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Astron. Astrophys. 364, 887-893 (2000)

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1. Introduction

The capture of comets from the Oort Cloud (Oort 1950) is a subject with a long history and fruitful results (e.g. Newburn et al. 1991). Up to now there are nearly 940 comets with computed orbits recorded (end of 1997), of which about [FORMULA] are long-period (with period [FORMULA] yr) comets (Fernández 1999). Most of the discovered long-period (LP) comets have the perihelion distance q smaller than a few AU. Only 10 have perihelia beyond Jupiter's orbits ([FORMULA]AU), the comet C/1991 R1 (McNaught-Russel) being the farthest with [FORMULA]AU. The study of evolution of the LP comets subject to the perturbations of the outer planets led to the idea that the short-period (SP) comets could be the end products of the dynamical evolution of LP comets. The short-period (SP) comets are divided into two families: Halley-family comets (20yr[FORMULA]yr or [FORMULA], where T is the Tisserand parameter with respect to Jupiter) and Jupiter-family comets ([FORMULA]yr or [FORMULA]). Due to the flat near-ecliptic distribution, the Jupiter-family comets (JFCs) are believed to originate from a flat trans-Neptunian source (Duncan et al. 1995). As the Halley-family comets (HFCs) may come from the Oort Cloud, the question as to whether this mechanism is sufficient to maintain a steady-state population of the HFCs is still open (Fernández 1999).

One of the major difficulties in the statistical study of the comet dynamics is that one needs to integrate orbits of millions of comets over the lifetime of the Solar System, which is beyond the capacity of existing computers. Consequently, Monte Carlo simulations have been used (see, e.g. Valtonen et al. 1998). In recent years the map approach has been used widely in the study of long-term evolution of celestial bodies. It approximates the differential equation system with a map system, with the main properties of the original system being kept. The use of a map instead of integrating the original system saves much computing time, and it is easier to handle both analytically and numerically (for a review, see Froeschlé 1998).

For the study of comets captured from the Oort Cloud, Petrosky & Broucke (1988) and Liu & Sun (1994) have derived two-dimensional area-preserving maps, approximating the model of the restricted three-body problem. Recently, for the evolution of comets in high-eccentricity planet-crossing orbits, Malyshkin & Tremaine (1999) obtained a two-dimensional map similar to the Keplerian map obtained by Petrosky & Broucke (1988), and studied the role of resonance sticking on the evolution of cometary orbits. They have also compared the results obtained by the map with those by direct integrations of the cometary orbits. A good correspondence between both proved the map to be very helpful in the study of comet dynamics.

In this paper we study the transfer of comets from the Oort Cloud to the HFCs. The arrangement of the paper is as follows. In Sect. 2, we present the map model adopted for this work. In Sect. 3 the map is used to study the transfer of comets from near-parabolic orbits to short-period ones. The dependence of transfer probability and of the average capture time on the perihelion distance of cometary orbits and on the mass of the planet is computed in this section. Conclusions of the paper are given in the final section.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001