Oort Cloud Formation in a Dense Galactic Environment

It is now known that most stars form in clusters. In [47], it was pointed out that a denser galactic environment would have exerted a stronger tide on the scattered planetesimals. In addition, stellar encounters would have been more effective, because of the slower relative velocities and smaller approach distances typical of a cluster environment. As a consequence, the threshold semi-major axis value beyond which planetesimals could be decoupled from the planets would have been ~1,000AU, instead of the current value of ~10,000AU. In other words, the Oort cloud would have extended closer to the Sun, covering the region with binding energy down to 10-3 in normalized units. Because this width is of the same order as the energy change suffered by planetesimals crossing the orbits of Jupiter and Saturn, the role of these gas giants in building the Oort cloud would be greatly enhanced.

Simulations of Oort cloud formation in a dense environment have been done in [49]. Three kinds of environments were considered: (i) a loose cluster with 10 stars pc-3; (ii) a dense cluster with 25 stars pc-3; and (iii) a superdense cluster with 100 stars pc-3. In all cases, all stars were assumed to have a solar mass (compare with the current stellar density of 0.041 M0 pc-3 [33]). The average relative velocity among the stars was assumed to be 1kms-1, typical of star clusters [11] (instead of the current ~40kms-1). In addition, a placental molecular cloud containing 105 molecules of Hydrogen per cm3 was assumed (the current molecular density is ~3gcm-3). The initial conditions of the planetesimals were similar to those in [36]. Comets were placed on initial orbits with 100 < a < 250 AU and q ranging from 4 to 30 AU.

Figure 25 shows the result of these simulations. As expected, the denser the cluster, the more tightly the resulting Oort cloud is bound to the Sun. Notice, however, that the outer part of the cloud (beyond 104 AU) becomes totally empty, because all comets beyond this limit are stripped off by the loose dense superdense

Fig. 25. A sketch showing how comets trapped in the Oort cloud would appear distributed in the circumsolar space, for three kinds of star clusters surrounding the Sun. The radii of the circles are expressed in AU. Stars denote comets coming from Jupiter-Saturn zone, while open circles denote bodies from the Uranus-Neptune zone. From [49]

Fig. 25. A sketch showing how comets trapped in the Oort cloud would appear distributed in the circumsolar space, for three kinds of star clusters surrounding the Sun. The radii of the circles are expressed in AU. Stars denote comets coming from Jupiter-Saturn zone, while open circles denote bodies from the Uranus-Neptune zone. From [49]

passing stars. Thus, a mechanism would be required to transfer the comets from the massive inner Oort cloud to the outer cloud, to explain the current flux of LPCs (which come from the outer cloud only). Less effective stellar encounters, occurring during the dispersal of the cluster and in the current galactic environment, might be responsible for this process.

In terms of efficiency of Oort cloud formation, [49] found that about 30% of the initial planetesimals were trapped in the cloud, a factor of 6 higher than in [33]. However, this new efficiency is of the same order of that found in [36], which used initial conditions similar to those in [49], but no star cluster. Thus, it is unclear if the difference in efficiency between [49] and [33] is due to the different choice of initial conditions (in which case the efficiency in [33] is more accurate because the initial conditions are more realistic) or to the presence of the cluster. Moreover, a totally unexpected result was that the final contribution of Jupiter and Saturn to the formation of the Oort cloud (i.e., the fraction of the planetesimal population with initial q < 10 AU that ended in the cloud) was minimal. This happened because the planetesimals scattered by Jupiter and Saturn typically ended up in the outer part of the cloud and were subsequently stripped away by the numerous stellar encounters.

More recently, [15] revisited the problem and simulated the evolution of particles initially on circular and coplanar orbits in the Jupiter-Saturn region in presence of a local clusters of various densities. The authors found that, for clusters with densities (gas plus stars) of 5 x 103-104 M0 pc~3 in the vicinity of the Sun, about 10-15% of the simulated particles are trapped in the inner Oort cloud (extending from a few 100 AU to ~10,000AU) at the end of the simulation.

The study of the formation of the Oort cloud in a dense environment is not finished, however. It is still necessary to quantify which mechanism could transfer the comets from the massive inner Oort cloud - produced in the dense environment - to the outer Oort cloud - where comets must reside at the current time to produce LPCs, and the efficiency of this process. Moreover, it would be more realistic to re-do the simulations in [15], taking into account the effect of gas drag, given that the gas-disk was present for most of the time that the Sun spent in the cluster. Gas drag could protect comets from ejection (Levison, private communication), thus increasing further the fraction of planetesimals from the Jupiter-Saturn zone that are trapped in the cloud.

Sedna: An Inner Oort Cloud Object?

One piece of evidence for a moderate stellar cluster surrounding the early Sun is provided by Sedna. The distribution of the Extended Scattered disk bodies shows a clear tendency. In the 50-60 AU region 2004 XR190 has q ~ 50 AU, but this region is affected by many resonances that can raise the perihelion distance (see Sect. 4.2). Further out, the perihelion distance is larger for bodies with larger semi-major axis: up to ^200 AU the Extended Scattered disk bodies have q < 41.5 AU; 2000 CR105 (a = 222 AU) has q = 44.3AU and

Sedna (a = 495 AU) has q = 76 AU. Although only a few such bodies are known - and one should be careful about small number statistics - the lack of objects with perihelion distances comparable to those of 2000 CR105 and Sedna but smaller semi-major axes seems significant. In fact, observational biases (given an object's perihelion distance and absolute magnitude, and a survey's limiting magnitude of detection) sharply favor the discovery of objects with smaller semi-major axes. So, it would be unlikely that the first two discovered bodies with q> 44 AU have a> 200 AU if the real semi-major axis distribution in the Extended Scattered disk were skewed toward smaller a.

Assuming that the Extended Scattered disk bodies belonged to the Scattered disk until a perturbation lifted their perihelion distance beyond Neptune's reach, the fact that q increases with a is a clear signature that the perturbation had to grow in magnitude with increasing heliocentric distance. Passing stars produce this very signature [49,129,146]. In particular, it was shown in [129] that an encounter with a solar mass star at 800 AU with an unperturbed relative velocity of 1kms_1 (see Fig. 26) would have produced

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