1 Introduction

It is nowadays well established that molecules are an important component in many different astronomical environments, that they can be used as efficient diagnostic tools of the physical and chemical state of such regions, and that—with about 200 different molecules discovered to date—chemical complexity can be developed in the outer space, with potential implications for the appearance of life. Scientists have wondered how molecules are synthesized in situ in harsh environments where, a priori, the survival of molecules does not seem favorable, and in this way, Astrochemistry and the development of chemical models have come to aid in the search for answers to these questions (see, e.g., Herbst and Yates 2013).

The aim of this chapter is to provide an introduction on how chemical models are constructed, which are the key physical and chemical data needed to feed them, and how models assist in the interpretation of astronomical observations. Although the basics behind the chemical models to be described can be applied to different types of astronomical sources, such as interstellar clouds, circumstellar envelopes, or planetary atmospheres, this chapter focuses on the theoretical description of interstellar chemistry. Section 14.2 presents the basic equations that enter into a chemical model, Sects. 14.3 and 14.4 describe the main gas-phase and grain-surface processes and their associated parameters, Sect. 14.5 discusses some types of chemical models developed for specific classes of interstellar regions, and finally, in Sect. 14.6 some concluding remarks are presented.

2 Construction of a Chemical Model

The low densities and temperatures prevailing in most interstellar regions make their chemical composition to be completely out of thermochemical equilibrium. That is, the composition is by no means determined by the minimum of the Gibbs energy of the system, but by chemical kinetics. This fact is key for the way interstellar chemistry works. First, time is a key quantity, i.e., the chemical composition may evolve with time and the current composition of a certain interstellar region is the consequence of the chemical evolution from a given initial time to the current age of that region. Therefore, to theoretically describe the chemical evolution the composition at the initial time must be known. In the practice, however, this is an important handicap of chemical models since the definition of the time zero and the knowledge of the composition at that time are not straightforward. Second, the chemical evolution of matter is the result of the competition between the rates at which the different physical and chemical processes take place.

The key equations behind a chemical kinetics model are differential equations that describe the variation of the abundance of each species i with time. This variation is given by the rate at which the species i is produced by any physical or chemical process minus the rate at which this species is destroyed by any process, i.e.

$$ {\fontsize{8.8}{10.8}\selectfont{\begin{aligned}\frac{d{n}_i}{dt}=\sum_{j,k}{k}_{jk}{n}_j{n}_k-{n}_i\sum_l{k}_{il}{n}_l+\left(\sum_m{K}_m{n}_m-{K}_i{n}_i\right)+\left[{R}_i^{des}{n}_i^{s, desorbable}-{R}_i^{ads}{n}_i\right]\end{aligned}}} $$
(14.1)
$$ \frac{d{n}_i^s}{dt}=\left\{\sum_{j,k}{k}_{jk}^s{n}_j^s{n}_k^s-{n}_i^s\sum_l{k}_{il}^s{n}_l^s\right\}+\left[{R}_i^{ads}{n}_i-{R}_i^{des}{n}_i^{s, desorbable}\right] $$
(14.2)

where n and n s stand for the abundances of the different species (i, j, k, l, m, n) in the gas phase and on the surface of dust grains, respectively. These abundances are usually expressed as volume densities, i.e., number of particles per cubic centimeter, following the cgs system of units. The quantities n s are a convenient way to express abundances on grain surfaces from a mathematical point of view, although they are not very intuitive. The abundance of a species i on grain surfaces, n is, can be expressed as n is = N is × n d, where N is is the number of particles of species i on the surface of an average dust grain and n d is the volume density of dust particles. There is a subtle aspect to take into account about desorption, which is that not all ice particles can efficiently desorb but only those in the top monolayers. This fact makes necessary to introduce the quantity n is,desorbable, which is the volume density of particles of species i in the top desorbable monolayers. This quantity is simply equal to n is when these layers are not fully occupied and to n is corrected by the fraction of ice particles in the top desorbable monolayers otherwise (see, e.g., Aikawa et al. 1996; Woitke et al. 2009; Cuppen et al. 2017).

