Fig. 45. Indication for an extended source for CO by the NMS spectrometer on board Giotto 
By high-resolution near-IR long-slit spectra, it has been possible to spatially separate the nucleus CO source in several long-period comets since the mid-1990s. The results of observations of six comets are summarized in . Studies of the variation of CO abundances with heliocentric distance in comet Hale-Bopp  showed that beyond about 2 AU only the nucleus CO source seemed to be present, whereas closer to the Sun about half of CO came from the nucleus and extended coma sources. Part of the extended coma source of CO molecules in the coma is photodissociation of formaldehyde. However, the abundance of H2CO in comets is too low to fully explain the extended CO coma source. Several mechanisms have been proposed, including CHON grains, sublimation of the outer mantle of unaltered interstellar grains, or polymerized formaldehyde (POM: polyoxymethylene) (e.g., [66,68]). A discussion of possible mechanisms to explain the Halley measurements and an overview of the proposed ideas to explain extended coma sources can be found, for example, in .
Formaldehyde, H2CO, has been observed by its radio transitions, but also in the IR-range, in many comets with abundances of 0.13-4% [32,43,60,191, 197]. In situ measurements of H2CO in comet Halley [89,134] show the release by an extended coma source. Possibly, formaldehyde is completely released from a source in the coma and not a parent ice molecule . However, the relatively easy synthesis of formaldehyde in ice mixtures containing H2O and CO makes it unlikely that no H2CO at all should be present in the nucleus . H2CO molecules can polymerize and form polyoxymethylene (POM: (-CH2-O-)„). It has therefore been suggested that the distributed H2CO source consists of formaldehyde polymers on grains releasing single H2CO molecules during sublimation [111,113,155]. Laboratory studies  showed that a combination of photodegradation and thermal degradation of POMs could provide sufficient H2CO in the coma, in agreement with the measurements in comet Halley . Unfortunately, our knowledge of the organic
Fig. 46. Indication for an extended source for CO in comet Hale-Bopp 
Fig. 46. Indication for an extended source for CO in comet Hale-Bopp 
refractory component of cometary grains is still poor and allows us only to set constraints on the extended gas sources. Improvements are expected from further laboratory measurements and the direct analysis of cometary grains, for example of probes from the Stardust mission.
Observations of cometary plasma tails show H2O+ and CO+ ions to be their dominant constituents. These ions are formed by photoionisation:
In the inner coma, however, NH+ and H3O+ dominate inside a few 104 km. We take the formation and destruction of H3O+ as an example. H3O+ is formed by ion-neutral reactions of water ions with neutral water molecules and is destroyed by dissociative recombination.
In general, ion destruction by dissociative electron recombination is a major loss process for the dominant ions in the inner cometary coma. Figure 47 shows the spatial distribution of ions of the mass/charge range 16-19 amue-1 as measured by Giotto IMS  in the inner coma of comet Halley. Surprisingly, the peak number density was not near the nucleus, but at about 104 km distance (called "ion pile-up region" by ). The formation of the enhanced ion region was a puzzle for some time. The most likely explanation is that no ion enhancement is seen, but instead a decreased ion density in the innermost coma region. The decrease in ion density is caused by a sudden drop in electron temperature, Te, in the inner coma because of efficient cooling of electrons by collisions with water molecules (Te ~ Tgas inside the come-topause) (Fig. 39). The rate coefficient for dissociative electron recombination is a strong function of Te, and decreasing Te therefore results in efficient ion dissociation in the inner coma. The major difficulty of modeling the observed distributions of H3 O+ and other ions was caused by the fact that Te in the energy range relevant for these reactions could not be measured by Giotto. As a result, many attempts have been made to determine the correct position of the sudden change in Te (see summary in , Fig. 47). However, a good agreement of modeled and measured H3 O+ ion density was finally obtained .
Radio observations of HCO+ ions in comet Hale-Bopp from the ground also showed a region of decreased density around the nucleus . Again, destruction of HCO+ ions by electron dissociative recombination seems to play a major role . Radio observations therefore allow us to image from ground the region where electron dissociation is important (see also discussion in ), at least for exceptionally bright comets. However, determining the low-energy electron temperature to model the inner coma ion densities remains difficult if no in situ data are available.
6 Gas Production Rates
Our knowledge of the chemical composition of cometary nuclei, its variation among comets and its variation with time and heliocentric distance is based on the measurements of production rates of molecules observed in the coma. When accurate coma production rates are available, models of the out-gassing processes in the nucleus help to translate coma observations to nucleus abundances. Parent molecule production rates are best measured by direct observations of their emission lines, mainly in the radio and IR domain. Observations of daughter products in the optical range complement these observations. They significantly extend the range of heliocentric distances covered for many species and allow to include observations of faint comets.
The first step to derive gas production rates is to convert the measured emission fluxes into column densities or the number of molecules in the field-of-view (FOV) of the observation. This requires knowledge of the excitation mechanism of the observed emission as described in Sect. 4.
The detailed physical and chemical coma processes are often not taken into account when interpreting ground-based observations of comets. Only simple models of the cometary coma are used because fundamental parameters such as velocities and temperatures can often not be measured, in particular at large rh. When discussing cometary gas activity and composition, it is therefore important to have in mind the various difficulties encountered.
