Formation of the spectrum
Most of the direct evidence we have on the physical conditions in stars is obtained from their spectra. The energy that finally reaches us from a star was originally created in the nuclear reactions in the star’s deepest interior. This energy gradually filters out through the gas of which the star is composed; the light energy that finally leaves the surface has a spectrum which is governed by the temperature, density and chemical composition of only a thin layer of gas whose thickness is 10-3 or less of the star’s radius.

Moving outwards from the centre of a star, there is a gradual decrease in temperature and density. A star has no sharply-defined surface because the density of gas just dwindles gradually until it is virtually zero. In general, as the density of the stellar material decreases, its opacity to light does too, so there is a region in the outer part of a star where the material becomes transparent to light. As this transition region is very thin compared with the size of the star as a whole, the visible disc is fairly sharply defined. This is obvious in the ease of the Sun, which is the only star whose disc is resolvable by eye. The visible disc is called the photosphere, and it is precisely this layer in the star which is responsible for the characteristic spectrum. The decrease in opacity through the photosphere manifests itself as limb darkening, which is directly observed on the solar disc.

In the case of the Sun, it is possible to investigate the layers of more tenuous gas overlying the photosphere, the chromosphere and corona whose spectra can be obtained during total eclipse. It is reasonable to suppose that similar structures exist in the outer¬most parts of other stars. The photosphere and overlying regions of a star are known as the STELLAR ATMOSPHERE, but, there is no precise boundary between this atmosphere and the interior.

A typical stellar spectrum is an ABSORPTION-LINE SPECTRUM; that is, it consists of a continuous background of light crossed by dark absorption lines at particular wavelengths. In a simple approximation, the stellar atmosphere may be thought of as a layer of cool, transparent gas overlying the hotter region below. The region beneath the photosphere produces the continuous spectrum, while atoms and molecules in the cool atmosphere are responsible for the absorption lines. This picture is an over¬simplification of the true state of affairs, for there is no dividing line between these regions. In fact, every part of the stellar gas both emits and absorbs light, but on the whole less light finally emerges at those precise wavelengths that are absorbed by the various atoms and molecules present in the atmosphere, and so absorption lines are formed.

Not surprisingly, the appearance of a star’s spectrum depends strongly on the temperatures prevailing in the stellar atmosphere. As a star has no solid surface, and the temperature is different in different regions of the atmosphere, what exactly is meant by the TEMPERATURE of a star? It is necessary to choose a precise definition which is physically significant and can be used to compare one star with another. The EFFECTIVE TEMPERATURE (Teff) of a star is taken as the temperature of a black body whose rate of energy radiation is equal to the star’s. In practice, this temperature turns out to be the actual temperature somewhere in the middle of the photospheric layer.

Temperatures of normal stars cover a large range: between about 3000 and 40000K, but typically, the temperature in a stellar atmosphere is around several thousand degrees. At these temperatures many atoms are ionized, so the stellar material contains free electrons and positive ions as well as neutral atoms. The proportion of any particular element which is ionized depends on the temperature, the ionization potential of the element, and the density. At higher temperatures, more atoms will be stripped of electrons, but if the density is high, it is easier for the ions to re¬capture their electrons, so that a high density limits ionization. The higher the ionization potential of an element, the more energy is required to produce ionization, so higher temperatures are required. The degree of ionization in a star’s atmosphere strongly influences the appearance of its spectrum. In physics the ionization state of an atom is conventionally represented by plus signs following the usual chemical symbol: thus H°, Fe°, Mg° represent neutral atoms of hydrogen, iron and magnesium respectively; Fe+, Ti+ represent singly ionized iron and titanium; N2+ means doubly-ionized nitrogen etc. In astronomy it has been traditional to use the chemical symbol followed by Roman numerals: e.g. HI, Fel, Mgl for neutral atoms, Fell, Till for singly-ionized atoms, NIII for doubly-ionized and so forth. In this book we often use the physics convention, not the astronomical tradition.

The classification of stellar spectra
chief features of the appearance of a stellar spectrum are governed primarily by the star’s effective temperature. An unusual chemical composition can alter the spectrum radically, but the vast majority of stars, those termed normal, have a composition closely resembling the Sun’s, and it is only these that will be con¬sidered here. The wide temperature range of stars means that there is also a wide variety in spectral appearance.

