Simulation of the water and carbon monoxide production rates of comet Hale–Bopp using a quasi 3-D nucleus model

doi:10.1016/S0032-0633(98)00057-9

Planetary and Space Science

Volume 46, Issue 8, 1 August 1998, Pages 851-858

https://doi.org/10.1016/S0032-0633(98)00057-9 Get rights and content

Abstract

The activity of comet C\1995 O1 (Hale–Bopp) has been simulated using a multidimensional comet model (Enzian et al., 1997). In this model the comet nucleus is considered to be formed by a fluffy ice-dust matrix. Heat and gas diffusion inside the rotating nucleus is taken into account in radial and meridional direction. A quasi tri-dimensional solution is obtained through the dependency of the boundary conditions on the hour angle. The ice phase is considered to be amorphous water ice including solid carbon monoxide, both trapped in amorphous water ice and as an independent phase. Comet Hale–Bopp is of particular interest due to its strong activity and the significant CO production at large heliocentric distance. The model results provide a satisfying fit to the observed CO production rates (until perihelion) in the case of an amorphous ice composition and a CO source located below the surface, and not at the surface. During the ACM96 meeting in June 1996 we predicted that the increase in carbon monoxide production levels off at about 3 AU and that the production rates increase again at about 1.5 AU (inbound). The gas production rates will then reach their maximum slightly after the comets perihelion : 6×10³⁰ molecules s⁻¹ for CO and 2×10³¹ molecules s⁻¹ for H₂O (upper limit for a nucleus with a radius of 20 km). An attempt is made to take an extended H₂O source in the coma into account. These predictions were compatible with recent observations of comet Hale–Bopp.

Introduction

Comet Hale–Bopp (C\1995 O1) is an intrinsically bright comet that was discovered in July 1995 at 7.2 astronomical units (AU) from the sun (Hale and Bopp, 1995). At that time comet Hale–Bopp was more than 100 times brighter than comet Hally at the same heliocentric distance (r_h). Most of the light reflected from a comet is due to sunlight scattered by micrometre-sized grains which are dragged out from an ice-dust nucleus. Spectra obtained from ground-based radiotelescopes (Jewitt et al., 1996 ; Biver et al., 1997 ; Biver, 1997) show the progressive release of CO, CH₃OH, HCN, H₂O (from OH), H₂S, CS, H₂CO, CH₃CN and HNC as comet Hale–Bopp approached the sun from 6.9–1.4 AU. Many of these species are also the main observed constituents of ices in interstellar molecular clouds. The more volatile molecules were relatively more abundant in the coma far from the sun, however, no direct relation between overabundance and volatility can be seen. Such a behaviour reflects the number of physical and chemical processes taking place inside a comet nucleus as a result of solar heating, causing chemical differentiation. For example, the CO gas production rate (Q̇_CO) increased from 3×10²⁸ at 6.6 AU in August 1995 to 1×10²⁹ molecules s⁻¹ at 1.4 AU in January 1996, whereas the H₂O production rate increased from 2×10²⁸ at 4.8 AU in April 1996 (Weaver et al., 1997) to 2×10³⁰ at 1.4 AU (Biver et al., 1997). The observed water production rates at large heliocentric distance were unexpected. Free surface sublimation from a nucleus with a size of a few tenths of a kilometre cannot account for this H₂O production. Hence, one assumes an extended H₂O source due to sublimating ice grains ejected from the nucleus. Such grains are likely to be present in the coma of comet Hale–Bopp as suggested by the water ice absorption band at 2.04 μm in infrared spectra (Davies et al., 1995) and by the OH line shape of the radio spectra (Biver et al., 1997).

Comet Hale–Bopp follows a quasi-parabolic orbit (actual eccentricity ε = 0.995) with an inclination of almost 90° with respect to the ecliptic plane. The comet passed through perihelion on 1 April 1997 at a distance to the sun of 0.91 AU.

Trying to predict the future brightness and production rates of comets is very difficult. Here we report a numerical simulation of the outgassing of carbon monoxide and water vapour of comet Hale–Bopp. We analyze in particular the influence of an additional heat source. As an example we have chosen the crystallisation of amorphous water ice. The predictions of the future activity (CO and H₂O production) of comet Hale–Bopp presented at the ACM meeting in June 1996 were confirmed until perihelion by recent observations of comet Hale–Bopp.

