General discussion of binaries

For the stars for which angular diameters have been measured we can, of course, determine the radii by multiplying the angular radius by the distance to the star, provided we know the distance. For stars further away than about 20 pc we cannot measure trigonometric parallaxes accurately, we can therefore determine distances only in indirect ways. Star stream parallaxes (see for instance Becker, 1950) have been used to determine the distance to the Hyades cluster, but it turned out that the photometric parallaxes were more accurate. Fortunately, we can also determine radii for stars in special binary systems, namely in eclipsing binaries. For these binaries we can also determine the masses of the stars. We shall therefore devote this section to the discussion of binaries in general, and the next sections to the discussion of the special types of binaries for which stellar radii can be determined, namely eclipsing binaries, and for those binaries for which stellar masses can also be determined, again the eclipsing binaries and also the visual binaries.

We can determine stellar masses for binaries using Kepler's third law. Let us briefly discuss the mechanics of a binary system.

From the solar system we are accustomed to the case that one body, the sun, has a much larger mass than the other bodies, the planets. For binaries with two stars we have to take into account that both bodies have elliptical (or perhaps circular) orbits around their center of gravity S (see Fig. 9.1).

General discussion

We are all accustomed to the fact that our Earth has a magnetic field whose shape comes rather close to that of a dipole field, with the magnetic axis not being very different from the rotational axis of the Earth. This raises the suspicion that the magnetism is due or at least related to the rotation of the Earth. We may therefore wonder whether stars which have much higher rotational velocities than the Earth might have much stronger magnetic fields than the Earth. It seems very interesting to check. The question arises: how can we measure magnetic fields on stars? We clearly cannot take a magnetometer to the star's surface. All we can get from the star is its light. Fortunately, nature has provided an effect of a magnetic field on the light which can be used to measure magnetic fields of stars. This is the Zeeman effect, named after its discoverer.

The Zeeman effect

Zeeman discovered that for a laboratory light source which emits an emission line spectrum in a laboratory magnetic field, the spectral lines generally split into several components. If you observe the light in an arbitrary direction with respect to the direction of the magnetic field, you will, in the simplest case, see a line split into three components, the socalled Lorentz triplet. The central component remains at the original wavelength λ0, which the line had without a magnetic field.

The coordinate system

If we want to study stars, the first thing to look at might be their positions in the sky. This in itself does not tell us much about the nature of the stars, but it is very helpful when we want to find a particular star or a group of stars in the sky. We have to have a reference point with respect to which we can describe the position of the star in which we are interested. We all know or have at least heard about the constellations of stars which in earlier times were extremely helpful in describing the positions of stars with respect to a given star in a particular constellation. We still name the brightest stars according to the constellations in which they are found, but we like to have a more general description of the positions. When looking at the sky we can measure the positions only as projected against the sphere of the sky, i.e., against a two-dimensional surface. We can therefore describe the positions of the stars by two quantities. Since the surface against which we measure the positions is a sphere, we use spherical polar coordinates. Since our telescopes are fixed on the Earth, we use a coordinate system which is fixed with respect to the Earth. The Earth is rotating, but we do not want to have a rotating coordinate system, which would cause many problems.

Color magnitude diagrams of nearby stars

For nearby stars, say within 20 pc, we can determine the distances from trigonometric parallaxes. From the apparent magnitudes and the distances we can calculate the absolute magnitudes, i.e., the magnitudes which the stars would have if they were at a distance of 10 pc. This means that for absolute magnitudes we compare the brightness the star would have if it were at a distance of 10 pc with the actual brightness of Vega at its actual distance, i.e. with its apparent brightness. It turns out to be quite instructive to plot the absolute magnitudes of the stars as a function of their B – V colors. In Fig. 5.1 we do this for the nearby stars. While we might have expected that stars with a given color could have quite different absolute magnitudes, it turns out that this is generally not the case. Most of the stars with a given B – V color have the same absolute magnitude. Most of the stars fall along one line in the color magnitude diagram. This line is called the main sequence. The intrinsic brightnesses and the colors of these stars are obviously determined by just one parameter, since they follow a one-dimensional sequence. It turns out, as we shall see in Volume 3, that this one parameter is the mass of the star.

Supernovae

Classification of novae and supernovae

The ancient astronomers had already noted that sometimes new stars became visible in the sky and after some time disappeared again. In the Middle Ages the astronomers called these stars novae, which is the Latin word for new stars. Some of these new stars were exceedingly bright, and were later called supernovae. Three of these supernovae were observed in historic times: Tycho de Brahe's supernova, which occurred in the year 1572, Kepler's supernova which became very bright in the year 1604, and a supernova which was observed by Chinese astronomers in the year 1054. At the location of the Chinese supernova we now see the Crab nebula in the constellation of Taurus. The nebula got its name from its appearance which reminds us of a crab. The Crab nebula still expands with velocities of about 1400 km s−1, showing that a truly gigantic explosion must have occurred 900 years ago.

What are these novae and supernovae? How often do they occur? What kinds of objects are their progenitors? What leads to such gigantic explosions? What distinguishes novae and supernovae? Are all supernovae similar events or do we have to distinguish different kinds of novae or supernovae? These are questions for which we would like to find the answers.

Both novae and supernovae are objects which suddenly increase their light output by many orders of magnitude.

General discussion

In the previous sections we have discussed stars which are generally considered to be normal stars, which means their spectra fit into the two-dimensional classification scheme according to spectral type and luminosity. True, the weak-lined stars, or population II stars, do not fit into that scheme, but generally their peculiarity can be understood by the change of just one parameter, the ratio of the metal abundance to the hydrogen abundance, though recently it has been found that this may not always be the case. More than one parameter may actually be necessary to describe the abundances of the heavy elements. The population II stars are still generally considered to be ‘normal’ stars because we believe that all their peculiarities can apparently be traced back to different chemical abundances. For the stars we are going to discuss in this chapter, this does not seem to be the case. There are, of course, a large number of different kinds of peculiar stars, but we are not able to discuss all of them in the framework of this introduction to stellar astrophysics. We shall only discuss the most frequent kinds of peculiar stars and those which are of special interest in the framework of understanding stellar structure and evolution.

Peculiar A stars, or magnetic stars

The observations

In the previous section we saw that some stars with very strong magnetic fields are found among the early A stars.

Introduction

Probably the most radical advance in X-ray instrumentation in the past five years has been the development of the single photon calorimeter, in which X-rays are detected via the temperature pulses they induce in a small (< 1 mm3) absorber, cooled to a fraction of a degree kelvin.

The detection of individual 5.9 keV X-rays (fig. 6.1) was first demonstrated by groups at NASA's Goddard Space Flight Center (GSFC) and the University of Wisconsin in 1984, using a silicon microcalorimeter operating at 0.3 K (McCammon et al, 1984). This work was specifically directed towards the production of a high-efficiency, non-dispersive focal plane spectrometer with energy resolution comparable to that of a Bragg crystal. It can, however, still be seen as the culmination of several decades’ research in fields other than X-ray astronomy, originally in nuclear physics and latterly in infrared astronomy. Andersen (1986) and Coron et al (1985a) trace calorimeter development back as far as 1903, and the radioactivity studies of Pierre Curie. They record how, by the mid-1970s, the sensitivity (in detectable watts) of IR bolometers operating at liquid helium temperatures, where heat capacities are very low, had reached the point where Niinikoski and Udo (1974) could identify the extraneous spikes seen in the output of balloon-borne bolometers with local heating produced by the passage of cosmic rays. Niinikoski and Udo appear to have been the first to suggest that it might be possible to thermally detect single photons or particles, rather than continuous fluxes.