C/1995 O1 (Hale-Bopp): Gas Production Curves And Their Interpretation

The discovery of C/1995 O1 (Hale-Bopp) at 7 AU from the Sun provided the first opportunity to follow the activity of a bright comet over a large range of heliocentric distances r_h. Production rates of a number of parent molecules and daughter species have been monitored both pre- and postperihelion. CO was found to be the major driver of the activity far from the Sun, surpassed by water within 3 AU whose production rate reached 10³¹ s⁻¹ at perihelion. Gas production curves obtained for various species show several behaviours with r_h. Gas production curves contain important information concerning the physical state of cometary ices, the structure of the nucleus and all the processes taking place inside the nucleus leading to outgassing. They are relevant to the study of several other phenomena such as the sublimation from icy grains, dust mantling or seasonal effects. For some species, such as H₂CO or HNC, they permit to constrain their origin in the coma. We discuss models of subsurface gas production in distant comets and predictions of how such a source may vary as the comet moves along its orbit, approaching perihelion and receding again. Features in the observed gas production curves of comet Hale-Bopp are generally interpretable in terms of either subsurface production (typical example: CO at large r_h) or free sublimation (typical example: H₂O). Possible implications for the vertical stratification of the cometary ices are reviewed, and preference is found for a model with crystallization of amorphous ice close to the nuclear surface. This revised version was published online in July 2006 with corrections to the Cover Date.     

Millimeter-wave experiments for cometary space missions

Predicted brightness temperatures for a variety of cometary nucleus models, consisting of homogeneous layers comprised of mixtures of water ice and refractory grains, are presented as functions of wavelength. These illustrative spectra are computed using simple radiative transfer techniques adapted from modeling of terrestrial ice and snow fields. The computed millimeter-wave spectra are sensitive to the values of physically significant nucleus parameters such as crust thickness, the subsurface temperature gradient, and the boundary temperature of the sublimating surface. It appears that millimeter-wave sensing from an interplanetary spacecraft is an effective means for distinguishing between alternate models of the nucleus and for inferring the rough physical state of substrata; modern theories on the nature of the nucleus indicate that sublimation from the substrata provides the gas phase cometary volatiles that are actually observed from ground-based and Earth-orbiting instruments. Antenna beam dilution is a major obstacle for ground-based molecular spectral line radio observations (e.g., water and ammonia) of comets but a modest millimeter-wave radiometer system in the near vicinity of the comet would not be subject to this problem. Such a system can make definitivebservations of several candidate parent molecules in the gas phase and should contribute to the understanding of the physics of the inner coma.     

Coma expansion and photometry of comet Bowell (1980b)

Optical and infrared observations of comet Bowell are presented. The optical observations indicate that the solid grain coma is expanding at only 0.9 ± 0.2 m sec^?1. This is two orders of magnitude slower than the local gas sound speed and may suggest that gas drag is not responsible for stripping the grains from the nucleus. The hypothesis of “electrostatic snap-off” is tentatively advanced to account for the ejection of the grains. Alternatively, the grains may have an unusual size distribution. The extrapolated motion of the grains suggests that the bulk of the coma was formed when the comet was at a heliocentric distance $\text{R ? 10}\text{AU}$. Any water ice in the nucleus would be too cold to give rise to the observed grain coma by equilibrium sublimation at this R. Further evidence against the production of the grain coma by equilibrium sublimation of the nucleus is provided by broadband (J) photometric observations. Almost all of the observed photometric variations of comet Bowell can be ascribed to geometric effects. Simple models indicate that the total grain cross section has been nearly constant since the time of the earliest observations. The present observations, which suggest that water ice sublimation does not control either the optical morphology or the near infrared photometric behavior of comet Bowell, are contrasted with reported high OH production rates. It is concluded that the grain coma may be largely a relic of activity occurring on the nucleus at $\text{R ? 10}\text{AU}$ while the OH may indicate sublimation from the nucleus near perihelion and from coma grains near $\text{R ? 4.6}\text{AU}$.     

Hale-Bopp: What Makes a Big Comet Different? Coma Dynamics: Observations and Theory

Comet Hale-Bopp was the largest comet by almost any definition, observed at least since the advent of modern observing techniques. In a more typical comet both the chemical and dynamical influences of collisional processes are limited by the short time a parcel of gas sublimated from the nucleus remains in the dense part of the coma. The resulting large size of the collisional coma in comet Hale-Bopp had important consequences on the dynamics of the coma, which in turn has important consequences on how observations are interpreted with standard models. Measured velocities of typical gas species (mostly the observed radicals) as well as dust were larger than normal comets. Conversely, velocities of super thermal atomic hydrogen were smaller than normal because of the samecollisional processes. Furthermore, as a consequence, dust particles, which are dragged by the outflowing gas, were also accelerated to larger velocities. Such larger velocities are not simply an interesting curiosity in their own right, because nearly all observations of dust and gas are interpreted with models of the coma that depend directly on some measurement or assumption with regard to velocity. In this presentation both observations and theory regarding the dynamical conditions in the coma of comet Hale-Bopp are summarized.     

