Orbital linkages of Comet 6P/d'Arrest based on its asymmetric light curve

We present an investigation of different models of the nongravitational acceleration on Comet 6P/d'Arrest, as used in orbital linkages spanning 150 years from the discovery of the comet in 1851 until the recent observations made in 2001. Some of our models use the time-shifted g-like function to represent the variation of outgassing rate, but the main thrust is on models using instead a production curve that is fitted to recent light curve observations—mainly those in 1976. We pay special attention to the proper scaling of such a production curve, when applied to other apparitions with a different perihelion distance q, and we find a best fit with a q^−1.6 power-law. Generally, the best fit is found with models, in which the acceleration components are expressed in terms of the angular parameters of the rotating nucleus. We thus find the orientation of the spin axis, and using the orbital evolution we are able to predict a variable time shift of the outgassing curve. The very best results are found when applying this time shift to the light-curve based, angular models. The totality of the 1851-2001 observations can then be linked with a mean residual of less than 4″. This may be brought down to ∼^2″ by solving for individual ‘activity parameters’ of all apparitions, which are multiplicative factors applied to the acceleration amplitudes. These turn out to be within 10% of unity for the best fit. We have also performed a linkage to the observations of Comet 1678 (La Hire) using our models. We find an indication of a secular increase of the amount of asymmetry of the outgassing with respect to perihelion, part of which is due to the variable time shift caused by the orbital evolution.     

Comet 9P/Tempel 1: Sublimation beneath the dust cover

In the current work we analyze properties of the dust mantle, its thickness and thermal conductivity, necessary to reproduce observed rate of water production of Comet 9P/Tempel 1. For this purpose we considered simplified shape of the comet nucleus approximated by the symmetric prolate ellipsoid with smooth surface. We have performed simulations, using models with dust mantle of the thickness either constant, but nonuniform (Model A), or evolving (Model B). The simulated profiles of water production versus time were compared with observations. In addition, we compared the calculated surface temperature with the real temperatures derived from IR observations (the Deep Impact mission). This new double-stage verification procedure, shows that our model A is a good representation for the nucleus of Comet Tempel 1. This indicates, that the dust mantle thickness should be nonuniform, but does not change significantly with time. We show, that reproducing observed high temperatures of the nucleus requires dust mantle, that is almost everywhere thick and has extremely low thermal inertia. The latter should be close to zero as already predicted by others. The agreement between the simulated and measured water production can be obtained when the dust is regionally thin and has the thermal inertia higher than average, according to our simulations about 100 W s^1/2 K⁻¹ m⁻². Such regions should be located in the south hemisphere of the nucleus.     

Comet 17P/Holmes: Possibility of a CO driven explosion

This work is a continuation of our previous paper about brightening of Comet 17P/Holmes (Kossacki, K.J., Szutowicz, S. [2010]. Icarus 207, 320–340). In that paper we presented results of simulations indicating that the nonuniform crystallization of amorphous water ice itself is probably not sufficient for an explosion. In the present work we investigate the possibility that the explosion is caused by a rapid sublimation of the CO ice leading to the rise of gas pressure above the tensile strength of the nucleus. We simulated evolution of a model nucleus in the orbit of Comet 17P/Holmes. The nucleus is composed of water ice, carbon monoxide ice and dust and has the shape of an elongated ellipsoid. The simulations include crystallization of amorphous ice in the nucleus, changes of the dust mantle thickness, and sublimation of the CO ice. In our model CO is mantling grains composed of dust and amorphous water ice. Orientation of the nuclear spin axis in space is the same as derived in Moreno et al. (Moreno, F., Ortiz, J.L., Santos-Sanz, P., Morales, N., Vidal-Nunez, M.J., Lara, L.M., Gutierrez, P.J. [2008]. Astrophys. J. 677, L63–L66) for Comet Holmes during recent brightening event. Hence, the angle between the orbital and the equatorial planes of the comet is I = 95°, and the cometocentric solar longitude at perihelion is Φ = 210°. The calculations are performed for the south pole being the sub-solar point close to time of the outburst. Our computations indicate, that the CO pressure within the comet nucleus can rise to high values. When the layer between the dust mantle and the crystallization front of the amorphous water ice is very fine grained, few microns in radius, the CO pressure within the nucleus can exceed 10 kPa. This value is the lowest estimate for the tensile strength of the nucleus of Comet Holmes (Reach, W.T., Vaubaillon, J., Lisse, C.M., Holloway, M., Rho, J. [2010]. Icarus 208, 276–292). Hence, when the gas pressure reaches this value the nucleus may explode.     

