White dwarfs

Objects lying five or more magnitudes below the main sequence are called ‘white dwarfs’.

The name was attributed to them because the spectrum of the first star analysed, 40 Eri B (Adams 1914), was of type A and the star white, whereas dwarfs were thought to be all of type M and therefore red. So the term calls attention to the inconsistency between the color or spectral type and the luminosity (or absolute magnitude) of the star. Since, however, the stars are neither white nor dwarfs, it would be more logical to call them ‘degenerates’ (D) because of the equation of state of the matter composing them. We shall use the latter term.

Detection methods. Degenerates, being intrinsically faint, are difficult to single out among the large number of faint stars. (Let us remember that there are about 2 × 107 stars brighter than B = 15.) Detection methods are thus of fundamental importance. Essentially three methods have been used to isolate candidates. The first is to search for nearby stars through their proper motion, and retain those which are blue. The second is to search spectroscopically for blue stars where no intrinsically bright stars are expected. The third is to search for faint companions to brighter nearby stars.

The first method was proposed and exploited by Luyten, from 1931 on. From an examination of about 108 star images on plates taken at different epochs, Luyten selected those stars whose proper motion is larger than a given amount (for instance 17″).

Normal stars

An O-type spectrum is characterized by the simultaneous presence of lines of neutral and ionized helium. If ionized helium is absent, the spectrum corresponds to a B-type. The lines of ionized helium strengthen toward earlier stars, whereas neutral helium lines and hydrogen lines decline toward earlier types. Table 8.1, taken from Conti (1973), illustrates this by way of the equivalent widths of some of the stronger lines.

Because of this antagonistic behavior of He ii and He i, we can use them for classification. The MK system uses the ratio He ii λ4541/He i λ4471 as the criterion for spectral type for the interval 03–09 (for an illustration, see figure 8.1). The He ii lines are grouped in the so-called Pickering series (analogous to the Bracket series of hydrogen) with lines at λλ5414,4850,4542,4339,4200,4100, 4025 and 3968,…, and the Fowler series (analogous to the Paschen series of hydrogen) with lines at λλ4656,3204,…

Besides helium, some other elements are also present in O-type spectra. Among these we have Si iv(λ4089) and C iii(λλ4068,4647 and 4651) in late O-type stars. N iii(λλ4634,4640) if present is only seen in emission.

In these stars emission lines are very often present and can appear with varying degrees of intensity, from barely perceptible to rather strong, although they are never as broad and intense as in Wolf–Rayet stars. They can appear in different objects as a weak central emission on a wider absorption, or as a complete fill-in, or as a moderately strong emission.

Normal stars

The spectra of stars of class M are characterized by strong absorption bands of TiO, and by the great number and strength of metallic lines which practically block the spectrum for λ < 4000 Å.

In the Harvard system four subdivisions of M-type stars were kept: Ma, Mb, Mc and Md. The Mt Wilson observers replaced these types by the decimal subdivisions M0, 1,…, 6 in which Ma corresponds to M0–M2, Mb to M3–M5, and Mc to M5 and later. The last group, Md, is characterized by variable emission lines, so that any Md object should be denoted Mxe, x standing for the decimal subtype and e for emission. The Mt Wilson system uses mainly the intensities of the TiO bands for classification and this is also done in the Yerkes system. The reason is that the bands strengthen so rapidly with advancing type that it becomes difficult to find stretches of continuum where atomic lines can be compared reliably, except for the earlier subtypes. The most important TiO bands are listed in table 14.1.

The first bands which appear in the yellow and red are λ5167 and λ7054, and λ4954 in the blue at M0. After M2 many others can be seen; the ones especially useful are marked with an asterisk in table 14.1.

Taxonomy, according to the dictionary, is the classification of objects into ordered categories. All natural sciences – botany, zoology, geology – classify the objects of their study: in a certain sense, taxonomy is the backbone of everything else.