Is Hale–Bopp A ‘Juvenile’ Comet – Study Of The Energy Balance To Explain The Vapor Flux Of Volatiles From The Surface

Sublimation of minor gases from ices inside of a porous comet nucleus strongly depends on the effective energy input. Our model meant to describe the gas flux inside and out of the porous nucleus has been used to study the influence of physical and structural parameters on the effective energy input. We solve the conservation equations for H₂O and CO as the most abundant minor component of higher volatility under appropriate boundary conditions. From the calculations we obtain the gas flux from volatile, icy components inside the porous nucleus, temperature profiles, changes in relative chemical abundances, and the gas flux into the coma for each of the volatiles. We will show results from our calculations for a model comet in the orbit of Hale-Bopp (C/1995 O1). In this paper we focus on the energy balance at the surface. We will also relate measurements of molecule fluxes to available energies and try to provide hints about the evolutionary status of the comet. This revised version was published online in July 2006 with corrections to the Cover Date.     

Chemical and physical properties of gas jets in comets: I. Monte Carlo model of an inner cometary coma

We describe a 3-dimensional, time-dependent Monte Carlo model developed to analyze the chemical and physical nature of a cometary gas coma. Our model includes the necessary physics and chemistry to recreate the conditions applicable to Comet Hale-Bopp when the comet was near 1 AU from the Sun. Two base models were designed and are described here. The first is an isotropic model that emits particles (parents of the observed gases) from the entire nucleus; the second is a jet model that ejects parent particles solely from discrete active areas on the surface of the comet nucleus, resulting in coma jets. The two models are combined to produce the final model, which is compared with observations. The physical processes incorporated in both base models include: (1) isotropic ejection of daughter molecules (the observed gases) in the parent's frame of reference, (2) solar radiation pressure, (3) solar insolation effects, (4) collisions of daughter products with other molecules in the coma, and (5) acceleration of the gas in the coma. The observed daughter molecules are produced when a parent decays, which is represented by either an exponential decay distribution (photodissociation of the parent gas) or a triangular distribution (production from a grain extended source). Application of this model to the analysis the OH, C₂ and CN gas jets observed in the coma of Comet Hale-Bopp is the focus of the accompanying paper [Lederer, S.M., Campins, H., Osip, D.J., 2008. Icarus, in press (this issue)].     

On the Relationship of Chemical Abundances in the Nucleus to Those in the Coma

One of the goals of comet research is the determination of the chemical composition of the nucleus because it provides us with the clues about the composition of the nebula in which comet nuclei formed. It is well accepted that photo-chemical reactions must be considered to establish the abundances of mother molecules in the coma as they are released from the comet nucleus or from distributed dust sources in the coma. However, the mixing ratios of mother molecules in the coma changes with heliocentric distance. To obtain the abundances in the nucleus relative to those in the coma, we must turn our attention to the release rates of mother molecules from the nucleus as a function of heliocentric distance. For this purpose, we assume three sources for the coma gas: the surface of the nucleus (releasing mostly water vapor), the dust in the coma (the distributed source of several species released from dust particles), and the interior of the porous nucleus (the source of many species more volatile than water). The species diffusing from the interior of the nucleus are released by heat transported into the interior. Thus, the ratio of volatiles relative to water in the coma is a function of the heliocentric distance and provides important information about the chemical composition and structure of the nucleus. Our goal is to determine the abundance ratios of various mother molecules relative to water from many remote-sensing observations of the coma as a function of heliocentric distance. Comet Hale-Bopp is ideal for this purpose since it has been observed using instruments in many different wavelength regions over large ranges of heliocentric distances. The ratios of release rates of species into the coma are than modeled assuming various chemical compositions of the spinning nucleus as it moves from large heliocentric distance through perihelion. Since the heat flow into the nucleus will be different after perihelion from that before perihelion, we can also expect different gas release rates after perihelion compared to those observed before perihelion. Since not all the data are available yet, we report on progress of these calculations. This revised version was published online in July 2006 with corrections to the Cover Date.     