Evolution of depressions on Comet 67P/Churyumov-Gerasimenko: Role of ice metamorphism

This work is intended to investigate the influence of temperature-dependent metamorphism of ice on the shape of small depressions in the surface of cometary nuclei. We are mainly interested in the role of initial cohesivity of a nucleus. For this purpose we simulate sublimation of ice from the facets of initially cylindrical depressions in ice of different initial structure. The simulations account for the diurnal and orbital changes of insolation and its dependence on the current shape of the depressions. Our model includes heat transport in the cometary material and metamorphism of ice. We present the results obtained for the nucleus of the Comet 67P/Churyumov-Gerasimenko, target of the ESA cornerstone mission Rosetta.     

Comet 67P/Churyumov-Gerasimenko: Modeling of orientation and structure

The comet 67P/Churyumov-Gerasimenko is the current target of the mission Rosetta, initially planned to investigate comet 46P/Wirtanen. These two comets have similar orbits, except the distance to the Sun at perihelion, but different orbital histories and different masses. Thus, structures of the nuclei can be significantly different. The evolution of comet Wirtanen was simulated by several authors, while comet Churyumov-Gerasimenko became an object of high interest only recently and is not well investigated. In the present work we simulate the evolution of the nucleus, down to tens of meters below the surface, using an extended version of the model previously applied for comet Wirtanen [Kossacki et al., 1999. Comet 46P/Wirtanen: evolution of the subsurface layer. Icarus 142, 202-218.]. The model includes strengthening of the nucleus due to sintering of the ice grains. Simulations are performed for different latitudes, accounting for the evolution of the orbit and for changes of the nucleus orientation, as well as diurnal and seasonal changes of insolation. The calculated loss of water vapor from the comet is integrated over the nucleus surface and is compared with the observational data. We have found, that the sublimation through the dust mantle can be large enough to reproduce the profile of the total water production as a function of time from perihelion. The required dependence of thickness of the dust layer on latitude qualitatively matches present distribution of the absorbed solar flux. The non-gravitational acceleration in the comet motion together with the simulated sublimation flux are used in order to estimate the mass and the bulk density of the nucleus.     

HCN and CN in Comet 2P/Encke: Models of the non-isotropic, rotation-modulated coma and CN parent life time

Axisymmetric models of the outgassing of a cometary nucleus have been constructed. Such models can be used to describe a nucleus with a single active region. The models may include a solar zenith angle dependence of the outgassing. They retrieve the outgassing flux at distances from the nucleus where collisions between molecules are unimportant, as function of the angle with respect to the outgassing axis. The observed emissions must be optically thin. Furthermore the models assume that the outflow speed at large distance from the nucleus does not depend on direction. The value of the outflow speed is retrieved. The models are applied to CN images and HCN spectra of Comet 2P/Encke, obtained nearly simultaneously in November 2003 with the 2 m optical telescope on Mount Rozhen, Bulgaria, and with the 10 m Heinrich Hertz Submillimeter Telescope on Mount Graham, Arizona, USA. According to Sekanina (1988), Astron. J. 95, 911-924, at that time a single outgassing source was active. Input parameters to the models like the rotation period of the nucleus and a small correction to Sekanina’s rotation axis are determined from a simpler jet position angle model. The rotation is prograde with a sideric period of 11.056 ± 0.024 h, in agreement with literature values. The best fit model has an outflow speed of 0.95 ± 0.04 km s⁻¹. The same value has been derived from the corkscrew appearing in the CN images. The location of the outgassing axis is at colatitude δ_a = 7.4° ± 2.9° and longitude λ_a = 235° ± 17° (a definition of zero longitude is provided). Comet Encke’s outgassing corresponds approximately to the longitudinally averaged solar input on a spherical nucleus (i.e. very likely comes from deeper layers) but with some deficiency of outgassing at mid-latitudes and non-zero outgassing from the dark polar cap. The presence of gas flow from the dark polar cap is explained as evidence of gas flow across the terminator. The models rely mostly on the CN images. The HCN spectra are more noisy. They provide information how to determine the best fit outflow velocity and the sense of rotation. The model HCN spectra are distinctly non-Gaussian. Within error limits they are consistent with the observations. Models based solely on the HCN spectra are also presented but, because of the lower quality of the data and the unfavorable observing geometry, yield inferior results. As a by-product we determine the CN parent life time from our CN observations. The solar EUV and Lyα radiation field at the time of our observations is taken into account.     

