We summarize the results of recent quantum mechanical calculations of cross sections and rate coefficients for the rovibrational excitation of H2 and HD by the principal perturbers, H, He, and H2. These results have been used to evaluate the rate of cooling of astrophysical media by H2 and HD molecules; these calculations are also described. The cooling of the primordial gas by rotational transitions of H2 is considered as a special case.

All the numerical results and related software are available from http://ccp7.dur.ac.uk/.

Introduction

Molecular hydrogen is recognized as a major contributor to the cooling of astrophysical media. Its role is all the more significant under conditions, such as those which prevailed in the primordial gas, where few other coolants were present; but H2 is also an important, sometimes the dominant coolant of low density interstellar gas, for kinetic temperatures T > 100 K. Interstellar gas can be heated to such temperatures by shock waves, by the dissipation of turbulence, or by absorbing energy from the local ultraviolet radiation field, as in photon-dominated regions.

Although the elemental abundance of deuterium is approximately 5 orders of magnitude less than that of hydrogen, it turns out that cooling by HD must often be taken into account, essentially for two reasons. First, chemical fractionation can, in media which are only partially molecular, enhance the abundance of HD, relative to that of H2.

We review recent H2 absorption line measurements in the diffuse interstellar medium, using FUV spectra from the Orbiting and Retrievable Far and Extreme Ultraviolet Spectrometer (ORFEUS). We investigate molecular hydrogen gas along lines of sight toward 5 stars in the Magellanic Clouds and toward 3 stars within the Milky Way. Molecular fractions in gas within the Magellanic Clouds are significantly lower than typically found in gas in the Milky Way, most likely caused by the lower dust content. The finding of H2 in a Galactic high-velocity cloud led us to speculate that the high-velocity gas in front of the Magellanic Clouds is part of the Galactic fountain. Sight lines toward the Galactic stars show well defined absorption by molecular hydrogen, deuterium and metals, allowing the study of physical and chemical conditions in the local interstellar gas in great detail.

Introduction

Molecular hydrogen is by far the most abundant molecule in the interstellar medium. Its measurement, however, is difficult: H2 has no permanent dipole moment and no radio emission is seen from H2, in striking contrast to the second most abundant molecule in the ISM, carbon monoxide (CO). For the study of the diffuse interstellar medium the FUV absorption spectroscopy is the only method to obtain information about the molecular hydrogen content, but satellites are required for this method, since the earth's atmosphere is opaque for radiation in the FUV domain.

Molecular hydrogen is a key species for the formation of the first luminous objects in the early universe. It is therefore crucial to understand the various physical processes leading to its formation and destruction and the feedbacks regulating this chemical network. Here we review both the radiative and SN-induced feedbacks and we assess the role of the objects relying on H2 for their collapse in the evolution of the reionization of the universe.

Introduction

At z ≈ 1100 the intergalactic medium (IGM) is expected to recombine and remain neutral until the first sources of ionizing radiation form and reionize it. Until recently, QSOs were thought to be the main source of ionizing photons, but observational constraints suggest the existence of an early population of pregalactic objects (Pop III hereafter) which could have contributed to the reheating, reionization and metal enrichment of the IGM at high redshift. In order to virialize in the potential well of dark matter halos, the gas must have a mass greater than the Jeans mass (Mb > MJ), which, at z ∼ 20 – 30 corresponds to very low virial temperatures (Tvir < 104 K). To have a further collapse and fragmentation of the gas, and to ignite star formation, additional cooling is required. It is well known that in these conditions the only efficient coolant for a plasma of primordial composition, is molecular hydrogen (Abel et al. 1997; Tegmark et al. 1997; Ciardi, Ferrara & Abel 2000 [CFA]).

Molecular hydrogen is formed on interstellar grains by two main processes. In the first, or Langmuir-Hinshelwood, mechanism, hydrogen atoms land on a grain and diffuse over the surface by either tunneling or hopping until they find each other. In the second, or Eley-Rideal, mechanism, hydrogen atoms landing on grains are fixed in position. Reaction occurs only when a gaseous hydrogen atom lands atop an adsorbed one. Based on new experimental results concerning the rate of diffusion of H atoms on interstellar-like surfaces, it is clear that the rate is significantly slower than estimated in the past. The range of temperatures over which diffusive formation of H2 occurs is correspondingly reduced although sites of strong binding can raise the upper temperature limit. The surface formation of molecules heavier than hydrogen is still not well understood.