The first two terms in Eq. (14.1) describe the formation and destruction of species i by bimolecular gas-phase chemical reactions, and thus, in these two terms, k jk represents the rate coefficients of reactions between species j and k that produce i, while k il stands for the rate coefficients of reactions in which species i reacts with other reagent l. Both k jk and k il have cgs units of cm3 s−1. The terms in parentheses in Eq. (14.1) describe the formation and destruction of species i by processes that follow a first-order kinetics, with rate coefficients K m and K i, respectively, both of which have cgs units of s−1. The coefficient K i takes into account all unimolecular processes of destruction of species i, which in the interstellar medium are mainly ionization or dissociation induced by cosmic rays or ultraviolet photons. Apart from unimolecular and bimolecular processes, termolecular reactions, i.e., those in which the reactive collision takes place between three bodies—the third one is chemically inert but carries out the excess of energy of the reaction—are a priori possible, although the low volume densities prevailing in the interstellar medium prevent these processes from being efficient, and are not included in Eqs. (14.1) and (14.2).

If a gas phase species i can be efficiently adsorbed onto dust grains, where it may experience some chemical transformations, then it is necessary to include the terms in square brackets in Eq. (14.1) and it is also necessary to describe the variation of the abundances of the ice species, n s, with time according to Eq. (14.2). The terms in square brackets in Eqs. (14.1) and (14.2) describe the adsorption (desorption) of a species i on (from) the surface of dust grains. The kinetics of adsorption is regulated by the rate coefficient R iads (with units of s−1), which depends on the abundance and size of dust grains. The kinetics of desorption is described by the rate coefficient R ides (with units of s−1), which results from the sum of the contributions of different desorption mechanisms. As long as chemical reactions can take place on the surface of dust grains, the chemical composition of the ice mantle can change and so the abundances of the adsorbed species. The kinetics of these grain-surface reactions is described by a formalism rather similar to that used to describe the kinetics of gas-phase chemical processes (Hasegawa et al. 1992). In this case, k jks stands for the rate coefficients of formation of the ice species i through reactions between ice species j and k, and k ils represents the rate coefficients of grain-surface reactions that deplete the ice species i. Both k jks and k ils have cgs units of cm3 s−1. This “rate-equation approach” has been widely used to deal with grain surface chemistry because it can be easily implemented in chemical models including a large number of species. This approach however lacks a proper description of grain surface chemistry at a microscopic level. Simulations using a stochastic treatment of the kinetics on a grain surface have come to assist here (e.g., Cuppen et al. 2013), although they are computationally expensive and still cannot be used to simultaneously model the chemistry of many species.

Once the main processes of chemical transformation have been identified and their rate coefficients are known or can be estimated, it is possible to write an equation with the source and sink terms for each gas-phase and ice species and build the full system of equations for all species included in the model. Usually, chemical models of interstellar clouds involve hundreds of species, which are linked by thousands of physical and chemical processes. The system of equations can be solved either at steady state or as a function of time. In the first case, the left-side terms in Eqs. (14.1) and (14.2) are set to zero and we are left with a system of algebraic equations. In this case we do not need to care about the initial conditions. In the time-dependent case, we have a system of ordinary differential equations (ODE), which can be solved as a function of time starting from some initial conditions, i.e., some initial abundance for every gas-phase and ice species considered in the model. The rate coefficients of these processes depend on parameters such as the gas kinetic temperature (e.g., for bimolecular gas-phase chemical reactions), the dust temperature (e.g., in the case of grain-surface chemical reactions), or the intensity and energy distribution of energetic radiation fields (e.g., in the case of ionizations and dissociations induced by ultraviolet photons). The chemical model thus has to be fed with some physical knowledge of the region to be studied. In a time-dependent chemical model, the abundances of all species are computed as a function of time under fixed or varying physical conditions. The former case is known as “pseudo time-dependent chemical model” and is a good approximation when the chemistry occurs on timescales shorter than those associated to the physical evolution of the interstellar region. If this is not the case, then the time-dependence of the gas and dust temperature, volume density, and strength of ultraviolet radiation must be taken into account.

