Info

Fig. 15. The differential distribution of LPCs as a function of the inverse semimajor axis. The big spike at 1/a < 10~4 is due to the new comets and is usually called the Oort spike. From [183]

a minimum and Z a maximum when U = 0°, 180°.8 The difference between the maximum and the minimum values of e and Z increases when a increases or Hz decreases. There is no variation of e and Z if Z = 0.

Thus, Oort cloud comets with high inclination relative to the galactic plane, under the effect of the tide, increase their orbital eccentricity; their perihelion distance decreases and the objects become a planet-crosser. If this evolution is fast enough that q decreases from beyond 10 AU to less than — 3 AU within half an orbital period, the comet becomes active during its first dive into the inner Solar System (i.e., without having interacted with Jupiter or Saturn during its previous orbits), namely it appears as a "new comet." The perturbations from the planets remove the planet-crossing comets from the Oort cloud, by either decreasing their semi-major axis or ejecting them from the Solar System on hyperbolic orbits. Thus, the high inclination portion of the Oort cloud is progressively depleted. The role of passing stars and GMCs is to reshuffle the comet distribution in the Oort cloud and to refill the high inclination region where comets are pushed into the planetary region by the disk's tide. Of course, stars and GMCs can also directly deflect the cometary trajectories, injecting the comets into the inner Solar System without the help of the galactic tide. This happens particularly during comet showers caused by close encounters between the Sun and these external perturbers [78,84]. These directly injected comets do not need to have a large inclination relative to the galactic plane.

The transfer of comets from the Oort cloud to the inner Solar System has been simulated by many authors, in particular by [78,178] and, more recently, [183]. In what follows I will mostly refer to this latter, most modern work.

In [183], the Oort cloud was modeled as a collection of objects with 10,000 < a < 50,000 AU, a differential distribution N(a)da <x a-15 and uniform distribution on each energy hyper-surface, consistent with an earlier model of Oort cloud formation [36]. The evolution of the comets was followed numerically, under the influence of the galactic disk's tide and of the four giant planets, with the latter assumed to be on coplanar circular orbits. Stellar and GMC passages, as well as the radial component of the galactic tide, were neglected. Figure 16a shows the cos) distribution of the simulated comets at their first passage within 3 AU from the Sun (the limit assumed for comet physical activity and visibility). The distribution peaks at cosZ= ±0.5 and is relatively depleted at cosZ = ±1 and 0. This is the signature of the galactic tide. Comets with Z — 0° (or equivalently, Z — 180°) have an oscillation in the perihelion distance that is too small to bring them from the trans-planet region into the visibility region. Comets with initial Z — 90° have their inclination decreased to lower values by the time that the perihelion distance is decreased below 3AU. Similarly, Fig. 17a shows the uU distribution. The

8Here I assume that I is defined in the range between —90° and 90° (negative I corresponding to retrograde orbits relative to the galactic plane), and by "maximum" and "minimum" I mean the maximum and minimum of \Z\

Fig. 16. The inclination distribution relative to the galactic plane for new comets. (a) (left): result of a numerical simulation. (b) (right): the observed distribution. Here I is defined in the range between 0° and 180°; values of I larger than 90° correspond to retrograde orbits relative to the galactic plane. From [183]

Fig. 16. The inclination distribution relative to the galactic plane for new comets. (a) (left): result of a numerical simulation. (b) (right): the observed distribution. Here I is defined in the range between 0° and 180°; values of I larger than 90° correspond to retrograde orbits relative to the galactic plane. From [183]

peaks at u ~ 1/4n and 3/4n are, again, a signature of the galactic tide. In fact, the precession of u is counter-clockwise, and the minimal q is achieved when u = n/2, 3/2n. Thus, the perihelion distance decreases below the imposed threshold q = 3AU when u is en route from 0 to n/2 or from n to 3/2n. Figures 16b and 17b show the same distributions for the observed new comets. The observed and simulated distributions are quite similar, which confirms the dominant role of the galactic tide. However, the peak and valleys observed in the simulated distributions are not nearly as pronounced as those in the observed dataset. This suggests that the direct injection of comets from the Oort cloud because of passing stars and/or GMCs (neglected in the simulation) has non-negligible importance.