Introduction

It is almost certain that H2 and a variety of other molecules are formed on the surfaces of low-temperature interstellar dust particles. On these surfaces, binding sites for adsorbates exist interspersed among regions of higher potential. On a grain of typical radius 0.1 µ there are roughly 106 such binding sites, onto which neutral gas-phase molecules stick with high efficiency. The binding energy, or energy required for desorption (ED), depends on the surface and on the adsorbate. For example, the binding energy of H atoms on olivine (a silicate-type material) has just been measured to be 372 K by Katz et al. (1999), who also measured the binding energy of H on amorphous carbon to be 658 K.

We describe the new capability provided by integral field spectroscopy for simultaneously mapping a wide range of shocked emission lines across outflows at high spatial resolution. We have used the MPE-3D near-IR integral field spectrometer on the AAT to carry out a detailed observational study of the physics of shocked H2 and [Fe II] excitation within individual bow shocks. Simultaneous measurement of line ratio variations with position across and along bow shocks will strongly constrain shock models in a number of outflow sources. In Orion, where broad H2 line widths had previously implied magnetically moderated C shocks, our higher resolution echelle observations of the H2 velocity profiles in two of the bullets (Tedds et al. 1999) contradict any steady-state molecular bow shock models. This suggests that instabilities or supersonic turbulence may be important in this case. 3D measurements of the corresponding H2 level populations will address this.

Introduction

The nature of molecular shocks, which play an important role in the processes of momentum and energy transfer within star forming molecular clouds (McKee 1989), is still uncertain (Draine & McKee 1993). In this paper we describe how new developments in integral field spectroscopy provide us with the opportunity to self-consistently distinguish between competing shock models. The Orion molecular cloud is the brightest known source of shocked H2 emission and as such has been the primary test bed for theoretical models.

This contribution summarizes experimental work which has been performed predominantly in our laboratory using ion guides and specific traps for studying ions, molecules and dust particles under astrophysical conditions. After a short reminder of the basics of the technique and a brief discussion of our newest device, the nanoparticle trap, we shall review experimental results for low temperature gas phase collisions with H2. In the last part we will summarize our present activities related to chemistry involving cold H atoms.

Introduction

Despite the fact that our knowledge on the role of hydrogen in space has significantly increased in recent years due to a combination of extensive new observations and astrophysical model calculations with fundamental theory and detailed innovative experiments, there are still many unsolved problems related to the interaction of H or H2 with ions, radicals, surfaces and also photons. The most obvious example is the formation of H2 itself; other examples include specific state-to-state cross sections, ortho-para transitions in H2, H-D isotopic scrambling, formation and destruction of the molecule, or the role of hydrogen clusters and anions. In addition to gas phase reactions we will discuss in this paper our most ambitious goal, the detection of catalytic formation of H2 molecules on an interstellar dust analogue localized in a cold trap.

Experimental: Ion guides and particle traps

Inhomogeneous RF or AC fields

From the point of view of experimental techniques, our research is predominantly based on the use of specific inhomogeneous, time-dependent, electrical fields, E0(r,t) = E0(r) · cos(Ωt).

Introduction

Dipole absorption to excited states of diatomic hydrogen lying above 13.6 eV is not usually considered in the discussion of interstellar photophysical processes. The purpose of this contribution is to provide a brief survey of these states, their structure and decay dynamics, and in particular of the theoretical methods used to describe them.

Above about 14.6 eV excitation energy the density of electronic states of H2 increases dramatically so that above 14.8 eV the spacing of successive electronic states becomes smaller than a vibrational quantum, and at an energy about 0.04 eV below the ionization potential (I.P. = 15.4254 eV) it becomes even smaller than a rotational quantum of energy. This means that the usual Born-Oppenheimer description of molecular structure becomes inadequate: rather than considering the rotational/vibrational motion of the nuclei as being slow and determined by the average field of the rapidly moving electrons, one must also take account of the opposite limit, corresponding to a rapidly rotating and vibrating ion core interacting with a highly excited, distant, and slowly orbiting electron. In terms of the level structure this means that for given electronic inversion symmetry (g/u) and electron spin (0/1) the electronic states n,(l),∧ with associated vibrational structure v,N and parity (– 1)p (p = 0, 1) are progressively reordered and eventually form Rydberg series. These series are appropriately labelled n, v+,N+ for each (l), N and parity (– l)p. l is the electron orbital quantum number which is is put into brackets because (albeit useful for book-keeping purposes) it is not always a good quantum number.

