4:00 PM - 4:15 PM
[PPS05-03] Formation of Martian moons from small bodies encountering proto-Mars with temporary capture orbit
Keywords:Martian moons, capture theory, planetary accretion
The Martian moons Phobos and Deimos have reflectance spectra similar to those of D-type asteroids, which has raised so far the capture theory for the origin of the Martian moons. On the other hand, the fact that both moons have very small orbital inclinations within 2 degrees to the equatorial plane of Mars challenges the capture theory. This is because the probability of the formation of two moons with such small inclinations seems extremely low, assuming that the capture occurred from a planetesimal population with random areocentric inclinations. This was one of the major motivations for the giant impact theory (e.g. Rosenblatt+ 2016), another current leading theory for the formation of Martian moons. However, the giant impact theory seems inconsistent with the expected volatile-rich composition of the moons predicted by the D-type asteroid-like spectra, because the moon-forming materials should experience high temperatures by the giant impact (Hyodo+ 2017).
The apparent inconsistency of the orbital characteristics of the Martian moons with the capture theory may be resolved if there are
1) feasible processes of lowering the orbital inclination of the moon and/or
2) an enhancement of capture probability for a planetesimal population encountering Mars with small areocentric inclinations.
For the first possibility, our previous studies (e.g. Matsuoka & Kuramoto 2019, JpGU) have shown that the orbital inclination of a moon can be lowered by taking into account the orbital energy dissipation due to gas drag from the rotating atmosphere. The extended atmosphere to the orbits of the Martian moons is thought to have been created by the accumulation of nebular gas trapped by the gravity of Mars.
In this study, we explore the second possibility to reconcile the capture theory to the low orbital inclination moons. A small body entering the sphere of Martian gravity from Lagrange point L1 or L2 with low initial velocities can experience multiple encounters with Mars during its stay in the sphere because its outgoing orbit after an encounter is reflected by the wall of the Hill effective potential unless it moves toward L1 or L2 points. Such a state, in which a body remains in the Hill sphere for a long period of time is known as "temporary capture". During the temporary capture, the small body has a low orbital inclination to the heliocentric orbital plane of the planet at every encounter. If proto-Mars have an extended atmosphere, atmospheric gas drag may transform it into a permanently captured Martian moon with a low inclination.
We have performed orbital calculations assuming a Hill sphere fulfilled with a static atmosphere and the injection from a Lagrange point as the orbital initial condition. The conditions for such bodies to achieve capture have also been determined numerically and analytically. In the cases of capture, the simulation results show that the final orbital inclination of the moon is much smaller than the initial inclination of the moon precursor. The upper limit of the areocentric orbital inclination during a close encounter is approximately given by 10 deg × v0/(20 m/s), where v0 is the initial velocity. If the initial velocity of the precursor is small, a moon with a low inclination will be formed.
Our results show that the fraction of temporarily captured moon precursors that achieve permanent capture depends on their initial velocity, but is in the order of 0.1--1.0, assuming a nebular density of the minimum-mass solar nebula and a Phobos-size precursors. On the other hand, Higuchi & Ida (2017) estimate that temporary capture to Mars occurs at ~2×10-4 for the case of small bodies entering the Hill sphere. The ratio of temporary captures to impacts on Mars is probably larger than this value, since impacts on Mars are considered to be rarer than Hill sphere entries. If the sources of the accretion of Mars were predominantly of Phobos-mass planetesimals, it is estimated that at least 0.02--0.2% of Mars mass would have been required for such a capture to occur twice. Therefore, if the Martian moons are survivors of bodies captured via temporary capture orbits, then Phobos and Deimos are representative samples of bodies accreted in the later stage of the accretion of Mars, when the nebula existed.
The apparent inconsistency of the orbital characteristics of the Martian moons with the capture theory may be resolved if there are
1) feasible processes of lowering the orbital inclination of the moon and/or
2) an enhancement of capture probability for a planetesimal population encountering Mars with small areocentric inclinations.
For the first possibility, our previous studies (e.g. Matsuoka & Kuramoto 2019, JpGU) have shown that the orbital inclination of a moon can be lowered by taking into account the orbital energy dissipation due to gas drag from the rotating atmosphere. The extended atmosphere to the orbits of the Martian moons is thought to have been created by the accumulation of nebular gas trapped by the gravity of Mars.
In this study, we explore the second possibility to reconcile the capture theory to the low orbital inclination moons. A small body entering the sphere of Martian gravity from Lagrange point L1 or L2 with low initial velocities can experience multiple encounters with Mars during its stay in the sphere because its outgoing orbit after an encounter is reflected by the wall of the Hill effective potential unless it moves toward L1 or L2 points. Such a state, in which a body remains in the Hill sphere for a long period of time is known as "temporary capture". During the temporary capture, the small body has a low orbital inclination to the heliocentric orbital plane of the planet at every encounter. If proto-Mars have an extended atmosphere, atmospheric gas drag may transform it into a permanently captured Martian moon with a low inclination.
We have performed orbital calculations assuming a Hill sphere fulfilled with a static atmosphere and the injection from a Lagrange point as the orbital initial condition. The conditions for such bodies to achieve capture have also been determined numerically and analytically. In the cases of capture, the simulation results show that the final orbital inclination of the moon is much smaller than the initial inclination of the moon precursor. The upper limit of the areocentric orbital inclination during a close encounter is approximately given by 10 deg × v0/(20 m/s), where v0 is the initial velocity. If the initial velocity of the precursor is small, a moon with a low inclination will be formed.
Our results show that the fraction of temporarily captured moon precursors that achieve permanent capture depends on their initial velocity, but is in the order of 0.1--1.0, assuming a nebular density of the minimum-mass solar nebula and a Phobos-size precursors. On the other hand, Higuchi & Ida (2017) estimate that temporary capture to Mars occurs at ~2×10-4 for the case of small bodies entering the Hill sphere. The ratio of temporary captures to impacts on Mars is probably larger than this value, since impacts on Mars are considered to be rarer than Hill sphere entries. If the sources of the accretion of Mars were predominantly of Phobos-mass planetesimals, it is estimated that at least 0.02--0.2% of Mars mass would have been required for such a capture to occur twice. Therefore, if the Martian moons are survivors of bodies captured via temporary capture orbits, then Phobos and Deimos are representative samples of bodies accreted in the later stage of the accretion of Mars, when the nebula existed.