STELLAR SPECTRA are classified into seven main groups which form a temperature sequence. Each class is designated by a letter of the alphabet. From hottest to coolest they are:0, B, A, F G K M. This rather odd sequence of letters arose from an empirical classification method, developed at Harvard in the early twentieth century, which was originally in alphabetical order Historically the first classes chosen were absorption –line spectra in order of increasing strength of the hydrogen lines .Classes O and onwards were characterized by emission lines in the spectra and included the spectra of nebulae as well as stars. However it later became clear that some classes were spurious, resulting from lack of uniformity in the photography, and that it would be better order the classes as a temperature sequence .The Classification of nebular spectra was also discarded .On Revision the original letter names for the remaining classes wre kept .There is a well –known mnemonic which helps to recall the sequence O Be A Fine Girl kiss me!’ Each class is further divided into 10 sub –classes numbered from 0 to 9.Examples of spectral classes are A0,F5,G2

At One Time it was supposed that the sequence of spectral classes might form an evolutionary sequence .This is now known to be entirely false but, unfortunately ,the attendant terminology has never been dropped .As a result O and B stars are referred to as EARLY-type STARS and K and M stars as LATE-TYPE STARS .Where possible we avoid this misleading terminology
.
The criteria by which spectral classes are judged are: the absence or presence of particular spectral lines, and/or the ration of the intensities of certain spectral lines. These criteria have been proposed to enable classification from low-dispersion spectro¬grams without the necessity of determining the temperatures of stars from detailed analysis. W.W.Morgan arid P.O.Keenan were largely responsible for the development of this system and their names are often linked with this classification scheme. The main features of each class are listed below and examples of spectra of several classes are illustrated
O:lines of He+, He0, C2+ Si3+ and other highly-ionized ions of the
lighter elements.
B: He+ disappears after B5. He0 reaches a maximum at B2. 0+, N+ etc. replace the more highly ionized atoms. Lines of H° become more prominent.
A: He0 disappears and the spectrum is dominated by very strong lines of H° which reach their maximum in classes AO to A3. Lines of Ca+, Fe+, Cr+, Ti+, Fe°, Cr° and other neutral and singly-ionized heavier atoms gradually increase in strength through this class.
F: The spectrum is dominated by the many lines of neutral and singly-ionized metals and heavy atoms. The H° lines are much weaker than in class A, but the lines of Ca+ become very strong. G: Lines of neutral metals dominate. The molecular bands of CN
And CH appear.
K: The lines of neutral metals and the molecular bands become even stronger than in class G. Bands of TiO appear about class K5.
M: The TiO bands intensify and many other molecular bands and
lines of neutral metals are present.

No comment has been made so far on the way that the conti¬nuum radiation also varies through the sequence of spectral lasses. The continuum radiation is distributed with wavelength in a way which closely resembles that emitted by a black body at the effective temperature of the star. Thus, the total amount of energy radiated is greatest for the hottest stars, and the hotter a star, the radiation is emitted at shorter wavelengths.

The different ranges of continue us radiation emitted by stare of various temperatures result in their appearing different colours to the eye. Of course, the eye is taking in a mixture; of light at many wavelengths simultaneously, so the sensation of colour depends on how the brain responds to the particular mixture of wavelengths. A fairly uniform mixture of light of all wavelengths gives the sensation of white. Sirius and Vega, both A stars, appear white. Hotter stars such as Spica may look bluish, as there is more blue light than red. The Sun is of spectral class G, arid as all know, is distinctly yellow. Cooler stars, such as Betelgeuse and Antares are very red in colour.

Although the continuous spectra of stars resemble those of black bodies in general, the detailed shape of the curve is altered by the absorption by hydrogen and other atoms. As some 75 per cent of the material of which normal stars are made is hydrogen, it is not surprising that the chief spectral lines in the visible region, the Balmer series, are very prominent in the temperature range that gives rise to favourable physical conditions for hydrogen absorp¬tion. As many as 20 distinct lines in the Balmer series may com¬monly be detectable, but at shorter wavelengths the lines, which are getting closer together, all coalesce. This means that hydrogen is considerably more opaque to light of wavelengths less than about 3(55nm than that of longer wavelength. This results in a sharp reduction in the level of continuum radiation output below 365 nm, a phenomenon called the Balmer discontinuity. The size of the dis¬continuity depends on spectral class, and may be used as a criterion for spectral classification. There are also discontinuities at the limits of the other series of hydrogen lines which lie outside the visible region. Less conspicuous discontinuities occur in the con¬tinuum owing to similar effects caused by other elements less abun¬dant than hydrogen. Figure 2.7 shows graphically the continuous spectra of stars of various types.