Fig. 17. The same as Fig. 16, but for the distribution of the argument of perihelion relative to the galactic plane. From [183]

0 2x10-" 4x10-" 6x10-" 8x10-" 0.0001 1/a (1/AU)

Fig. 18. The distribution of 1/a of the comets at their first appearance (q < 3AU) from the Oort cloud, according to [183]. The sharp fall-off at 1/a = 2 x 10-5 AU-1 is due to the choice of the initial conditions (a < 50, 000 AU)

0 2x10-" 4x10-" 6x10-" 8x10-" 0.0001 1/a (1/AU)

Fig. 18. The distribution of 1/a of the comets at their first appearance (q < 3AU) from the Oort cloud, according to [183]. The sharp fall-off at 1/a = 2 x 10-5 AU-1 is due to the choice of the initial conditions (a < 50, 000 AU)

Figure 18 shows the distribution of 1/a for the comets at their first apparition, still according to the simulation in [183]. Notice the sharp fall off at a < 20,000 AU (1/a > 5 x 10~5 AU-1) that reproduces the one observed in the 1/a distribution of LPCs (see Fig. 15). Thus, essentially all comets at their first apparition have semi-major axes beyond 20,000 AU and therefore would be classified as "new comets" by an observer. This sharp fall off is due to the so-called Jupiter barrier. The fact is that new comets must have decreased their q from > 10 AU to < 3 AU in less than one orbital period, otherwise they would have encountered Jupiter and Saturn during an earlier revolution, and most likely would have been ejected from the Solar System. This condition is fulfilled only if the semi-major axis is larger than ^20,000 AU. The implication of this result is that LPCs do not probe the Oort cloud inside this semi-major axis threshold, except during rare showers because of a very close encounter between a passing star and the Solar System (which allows a rapid decrease of q even for a <20,000 AU; see [77]). Therefore, our information on the inner Oort cloud does not come from the observations of comets, but solely from models of Oort cloud formation (see Sect. 3).

From the fraction of the Oort cloud population that enters the visibility region per unit time, and the flux of new comets with H10 < 11 and q < 3AU estimated from observations, [183] concluded that the Oort cloud population with a >20,000 AU and H10 < 11 is ~ 1012. This estimate agrees with [179], and is two times higher than that in [78], which gives a measure of its uncertainty. For the reason explained above, the estimated population in the Oort cloud with smaller semi-major axis is totally dependent on the model of Oort cloud formation.

The evolution of the comets, from their first apparition to their ultimate dynamical elimination, has also been followed in [183]. If the orbital elements of all comets at every passage at q < 3 AU are added up (without limitation

Fig. 19. The distribution of the inverse semi-major axis of all LPCs, independent of the number of perihelion passages within 3 AU, according to the simulation in [183]. This distribution is very different from that observed, illustrated on the same scale in Fig. 15

Fig. 19. The distribution of the inverse semi-major axis of all LPCs, independent of the number of perihelion passages within 3 AU, according to the simulation in [183]. This distribution is very different from that observed, illustrated on the same scale in Fig. 15

on the number of perihelion passages that they already suffered), the resulting distribution of 1/a (Fig. 19) is very different from the observed distribution (Fig. 15). In particular, the ratio between the number of comets in the Oort spike and the number of returning comets is much smaller than observed. This problem was already pointed out in [140]. As suggested by Oort himself, this mismatch indicates that comets from the Oort cloud have a very limited physical lifetime: after a few perihelion passages, they fade away from visibility, either by becoming inactive or disintegrating. In [183], it was shown that a very good match with the observed distribution of LPCs can be achieved if one assumes that the probability Pm that a comet is still active after m perihelion passages within 3 AU decays as m-0 6. This fading law implies that only 10% of the comets survive more than 50 passages and only 1% of them survive more than 2,000 passages. Other equally drastic fading laws, such as Pm = 1 for m < 6 and pm = 0.04 for m > 6 [177], can also reproduce the observed distribution of LPCs.

Therefore, the conclusion is that comets from the Oort cloud fade very quickly, in just a few revolutions. This is very different behavior to that of JFCs, which have a physical lifetime of ~ 10, 000 years (they remain active for about 1,000 revolutions). The fate of faded comets (disruption versus inactivity) for both LPCs and JFCs is discussed in Sect. 2.4.

2.3 Note on Halley-Type Comets

The HTCs have traditionally been considered as the low semi-major axis end of the returning LPC distribution. Indeed, at a first glance, the distribution of HTCs and of returning LPCs (apart from the semi-major axis range that they cover) appear fairly similar.