3 Processes in the Gas Phase

3.1 Interactions with Energetic Radiation

Interstellar gas-phase species can be exposed to energetic radiation (ultraviolet, X-rays, γ-rays, cosmic-rays) of different degrees of intensity, and thus can interact with this energetic radiation suffering chemical transformations such as ionization and molecular dissociation. Here we concentrate on cosmic rays and ultraviolet photons, both of which are important drivers of the chemistry in the interstellar medium.

Cosmic rays are present allover our Galaxy—probably arising from supernovae remnants—and thus permeate the interstellar medium, being able to penetrate large columns of interstellar matter and ionize atoms and molecules in places where ultraviolet photons are not able to penetrate. For astrochemical purposes, the cosmic-ray flux is quantified through the ionization rate of H2 molecules, ζH2 (with units of s−1), which is the integral of the product of the ionization cross section of H2 by the cosmic-ray flux integrated over the energy spectrum of cosmic rays (see, e.g., Padovani et al. 2009). In the local interstellar medium, ζH2 takes values in the range (1–5) × 10−17 s−1 (Dalgarno 2006). The ionization rates of species other than H2 are usually expressed in terms of ζH2 through a scaling factor, which can be found in astrochemical databases.

The ionization of H2 by cosmic rays results in high energetic electrons, which lose energy through collisions with the gas, exciting H2 molecules to high-energy electronic states. The desexcitation of H2 molecules produces a cascade of ultraviolet photons, which can further ionize and dissociate species other than H2. This source of secondary ultraviolet photons induced by cosmic rays, known as Prasad-Tarafdar mechanism, has an ionizing power ∼1000 times greater than the direct ionization by cosmic rays, and is of particular importance in the interior of cold dense clouds, where external ultraviolet photons cannot penetrate due to the large extinction (Gredel et al. 1989).

The interstellar medium is exposed to an ultraviolet radiation field originated by the emission of ambient hot stars (Draine 1978). Interstellar molecules are efficiently photoionized and photodissociated by ultraviolet photons with wavelengths from 91.2 nm (this is the ionization threshold of H, which corresponds to 13.6 eV, and shorter-wavelength photons are efficiently absorbed by interstellar atomic hydrogen) to 200–300 nm (longer-wavelength photons have little ionizing and dissociating power). The photoionization and photodissociation rates of a given species i is given by the integral of the relevant cross section over the spectral shape of the ultraviolet radiation field:

$$ {K}_i={\int}_{91.2\ nm}^{\lambda_i}4\pi J\left(\lambda \right){\sigma}_i\left(\lambda \right) d\lambda $$
(14.3)

where the integral extends from 91.2 nm up to a wavelength λ i that depends on each species i, J(λ) is the mean specific intensity (with units of photon cm−2 s−1 nm−1 sr−1) of the radiation field, which can be the interstellar radiation field, the secondary radiation field induced by cosmic rays, or any other, e.g., arising from nearby hot stars. The ionization/dissociation cross section σ i(λ) is expressed in cgs units of cm−2. Because of the energy cutoff of the interstellar ultraviolet radiation field at 13.6 eV, a given species with an ionization potential IP i can only be ionized by interstellar ultraviolet photons with energies in the range IP i –13.6 eV. If the ionization potential is above 13.6 eV, that species cannot be ionized by interstellar ultraviolet photons. As concerns photodissociation of interstellar molecules, the cross section is delimited at the high-energy edge by the cutoff at 13.6 eV and at the low-energy edge by the dissociation energy of the molecule. The shape of the photodissociation cross section depends on the type of mechanism that dominates the photodissociation process, which can occur through discrete lines or a continuum (van Dishoeck 1988).