The contribution of icy grains to the activity of comets: I. Grain lifetime and distribution

We have developed a computer code (GEM—grain evolution model) to simulate the behavior of ice grains in a comet coma. The grains are assumed to be composed of water-ice with an admixture of dark material (“dirt”). An initial size distribution of grains is assumed to be ejected from the nucleus. The ejected mass is taken to be proportional to the rate of gas production by the nucleus. The efficiency for absorption and re-radiation of sunlight is computed from Mie scattering theory. The grain temperature and sublimation rate at a given heliocentric distance is then derived from energy balance considerations. The evolution of the grain size distribution is followed as a function of distance from the nucleus.     

Comet color changes with solar distance

JHK colors of 14 comets are correlated with cometary distance from the Sun. The correlation could be explained by (1) changes in coma particle size as comets approach the Sun, (2) decrease in the ice/dirt ratio in coma grains as comets approach the Sun, and/or (3) phase reddening. Short-term color changes in individual comets at fixed phase angles suggest that phase reddening does not explain all color changes. Short-term changes are consistent with jets injecting fresh (high ice/dirt) nuclear material into parts of the coma. All colorimetric data are consistent with pristine coma material being relatively low-albedo dirty ice grains colored by carbonaceous dirt like that in RD-type asteroids. Ice sublimation near the Sun may leave residual pure RD dirt grains, explaining the observed color changes.     

Estimating the Size of Hale-Bopp's Nucleus

A variety of independent methods have been used to estimate the size of the nucleus of comet Hale-Bopp. Several groups have analyzed optical and infrared images of the comet and claim to detect the signature of the nucleus, despite the presence of a strong coma. A detection of the nucleus was also claimed during mm- and cm-wave observations of Hale-Bopp shortly before perihelion. A team of observers detected the occultation of a star by the nucleus of Hale-Bopp in October 1996. The maximum observed gas production rate of the comet near perihelion can be used to place a lower limit on the size of the nucleus. This paper critically reviews the many different methods used to constrain the size of Hale-Bopp's nucleus. All of the techniques are affected by systematic errors that can be difficult to quantify precisely. Nevertheless, the available evidence strongly suggests that the nucleus of Hale-Bopp has an effective radius of at least 15 km and is probably in the range 20–35 km. Thus, the prodigious gas and production rates from this comet are naturally explained by its unusually large size. This revised version was published online in July 2006 with corrections to the Cover Date.     

A note on the snow line in protostellar accretion disks

Abstract— The temperature of ice grains in a protostellar disk is computed for a series of disk models. The region of stability against sublimation is calculated for small ice grains composed of either pure ice or “dirty” ice. We show that in the optically thin photosphere of the disk the gas temperature must be around 145 K for ice grains to be stable. This is much lower than the temperature of 170 K that is usually assumed.     

The Infrared Spectral Energy Distribution And Polarization Of Comet C/1995 O1 (Hale–Bopp) During 1997

Comets, such as C/1995 O1 (Hale-Bopp), are important to studies of the origins of the solar system because they are believed to be frozen reservoirs of the most primitive pre-solar dust grains and ices. Here, we report 1.2–18.5 μm infrared (IR) spectrophotometric and polarimetric observations of comet Hale-Bopp. Our measurements of the spectral energy distribution (SED) and IR polarization near perhelion passage suggest that emission from the coma was dominated by scattering and thermal emission from sub-micron sized dust grains. Hale-Bopp's surprising brightness may have been largely a result of the properties of its coma grains rather than the size of its nucleus. The thermal emission continuum from the grains had a superheat of S = T_color/T_BB ≥ 1.7, the peak of the 10 μm silicate emission feature was 1.7 mags above the carbon grain continuum, and the albedo (reflectivity) of the grains was ≥ 0.4 at a scattering angles, θ ≥ 135° This revised version was published online in July 2006 with corrections to the Cover Date.     

The contribution of grains to the activity of comets: II. The brightness of the coma

We use the model of grain behavior in the coma developed by Beer et al. [Beer, E.H., Podolak, M., Prialnik, P., 2006. Icarus 180, 473-486] to compute the contribution of ice grains to the brightness of the coma. The motion of an ice grain along the comet-Sun axis is computed, taking into account gas drag, the gravity of the nucleus, and radiation pressure of sunlight. The sublimation of the grains is also included. We assume that the maximum distance that a grain travels along this axis is indicative of the size of the coma, and we compute the resultant brightness as a function of heliocentric distance. The results are then compared to observations.     

