T. Paulech

The simulation of the outer Oort cloud formation - The first giga-year of the evolution

Aims. Considering a model of an initial disk of planetesimals that consists of 10 038 test particles, we simulate the formation of distant-comet reservoirs for the first 1 Gyr. Since only the outer part of the Oort cloud can be formed within this period, we analyse the efficiency of the formation process and describe approximately the structure of the part formed. Methods. The dynamical evolution of the particles is followed by numerical integration of their orbits. We consider the perturbations by four giant planets on their current orbits and with their current masses, in addition to perturbations by the Galactic tide and passing stars. Results. In our simulation, the population size of the outer Oort cloud reaches its maximum value at about 210 Myr. After a subsequent, rapid decrease, it becomes almost stable (with only a moderate decrease) from about 500 Myr. At 1 Gyr, the population size decreases to about 40% of its maximum value. The efficiency of the formation is low. Only about 0.3% of the particles studied still reside in the outer Oort cloud after 1 Gyr. The space density of particles in the comet cloud, beyond the heliocentric distance, r ,o f 25 000 AU is proportional to r −s ,w heres = 4.08 ± 0.34. From about 50 Myr to the end of the simulation, the orbits of the Oort cloud comets are not distributed randomly, but high galactic inclinations of the orbital planes are strongly dominant. Among all of the outer perturbers considered, this is most likely caused by the dominant, disk component of the Galactic tide.

Probing the relation between the structure of initial proto-planetary disc and the Oort-cloud formation

Aims. The Oort cloud consists of cometary nuclei which were ejected from the once existing proto-planetary disc to large heliocentric distances by the giant planets. The process of the cloud formation depended on the initial structure and mass of the disc. Considering four models of an initial proto-planetary disc, we roughly probe this dependence. Methods. We use the resultant data of our previous simulation of the Oort cloud formation for the first two Gyr. The considered disc models consist of a set of representative test particles. The new models are created subtracting a fraction of the particles from the model considered in our previous work, in a way to obtain the required heliocentric-distance distribution. Specifically, we focus on the situations in which a part of the small bodies in the disc is assumed to be already spent in the previous process of the giant planet formation. We omit the particles from an originally smooth profile in the regions adjacent to the planet orbits. With the reduced data, we construct the comet cloud characteristics we are interested in. Results. We find that it is difficult to construct the proto-planetary disc if (i) the amount of heavy chemical elements in Jupiter and Saturn is as high as currently accepted (≈20 and ≈29 M⊕; respectively) and (ii) the total mass of the minimum-mass solar nebula is assumed to be lower than ≈0.05 M . The behaviour of the Oort cloud formation does not crucially depend on the initial disc model. Some quantitative differences in its structure are obvious: since the cloud is known to be filled mainly by Uranus and Neptune, the efficiency of its formation is higher if the initial amount of particles in the Uranus-Neptune region is relatively higher. The efficiency is also higher in the gapped-disc models because a less amount of particles experience a very close encounter with a planet resulting in their ejection into the interstellar space.

Notes on the outer-Oort-cloud formation efficiency in the simulation of Oort cloud formation (Research Note)

Aims. The formation efficiency of the outer Oort cloud, obtained in the simulation performed in our previous work, appeared to be very low in a comparison with the corresponding results of other authors. Performing three other simulations, we attempt to find if any of three possible reasons can account for the discrepancy. Methods. The dynamical evolution of the particles is followed by numerical integration of their orbits. We consider the perturbations by four giant planets on their current orbits and with their current masses, in addition to perturbations by the Galactic tide and passing stars. Results. The omission of stellar perturbations causes only a small increase (about ≈10%) in the population size, because the erosion by stellar perturbations prevails upon the enrichment due to the same perturbations. As a result, our different model of them cannot result in any huge erosion of the comet cloud. The relatively shorter border, up to which we followed the dynamics of the test particles in our previous simulation, causes a significant (about a factor of ≈2) underestimate of the outer-Oort-cloud population. Nevertheless, it by itself cannot fully account for an order-of-magnitude difference in the formation-efficiency values. It seems that the difference could mainly stem from a large stochasticity of the comet-cloud formation process. Our maximum efficiency can grow to more than three times the corresponding minimum value when using some subsets of test particles.