Computing a photorate using Eq. (14.3) requires the knowledge of the ultraviolet radiation field, which may involve radiative transfer calculations. For the standard interstellar medium it is usual to parameterize photorates as a function of the visual extinction. The visual extinction, A V, is a measure of the attenuation of radiation at optical wavelengths (in the V band centered at 550 nm) by a column density of interstellar material (essentially due to dust absorption and scattering), and is measured in magnitudes. A visual extinction of 1 magnitude implies that the intensity in the V band decreases by a factor of ∼2.5, according to the definition of a magnitude in astronomy. In the local interstellar medium, A V is proportional to the column density of H nuclei according to A V = N H/1.87 × 1021 cm−2 (Bohlin et al. 1978), and photorates can be expressed as:

$$ {K}_i=\kern0.5em {\alpha}_i\ \mathit{\exp}\left(-{\gamma}_i{A}_V\right) $$
(14.4)

where αi (with units of s−1) is the photorate of species i under the unattenuated interstellar radiation field of Draine (1978) and γi is a parameter used to take into account the increased dust extinction at ultraviolet wavelengths compared to the V band.

3.2 Gas-phase Chemical Reactions

Bimolecular gas-phase chemical reactions are one of the most important drivers of chemical complexity in the interstellar medium. In most interstellar regions the gas kinetic temperature is low and thus only exothermic reactions without important activation barriers play an important role. In warm regions where temperatures reach some hundreds of degrees Kelvin, endothermic reactions and reactions with moderate activation barriers may become important as well. In general, the rate coefficients of gas-phase chemical reactions depend on temperature, and this dependence is usually expressed through a modified Arrhenius equation:

$$ k=\kern0.5em \alpha {T}^{\beta}\exp \left(-\frac{\gamma }{T}\right) $$
(14.5)

where T is the gas kinetic temperature and α, β, and γ are three empirical parameters: α has cgs units of cm3 s−1, β is a dimensionless exponent, and γ is usually interpreted in terms on an endothermicity or activation barrier and is expressed in K. Although most molecules identified in the interstellar medium are neutral, ions play an important role in interstellar chemistry. Thus, gas-phase chemical reactions between neutral species as well as those involving ions are both important and necessary to build a realistic chemical model of any interstellar region.

The kinetics of a bimolecular gas-phase reaction between an ion and a neutral species is relatively simple. If such a reaction is exothermic, then it is usually rapid, even at very low temperatures. If the neutral species is non-polar, long-range capture theories indicate that the rate coefficient is independent of temperature and given by the Langevin expression:

$$ {k}_L=\kern0.5em 2\pi e{\left(\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$\mu $}\right.\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=2.3420\times {10}^{-9}{cm}^3{s}^{-1}\sqrt{\raisebox{1ex}{$\alpha \left[{\AA}^3\right]$}\!\left/ \!\raisebox{-1ex}{$\mu \left[ amu\right]$}\right.} $$
(14.6)

where e is the electric charge of the ion, α is the polarizability of the neutral species, and μ is the reduced mass of the reactants. For a single charged ion, as is usually the case in interstellar chemistry, the Langevin rate coefficient is given by the expression at the right side of Eq. (14.6). Most molecules of astrophysical interest have polarizabilities around 1 Å3 and reduced masses are usually a few atomic mass units (amu), so that rate coefficients are typically around 10−9 cm3 s−1. In the case of polar neutral species, the kinetic behavior becomes more complex because the potential describing the interaction depends on the orientation of the dipole moment and thus it is no longer isotropic. In this case, rate coefficients usually show a negative temperature-dependence (i.e., the lower the temperature the faster the reaction is) in a way that can be theoretically described according to classical trajectory calculations. A commonly used expression is the Su-Chesnavich one (see details in Wakelam et al. 2010). Measurements of rate coefficients of ion–neutral reactions have shown that the kinetics of most such reactions can be well described by long-range capture theories. This fact is extremely important because, in the absence of experimental data, it permits to predict to a fair degree of accuracy the rate coefficients of ion–neutral reactions.