The classification can be done on the basis of a single observable property of the objects, or a combination of properties. For instance, Linnaeus used plants' flowers for his botanical classification system, but modern authors use a variety of plant characteristics. In astronomy, the main difficulty consists in that the objects are far away and we can study certain properties only for a rather small number of objects. Whereas for a plant, an animal or a rock we can search leisurely for those parameters which are best for classification purposes, and then measure the parameters in all plants of a certain type, such an operation is impossible in astronomy. In fact the astronomer must use those parameters which are available for a large number of stars, even if they might turn out not to be the best for classification. Stellar parameters that can be estimated or measured are temperature, color, spectral type, proper motion, radial velocity, radius, magnetic field, rotational velocity, chemical composition and so on. It is obvious that one essential condition for classification is that the parameter used should be known for a large number of objects. Table 1.1 summarizes for how many stars these parameters are known; the numbers are taken from compilations existing at the Centre de Données Stellaires (CDS).

The purpose of this book is to provide an outline of the methods and the results of classification. Classification is one of the fundamental branches of astronomy, in the same way as astrometry is. Classification is used whenever we need to order a large number of objects, or a variety of phenomena. Classification methods appeared in astronomy in the nineteenth century when a large number of stellar spectra suddenly became available, through two technical developments – the objective prism and the photographic plate.

Because the number of spectra was so large, it was impractical to study each of them in detail and later to generalize the similarities found between them. In fact, classification takes just the opposite approach: first groups of similar members are formed from the N individuals, and then typical members of each group are studied in detail. Since the members of a group are similar, the conclusions of the detailed study of typical objects can then be applied to all group members. By replacing a large number of individual stars by a much smaller number of groups and typical objects, a significant economy of work is achieved.

Classification methods use observational data, like objective prism spectra, with minimal interpretation. This stems from the fact that large amounts of data are used, let us say several thousand spectra; if the data were interpreted in a elaborate way, one would be performing analysis and not classification.

Spectral classification started in the second half of the nineteenth century and has had a long and interesting development, which is detailed by Curtiss (1932), Fehrenbach (1958) and Seitter (1968). Instead of following the historical developments in their complicated interactions, we shall study in detail only two classification systems, because they synthetize the developments. These two systems are the Harvard and Yerkes systems. In the last section of this chapter we shall consider briefly classifications at higher plate factors.

The Harvard system

The material for this system consists of objective prism spectra of a large number of stars. Regrettably not all spectra were obtained with the same cameras and/or objective prisms, and this produced some undesirable consequences. In particular, brighter stars were observed with lower plate factors than fainter ones, the latter having a total length of 2.2 mm between Hβ and Hε. For stars of intermediate brightness this length was 5.6 mm and for the brightest stars up to 80 mm. However, all spectra were widened considerably to more than 2 mm.

The Harvard scheme divided the spectra into classes symbolized by capital letters, arranged in alphabetic order. Class A was described as ‘only the hydrogen series and generally K are visible’. In class B the lines of class A were supplemented with λ4026 and λ4471 of He i. Class C was the class of stars of types A and B but with Hδ and Hγ observed as double lines.

This chapter describes spectral classification in general, without referring to a particular classification system.

We start by discussing certain specifications of the spectroscopic material. Then we describe the features of the spectra and the factors which may affect them. Next we consider the process of classification itself and finally we deal with certain aids to classification.

The material of spectral classification

A spectrum is the display of stellar radiation as a function of wavelength. The names of the different wavelength regions are given in table 2.1. Astronomers also talk of the ‘ultraviolet spectrum’ of a star; this is a short way of speaking of the ‘ultraviolet region of the spectrum’ of the star.

Once a spectrum has been obtained, certain details about it must be provided. In first place, what and how it was observed must be specified. Among the most important specifications is the wavelength range covered. Note that one should specify what the (usable) spectrum region is, rather than state that ‘103aO plates used’ because in a few years this will not be understandable. Next the plate factor (D) should be specified, which is the number of angstroms of the spectrum entering 1 mm length of receiver. Much confusion originates here because astronomers call D the ‘dispersion’, whereas opticians call it (correctly) the ‘reciprocal dispersion’. A small plate factor D implies highly dispersed spectra (i.e. large scale), and a large value of D, low dispersion spectra.

The second part of this book is devoted to the description of the different groups of stars which have been defined over the years. We shall start with the hottest stars and work toward the cooler ones, each chapter dealing with one type of object. The material is arranged broadly into ‘families’ (chapters), so that stars which are similar appear together.

Stars with peculiar spectra are dealt with in sections added to the relevant chapter. Since many groups are not limited to one spectral class, the place of a given group in the book is usually the one corresponding to the first appearance of the group. So, for example, Am stars are discussed in section 10.1 of the A-type stars, despite the fact that some Am stars are found among F-type objects.

