Among the most extensive applications of atomic physics in astronomy is the precise computation of transfer of radiation from a source through matter. The physical problem depends in part on the bulk temperature and density of the medium through which radiation is propagating. Whether the medium is relatively transparent or opaque (‘thin’ or ‘thick’) depends not only on the temperature and the density, but also on the atomic constituents of matter interacting with the incident radiation via absorption, emission and scattering of radiation by particular atomic species in the media. Since optical lines in the visible range of the spectrum are most commonly observed, the degree of transparency or opaqueness of matter is referred to as optically thin or optically thick. However, it must be borne in mind that in general we need to ascertain radiative transfer in all wavelength ranges, not just the optical. Macroscopically, we refer to optical thickness of a whole medium, such as a stellar atmosphere. But often one may observe a particular line and attempt to ascertain whether it is optically thick or thin in traversing the entire medium.

Radiative transfer and atomic physics underpin quantitative spectroscopy. But together they assume different levels of complexity when applied to practical astrophysical situations. Significantly different treatments are adopted in models for various astrophysical media. At low densities, prevalent in the interstellar medium (ISM) or nebulae, ne <; 106 cm-3, the plasma is generally optically thin (except for some strong lines, such as the Lyα, that do saturate), and consideration of detailed radiative transfer effects is not necessary.

This text is aimed at students and researchers in both astronomy and physics. Spectroscopy links the two disciplines; one as the point of application and the other as the basis. However, it is not only students but also advanced researchers engaged in astronomical observations and analysis who often find themselves rather at a loss to interpret the vast array of spectral information that routinely confronts them. It is not readily feasible to reach all the way back into the fundamentals of spectroscopy, while one is involved in detailed and painstaking analysis of an individual spectrum of a given astrophysical object. At the same time (and from the other end of the spectrum, so to speak) physics graduate students are not often exposed to basic astronomy and astrophysics at a level that they are quite capable of understanding, and, indeed, that they may contribute to if so enabled.

Therefore, we feel the need for a textbook that lays out steps that link the mature field of atomic physics, established and developed for well over a century, to the latest areas of research in astronomy. The challenge is recurring and persistent: high-resolution observations made with great effort and cost require high-precision analytical tools, verified and validated theoretically and experimentally.

Historically, the flow of information has been both ways: astrophysics played a leading role in the development of atomic physics, and as one of the first great applications of quantum physics.

An elaborate radiative transfer treatment (Chapter 9) is necessary for stellar atmospheres through which radiation escapes the star. But that, in a manner of speaking, is only the visible ‘skin’ of the star, with the remainder of the body opaque to the observer. Radiation transport throughout most of the star is therefore fundamentally different from that through the stellar atmosphere. Since radiation is essentially trapped locally, quite different methods need to be employed to determine the opacity in the interior of the star. However, since there is net outward propagation of radiation from the interior to the surface, it must depend on the variation of temperature and pressure with radius, as in Fig. 10.5.

Perhaps nowhere else is the application of large-scale quantum mechanics to astronomy more valuable than in the computation of astrophysical opacities. Whereas the primary problem to be solved is radiation transport in stellar models, the opacities and atomic parameters needed to calculate them are applicable to a wide variety of problems. One interesting example is that of abundances of elements in stars, including the Sun. Observationally, the composition of the star is inferred from spectral measurements of the atmospheres of stars, i.e. surface abundances, because most of the interior of the star is not amenable to direct observation. However, radiative forces acting on certain elements may affect surface abundances that may be considered abnormal in some stars.

Spectral formation depends on a variety of intrinsic atom–photon interactions. In addition, external physical conditions, such as temperature, density and abundances of elements determine the observed spectrum. As described in later chapters, spectral analysis is therefore often complicated and it is difficult to ascertain physical effects individually (and even more so collectively). The main aim of this chapter is to provide a unified picture of basic atomic processes that are naturally inter-related, and may be so considered using state-of-the-art methods in atomic physics. A quantum mechanical treatment needs to take the relevant factors into account. An understanding of these is essential, in order to decide the range and validity of various theoretical approximations employed, and the interpretation of astrophysical observations. From a practical standpoint, it is necessary to determine when and to what extent a given effect or process will affect spectral lines under expected or specified physical conditions.

