Temperature and Gas Production Distributions on the Surface of a Spherical Model Comet Nucleus in the Orbit of 46P/Wirtanen

doi:10.1006/icar.1998.6050

Icarus

Volume 138, Issue 1, 1 March 1999, Pages 74-84

THIS PAPER IS DEDICATED TO OUR FRIEND AND COLLEAGUE DR. HERVÉ CABOT, WHO DIED IN A TRAGIC AVALANCHE ACCIDENT DURING THE DESCENT FROM PIC BLANC DU GALIBIER, FRANCE, ON JANUARY 4, 1998

https://doi.org/10.1006/icar.1998.6050 Get rights and content

Abstract

A multidimensional comet nucleus model is used to estimate the temperature and gas production distributions on the surface of a comet nucleus in the orbit of 46P/Wirtanen. The spherical model nucleus is assumed to be made up of a porous dust-ice (H₂O, CO) matrix. Heat and gas diffusion inside the rotating nucleus are taken into account in radial and meridional directions. A quasi-3D solution is obtained through the dependency of the boundary conditions on the local solar illumination as the nucleus rotates. As a study case, we consider a homogeneous chemical composition of the surface layer which is assumed to contain water ice. The model results include the distributions of temperature and gas production on the surface. For the chosen test case of a nucleus spin axis perpendicular to the orbital plane we found that the CO gas production on the surface is quasi-uniformly distributed in contrast to the nonuniform water outgassing. The mixing ratio at a specific point on the comet nucleus surface is not representative of the overall mixing ratio which is observed in the coma.