Under the effect of close encounters with Jupiter and Saturn, some returning comets can have their semi-major axis decreased to less than 34.2 AU. At that point, their orbital period becomes shorter than 200 years, so that, by convention, they are classified as SPCs. They are predominantly HTCs, and not JFCs, because their Tisserand parameter relative to Jupiter is typically smaller than 2. The reason for this is that new comets from the Oort cloud, having q < 3, a ~ ro, e ~ 1 must have Tj < 2.15, and the Tisserand parameter remains roughly conserved during the subsequent evolution down to the SPC region, because of the dominance of Jupiter's perturbations. The transfer of comets from the Oort spike to the HTC region typically requires a large number of revolutions. Thus, the HTCs should belong to the small fraction 4%) of Oort cloud comets that do not fade away rapidly.

This transfer process from the Oort cloud to the HTC region has been revisited recently in [109], using state-of-the-art numerical simulations. It was found that, although the semi-major axis distribution of the HTCs obtained in the simulations is a reasonable match for the observed distribution, the inclination distributions are profoundly different (Fig. 20). In particular, the median inclination distribution of the observed HTCs is 45°, and 80% have a prograde orbit, whereas the median inclination of the HTCs obtained in the simulation is 120° and only 25% of them have prograde orbit. The reason that the simulated distribution is skewed toward retrograde objects is that such orbits have a longer dynamical lifetime (100,000 years, as opposed to 60,000years for prograde HTCs).

In [109], to solve the mismatch between the inclination distributions, the authors proposed that part of the HTCs come from the inner Oort cloud (a < 20,000 AU) and that this reservoir has a disk-like structure, with

Sent-rMjMAxts.stAUJ lrfnalDn, 1 (Deg>

Fig. 20. Comparison between the cumulative orbital element distributions of the observed HTCs (dotted line) and those produced in the integrations of [109] (solid line). (a) Semi-major axis distributions; (b) inclination distributions. Note the significant disagreement in the inclination distributions. Only comets with q < 1.3AU are considered

Sent-rMjMAxts.stAUJ lrfnalDn, 1 (Deg>

Fig. 20. Comparison between the cumulative orbital element distributions of the observed HTCs (dotted line) and those produced in the integrations of [109] (solid line). (a) Semi-major axis distributions; (b) inclination distributions. Note the significant disagreement in the inclination distributions. Only comets with q < 1.3AU are considered inclinations within 50° of the ecliptic. However, modern formation models of the Oort Cloud (see Sect. 3 and Fig. 23) show that retrograde orbits in the Oort cloud start to appear beyond 6,000-7,000 AU, and a flattened region can only be found inside this boundary in semi-major axis. However, this region is too tightly bound to the Sun to be an abundant source of comets.

In [116], it has been recently proposed that part of the HTC population comes from the distant end of the Scattered disk. They would be objects that, pushed outward by Neptune, eventually feel the galactic tide and have their perihelion decreased further into the planetary region (q < 25 AU). Subsequent encounters with the giant planets then bring these objects into the HTC region. Reminiscent of its Scattered disk origin, this population would be predominantly prograde. The final HTC population would be a combination of this population with that of comets coming from Oort cloud as described above [109]. This would explain why the observed HTC inclination distribution, while ranging from 0 to 180°, is skewed toward prograde values (see Fig. 20).

Probably, the last word on the problem of the inclination distribution of HTCs has not yet been said. It is possible that part of the solution is that HTCs, even if longer-lived than new LPCs, cannot be active for more than ~ 10, 000 years, as it is the case for JFCs. This would bring the median value of the inclination distribution of the simulated "active" comets down to ~ 90°, or even less [46]. Moreover, the median inclination of the currently observed HTCs might be smaller than the real value, because of observational biases and/or small number statistics. In fact, an update of the HTC catalog with respect to that used in [109] shows an increase of the median inclination from 45 to 60°. In addition, the HTC catalog might be contaminated by a few prograde objects coming from the JFC population (see Sect. 2.1). Finally, I notice that in the simulations of [183], 65% of the SPCs were on prograde orbits. Why this result is different from that in [109] (25%) is not clear. The efficiency of transfer of comets from the Oort cloud to the SPC region is very small, so that it is possible that the results of any model based on numerical simulations is dominated by small number statistics. Definitely, the issue of the origin of HTCs needs to be investigated further.

Was this article helpful?

0 0

Post a comment