For example, at low temperatures and densities we may expect only the low-lying atomic levels to be excited, which often give rise to infrared (IR) and optical forbidden emission lines. But the presence of a background ultraviolet (UV) radiation field from massive young stars in star-forming regions of molecular clouds (e.g., the Orion Nebula discussed in Chapter 12), may excite low-lying levels via UV absorption to higher levels and subsequent radiative cascade of emission lines that would appear not only in the UV but also contribute to the intensities of the IR/optical lines.

Stars exist in great variety. They are among the most stable, as well as occasionally the most unstable, objects in the Universe. While extremely massive stars have short but very active lifetimes of only millions of years after birth, the oldest stars have estimated ages of up to 14 billion years at the present epoch, not much shorter (though it must be) than the estimated age of the Universe obtained by other means, such as the cosmological Hubble expansion. In fact, the estimates of the age of the Universe are thereby constrained, since the Universe cannot be younger than the derived age of the oldest stars – an obvious impossibility. Stellar ages are estimated using well-understood stellar astrophysics. On the other hand, variations in the rate of Hubble expansion may depend on the observed matter density in the Universe, the gravitational ‘deceleration parameter’, the ‘cosmological constant’, ‘dark’ (unobserved) matter and energy, and other exotic and poorly understood entities. Needless to say, this is an interesting and rather controversial area of research, and is further discussed in Chapter 14.

But stars are the most basic astronomical objects, and astronomers are confident that stellar physics is well-understood. This confidence is grounded in over a century of detailed study of stars, with the Sun as the obvious prototype. Most of this knowledge is derived from spectroscopy which, in turn, yields a wealth of information on nearly every aspect of stellar astrophysics; stellar luminosities, colours, temperatures, sizes, ages, composition, etc.

Atomic astrophysics and spectroscopy

Spectroscopy is the science of light–matter interaction. It is one of the most powerful scientific tools for studying nature. Spectroscopy is dependent on, and therefore reveals, the inherent as well as the extrinsic properties of matter. Confining ourselves to the present context, it forms the link that connects astronomy with fundamental physics at atomic and molecular levels. In the broadest sense, spectroscopy explains all that we see. It underlies vision itself, such as the distinction between colours. It enables the study of matter and light through the wavelengths of radiation (‘colours’) emitted or absorbed uniquely by each element. Atomic astrophysics is atomic physics and plasma physics applied to astronomy, and it underpins astrophysical spectroscopy. Historically, astrophysical spectroscopy is older than modern astrophysics itself. One may recall Newton's experiments in the seventeenth century on the dispersion of sunlight by a prism into the natural rainbow colours as an identification of the visible band of radiation. More specifically, we may trace the beginning of astrophysical spectroscopy in the early nineteenth century to the discovery of dark lines in the solar spectrum by Wollaston in 1802 and Fraunhofer in 1815. The dark lines at discrete wavelengths arise from removal or absorption of energy by atoms or ions in the solar atmosphere. Fraunhofer observed hundreds of such features that we now associate with several constituent elements in the Sun, such as the sodium D lines.

In ionized plasmas spectral formation is due to particle collisions or radiative excitations. In astrophysical situations there is usually a primary energy source, such as nuclear reactions in a stellar core, illumination of a molecular cloud by a hot star or accretion processes around a black hole. The ambient energy is transferred to the kinetic energy of the particles, which may interact in myriad ways, not all of which are related to spectroscopy.

Electron collisions with ions may result in excitation or ionization. The former process is excitation of an electron into discrete levels of an ion, while the latter is excitation into the continuum, or ionization, as shown in Fig. 3.1 and discussed in Chapter 3. A practically complete description of the (e + ion) excitation process requires collisional information on the ions present from an observed astrophysical source, and for all levels participating in spectral transitions. As the excitation energy from the ground state to the higher levels increases, the ionization energy EI is approached. The negative binding energy of the excited states increases roughly as E ~ –z2/n2, where z is the ion charge. As n → ∞, E → 0, i.e., the electron becomes free.