As far as possible, each chapter has the following structure. First, we define each group, taking in as much history as we need, but without trying to write the whole history of the group. Then we describe the spectrum of the type of star, usually in the classical region, but, if information exists, also in the ultraviolet, infrared and radio regions. Rotation is also included here. Next we examine what photometry can tell us about the group; then we consider the absolute magnitude, whether any of the group are binaries and finally statistical properties like presence in clusters, distribution on the sky and the frequency of the stars of the group.

In this chapter we shall study two photometric systems in order to show in detail some of the uses of a photometric system. We have chosen the UBV and the uvby or Strömgren system. For other photometric systems the reader is advised to consult Golay (1974) or Straizys (1977).

The UBV system

The UBV system was developed in the fifties by Johnson (see Johnson and Morgan 1953) for the photometric study of stars classified in the Yerkes system.

It uses three wide passbands, each about a thousand angstroms wide, called U (ultraviolet), B (blue), and V (visual), with λ0 around λ3500, λ4300 and λ5500 respectively. The choice of the passbands was made in part for historical reasons. V corresponds approximately to the ‘visual magnitudes’ handed down essentially from Ptolemy. B corresponds on the average to the ‘photographic magnitudes’ of the end of the nineteenth century. Finally U was chosen so as to get as much ultraviolet light as possible. The functions S(λ) are tabulated in table 5.1, but readers should be warned that different authors use slightly different S(λ). The system is thus not suited for very high precision. Furthermore the S(λ) of the U color goes down to λ3000, whereas the atmosphere usually cuts off the spectrum below λ3300. The ultraviolet limit of the U band is therefore not fixed by the filter system, but differs from place to place (for instance with the elevation of the observatory) and sometimes from night to night.

Introduction

Proof of the existence of interstellar gas was first provided by observations of narrow absorption lines in the visible spectra of distant stars. In 1904, J. Hartmann identified lines of Ca II that did not share the periodic variations in Doppler shift exhibited by the principal stellar absorption lines in a spectroscopic binary star, and attributed these ‘stationary lines’ to foreground material outside the stellar system. Somewhat more than three decades later, the first interstellar molecules, CH, CH+, and CN, were discovered in similar ways. There is a similarly long history of related investigations in laboratory spectroscopy and in theoretical interpretation.

The interstellar absorption lines tend to be very narrow compared with the photospheric absorption features in the spectra of the hot stars used as background light sources. In terms of line broadening by thermal motions and frequent atomic collisions, this suggests low densities and low temperatures for the absorbing material. In most cases, the observed lines arise only in the lowest states of atoms and molecules, indicating also that the densities and temperatures are too low to maintain significant excited state populations. As we will see, it is possible to infer from such observations quite a lot of information about element abundances, temperatures, densities, cosmic-ray fluxes, and intensities of radiation inside particular clouds.

The term ‘diffuse interstellar cloud’ has no precise denotation and distinctions between different kinds of interstellar clouds – e.g., diffuse, dark, and giant molecular – are somewhat poorly defined.

Discovery

In Ptolemy's Almagest, six objects are listed as ‘stella nebulosa’, hazy, luminous spots on the Celestial Sphere. Once viewed telescopically, these six objects were resolved into clusters of stars; however, other nebulous objects were noticed. The first, in Orion, appears to have been discovered by Fabri de Peiresc in 1610. Two years later, Simon Marius noted a nebula in Andromeda that had also been recorded by Al Sufi in the tenth century. The discoveries continued and, in 1781, Charles Messier compiled a list of nebulae and star clusters. The 105 objects he catalogued are still identified by their Messier number; the Orion Nebula is M42 while the Andromeda Nebula is M31.

An all-sky survey carried out by the Herschels at the turn of the nineteenth century resulted in a General Catalogue containing over 5000 nebulous objects. In 1888 a New General Catalogue was published by J. L. E. Dreyer; later editions included Index Catalogues and tabulated more than 13000 objects. The Orion Nebula, M42, is also identified as NGC 1976; the Andromeda Nebula, M31, is NGC 224.

About the middle of the nineteenth century, Lord Rosse constructed a sixfoot reflector in Ireland with which he made numerous visual sketches of nebulae and applied names to them by which they are still referred. M97 (NGC 3587) is called the ‘Owl’, while M51 (NGC 5194) is known as the ‘Whirlpool’, indicative of its spiral form.