In the case of reactions between neutral species, if both reactants are stable species, i.e., both are closed-shell electronic molecules, reactions tend to have large activation barriers, and thus negligible rate coefficients at low temperatures, so that they can be neglected for interstellar chemistry. Exothermic reactions in which at least one of the reactants is a radical may or not occur fast at low temperatures. Unlike in the case of ion–neutral reactions, here it is difficult to anticipate theoretically whether or not the reaction has an activation barrier, and experiments are needed. There is a vast experimental literature on the kinetics of neutral–neutral reactions, although most measurements have been done at room (and higher) temperature for reactions of interest in areas such as combustion chemistry or Earth atmospheric chemistry. In the last years, thanks to development of the CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme) technique, great efforts have been carried out to measure rate coefficients of neutral–neutral reactions of astrophysical interest at very low temperatures (Smith 2006). The emerging paradigm is that many more exothermic neutral–neutral reactions than previously thought are very rapid (∼10−10 cm3 s−1) at low temperatures, and even some of them experience spectacular enhancements in their reactivity when the temperature decreases from 300 K to 10 K. Moreover, recent experiments have put on the table that reactions with moderately small activation barriers can still be very rapid at very low temperatures, presumably due to quantum tunneling or roaming effects (Shannon et al. 2013; Zanchet et al. 2018).

Apart from ion–neutral and neutral–neutral reactions, there are other types of bimolecular gas-phase chemical reactions that are also important in interstellar chemistry. Among them, we have dissociative recombination of positive molecular ions and electrons, which are usually very fast. From a theoretical point of view the rate coefficient of these reactions should be around 10−7 cm3 s−1 (Bates 1950), something that has been verified experimentally. Moreover, the rate coefficient tends to increase with the size of the molecular ion, and there is a more or less marked dependence with temperature of the type k ∝ T −n (where n takes values in the range 0–2), i.e., the rate coefficient increases with decreasing temperature. Another type of reactions of interest for interstellar chemistry is radiative association, in which two species form an activated complex that can decay to a stable state through radiative emission. These reactions are usually slow, although in certain cases, in particular when ions of a certain size are involved, they can be fast enough to compete with other types of reactions (Gerlich and Horning 1992).

4 Processes Involving Dust Grains

Dust grains, which are ubiquitous in the interstellar medium, are active agents in regulating the chemical state of clouds. These tiny particles provide a reservoir where gas-phase material can be deposited in the form of ices. These ices can experience chemical transformations through reactions taking place on the surface of grains, and later on this chemically processed material can be injected back into the gas phase.

4.1 Gas-grain Exchange: Adsorption and Desorption

The adsorption of a gas-phase particle i onto the surface of a dust grain particle occurs through collisions between these two particles with a rate (with units of s−1) given by:

$$ {R}_i^{ads}=\kern0.5em {S}_i{v}_i\left\langle {\sigma}_d{n}_d\right\rangle $$
(14.7)

where S i is the sticking efficiency of species i, in the absence of better constraints it is usually assumed to be 1 for most species, and v i is the thermal velocity of the gas species i, which can be evaluated as \( \sqrt{3{k}_BT/{m}_i} \), where k B is the Boltzmann constant, T is the gas kinetic temperature, and m i is the mass of species i. The term 〈σ dn d〉 in Eq. (14.7) is the product of the geometric cross section and the volume density of dust particles averaged over the grain size distribution, which in the interstellar medium is given by the power law n(a) ∝ a −3.5, where n(a) is the number of grains of radius a (Mathis et al. 1977).