At first sight, therefore, it might seem like a very large number of levels need to be considered for a given atomic system in order to interpret its spectrum completely.

The origin of spectral lines depends on the matter and radiation fields that characterize the physical conditions in the source. However, the lines actually observed also depend on the intervening medium towards the observer. The wide variety of astrophysical sources span all possible conditions, and their study requires both appropriate modelling and necessary atomic parameters. The models must describe the extremes of temperature, density and radiation encountered in various sources, from very low densities and temperatures in interstellar and intergalactic media, to the opposite extremes in stellar interiors and other environments. As such, no single approximation can deal with the necessary physics under all conditions. Different methods have therefore been developed to describe spectral formation according to the particular object, and the range of physical conditions under consideration.

This is the first chapter devoted mainly to astrophysical applications. The theoretical formulation of atomic spectroscopy described hitherto is now applied to the analysis of emission-line observations in three widely disparate regions of the electromagnetic spectrum: the visible, X-ray and far-IR. Examples include some of the most well-known and widely used lines and line ratios. Emission line analysis depends on accurate calculations of emissivities, which, in turn, are derived from fundamental parameters such as collision strengths for (e + ion) excitation and recombination, and radiative transition probabilities. However, spectral models in complicated situations, such as line formation in transient plasmas and in the presence of external radiation fields, assume a level of complexity that requires consideration of a variety of processes and parameters.

Which atoms were formed first, in what proportion and when? The relationship between atomic spectroscopy and cosmology rests on the answer to these questions. According to big bang nucleosynthesis (BBN), before the creation of the first atoms, the Universe would have been filled with a highly dense ensemble of nuclei, free electrons, and radiation. The standard model from high-energy particle physics implies that most observable matter is made of baryons, such as protons and neutrons; electrons are leptons and much less massive. The baryons are themselves made of more exotic fundamental particles, such as quarks, gluons and so forth. According to the BBN theory, given a fixed baryon-to-photon ratio in the first three minutes of origin, a few primordial nuclear species made of baryons appeared. The atomic nuclei created during the BBN were predominantly protons and helium nuclei (2He3, 2He4), with very small trace amounts of deuterium (heavy hydrogen 2H1) and lithium (3Li6, 3Li7). Atomic physics then determines that singly ionized helium He II (not hydrogen!) would have been the first atoms(ions) formed.

The process of formation is (e + ion) recombination: He III + e → He II + hν. This temporal marker in the history of the Universe is referred to as the recombination epoch. The reason that He II was the first atomic species is not difficult to see, given the extremely hot plasma that preceded the recombination epoch when nuclei and electrons were free in the fully ionized state.

Ionized hydrogen or H II regions and gaseous nebulae are generally low-density objects that appear as extended and diffuse clouds. Typical electron temperatures are of the order of 104 K, or ~ 1 eV, and densities are between 102 and 106 cm-3. But ionizing sources of H II regions in general are quite diverse. Among the most common variety are those found in giant molecular clouds photoionized by newly formed hot stars with sufficient UV flux to ionize hydrogen and several other elements to low ionization states. Similar H II regions are commonplace in astronomy, as part of otherwise unrelated objects, such as active galactic nuclei (Chapter 13) and supernova remnants. Such regions are also easily observable, since they are largely optically thin. Furthermore, a number of nebular ions are commonly observed from a variety of gaseous objects. In fact, in Chapter 8 we had developed the spectral diagnostics of optical emission lines, as observed from the Crab nebula in Fig. 8.3. That nebula is the remnant of a supernova explosion, in the constellation of Taurus, witnessed in AD 1054 by Arab and Chinese astronomers. The central object is a fast spinning neutron star – pulsar – energizing the surrounding nebula. Nebular spectroscopy therefore forms the basis of most spectral analysis in astrophysics.

We describe the essentials of nebular astrophysics with emphasis on spectroscopic analysis, and address the pervasive problem of atomic data sources of varying accuracy.