Introduction

The analysis of the spectra of astrophysical systems provides valuable information about their composition and dynamics. The purpose of this brief chapter is to introduce some basic concepts of atomic and molecular spectroscopy that are needed to appreciate the role played by spectra in astrophysics. The ideas developed in this chapter will be used in the study of stellar atmospheres, the interstellar medium (Vol. II), and in extragalactic astronomy (Vol. III).

Width of Spectral Lines

When a system makes a transition between two discrete energy levels E2 and E1 emitting a single photon, the frequency of the photon should be equal to ω = (E2 - E1)/ħ. Such a transition should lead to a sharp spectral line of infinite intensity and zero width. In reality, the frequency of the photon that is emitted is not precisely determined and the observed spectral line will have a finite width and intensity. The nature of the width of the spectral line contains important information about the state of the physical system.

The finite width of the spectral line can arise because of several reasons, among which three particular processes are of importance in astrophysics. To begin with, all energy levels (except the ground state) have a finite intrinsic width, that is, the energy of an excited state can be ascertained within only a finite accuracy ΔE2 around a mean value E2. This is because all excited states have a nonzero probability per second P for making a spontaneous transition to lower energy levels.

Introduction

This chapter deals with the dynamics of electrically conducting fluids, usually called plasmas. The emphasis is on concepts that are of direct relevance to astrophysics. The basic ideas that are covered here will be used in several chapters of Vols. II and III.

The Mean Field and Collisions in Plasma

Several astrophysical systems are made of fully ionised gases, usually called plasmas, in which electromagnetic interactions between the constituents play a vital role. In this chapter, we treat fully ionised plasma as having two components: electrons of charge -e and positive ions of charge Ze. We begin by discussing several assumptions and approximations that will be inherent in our description.

The effective use of statistical methods in the study of neutral gases relies on the fact that the interaction between constituent particles are of short range and random in nature. This assumes that the gas is sufficiently rarefied and can be treated as ideal. To treat a plasma as a fluid, it is necessary to impose a corresponding condition that, however, has some important conceptual differences from that of neutral gases.

The condition for a plasma to be treated as ideal requires that the random kinetic energy of the particles be large compared with the electrostatic potential energy between two particles, that is, kBT ≫ e2/r ∼ e2nfrac13;, where T is the temperature, n is the number density of particles, and r ≃ n-⅓ is the mean interparticle distance.

Introduction

This chapter begins with a rapid overview of concepts from special relativity and develops the four-vector notation. Several aspects of electrodynamics are then introduced using special relativity and four-vector notation. Finally, this formalism is used to discuss some aspects of principles of optics that are relevant to astronomy. The concept of distribution functions, developed in Section 3.6, will be used extensively in several later chapters. This chapter will also be needed in the development of radiative processes (Chaps. 4 and 6), general relativity (Chap. 11), and in the study of cosmology in Vol. III.

The Principles of Special Relativity

The description of physical processes requires the specification of spatial and temporal coordinates of events that may be combined into a single entity characterised by the four numbers xi = (t, x). Throughout this chapter, the Latin indices a, b, …, i, j, etc., run over 0, 1, 2, and 3, with the 0 index denoting the ‘fourth’ dimension and 1, 2, and 3 denoting the standard space dimensions. The actual values of xi, attributed to any given event P, will depend on the specific coordinate system which is used. We pay special attention to a subset of all possible coordinate systems called inertial coordinate systems. Such coordinate systems are defined by the property that a material particle, far removed from all external influences, will move with uniform velocity in such systems.

Introduction

This chapter develops several basic ideas of dynamics, emphasizing general principles that are useful in classifying the behaviour of dynamical systems. The reader is assumed to be familiar with elementary concepts of classical mechanics. Concepts developed here will be needed in the study of special relativity (Chap. 3), statistical mechanics (Chap. 5), general relativity (Chap. 11), Sun and solar system (Vol. II), binary stars (Vol. II), and galactic dynamics (Vol. III).

Time Evolution of Dynamical Systems

Many systems encountered in nature can be described by a finite set of N real variables [q1(t), q2(t), …, qi(t), …, qN(t)] t h a t evolve in time. For example, in the study of two stars, moving under the influence of their mutual gravitational force, we are interested in the positions of the stars as functions of time. The position of each star can be described by three coordinates (in three-dimensional space) so that the full system can be described by a total of six functions of time. The quantities qi(t) (with i = 1,2, …, N) are called dynamical variables; obviously, we are free to choose any other set of N independent, single-valued functions of qi as dynamical variables to describe the system, with the particular choice often dictated by mathematical convenience. The central problem of dynamics is related to determining the time dependence of qi(t) and studying the general characteristics of motion.