During the initial discovery period of nebulae, a debate was ongoing as to whether or not all nebulae could be resolved into stars if a telescope of sufficient light-gathering power and resolution were available.

Introduction

Stellar spectra differ widely. Lines of atomic hydrogen are strong in the spectrum of the bright star Sirius, relatively weak in the solar spectrum, while lines of iron and other metals are strong in the solar spectrum, weak or absent in the spectrum of Sirius. Do such differences in the relative strengths of spectral lines reflect differences in relative abundances? Can we conclude that the atmosphere of Sirius is made up largely of hydrogen while the solar atmosphere consists largely of metal atoms?

Since the early 1920s astronomers have understood that the most conspicuous differences between stellar spectra arise from differences in the temperature of the atmospheric layers where the spectral lines are formed, rather than from differences in the relative abundances of the chemical elements. To absorb light at the frequency of one of the Balmer lines, a hydrogen atom must be in its first excited state. The fraction of hydrogen atoms in this state depends on the temperature (and, much more weakly, on the pressure). At the temperature of the solar photosphere (the visible layer of the Sun's atmosphere), nearly all of the hydrogen atoms are in the ground state, where they can absorb lines of the ultraviolet Lyman series. The spectrum of Sirius is formed at a temperature of around 10000 K. A much larger (though still numerically small) fraction of the hydrogen atoms is in the first excited state at this temperature. At still higher temperatures hydrogen is almost fully ionized, so the relative population of the first excited state is again very low.

Introduction

The solar corona is the most thoroughly explored example of a hot, dilute, extended stellar atmosphere. Because we are so near the Sun, we can resolve and observe individual structures. Using atomic physics, we can develop and test spectroscopic methods and apply them to construct coronal models that accurately represent the run of temperature, density, and velocity.

The solar corona turns out to be a fascinating astrophysical environment. Beyond its own intrinsic interest, it is also important because it is typical of many other stellar atmospheres. X-ray detectors aboard the HEAO-2 satellite (‘Einstein’) have revealed soft X-ray emission from stars of every spectral type and luminosity class. Thus, the diagnostic techniques developed with solar observations may help us to understand the nature of stellar coronae in general.

Despite our advantage of being near the Sun, we have as yet very incomplete ideas about some of the basic coronal processes. For example, we are not yet certain how the corona is heated, or how it replenishes the material it loses to the solar wind. Better observations and improved diagnostic techniques will help us to answer these large questions.

In this chapter, I will focus on the spectroscopic diagnostic techniques that have been devised for the study of the solar corona (and which are applicable, in principle, to other coronae) and mention some of the results that have come to light. After briefly discussing monochromatic imaging of the corona, I will consider how coronal temperature density, velocity and magnetic field have been measured by spectroscopic techniques.

Introduction

The neutral interstellar gas in the Milky Way is largely confined to the galactic plane with a density stratification away from the plane that is approximately given by n(HI)≈n(HI)0e-|z|/h, with n(HI)0≈1.2 atoms cm-3 and h≈0.12 kpc. However, this simple exponential distribution does not adequately describe a very extended and highly ionized component of the interstellar gas that is commonly referred to as galactic halo gas or galactic corona gas. The density stratification of the halo gas is very uncertain but may have a scale height that exceeds by a factor of 30 that of the neutral disk gas.

The observational study of galactic halo gas is a very young field – the youngest of those subjects included in this volume. That a hot (104–106 K) and extended (z ≈10–30 kpc) gaseous halo surrounds the Milky Way was suggested by Shklovsky (1952) based on measurements of non-thermal radio emission from the galaxy and by Spitzer (1956) based on the apparent stability of high-latitude interstellar clouds. Spitzer noted that stars at z distances exceeding 0.5 kpc more frequently exhibit high velocity interstellar Ca II optical absorption lines than do stars at smaller z. He concluded that an appreciable fraction of the high-velocity clouds producing these absorption features must exist more than 0.5 kpc from the plane. The basic problem associated with a cloud at z > 0.5 kpc is its instability to outward expansion unless the cloud is in near pressure equilibrium with an external medium. The external medium was postulated to be a high-temperature low-density gas – the galactic corona.