Species that have been adsorbed on dust grains forming ice mantles can return to the gas phase via a variety of mechanisms, such as thermal desorption, photodesorption, or cosmic-ray induced desorption. Thermal desorption depends on the dust temperature T d and the binding energy of adsorption of each species i (E D,i). The thermal desorption rate, in units of s−1, of an adsorbed species i is given by

$$ {R}_i^{des, th}=\kern0.5em {\nu}_{0,i}\mathit{\exp}\left(-{E}_{D,i}/{T}_d\right) $$
(14.8)

where E D,i is expressed in units of K, ν 0,i is the characteristic vibration frequency of the adsorbed species i, which can be evaluated as \( \sqrt{2{n}_s{k}_B{E}_{D,i}/{\pi}^2{m}_i} \), where n s is the surface density of sites, typically ∼1.5 × 1015 cm−2 (see Hasegawa et al. 1992). Thus, the fundamental parameters needed to describe the kinetics of thermal desorption in the interstellar medium are the binding energies E D,i, which can be measured using temperature programmed desorption (TPD) experiments. There are, however, some issues concerning the applicability of the laboratory data to model the chemistry of interstellar clouds. For example, different results may be obtained depending on whether sublimation occurs at the sub-monolayer or multilayer regime, or depending on the nature of the substrate (e.g., binding energies tend to be higher if the substrate is water ice instead of silicates; e.g., Noble et al. 2012).

The absorption of ultraviolet photons (emitted by nearby stars, from the ambient interstellar radiation field, or generated through the Prasad–Tarafdar mechanism) by icy dust grains can induce desorption of molecules on the ice surface. In regions where dust is too cold to allow for thermal desorption, photodesorption can provide an efficient way to bring molecules to the gas phase. The photodesorption rate, in units of s−1, of an adsorbed species i is given by

$$ {R}_i^{des, ph}=\kern0.5em {Y}_i{F}_{UV}\frac{\left\langle {\sigma}_d{n}_d\right\rangle }{4\left\langle {\sigma}_d{n}_d\right\rangle {n}_s{N}_l} $$
(14.9)

where Y i is the yield of molecules desorbed per incident photon, F UV is the ultraviolet flux (in units of photon cm−2 s−1), and molecules are assumed to desorb only from the top N l monolayers. Experimental work using isotopic markers (Bertin et al. 2012, 2013) and molecular dynamics calculations (Andersson and van Dishoeck 2008) indicate that molecules desorb efficiently from the two (or even three) top monolayers. Experiments carried out to study the photodesorption of pure ices or binary ice mixtures suggest that the main underlying mechanism is the so-called indirect desorption induced by electronic transition (DIET). This mechanism involves absorption of ultraviolet photons in the ∼5 top monolayers and electronic excitation of the absorbing molecules, followed by energy redistribution to neighboring molecules, which can then break their intermolecular bonds and be ejected into the gas phase. This mechanism dominates over direct photodesorption of the absorbing molecule (see, e.g., Muñoz Caro et al. 2010; Bertin et al. 2012, 2013). If these electronic transitions are dissociative the situation complicates because, in addition to the redistribution of the excess energy to neighboring molecules, the fragments may desorb directly, recombine in the ice surface and then desorb, or diffuse through the ice and recombine with other species to form new molecules. These new molecules may immediately desorb due to the exothermicity of the recombination reaction (see chemical desorption below) and/or desorb later on upon absorption of new incoming photons (Fillion et al. 2014; Martín-Doménech et al. 2016). Photodesorption processes are described in more detail in Chap. 9.

