- Paper title: Jupiter: Friend or Foe IV: The Influence of Orbital Eccentricity and Inclination (arXiv:1111.3144)
- Authors: J. Horner, B. W. Jones
- First Author’s Affiliation: University of New South Wales, Sydney, Australia
The hunt is on to find habitable exo-Earths, but what does “habitable” actually mean? The traditional definition of habitability focuses on the surface temperature of the planet: specifically, is it in the correct range to support liquid water? However, there are many other components to habitability. For example, if the star is too active and the planet too close to it, stellar activity and radiation may create a hostile environment for life to form. Another constraint on habitability comes from meteorite impacts: if the planet is hit by the equivalent of a Yucatan impactor (i.e. the one that killed the dinosaurs) every few millenia, it will be challenging for complex life to evolve there!
In this paper, Horner and Jones focus on the impactor constraint for habitability. The existence of Jupiter is often cited as a factor in Earth’s habitability because the larger planet gravitationally shields Earth from most asteroid and cometary impacts. However, Jupiter is on a very sedate, low-eccentricity, low-inclination orbit, and the search for exoplanets has turned up gas giants with a wide range of inclinations and eccentricities. How would varying the eccentricity and inclination of Jupiter affect the impact rate on Earth? This is the question this paper asks. By understanding the influence of co-systemic giant planet eccentricity and inclination on the rate of impacts onto potentially habitable planets, it will be possible to more tightly focus the search for habitable exoplanets on systems that have giant planets in favorable configurations.
There are three families of possible impactors: Near-Earth Objects (NEOs, from the asteroid belt), short-period comets (SPCs), and long-period comets. The authors focused on NEOs and short period comets since long-period comets are a very small fraction of the total number of possible impactors, and since they orbit at such large distances that small changes in the orbit of Jupiter should not significantly impact their trajectories.
The authors used the MERCURY Hybrid integrator to model the orbits of families of 100,000 test particles over 10 million years. The integrator included the gravitational effects of Earth, Mars, Saturn, Uranus, Neptune, and the modified “Jupiter”. Jupiter has an actual eccentricity of .04, and an inclination of 1.3 degrees. The authors examined the impact rate for “Jupiters” with an eccentricity of .01, .04, and .1 (holding inclination at Jovian) and inclinations of 1.3, 5, and 25 degrees (holding eccentricity at Jovian). For each of these parameter choices, the mass of the giant “Jovian” planet was allowed to vary from 0.25-2 Jovian masses. In order to obtain a statistically significant number of impacts, the Earth’s radius was inflated from 6400 to 1 million kilometers increasing the cross-section and consequently the impact rate. Presumably this was to save on the computer time that would be required to integrate out to longer than 10 million years (Myr) or over more than 100,000 test particles. Relative differences in the impact rate should still be valid with this method since a smaller cross section can be compensated for by increased particle density and/or integration time
The present-day orbits of the SPCs and NEOs have been directly shaped by Jupiter, so for each “Jupiter” tested, a primordial population of asteroids was constructed under the assumption that the asteroid belt formed from a disk of cold material during planet formation. The unperturbed population of SPCs was built up based on the orbits of present-day Centaur comets, a group of comets with perihelia between Jupiter and Neptune thought to comprise most SPCs.
Figure 1 shows the number of impacts from NEOs expected over 10 Myr on an Earthlike planet having a co-systemic Jovian planet with a range of masses and eccentricities. Broadly speaking, increased eccentricity leads to an increased impact rate. This makes sense; as the planet grows more eccentric, it reaches deeper into the asteroid belt and gravitationally destabilizes more objects. This effect is significant; the high eccentricity case leads to as about 50% more impacts than the low-eccentricity case. The trend is not uniform with mass, however; as mass increases, the Jovian planet deflects more and more objects, leading to a rise in the impact rate. However, as the mass increases further, the planet begins to capture more of these objects instead of deflecting them, leading to a decline in the impact rate.
A similar trend holds for the SPCs, as shown in Figure 2. However, the effect is much weaker, possibly because the change in Jupiter’s range of orbits doesn’t put it as close to the SPC population as it does to the asteroid belt.
A truly remarkable result occurs when the authors consider the effect of inclination on asteroid impacts. As Figure 3 shows, the number of impacts rises very sharply with increased inclination. Indeed, for an inclination of 25 degrees, the bulk of the asteroid belt is cleared out within just 10 Myr! The authors note that this suggests a very remarkable constraint on habitability. Clearly having a low-inclination giant planet in the system favors habitability, as this leads to a lower impact rate from asteroids. However, for suitably high-inclination Jovian planets, the asteroid belt will be destabilized and depleted on short timescales relative to planet evolution, meaning that after an initial intense bombardment, an Earth in this system would enjoy a relatively asteroid-free existence – highly conducive to habitability!
The effect of inclination on impacts from SPCs is similarly favors the remarkable idea that higher inclinations may produce more beneficial impaction rates. As Figure 4 shows, the impact rate declines with increasing inclination, although this effect is weaker than for the asteroid population.
The implication is remarkable: while as we might have expected, having a low-inclination, low-eccentricity planet in the system leads to a low impact rate favorable to habitability, the very lowest impact rates might instead be produced by the presence of a low-eccentricity, high-inclination Jovian planet! This result is a reminder that what man proposes, nature disposes; nature always has a way of being more clever than humans can ever be.