Section snippets

Composition

The model nucleus is composed of fluffy ice–dust aggregates. The dust component stands for a non-volatile phase which reduces the visible albedo of the ice. The ice constituent is composed of carbon monoxide enriched water ice which is initially in the amorphous state. Some amount of the condensed CO may evaporate by temperature controlled sublimation. However, as shown by Schmitt et al. (1989), a small fraction is trapped by the amorphous ice and can only escape during the crystallisation of

Physical and numerical parameters

The initial composition of the model nucleus is homogeneous containing dust, amorphous (or crystalline) water ice and carbon monoxide, both trapped (10% molar) in amorphous water ice and as an independent phase (10% molar). The initial nucleus temperature is assumed with 20 K so that the solid CO is conserved. The initial dust to ice mass ratio is ψ = 1 which corresponds to the lower value evaluated for comet P\Halley (McDonnell et al., 1991). The compact dust density is assumed with ρ_d = 3000

Results

The simulated gas production rates are strongly dependent on the chosen parameters and on the model hypothesis. We have carried out a detailed sensitivity analysis on the parameters such as initial chemical composition, heat conductivity, rotation period and orientation of the nucleus spin axis. The sensitivity analysis can be found in Enzian et al., 1997. It can be shown that the value of the thermal diffusivity determines how steep the CO outgassing rate increases before perihelion and

Extended water source

Grains of various kinds of ices are likely to be ejected by CO. Particles of frozen H₂O were found in the coma surrounding Hale–Bopp at 6.8 AU from the Sun (Davies et al., 1995). Radio wavelength data show that water ice grains were still present at 3.5 AU. One can assume that an important fraction of the particles emitted from the cometary nucleus still contain volatile ices which continue to sublimate in response to solar irradiation after their lift-off. Owing to the efficiency at radiating

Conclusions

The thermal evolution of comet Hale–Bopp (C\1995 O1) has been studied by numerical simulation using a quasi tri-dimensional comet nucleus model (Enzian et al., 1997). It has been shown, for a nucleus composed of ice (H₂O and CO) and dust with a radius of 20 km, that free sublimation of water ice at the nucleus surface cannot explain the observed H₂O production rates beyond 3 AU. We found that the observed extended H₂O source due to sublimating icy grains is the dominant production mechanisms

Acknowledgements

. The computation of this work wwas performed on the CRAY T3D of the Institut du Développement des Ressources en Informatique Scientifique (Orsay\France) of CNRS. Part of this work was supported by the French Programme National de Planétologie and the Centre National dEtudes Spatiales. The authors thank the anonymous referees for interesting comments.

