The absorption-line spectra of stars allow astronomers to deduce the relative proportions or the ABUNDANCES of the various chemical elements in the stellar atmospheric layers where the absorption lines are formed. If the physical conditions in a stellar atmosphere can be discovered, then their effect on the appearance of the spec-trum lines of an element can be calculated and eliminated. The re¬maining factor is then the abundance of the element. Of course, the process of finding the abundances is only possible for elements that actually have lines visible, and it cannot tell us the composition of the star’s interior.

Many stellar spectra are still taken in the traditional way on photographic plates, but the use of direct photoelectric methods, in which the spectrum is produced as a graph of intensity against wavelength, is increasing. Photographic spectrograms have to be converted into intensity graphs, via a special instrument called a microphotometer. part of such an intensity trac¬ing. On the original photographic spectrograms, a DISPERSION (wavelength per unit length of the final spectrum) between 1 and 0.1 mm wavelength per rim of plate is considered desirable in order to resolve the spectral features as well as possible. Spectra are widened at right angles to the spread of lines by trailing the star image back and forth across the entrance slit of the spectrograph because a wide spectrum improves the meaningful signal, relative to the noise, in the final tracing. However, the wider the spectrum and the higher the dispersion, the more the starlight is being spread out over the photographic plate and the longer the exposure that is required. Even with very large telescopes only stars visible to the naked eye are bright enough for investigation at high dispersion, and astronomers have to be content with poorer quality data for the fainter stars.

The absorption lines appear as inverted bell-shaped the level of the continuous spectrum. The actual shape of a spectral line is called the LINE PROFILE. However, more often than not, especially when the lines are narrow, the recorded profile » partly a result of instrumental factors, rather than a true record of the light leaving the star. What is much less affected is the total absorption caused by each line. The quantity measured is called the EQUIVALENT WIDTH. The definition of equivalent width is illustrated m figure 2.15. Essentially it is the width (in units of wavelength) that the line would have if the absorption-line profile were a completely black rectangle. When the profiles of spectrum lines can be obtained accurately, they provide valuable additional information. The profiles of the hydrogen lines, for example, are particularly useful in determining the stellar temperature and luminosity.

The spectral lines from stars are not especially sharp, chiefly because the atoms responsible for the absorption are in random motion. The hotter the star, the more energy of motion the atoms possess; thus the Doppler effect spreads the absorption in a given line over a corresponding larger range of wavelengths. Stellar lines are usually rather broader than might be expected, and this extra width is thought to be due to small-scale motions (up to 5 knur1) of the gas as a whole, called MICROTURBULENCE. In giant and super-giant stars, the lines are often broadened in a way that indicates much larger-scale motion, that has come to be called MACROTURBULENCE (up to 50kms-1). There are other reasons why spectral lines are broadened: for example, collisions between atoms that particularly affect the line further from the line centre. A very strong line has much of its absorption in broad wings far from the line centre

The effect on the profile of a spectral line of in¬creasing the number of atoms that are effective at absorbing. Figure 2.18 shows the corresponding changes in the equivalent width, in a curve called the CURVE OF GROWTH. Now, in any one star, it is not possible to change the strength of one spectrum line, and so get the curve of growth experimentally. But if we assume that all the lines of one ion have similar curves of growth, then it is possible to construct the curve of growth for any given ion from the equivalent widths of several different lines of that ion. One problem encountered is that not all spectral lines have the same intrinsic strengths, so these latter have to be found experimentally in a laboratory or calculated. It is these quantities, properly weighted to account for the temperature effects, that are plotted on the hori¬zontal axis. Then the number of absorbing atoms (i.e. the abun¬dance) can be deduced from the relative position of the curve of growth along the horizontal axis.

The curve of growth method in its simplest form assumes that the stellar atmosphere can be represented by single values of tempera¬ture, pressure and so forth, but this is far from the truth. For¬tunately, powerful computers make it possible to simulate stellar atmospheres by mathematical models which take account of the different physical conditions in different layers. Using these models, astrophysicists predict the appearance of spectra for trial values of the abundances of the elements and choose the ones that best fit the observations of a particular star. Results from this more sophisticated method have, however, largely vindicated the use of the curve of growth, which has the advantage of simplicity even if it does lack elegance!

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