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Asymptotic thermal analysis of a rotating and sublimating sphere illuminated by a light source
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Small thickness of the boundary layer in a case of relatively small period of revolution makes application of full 3D models [19,20] for calculations of the temperature field in rotating nuclei impractical or even infeasible. Instead, a variety of approximate quasi-3D models have been proposed based on an intuitive assumption that the thermal transport is important only in the direction that is perpendicular to the body surface [17,21–30]. In the present work, in particular, it is shown that this assumption is not necessarily correct, and there are thermal regimes, when heat conduction in the latitudinal direction can not be neglected even if the Fourier number based on the body period of revolution is large.
The method of matched asymptotic expansions is applied for analysis of a generic unsteady three-dimensional (3D) thermal model of a rotating and sublimating homogeneous sphere asymmetrically illuminated by a light source and a series of approximate asymptotic models is proposed. The temperature field is described by heat conduction equation with a strongly non-linear boundary condition, accounting for the light absorption, thermal conductivity, self emission, and sublimation on the sphere surface. It is shown that properly generalized Van Dyke’s matching rule, accounting for non-linearity of the boundary condition, results in an asymptotic model, which provides accurate description of the temperature field even if the Fourier number Fo based on the sphere period of revolution is as small as 10. The asymptotic model is also capable for accurate description of the thermal boundary layer degeneration, when the angle between the rotational axis and the direction to the light source tends to zero or the effect of rotation vanishes locally. The accuracy of the asymptotic models is verified by the comparison of the computational results obtained based on the full 3D and asymptotic models. The asymptotic models are applied to study the effect of all dimensionless parameters on the total gas production rate of the sphere. It is found that in a large range of conditions the surface temperature field and gas production rate are independent of Fo, but determined by a new “rotational” parameter, which serves as measure of the sphere rotation rate.
Quasi-3-D model to describe topographic effects on non-spherical comet nucleus evolution
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Models such as the one of Benkhoff and Boice (1996) or Capria et al. (1996) consider the diurnal change in illumination of a point located at the equator (so-called 1.5-D model). A more elaborate model considering the two-dimensional lateral heat exchange over a meridian and the contributions of such wedges over one rotation was developed by Enzian et al. (1997, 1999) (so-called 2.5-D model). The last step is to take into account both the latitudinal and the longitudinal variations of illumination (see e.g. Capria et al., 2001; Cohen et al., 2003; De Sanctis et al., 2005; Sarid et al., 2005; De Sanctis et al., 2007).
A new quasi three-dimensional code is presented and used to explore the thermal evolution of non-spherical-shape cometary nuclei. Calculations are done for spherical nuclei with different obliquities, spherical nuclei with crater-like depressions and spheroid-shape nuclei. The results obtained for both the gas and dust fluxes agree with previous simulations. Local dust crust formation can occur when the comet is located far from the Sun (around 3.5 AU), creating active and inactive areas on the surface. For a given set of parameters, the H₂O production rate is comparable to the one observed for comets. A pre–post-perihelion asymmetry exists for H₂O, CO₂ and CO production rates. It is shown that crater-like depressions can be erased within the lifetime of a comet and that spheroid-shape nuclei have a higher production rate than equal area spherical nuclei.
A fully 3-dimensional thermal model of a comet nucleus
2007, New Astronomy
A 3-D numerical model of comet nuclei is presented. An implicit numerical scheme was developed for the thermal evolution of a spherical nucleus composed of a mixture of ice and dust. The model was tested against analytical solutions, simplified numerical solutions, and 1-D thermal evolution codes. The 3-D code was applied to comet 67P/Churyumov-Gerasimenko; surface temperature maps and the internal thermal structure was obtained as function of depth, longitude and hour angle. The effect of the spin axis tilt on the surface temperature distribution was studied in detail. It was found that for small tilt angles, relatively low temperatures may prevail on near-pole areas, despite lateral heat conduction. A high-resolution run for a comet model of 67P/Churyumov-Gerasimenko with low tilt angle, allowing for crystallization of amorphous ice, showed that the amorphous/crystalline ice boundary varies significantly with depth as a function of cometary latitude.
The effect of local topography and self-heating on the sublimation rate of cometary nuclei
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This work presents the results of calculation of the temperature regime and total flux of sublimation for a new physical model of local active areas on a cometary nucleus. As it was shown before a conical hole in the surface dust layer of a cometary nucleus can work as a concentrator of solar energy and, therefore, intensifies sublimation. The temperature of ice on the bottom and that of dust on the side of the crater is calculated for different geometrical parameters of the crater and different conditions of rotation of the nucleus. The dependence of the effect on the location of the active region as well as the effect of changing the solar zenith angle is studied.
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A model with subsolar water sublimation on a triaxial, ellipsoidal comet nucleus is presented for the calculation of reactive torques. The resulting differential equations describing the comet's rotation are then Hamiltonian, and gravity-gradients are trivial to include. While effects derived from a weak perturbing function are neither able to change the rotational excitation nor the spin magnitude of the nucleus, it is shown how the spin orientation of comets can change significantly over an orbital run. However, of the four comets studied, 1P, 19P, 46P and the Rosetta target 67P, 19P and 46P were the only objects clearly exhibiting this feature, thereby confirming a technique used to derive the consequences of a more elaborate model of sublimation induced torques. In particular, the rotational parameters of 67P were seen to be very stable, indicating that a highly kinematical model of its rotation for the mapping of the comet's gravitational field during the Rosetta mission can be used. The model's hierarchy with 1P/Halley as the object with highest excitation probability, is consistent with observations.
A practical tool for simulating the presence of gas comae in thermophysical modeling of cometary nuclei
2004, Icarus
Citation Excerpt :
Models in which the coupled heat transfer and gas diffusion equations are solved, and where a Dirichlet upper boundary condition is used for the latter equation (i.e., an explicit value for the surface gas density or pressure). The most common assumptions are zero surface pressure (e.g., Mekler et al., 1990; Prialnik, 1992; Prialnik et al., 1993; Podolak and Prialnik, 1996; Enzian et al., 1998, 1999; Orosei et al., 1999), or saturation surface pressure (e.g., Fanale and Salvail, 1984; Benkhoff and Spohn, 1991; De Sanctis et al., 1999; Capria et al., 2001). Models in which the coupled heat transfer and gas diffusion equations are solved, and where conservation of (the outgoing) mass flux is used as boundary condition for the latter equation (e.g., Rickman and Fernández, 1986; Rickman et al., 1990; Espinasse et al., 1991; Tancredi et al., 1994; Orosei et al., 1995; Capria et al., 1996; Enzian et al., 1997).
A longstanding problem in thermophysical modeling of cometary nuclei has been to accurately formulate the boundary conditions at the nucleus/coma interface. A correct treatment of the problem, where the Knudsen layer gas just above the cometary surface (which is not in thermodynamic equilibrium) is modeled in parallel with the nucleus, is extremely time-consuming and has so far been avoided. Instead, simplifying assumptions regarding the coma properties are used, e.g., the surface gas density is assumed equal to zero or set to the local saturation value, and the coma backflux is neglected or given some realistic but approximate value. The resulting inaccuracy regarding the exchange of mass, energy, and momentum between the nucleus and the coma, may introduce significant errors in the calculated nucleus temperature profiles, gas production rates, and momentum transfer efficiencies. In this paper, we present a practical, accurate, and time-efficient tool which makes it possible to consider the nucleus and the innermost coma of a comet (the former assumed to consist of a porous mixture of crystalline water ice and dust) as a coupled, physically consistent system. The tool consists of interpolation tables for the surface gas density and pressure, the recondensing coma backflux, and the cooling energy flux due to diffusely scattered coma molecules. The tables cover a wide range of surface temperatures and sub-surface temperature profiles, and can be used to improve the boundary conditions used in thermophysical models. The interpolation tables have been obtained by calculating the transmission distribution functions of gas emerging from sublimating porous ice/dust mixtures with various temperature profiles, which then are used as source functions in a Direct Simulation Monte Carlo model of inelastic intermolecular collisions in the Knudsen layer.

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^☆: R. L. Newburn, Jr.M. NeugebauerJ. Rahe

^f1: [email protected]

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Regular ArticleTemperature and Gas Production Distributions on the Surface of a Spherical Model Comet Nucleus in the Orbit of 46P/Wirtanen☆

Abstract

Planet. Space Sci.

Planet. Space Sci.

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Planet. Space Sci.

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Modeling the thermal properties and the gas flux from a porous, ice-dust body in the orbit of P/Wirtanen

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Evolution of the outgassing of Comet Hale–Bopp (C/1995 O1) from radio observations

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Infrared sounding of Comet P/Halley from Vega 1

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

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Temperature and size of the nucleus of Comet P/Halley deduced from IKS infrared Vega 1 measurements

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Regular Article
Temperature and Gas Production Distributions on the Surface of a Spherical Model Comet Nucleus in the Orbit of 46P/Wirtanen☆