The stellar spectra recorded on the surface of the Earth are further modified by the effects of Earth’s atmosphere. Particularly in the infrared and ultraviolet, the atmosphere blocks much of the incident radiation. Observations at ultraviolet and shorter wave¬lengths have to be made outside the atmosphere. As water vapour is one of the chief absorbers in the infrared region, it is possible to make observations at these wavelengths in areas with very dry climates. In practice, it is not difficult to tell which spectral lines have been superposed on the true stellar spectrum by the atmos¬phere as they have a different shape, and usually a different Doppler shift in wavelength.

There are many ways in which the spectral classes of large num¬bers of stars can be determined without the necessity of taking high-dispersion spectrograms. For example, certain photometric indices, such as (B-V). are correlated with spectral class and tem-perature. Alternatively, very low dispersion spectra of a whole field of stars can be obtained at one time by the object! prism technique: a narrow-angle prism placed over the telescope objective disperses each star image sufficiently to show up the chief spectral features

Luminosity classification
The total flux of radiation leaving Unit a star’s surface increases with temperature However, the total energy output of a star also depends on its Slze. A convenient measure of the energy output of a star is its absolute magnitude A graph of absolute magnitude against temperature (or spectral class, which is virtually equivalent to temperature) for a large sample of stars in the solar neighbourhood shows that the Vast majority lie in a narrow band stretching diagonally across -the graph, with only a very few lying below this band. Certainly, the points are very far from being randomly distributed.

Such a graph is an example of a HERTZSPRUNG-RUSSELL (HR) DIAGRAM, named after the astronomers who first conceived this technique. The concentration of points in the narrow band, called the MAIN SEQUENCE is a result of the fact that the effective tem¬perature that a star achieves increases with the mass of material it contains, and so also with size, in a clearly defined manner. Figure 2.11, which shows the HR diagram for the nearest 100 stars, also illustrates the fact that there are far more cool small stars than large hot ones in a sphere of space around the Sun. This suggests that there is probably a preponderance of small stars in the Galaxv as a whole, although as they are intrinsically so faint we can only see the nearby ones. The stars well below the main sequence are the white dwarfs, old stars whose origin is explained

The HR diagram of the 100 brightest stars presents a very dif¬ferent picture, as shown in figure 2.12. This includes intrinsically bright stars from a large volume of space, but only the nearest of intrinsically faint stars. Only the top portion of the main sequence is represented, and there are a considerable number of points lying well above the main sequence. These stars are very much more luminous than main-sequence stars of the same spectral type because of their vastly larger size. This variation in the size and luminosity of stars can be interpreted in terms of the evolution of stars. It is sufficient to mention here that a star spends most of its life using up its hydrogen fuel, and, according to its mass, lies at some point on the main sequence in the HR diagram. Such a star is referred to as a DWARF. When a significant proportion of the hydro¬gen has been consumed and converted into other elements, changes occur in the structure of the star which cause it to expand greatly and move into the GIANT or SUPERGIANT class. Finally it may end up as a WHITE DWARF when all the possible nuclear fuels have been exhausted.

The atmosphere of a giant star is very much more tenuous than that of a dwarf. Table 2.4 indicates the differences in structure between the atmospheres of dwarf and giant stars at 5000 and 10COOK. The much lower densities in the giants’ atmospheres cause subtle differences in the appearance of giant spectra, and so stars of different luminosities can be recognized even if their absolute magnitudes cannot be determined directly.

Spectral classification has been extended to include luminosity classes as well as a temperature class. Morgan and Keenan have developed a system in which the luminosity is represented by a Roman numeral. The correspondence between these actual absolute magnitudes for the different temperature classes is illustrated Supergiants are divided into classes Ia and Ib, giants into classes II and III. Members of class IV called subgiants, and class V is the main sequence. A few slightly sub-luminous stars called subdwarfs are allotted to class VI and white dwarf form class VII .Examples from among the the brightest stars

The temperature classes 0, B. A etc are based on the relative strengths of various spectral lines. As these strengths are also partially determined by the density, the spectral classes do not correspond to precisely the same effective temperature in giants and dwarfs. The effective temperature-spectral class relation¬ships for dwarfs, giants and supergiants

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