The impact of cosmic rays on icy dust grains can induce desorption of adsorbed molecules. The energy deposited on dust grains upon impact of relativistic heavy nuclei of Fe results in a local heating that induces the thermal desorption of the ice molecules present in the heated region. According to Hasegawa and Herbst (1993), the desorption rate induced by cosmic rays, in units of s−1, of a species i is given by

$$ {R}_i^{des, CR}=\kern0.5em 3.16\times {10}^{-19}{R}_i^{des, th}\left(70\ K\right) $$
(14.10)

where the numerical factor stands for the fraction of time spent by a grain in the vicinity of a temperature of 70 K, which is reached by the grain at the expense of the energy deposited upon impact of a relativistic Fe nucleus in the formalism of Hasegawa and Herbst (1993). The term R ides,th (70 K) is the thermal desorption rate of species i at 70 K, as given by Eq. (14.8).

The desorption mechanisms described above are not able to explain the presence of certain molecules in the interior of cold dense clouds. In these regions, temperatures are very low and thermal desorption is suppressed, interstellar ultraviolet photons cannot penetrate and photodesorption is restricted to the weak Prasad–Tarafdar radiation field, and the efficiency of cosmic-ray induced desorption remains low. Alternative desorption mechanisms have thus been invoked. One of them is chemidesorption (Garrod et al. 2007; Minissale et al. 2016), in which the energy released when an exothermic reaction takes place on the grain surface is in part used to inject the reaction products into the gas phase.

4.2 Grain-surface Chemical Reactions

In most chemical models of interstellar clouds, grain-surface reactions are assumed to occur through the Langmuir–Hinshelwood mechanism, in which two species undergo diffusion until finding one another and reacting. The kinetics of such a grain-surface chemical reaction between two species i and l can be expressed in terms of a rate coefficient k ils, with cgs units of cm3 s−1, in an analogous way to gas-phase bimolecular reactions (see details in Hasegawa et al. 1992). This rate coefficient can be expressed as

$$\vspace*{-3pt} {k}_{il}^s=\frac{\kappa_{il}\left({R}_i^{diff}+{R}_l^{diff}\right)}{n_d}\vspace*{-3pt} $$
(14.11)

where R idiff and R ldiff are the diffusion rates of species i and l, respectively, on the grain surface. For a given species i the diffusion rate, in units of s−1, is given by

$$\vspace*{-3pt} {R}_i^{diff}=\frac{1}{N_s}{\upsilon}_{0,i}\mathit{\exp}\left(-{E}_{b,i}/{T}_d\right)\vspace*{-3pt} $$
(14.12)

where N s is the number of adsorption sites on the surface of a grain, typically ∼106 for dust grains of 0.1 μm, and E b,i is the potential energy barrier between adjacent surface potential energy wells, usually E b,i∼0.3 E D,i. The parameter κ il in Eq. (14.11) is the probability for the reaction to happen upon an encounter between species i and l, which is unity for exothermic reactions without activation barrier. If an activation barrier is present, the reaction can proceed via quantum tunneling, with κ il < 1 (see Hasegawa et al. 1992).

5 Chemical Models of Different Types of Interstellar Clouds

Depending on the type of interstellar cloud (basically on the temperature, density of particles, intensity of ultraviolet radiation, and initial conditions and evolutionary history), different processes dominate the chemical composition of the gas and dust.

First, we have diffuse interstellar clouds (see Snow and McCall 2006), with typical densities of 100–1000 cm−3, temperatures of 30–100 K, and low extinction values (A V∼0.2–1). The results of a time-dependent pure gas-phase chemical model of a typical diffuse cloud (n H = 500 cm−3, T = 50 K, and A V = 1) are depicted in Fig. 14.1. It is seen that the degree of ionization is high (the fractional abundance of electrons is ∼10−4) as a result of the exposition to ultraviolet radiation, and most molecules are simple (diatomic and triatomic), with a certain importance of some exotic ions. A known failure of this model is the underestimation of the abundance of CH+ by 2–3 orders of magnitude. The chemistry of diffuse clouds is largely driven by ultraviolet photons arising from the ambient radiation field. In this sense, these regions are photon-dominated regions (PDRs), although the term is usually reserved for the edges of denser clouds located close to hot stars, and thus exposed to a far more intense ultraviolet field than in standard diffuse clouds. The Orion Bar and Horsehead Nebulae are good examples of such regions, where the higher densities and stronger ultraviolet radiation fields drive a faster and richer chemistry. Models aiming to describe the chemistry and physics of PDRs have been specifically developed (Hollenbach and Tielens 1997). These models couple processes driving chemical transformations to radiative and collisional processes driving the thermal balance, and solve them at different depths (or A V) from the edge to the internal regions of the cloud. Since in this case the system of equations becomes more complicated, only the solution at steady state (i.e., not as a function of time) is computed. This is a known handicap of these models. Whether or not the steady state assumption is good enough in PDRs is yet to be evaluated.