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Citation Excerpt :
This value was used in Kührt (1999) together with an argument Φ of 64° which is slightly below the lower range provided by Vasundhara and Chakraborty (1999). Enzian et al. (1998) set Φ to 0° which was probably also employed in Enzian (1999). Vasundhara and Chakraborty (1999) calculated the obliquity and the argument of the sub-solar meridian at perihelion.
An investigation of the activity of Comet C/1995 O1 (Hale-Bopp) with a thermophysical nucleus model that does not rely on the existence of amorphous ice is presented. Our approach incorporates recent observations allowing to constrain important parameters that control cometary activity. The model accounts for heat conduction, heat advection, gas diffusion, sublimation, and condensation in a porous ice–dust matrix with moving boundaries. Erosion due to surface sublimation of water ice leads to a moving boundary. The movement of the boundary is modeled by applying a temperature remapping technique which allows us to account for the loss in the internal energy of the eroded surface material. These kind of problems are commonly referred to as Stefan problems. The model takes into account the diurnal rotation of the nucleus and seasonal effects due to the strong obliquity of Hale-Bopp as reported by Jorda et al. (Jorda, L., Rembor, K., Lecacheux, J., Colom, P., Colas, F., Frappa, E., Lara, L.M. [1997]. Earth Moon Planets 77, 167–180). Only bulk sublimation of water and CO ice are considered without further assumptions such as amorphous ices with certain amount of occluded CO gas. Confined and localized activity patterns are investigated following the reports of Lederer and Campins (Lederer, S.M., Campins, H. [2002]. Earth Moon Planets 90, 381–389) about the chemical heterogeneity of Hale-Bopp and of Bockelée-Morvan et al. (Bockelée-Morvan, D., Henry, F., Biver, N., Boissier, J., Colom, P., Crovisier, J., Despois, D., Moreno, R., Wink, J. [2009]. Astron. Astrophys. 505, 825–843) about a strong CO source at a latitude of 20°. The best fit to the observations of Biver et al. (Biver, N. et al. [2002]. Earth Moon Planets 90, 5–14) is obtained with a low thermal conductivity of 0.01 W m⁻¹ K⁻¹. This is in agreement with recent results of the Deep Impact mission to 9P/Tempel 1 (Groussin, O., A’Hearn, M.F., Li, J.-Y., Thomas, P.C., Sunshine, J.M., Lisse, C.M., Meech, K.J., Farnham, T.L., Feaga, L.M., Delamere, W.A. [2007]. Icarus 187, 16–25) and with previous thermal simulations (Kührt, E. [1999]. Space Sci. Rev. 90, 75–82). The water production curve matches the production rates well from −4 AU pre-perihelion to the outgoing leg while the model does not reproduce so well the water production beyond 4 AU pre-perihelion. The CO production curve is a good fit to the measurements of Biver et al. (2002) over the whole measured heliocentric range from −7 AU pre- to 15 AU post-perihelion.
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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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This report is the follow-up of the paper of A. Drouart et al. (1999, Icarus140, 129) in which it was demonstrated that appropriate models of the solar nebula permit us to interpret the deuterium enrichment in water with respect to the protosolar D/H ratio measured in LL3 meteorites and comets. In the present report, we show that the models selected by Drouart et al. are also able to explain D/H in HCN measured in Comet C/1995 O1 (Hale–Bopp). We find that the D/H ratio in HCN entering the nebula is ∼4×10⁻³, which is significantly less than values measured in cold dark clouds, but consistent with values found in hot molecular cores. Both H₂O and HCN ices infalling from the presolar cloud onto the nebula discoid evaporated in the turbulent part of the nebula, isotopically exchanged with hydrogen, and mixed with water vapor coming from the inner part of the nebula. Subsequently, H₂O and HCN ices with D/H ratios measured in Comet Hale–Bopp condensed, agglomerated and were incorporated in cometesimals. In the light of these results, we discuss the story of molecules detected in comets coming from Oort cloud. Most molecules detected in Comet Hale–Bopp originated from ices embedded in the presolar cloud. Ices vaporized prior to entering into the nebula or in the early nebula, and subsequently recondensed, except highly volatile molecules. According to A. Kouchi et al. (1994, Astron. Astrophys.290, 1009), water ice condensed in crystalline form. We discuss the possibility that the most volatile species were then trapped in the form of clathrate hydrates. The oversolar C/N ratio and the strong depletion of Ne/O with respect to the solar abundance observed in comets are in agreement with the theory of clathrate hydrates of J. I. Lunine and D. J. Stevenson (1985, Astrophys. suppl. Ser.58, 493). Comets formed in the Kuiper belt may contain amorphous water ice and have kept the isotopic signature of the presolar cloud. New published models of interiors of Uranus and Neptune permit us to calculate that the D/H ratios in proto-uranian and proto-neptunian water ices are in agreement with those measured in comets. This confirms the current assumption that cometesimals and planetesimals that formed the cores of Uranus and Neptune had similar compositions.
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^fn1: Expanded version of a talk presented at the Asteroids, Meteors and Comets Meeting (Versailles, June 1996).

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Simulation of the water and carbon monoxide production rates of comet Hale–Bopp using a quasi 3-D nucleus modelfn1

Abstract

Introduction

Section snippets

Composition

Physical and numerical parameters

Results

Extended water source

Conclusions

Acknowledgements

Tectonophysics

Science

Moon and Planets

Science

Astronomy and Astrophysics

Icarus

Icarus

J. Chem. Phys.

The heat capacity of ice from