Combi et al.: Gas Dynamics and Kinetics in the Cometary Coma 523 Gas Dynamics and Kinetics in the Cometary Coma: Theory and Observations Michael R. Combi University of Michigan Walter M. Harris University of Washington William H. Smyth Atmospheric & Environmental Research, Inc. Our ability to describe the physical state of the expanding coma affects fundamental areas of cometary study both directly and indirectly. In order to convert measured abundances of gas species in the coma to gas production rates, models for the distribution and kinematics of gas species in the coma are required. Conversely, many different types of observations, together with laboratory data and theory, are still required to determine coma model attributes and parameters. Accurate relative and absolute gas production rates and their variations with time and from comet to comet are crucial to our basic understanding of the composition and structure of cometary nuclei and their place in the solar system. We review the gas dynamics and kinetics of cometary comae from both theoretical and observational perspectives, which are important for understand- ing the wide variety of physical conditions that are encountered. 1. INTRODUCTION and N. This description is most applicable for a typical comet observed in the range of a few tenths to about 2 AU Gases, primarily water, and entrained dust are liberated from the Sun. For comets much farther away, temperatures from the icy nucleus by solar heating when a comet is and velocities are smaller and reaction length scales are within a few astronomical units (AU) of the Sun and form larger. And for comets much closer (Sun-grazers), tempera- an outflowing cometary atmosphere. The cometary atmo- tures and velocities are much larger and reaction length sphere, or coma, expands to distances many orders of mag- scales are smaller. nitude larger than the size of the nucleus itself. Because of Our understanding of the conditions within a few times the ultimate expansion into vacuum and the very weak grav- the radius of the nucleus results largely from model pre- ity that affects only the largest dust particles, a Knudsen dictions that are only constrained by the gas fluxes and layer of a fraction to a few meters in thickness (a few times velocities hundreds of nucleus-radii from the nucleus, and the molecular collision mean free path) forms near the sur- are determined both by in situ and remote observations. face where the gas organizes itself into a transient stationary There are not many direct observations about the conditions thermal layer. The initiation of regular flow transforms this near the surface, beyond the images of 1P/Halley from the thermal layer into a rapid transonic dusty-gas flow with a Giotto and Vega spacecrafts and those of 19P/Borrelly from typical scale length of 10–100 m. Expansion and nearly adi- the Deep Space 1 spacecraft, which show only the dust dis- abatic cooling dominates the flow out to scales of ~100 km tribution. This region is described in detail in Crifo et al. where the dust becomes decoupled collisionally from the (2004). The photodissociation, photoionization and fast ion- gas. Here the gas flows with a speed of ~700 m s–1 and has neutral chemical reactions involving ultimately ~100 spe- a cool temperature of <30 K. The energetic photochemical cies and thousands of reactions forms a complex atmos- products of solar UV photodissociation then begin to heat phere/ionosphere that is described in detail in Rodgers et the gas faster than it can cool by adiabatic expansion or IR al. (2004). radiational cooling, and the gas kinetic temperature and The region of the coma accessible by remote ground- ultimately the outflow speed increase. Photoionization and based and Earth-orbit-based observations and by direct in charge impact ionization (~5–10% of the photodissociation situ sampling by spacecraft instrumentations (mostly by rate) forms a cometary ionosphere on scales of 103–104 km, neutral gas and plasma mass spectrometers) for detailed which ultimately interacts with the magnetized plasma of study generally covers distances larger than a few hundred the solar wind forming an ion tail on scales of 105–107 km. kilometers from the nucleus. Remote imaging observations Also, at large scales of 106–107 km, the neutral coma is of this region have provided information about the projected broken down into its atomic constituents, such as O, H, C, line-of-sight-integrated distribution of neutral gas and ion 523 524 Comets II species in two spatial dimensions on the sky plane and 2. FREE-EXPANSION MODELS sometimes the line-of-sight velocity distribution. Thus re- mote sensing provides somewhat convoluted, nonunique, 2.1. Eddington to Wallace and Miller global views of the coma, whereas in situ measurements Fountain Models have provided some detailed information about neutral gas and ion densities, velocities, and temperatures, but only for In Eddington’s fountain