Understanding measured water rotational temperatures and column densities in the very innermost coma of Comet 73P/Schwassmann–Wachmann 3 B

Direct sublimation of a comet nucleus surface is usually considered to be the main source of gas in the coma of a comet. However, evidence from a number of comets including the recent spectacular images of Comet 103P/Hartley 2 by the EPOXI mission indicates that the nucleus alone may not be responsible for all, or possibly at times even most, of the total amount of gas seen in the coma. Indeed, the sublimation of icy grains, which have been injected into the coma, appears to constitute an important source. We use the fully-kinetic Direct Simulation Monte Carlo model of Tenishev et al. (Tenishev, V.M., Combi, M.R., Davidsson, B. [2008]. Astrophys. J., 685, 659?677; Tenishev, V.M., Combi, M.R., Rubin, M. [2011]. Astrophys. J., 732) to reproduce the measurements of column density and rotational temperature of water in Comet 73P-B/Schwassmann–Wachmann 3 obtained with a very high spatial resolution of ～30 km using IRCS/Subaru in May 2006 (Bonev, B.P., Mumma, M.J., Kawakita, H., Kobayashi, H., Villanueva, G.L. [2008]. Icarus, 196, 241?248). For gas released solely from the cometary nucleus at a heliocentric distance of 1 AU, modeled rotational temperatures start at 110 K close to the surface and decrease to only several tens of degrees by 10–20 nucleus radii. However, the measured decay of both rotational temperature and column density with distance from the nucleus is much slower than predicted by this simple model. The addition of a substantial (distributed) source of gas from icy grains in the model slows the decay in rotational temperature and provides a more gradual drop in column density profiles. Together with a contribution of rotational heating of water molecules by electrons, the combined effects allow a much better match to the IRCS/Subaru observations. From the spatial distributions of water abundance and temperature measured in 73P/SW3-B, we have identified and quantified multiple mechanisms of release. The application of this tool to other comets may permit such studies over a range of heliocentric and geocentric distances.     

Modelling the circumnuclear coma of comets: objectives,methods and recent results

We investigate whether the modelling of the immediate vicinity of an active nucleus—currently unobservable—can, as the modelling of the outer, observable coma, be based on unrealistic simple assumptions such as those of nucleus and dust grains sphericity. We point out the inconsistency of models based on such assumptions, which, to manage compatibility with the observations, have to introduce additional assumptions that conflict with the previous ones, such as the existence of active areas of the nucleus. We argue that, while the outer coma models being phenomenological in nature, can perhaps tolerate such inconsistencies, the circumnuclear coma models must be predictive, having to obviate the lack of observational data, and therefore must exclude implausible and ad hoc assumptions, and advocate only well-understood physical processes and duly validated modelling methods. We describe the first steps of development of a predictive circumnuclear coma model, and present a set of results obtained with parameters fitted to comet P/Wirtanen, the target of the Rosetta mission, but of a quite general significance. Considering, first an inhomogeneous spherical nucleus with spherical dust grains, and then an aspherical homogeneous nucleus with spherical dust grains, we show that, in both cases (1) the surface temperature and initial gas parameters differ considerably from the Hertz–Knudsen values; (2) the near-surface gas and dust flows are not in general vertical, (3) the gas and dust density do not always monotonically decrease outwards, (4) the gas and dust velocity vary strongly from point to point, (5) shock structures are formed, which result in the formation of pseudo-jets of dust grains originating from various points of the surface. No simple method to distinguish between dust structures created by the surface inhomogeneity and by the surface orography is found. We show, for the first time, the deformation of the near-nucleus dust coma during a full rotation of an homogeneous, aspherical nucleus. We also show that identical active regions located at different points of an inhomogeneous spherical nucleus produce very different dust distributions, suggesting that the dust distribution is also strongly deformed during the rotation of such a nucleus. Finally, we consider, for the first time, a spherical homogeneous nucleus emitting aspherical dust grains. We show that, in such a case, the terminal grain velocity depends upon the shape, initial position, and even possibly upon the initial orientation of the grain at the surface, so that there cannot exist a precise relation between terminal velocity and dust grain mass. We conclude that, far from giving an approximate or average representation of the circumnuclear coma, the classical modelling approach yields in this region predictions that are in total conflict with the real behaviour of the gas and dust. As a most dramatic consequence, the use of this classical approach may have obscured completely the significance of the few direct and of the many indirect informations acquired hitherto on the nucleus activity.     

