between atoms and electrons and the absorption of 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.

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 consideration
of bulk stellar properties has been and will continue to be a major part of astronomical studies.

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 blackbody, or effective, temperature.

Since the total energy radiated by a star cannot be directly observed (except in the case of the Sun), the effective temperature is a derived quantity rather than an observed one. Yet, theoretically, it is the fundamental temperature. If the bolometric corrections are known, the effective temperature can be found for any star whose absolute visual magnitude and radius are known. Effective temperatures are closely related to spectral type and range from about 40,000 K for hot O-type stars, through 5,800 K for stars like the Sun, to about 800 K for brown dwarfs.

The mass of most stars lies within the range of 0.3 to 3 solar masses. One of the most massive stars determined to date is the O3-type star HD 93250, a giant that has perhaps 120 solar masses. There is a theoretical upper limit to the masses of nuclear-burning stars (the Eddington limit), which limits stars to no more than a few hundred solar masses. The physics of instability and fragmentation probably prohibits the formation of stars much more than 100 times the mass of the Sun. On the low mass side, most stars seem to have at least 0.1 solar mass. The theoretical lower mass limit for an ordinary star is about 0.075 solar mass, for below this value an object cannot attain a central temperature high enough to enable it to
shine by nuclear energy. Instead, it may produce a much lower level of energy by gravitational shrinkage. If its mass is not much below the critical 0.075 solar mass value, it will appear as a very cool, dim star known as a brown dwarf. Its evolution is simply to continue cooling toward eventual extinction. At still somewhat lower masses, the object would be a giant planet. Jupiter, with a mass roughly 0.001 that of the Sun, is just such an object, emitting a very low level of energy (apart from reflected sunlight) that is derived from gravitational shrinkage.

Brown dwarfs were late to be discovered, the first unambiguous identification having been made in 1995. It is estimated, however, that hundreds must exist in the solar neighbourhood. An extension of the spectral sequence for objects cooler than M-type stars has been constructed, using L for warmer brown dwarfs and T for cooler ones. A major observational difference between the two types is the absence (in L-type dwarfs) or presence (in T-type dwarfs) of methane in their spectra. The presence of methane in the cooler brown dwarfs emphasizes their similarity to giant planets. The class Y has been proposed for objects even cooler than those of class T.

Masses of stars can be found only from binary systems and only if the scale of the orbits of the stars around each other is known. Binary stars are divided into three categories, depending on the mode of observation employed: visual binaries, spectroscopic binaries, and eclipsing binaries.

Visual binaries can be seen as double stars with the telescope. True doubles, as distinguished from apparent doubles caused by line-of-sight effects, move through space together and display a common space motion. Sometimes a common orbital motion can be measured as well. Provided that the distance to the binary is known, such systems permit a determination of stellar masses,
m
₁
and
m
₂
, of the two members. The angular radius,
a
”, of the orbit (more accurately, its semimajor axis) can be measured directly, and, with the distance known, the true dimensions of the semimajor axis,
a
, can be found. If
a
is expressed in astronomical units, which is given by
a
(measured in seconds of arc) multiplied by the distance in parsecs, and the period,
P
, also measured directly, is expressed in years, then the sum of the masses of the two orbiting stars can be found from an application of Kepler's third law. (An astronomical unit is the average distance from Earth to the Sun, approximately 149,597,870 km [92,955,808 miles].) In symbols,

(
m
₁
+
m
₂
) =
a
³
/
P
²

in units of the Sun's mass.

For example, for the binary system 70 Ophiuchi,
P
is 87.8 years, and the distance is 5.0 parsecs; thus,
a
is 22.8 astronomical units, and

m
₁
+
m
₂
= 1.56

solar masses. From a measurement of the motions of the two members relative to the background stars, the orbit of each star has been determined with respect to their common centre of gravity. The mass ratio,
m
₂
/(
m
₁
+
m
₂
), is 0.42; the individual masses for
m
₁
and
m
₂
, respectively, are then 0.90 and 0.66 solar mass.

The star known as 61 Cygni was the first whose distance was measured (via parallax by the German astronomer Friedrich W. Bessel in the mid-19th century). Visually, 61 Cygni is a double star separated by 83.2 astronomical units. Its members move around one another with a period of 653 years. It was among the first stellar systems thought to contain a potential planet, although this has not been confirmed and is now considered unlikely. Nevertheless, since the 1990s a variety of discovery techniques have confirmed the existence of more than 300 planets orbiting other stars.