model the comet is assumed to a few fleeting threads along a few spacecraft trajectories. be a uniform and isotropic point source of emitters of light Information about kinetic and rotational temperatures has such that their density (e.g., gas or dust) would fall as the been obtained by both remote observations and in situ meas- inverse square of the distance from the source, except the urements. The spectroscopic measurements are discussed emitters are also subject to a uniform acceleration that in detail in Bockelée-Morvan et al. (2004) (for parent spe- pushes on them from a given direction (presumably from cies) and Feldman et al. (2004) (for nonparent species). the Sun’s direction). Eddington showed that such a model It is important to understand the physical state of the defines a paraboloid of revolution along a line parallel to coma and its variations because it is largely from analyses the acceleration and passing through the point source (the of observations of various species in the coma that we de- nucleus of the comet) such that termine the composition of the larger population of com- v2 v4 ets. Although in the last 20 years IR and radio astronomy x2 + y2 = 2z + (1) 2 have opened the possibility of directly observing parent gas a a species in comets, interpreting these observations is com- where the acceleration, a, is directed in the +z direction, x plicated by difficult excitation mechanisms, atmospheric and y complete the righthanded Cartesian coordinates, and extinction (in the IR), and generally weaker signal-to-noise v is the initial uniform outflow speed of the emitting par- when compared with visible and near-UV measurements of ticles. In this case the density, n, of emitting particles is daughter species. The interpretations of measurements of determined by two trajectories that cross any given point daughter species have their own sets of complicating issues within the paraboloid. Later work by Mocknatsche (1938), regarding production models and kinematics. However, which was independently rediscovered by Fokker (1953) routine observations of daughter species in the visible re- and later described by Wallace and Miller (1958), showed mains critically important for the foreseeable future because that the column density, which is what would be observed they are more sensitive for weak comets and especially for by a remote observer through an optically thin paraboloid those at large heliocentric distances. This is the only prac- of such particles, N, can be calculated after some algebraic tical way to characterize the composition and activity of the manipulation for any line-of-sight that passes within the entire population of comets and to compare with the large projected paraboloid for any angle between the Sun, comet, base of existent data. Observations of daughter species in and observer to simply be the visible should also be made and interpreted side-by-side Q with IR and radio observations of parent species for brighter N = (2) comets and those at generally smaller heliocentric distances 4vR to enable the entire complex picture to be unraveled. where Q is the global particle production rate and R is the In this chapter we concentrate on those aspects of photo- projected distance on the “sky” plane from the source (i.e., chemistry and dynamics that are important for understanding the nucleus). Interestingly, this is the same result as for a the overall physical state of the coma, and their variations point source without the acceleration. The projected shape from comet to comet, with changing heliocentric and com- of the paraboloid, of course, depends on the viewing geom- etocentric distance, and, most importantly, in the region etry. Such a model is still used to understand many basic sampled by observations, i.e., outside a few hundred kilo- properties of the observed dust distribution in comets. meters from the nucleus. We also discuss quantitative mod- els of the coma beginning with the original fountain model 2.2. Haser (1957) Model of Eddington (1910), which started the heuristic approach continued by Haser’s (1957) model that in turn later treated Most radiative emissions of gaseous species in comets the coma as a free expansion problem including produc- in visible light are caused by fluorescence with sunlight tion and loss processes. From there we move to physics- through an otherwise practically optically thin medium. based models that treat the energy budget, dynamics, and Early quantitative observations of gas species in the com- chemistry, leading to hydrodynamics, kinetic and hybrid etary coma indicated that the spatial variation of the ob- models. These models provide the basis for interpreting and served brightness of some emissions (e.g., C2, CN, etc.) linking together multiple diagnostic observations of com- deviated from the simple inverse distance relation of a ets that are becoming increasingly precise. Care must be simple fountain model.