Crystallization of ice in Comet 17P/Holmes: Probably not responsible for the explosive 2007 megaburst

Our work was inspired by the recent brightening of Comet 17P/Holmes. The recently observed increase in brightness of this comet was correlated with emission of dust, probably larger in mass than the dust mantle of the nucleus. We analyzed the hypothesis that the comet can eject a large mass of dust due to non-uniform crystallization of amorphous water ice. For this purpose, we simulated the evolution of a model nucleus on the orbit of Comet 17P/Holmes. The nucleus is composed of water ice and dust and has the shape of an elongated ellipsoid. The simulations include crystallization of amorphous ice in the nucleus, changes in the dust mantle thickness, and changes in the nucleus orientation in space. Our computations indicate that: (i) ejection of the dust cover triggers crystallization of ice independently on the material properties of the nucleus; (ii) moderate changes in the nucleus orientation (∼50°) may result in an acceleration of the crystallization of ice in the northern hemisphere, while a rather large change in the orientation (∼120°) is needed to cause a significant jump of the crystallization front in the southern hemisphere, where the emission of dust during the recent brightening was strongest. We investigated the possible reason for an explosion and we have found that the crystallization of the water ice itself is probably not sufficient.     

Main Belt Comet P/2008 R1 Garradd: Duration of activity

In this work we investigated changes of the water emission from a model comet of the size and orbital elements of Comet P/2008 R1 (Garradd). We performed simulations for model cometary nuclei of different compositions and two different orientations in space. Our simulations indicate, that the emission of water decreases from one orbital period to another one, but in some cases slowly. When the rotation axis of the nucleus lies in the orbital plane the seasonal maximum of water production during the first two orbital periods can be as high as about 10²⁶ mol s^?1, but decreases by two orders of magnitude during only 50 orbital periods. The highest rate of water production after many orbital periods is expected when the rotation axis is perpendicular to the orbital plane – the seasonal maximum of water production can be about 5 × 10²⁵ mol s^?1 during the first two orbital periods after activation of the comet and no more than 0.8 × 10²⁵ mol s^?1 500 orbital periods later. The upper estimate for the production of water derived from observations of P/2008 R1 (Garradd) by Jewitt et al. (Jewitt, D., Yang, B., Haghighipour, N. [2009]. Astron. J. 137, 4313–4321) is 5 × 10²⁵.     

A Study of Non-Gravitational Effects of Comet C/1995 O1 HALE–BOPP

The role of non-gravitational forces in the evolution of orbitalmotion of C/1995 O1 (Hale–Bopp) has been investigated. Inorbital calculations the observational material covering theperiod from April 1993 up to August 2001 was used. To model thenon-gravitational acceleration, observed and theoretical profilesof the H₂O production rates were employed. A set of forcedprecession models of a rotating cometary nucleus consistent withthe observed spin axis orientation was fitted to positionalobservations. The non-gravitational models allowed us to constrainthe mass and radius of the comet. The orbitalevolution of Comet Hale–Bopp was investigated over ±400 k yusing two sets of randomly varied orbital elements wellrepresenting all positional observations in the pure gravitationalcase, as well as in the non-gravitational case. The calculationsshowed that the comet's motion is predictable only over an interval ofa few orbital periods. The statistical conclusions changesignificantly when non-gravitational effects are included in the analysis.