Gas flow and dust acceleration in a cometary Knudsen layer

An analytical model of the innermost gas–dust coma region is proposed. The kinetic Knudsen layer adjacent to the surface of the cometary nucleus, where the initially non-equilibrium velocity distribution function of gas molecules relaxes to Maxwell equilibrium distribution function and, as a result, the macro-characteristics of gas and dust flows vary several-fold, is considered. The gas phase model is based on the equations for mass, momentum and energy flux conservation, and is a natural development of the Anisimov, 1968 and Cercignani, 1981 approaches. The analytical relations between the characteristics of the gas flow on the boundaries of the non-equilibrium layer and the characteristics of the returning gas flow adsorbed by the surface are determined. These values form a consistent basis both for hydrodynamic models of the inner coma and for jet force models. Three particular models are presented: (1) sublimation of a polyatomic one-component gas; (2) sublimation of a two-component polyatomic gas mixture, in both cases from a plane surface; and (3) sublimation of water ice through a porous dust mantle. We conclude that the characteristics of the gas flow emerging from the Knudsen layer over a porous dust mantle is not very sensitive to the structure of the mantle.We also treat the expansion of dust into the coma, concentrating on the interaction between a non-equilibrium gas flow and a test particle. The dynamics of a grain of idealized shape is explored by using several simplifying assumptions for the variation of the drag force. The velocity of a particle at the exterior boundary of the Knudsen layer is thus estimated. Examining various model behaviours of the drag force inside the Knudsen layer, we show that the dust velocity is not sensitive to these variations.     

Models of P/Wirtanen nucleus: active regions versus non-active regions

From the current understanding we know that comet nuclei have heterogeneous compositions and complex structures. It is believed that cometary activity is the result of a combination of physical processes in the nucleus, like sublimation and recondensation of volatile ices, dust grains release, phase transition of water ice, depletion of the most volatile components in the outer layers and interior differentiation.The evolution of the comet depends on the sublimation of ices and the release of different gases and dust grains: the formation of a dust crust, the surface erosion and the development of the coma are related to the gas fluxes escaping from the nucleus. New observations, laboratory experiments and numerical simulations suggest that the gas and dust emissions are locally generated, in the so-called active regions. This localized activity is probably superimposed to the global nucleus activity. The differences between active and inactive regions can be attributed to differences in texture and refractory material content of the different areas.In this paper we present the results of numerical models of cometary nucleus evolution, developed in order to understand which are the processes leading to the formation of active and non-active regions on the cometary surface. The used numerical code solves the equations of heat transport and gas diffusion within a porous nucleus composed of different ices—such as water (the dominant constituent), CO₂, CO- and of dust grains embedded in the ice matrix.By varying the set of physical parameters describing the initial properties of comet P/Wirtanen, the different behaviour of the icy and dusty areas can be followed.Comet P/Wirtanen is the target of the international ROSETTA mission, the cornerstone ESA mission to a cometary nucleus. The successful design of ROSETTA requires some knowledge of comet status and activity: surface temperatures, amount of active and inactive surface areas, gas production rate and dust flux.     

The composition and size distribution of the dust in the coma of Comet Hale-Bopp

We discuss the composition and size distribution of the dust in the coma of Comet Hale-Bopp. We do this using a model fit for the infrared emission measured by the Infrared Space Observatory (ISO) and the measured degree of linear polarization of scattered light at various phase angles and wavelengths. The effects of particle shape on the modeled optical properties of the dust grains are taken into account. Both the short wavelength (7-44 μm) and the long wavelength (44-120 μm) infrared spectrum are fitted using the same dust parameters, as well as the degree of linear polarization at twelve different wavelengths in the optical to near-infrared domains. We constrain our fit by forcing the abundances of the major rock forming chemical elements to be equal to those observed in meteorites. The infrared spectrum at long wavelengths reveals that large grains are needed in order to fit the spectral slope. The size and shape distribution we employ allows us to estimate the sizes of the crystalline silicates. The ratios of the strength of various forsterite features show that the crystalline silicate grains in Hale-Bopp must be submicrometer-sized. On the basis of our analysis the presence of large crystalline silicate grains in the coma can be excluded. Because of this lack of large crystalline grains combined with the fact that we do need large amorphous grains to fit the emission spectrum at long wavelengths, we need only approximately 4% of crystalline silicates by mass (forsterite and enstatite) to reproduce the observed spectral features. After correcting for possible hidden crystalline material included in large amorphous grains, our best estimate of the total mass fraction of crystalline material is ∼7.5%, which is significantly lower than deduced in previous studies in which the typical derived crystallinity is ∼20-30%. The implications of this low abundance of crystalline material on the possible origin and evolution of the comet are discussed. We conclude that the crystallinity we observe in Hale-Bopp is consistent with the production of crystalline silicates in the inner Solar System by thermal annealing and subsequent radial mixing to the comet forming region (∼30 AU).