Chemical models of molecular clouds

The complete chemical modelling of a cloud in the ISM looks tractable, if complicated, although there will always be assumptions, some of which will be rather gross, such as surface reaction rates, but they can all be refined in time. Molecular cloud modelling is at the frontier of astrochemistry and it would be hard to consider all of the results. The basic process of generating a kinetic model for a molecular cloud must follow the pathway  

The lifetime of molecular clouds has been the subject of much recent research, both observational and theoretical. The surprising result is that molecular clouds 

If we take the total observed mass in the Universe as 2 x 109MSun and divide this by the dynamic timescale for a GMC, this suggests that star formation is occurring at a rate of 500 MSun yr-1, which is 100 times the currently observed formation rate. This calculation is riddled with assumptions and approximations, including the efficiency of star formation. 

The lifetime of the molecular cloud is considered to be a time line running from cloud formation, star evolution and finally dispersion in a period that is several tci. The chemistry of the TMC and, to a good approximation, all molecular clouds must then be propagated over a timescale of at most 20 million years. The model must then investigate the chemistry as a function of the age of the cloud, opening the possibility of early-time chemistry and hence species present in the cloud being diagnostic of the age of the cloud. The model should then expect to produce an estimated lifetime and the appropriate column densities for the known species in the cloud. For TMC-1 the species list and concentrations are shown in Table 5.4. 

Binary ion-molecule reactions are indicated by thin arrows (c.t. indicates charge transfer), the radiative association reaction of C+ with H2 is indicated by the thick arrow and the dissociative recombination reactions are indicated by dashed arrows leading to the neutral molecules inside the compound brackets (e indicates free electrons). The molecules indicated in bold are known (observed) interstellar molecules. 

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The improvement in the rate of chemical reactions is reversed when temperature is cooler and at temperatures as low as 30 K (a warm comer of TMC-1) the exponential term is of order 10-279 and nearly all reactions between neutral species are frozen out at 50 K. Two important classes of reactions survive radical-radical chemistry and ion-molecule chemistry. The importance of these different reaction types will become apparent later with the construction of the models of molecular clouds. For the moment, however, laboratory measurements of reactions in radicals such as C2H have shown that even with temperatures as low as 15 K the rate constant for reactions of the type ... 

The first question to ask about the formation of interstellar molecules is where the formation occurs. There are two possibilities the molecules are formed within the clouds themselves or they are formed elsewhere. As an alternative to local formation, one possibility is that the molecules are synthesized in the expanding envelopes of old stars, previously referred to as circumstellar clouds. Both molecules and dust particles are known to form in such objects, and molecular development is especially efficient in those objects that are carbon-rich (elemental C > elemental O) such as the well-studied source IRC+10216.12 Chemical models of carbon-rich envelopes show that acetylene is produced under high-temperature thermodynamic equilibrium conditions and that as the material cools and flows out of the star, a chemistry somewhat akin to an acetylene discharge takes place, perhaps even forming molecules as complex as PAHs.13,14 As to the contribution of such chemistry to the interstellar medium, however, all but the very large species will be photodissociated rapidly by the radiation field present in interstellar space once the molecules are blown out of the protective cocoon of the stellar envelope in which they are formed. Consequently, the material flowing out into space will consist mainly of atoms, dust particles, and possibly PAHs that are relatively immune to radiation because of their size and stability. It is therefore necessary for the observed interstellar molecules to be produced locally. 

Much of our understanding of the chemistry of dense interstellar clouds derives from chemical models of these sources. A chemical model of an interstellar cloud is simply the solution of coupled differential equations that contain the time derivatives of the concentrations of individual molecular species. Each individual differential equation relates the time dependence of a specific molecular concentration to its formation and depletion rates. For example, consider the formation and depletion of a molecular ion labelled C" " ... 

Shocks were first invoked to explain the unusually high abundance of the radical CH+in diffuse clouds (n 100 cm-3 T = 100 K), where standard chemical models predict far too little of this substance which is reactive both with electrons and with atomic and molecular hydrogen.128 In a high temperature medium, however, the reaction,... 

In principle, it is now possible to construct a complete network of interconnecting chemical reactions for a planetary atmosphere, a hot molecular core or the tail of a comet. Once the important reactions have been identified the rate constants can be looked up on the database and a kinetic model of the atmosphere or ISM molecular cloud can be constructed. Or can it Most of the time the important reactions are hard to identify and if you are sure you have the right mechanisms then the rate constants will certainly not be known and sensible approximations will have to be made. However, estimates of ISM chemistry have been made with some success, as we shall see below. 

One useful trick in solving complex kinetic models is called the steady-state approximation. The differential equations for the chemical reaction networks have to be solved in time to understand the variation of the concentrations of the species with time, which is particularly important if the molecular cloud that you are investigating is beginning to collapse. Multiple, coupled differentials can be solved numerically in a fairly straightforward way limited really only by computer power. However, it is useful to consider a time after the reactions have started at which the concentrations of all of the species have settled down and are no longer changing rapidly. This happy equilibrium state of affairs may never happen during the collapse of the cloud but it is a simple approximation to implement and a place to start the analysis. 

There are some advantages of the temporal models of cloud chemistry associated with the concentrations of molecules at different times. Can we learn about the age of the cloud by its chemical composition or the age of an embedded star by the chemistry observed towards the object Can the molecular environment be understood from the inventory of chemicals Are there chemical diagnostics for planetary formation, star formation or even black holes All of these questions are at the frontier of Astrochemistry. 

In quantitative modeling of PESs the description of the molecular shape as a superposition of atomic components remains an attractive approach, but it is clear from the earlier discussion that it must be extended to accommodate two important factors. The atomic shape is not a rigid, but rather a soft, exponentially decaying electronic charge cloud. In addition, it should be anisotropic with the anisotropy depending not only on the atom itself, but also on its partner in the chemical bond. 

The impact of secondary aerosols on indirect radiative forcing is the most variable and is the least understood [3]. The reasons why the indirect effect of secondary aerosols is so difficult to describe is that it depends upon [1] (1) a series of molecular-microphysical processes that connect aerosol nucleation to cloud condensation nuclei to cloud drops and then ultimately to cloud albedo and (2) complex cloud-scale dynamics on scales of 100-1000 km involve a consistent matching of multiple spatial and time scales and are extremely difficult to parameterize and incorporate in climate models. Nucleation changes aerosol particle concentrations that cause changes in cloud droplet concentrations, which in turn, alter cloud albedo. Thus, macro-scale cloud properties that influence indirect forcing result from both micro-scale and large-scale dynamics. To date, the micro-scale chemical physics has not received the appropriate attention. 

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