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

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4. Conclusions

In this paper, we studied the dynamical transfer of comets from near-parabolic orbits to short period ([FORMULA]) orbits, under the perturbation of a large planet. Numerical results showed that due to the difference of average energy change per perihelion passage, the transfer of comets on planet-crossing orbits (with [FORMULA]) is more efficient than the transfer of comets in non-crossing orbits ([FORMULA]). The comets with [FORMULA] are easier to be transferred in both direct and retrograde motions. For the comets with [FORMULA], only those on direct orbits with q near 1 have a higher probability of transfer. According to our calculations, the flux of transferred comets with [FORMULA] is about 4 times as large as that of [FORMULA] on direct orbits. It is difficult to confirm this conclusion at the moment by observations since the small amount of observed SP comets.

The size of the HFCs comets population has been estimated by several authors (e.g. Fernández & Gallardo 1994). Even though the number of actually known HFCs is only somewhat more than 20, the observations are strongly biased towards small perihelion distances and bright absolute magnitudes. From the observed frequency of apparitions of new comets and making allowance for missed comets, the influx rate of new comets interior to Jupiter's orbit brighter than absolute magnitude 11 is about 0.5 yr-1AU-1 (Fernández & Ip 1991). This gives about 2.6 comets/year interior the Jupiter orbit. According to our results, the integral transfer propability is 0.12 for comets in direct motions and 0.067 for those in retrograde motions. Provided a mean value of transfer probability 0.09, the flux of HFCs transfered from the new comets flux is thus 0.23 comets per year in the regions [FORMULA] AU. Supposing the physical lifetime of a typical HFC as [FORMULA] year (e.g. Levison & Duncan 1994), the steady-state population of HFCs interior Jupiter's orbits is [FORMULA]. This can be compared with the steady-state population of 300 HFCs with [FORMULA]AU according to the estimate of Fernández & Gallardo (1994).

Among HFCs the retrograde comets represent less than [FORMULA] of the total population. We expect retrograde comet captures (in practice) only from [FORMULA], and also their [FORMULA] is generally lower than in direct orbits. According to our resluts, the retrograde comets should be [FORMULA]. This is somewhat overestimated. We think this is mainly due to the plannar approximation of the model. The actual ratio also depends on the width of the capture region in inclination which we have not studied here. However, from previous studies (e.g. Valtonen et al. 1992) we know that the capture probability as a function of inclination follows reasonably well the inclination distribution of Halley type comets.

The transfer of comets is a subject of orbital energy evolution under the perturbations of planets. In the case of Jupiter perturbations, the evolution of the orbital energy for a comet with [FORMULA] obeys the diffusion approximation, i.e., the relation (14) holds, due to the small average energy exchange per passage as compared with the total transferred energy -0.152. However for the comets with [FORMULA], due to the large average energy change, the evolution of the energy may not obey the diffusion approximation. This is related to the problem of the validity of the diffusion approximation on the comet evolution, which will be addressed in more detail in our future works.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001