Fig. 14.1
figure 1

Molecular abundances calculated as a function of time for a diffuse cloud using a pure gas-phase chemical model (the chemical network employed is UMIST 2012; McElroy et al. 2013) with typical physical conditions (n H = 500 cm−3, T = 50 K, and A V = 1). The calculated abundance of CH+ is severely underestimated with respect to the values derived from observations (see text)

Full size image

The interiors of cold dense clouds have densities significantly higher (104–105 cm−3) than those of diffuse clouds, very low temperatures (∼10 K), and large extinction values (A V > 10). In these regions the chemistry is driven by cosmic rays (see Agúndez and Wakelam 2013). Figure 14.2 shows the abundances of some molecules as a function of time as calculated with a pure gas-phase chemical model of a typical cold dense cloud (n H = 2 × 104 cm−3, T = 10 K, and A V = 30). In this case the degree of ionization remains relatively low (the fractional abundance of electrons is ∼10−8) and the absence of intense ultraviolet radiation allows gas-phase chemical reactions to develop a richer molecular complexity than in diffuse clouds. Pure gas-phase chemical models have known failures to correctly estimate the abundances of some molecules (dashed lines in Fig. 14.2). The abundance of CH3OH is severely underestimated by models and the abundances of O2 and H2O are much higher than observed. In the case of H2O, the disagreement can be explained by the lack of adsorption processes in the model, since water is probably in the form of ice on dust grains at the low temperatures of cold dense clouds.

Fig. 14.2
figure 2

Abundances of assorted molecules calculated as a function of time for a cold dense cloud using a pure gas-phase chemical model (the chemical network employed is UMIST 2012; McElroy et al. 2013) with typical physical conditions (n H = 2 × 104 cm−3, T = 10 K, and A V = 30; see Agúndez and Wakelam 2013). The calculated abundances of H2O, O2, and CH3OH are in severe disagreement with observations (see text)

Full size image

In more advanced evolutionary stages, when protostars are born at the cores of dense clouds (the so-called hot cores), the chemical composition experiences drastic changes. The switch on of the protostar at the core center injects energy into the cloud and heats up the gas and dust. Densities in hot cores are somewhat higher (∼106 cm−3) than in cold cores as a result of the more advanced stage of gravitational collapse of the cloud, and temperatures are much higher (some hundreds of degrees Kelvin) as a result of the heating produced by the protostar. These high temperatures make ice mantles to desorb thermally and activate endothermic gas-phase reactions, leading to a rich chemistry with many complex organic molecules being formed (Herbst and van Dishoeck 2009). Chemical models aiming to describe such regions must therefore account for grain-surface chemical processes and gas-grain exchange processes.

6 Concluding Remarks

A wide variety of molecules are present in the interstellar medium. Moreover, each type of interstellar region has its own chemical signature, that is, contains a specific type of chemistry and a very concrete type of molecules. Chemical models are needed to interpret observations of interstellar molecules and to understand the underlying physical and chemical processes that give rise to the chemical differentiation present in different types of interstellar clouds. For that purpose, laboratory and theoretical data of gas-phase and grain-surface processes are essential.