If the whole coma can be covered in the FOV of an observation and resonance fluorescence is the main excitation mechanism, the production rate, Q, can be derived from the measured flux, F, by the simple relation
equating the flux at geocentric distance, A, with the fluorescence efficiency, g, multiplied by the mean production rate of the molecules with lifetime t.
However, remote observations usually do not cover the whole coma in their FOV, and to correct for the molecules missed in the observations, a coma model needs to be applied. The most commonly used model is the Haser model , because it provides a simple analytic formula for the dependence of column density on nucleocentric distance. Exponential decay of a parent molecule and its daughter product is assumed. The number density of the daughter product versus nucleocentric distance r is then given as:
The column density is then derived by integrating the computed profiles along the line-of-sight to the comet. This results in an analytical expression of the column density with a series of Bessel functions .
The model assumes isotropic radial outflow of parent and daughter molecules. The velocities of parents and daughters are assumed to be constant and in most cases set equal to 1kms_1 at 1 AU. This is not in agreement with the real velocity profile in the coma, which depends on nucleocentric distance as a result of gas expansion, collisions, and photolytic heating (Sect. 3.1). However, constant velocities can reasonably well approximate high-resolution line profiles of the parent molecules observed at radio wavelengths and are a satisfying first approximation of the coma flow on the scales measured in remote ground-based observations. See Sect. 3 for a more detailed discussion on gas velocities.
To apply the Haser model, the scale lengths of the parent, lp, and daughter products, ld, need to be known. In principal, the scale lengths are given by the product of life time versus photodestruction and the gas velocity. However, as already mentioned, the gas velocity is not constant in the coma. In addition, temporal production rate variations, coma inhomogeneities, and extended sources can modify the spatial column density profiles. Furthermore, the observed daughter product may result from multiple parent molecules. In practice, therefore, scale lengths of daughter species and their parents are determined by approximating their observed spatial distribution with a column density profile derived from a Haser model.
We also add a word of caution when computing production rates at large heliocentric distances by simply extrapolating scale lengths determined near 1 AU. Such scale lengths might not correctly account for the changes in chemistry and gas flow occurring in the coma. Clearly, the Haser model serves only as a rough model of the coma flow, and it is often oversimplified.
Somewhat more sophisticated models of the coma flow used to compute production rates allow us to account for temporal variations of Q, for example due to nucleus rotation, and excess energies given to daughter products after formation from their parent molecules [49,81]. The more realistic modeling of the coma, however, is paid by the additional need of accurate values for the outflow velocities and the excess energies from photodissociation.
Realistic coma models need to take into account non-isotropic outgassing, temporal variability such as rotation, orbital variations, outbursts, as well as extended coma sources, and additional chemical processes other than simple two-step photoreactions. However, such models reach a state of complexity that makes them inconvenient to be used for fast production rate determinations. In addition, because of the large number of unknowns entering the modeling the reliability of the derived Q probably does not increase. The simple models, on the other hand, allow us to derive production rates relatively easy for a large number of comets. However, one needs to have their shortcomings in mind.
6.2 Abundance Ratios and Compositional Differences among Comets
The main volatile constituent of the nucleus is water ice, followed by carbon monoxide. Although the activity of cometary nuclei is dominated by these two main ices, the minor species with abundances of at most a few percent give important clues for the understanding of the origin and formation of comets. Their abundance ratios reflect the processes of condensation to cometary grains in the presolar nebula or preplanetary disc and the amount of re-processing during later phases of solar system evolution.
Until the first direct drilling experiments on cometary nuclei will be made, the composition of comets can only be derived from measurements of their coma composition. The abundance of minor volatiles is usually characterized by providing the production rate ratio to the main activity driver, H2O. In case of pure ices and in the regime where sublimation is controlled solely by the variation of solar insolation, all production rates vary with r-2 and the abundance ratios are constant. In a real comet, however, sublimation of the minor species also depends on the physical parameters of the nucleus (see Sect. 2), and the variation with heliocentric distance may not be the same as for water. In addition, the evolution of production rates obviously differs at larger distances where species are in the regime where their onset of activity occurs. Consequently, abundance ratios are distance dependent and comets can be compared only when observed at the same rh, or if the variation of their abundance ratio is known to be small over the distance range considered. Most of the parent abundance ratios presented below were determined near 1 AU. Many reviews discussing volatile abundances can be found, the most recent in .
Water ice, H2O, is the most abundant volatile constituent in cometary nuclei (80% by number in comet Halley ) and dominates the gaseous activity within about 3 AU heliocentric distance. The determination of H2O production rates is therefore of vital importance to characterize cometary activity. H2O emission bands in the infrared range were first observed from the Kuiper-airborne observatory  and from Earth orbit using infrared satellites, e.g. ISO and Spitzer. Unfortunately, observations from space can provide only poor coverage of comet activity because of the limited availability of IR-space telescopes and their restrictions by the solar elongation angle. Improvements in infrared technology allowed to detect water bands also from ground-based telescopes (e.g., [64, 162]). These observations require bright comets, and a sufficient Doppler shift if the observed transitions are affected by the telluric water absorption bands. The water production rate is therefore in most comets derived from its daughter products, mainly OH and O.
Abundance ratios of the minor parent species with respect to water are shown in Table 4.
Table 4. Production rate ratios relative to water. The minimum and maximum reported values are given for parent molecules from radio and infrared observations as summarized in  and . For optical daughter radicals, the ratios for typical and depleted comets are taken from 
Molecule Parent molecules Daughter radicals
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