Irregular moon

In astronomy, an irregular satellite is a natural satellite following a distant, inclined, often retrograde orbit and believed to be captured as opposed to a regular satellite, formed in situ.

Phoebe, the largest irregular satellite of Saturn.

Eighty-six irregular satellites have been discovered since 1997 orbiting all four giant planets. Before 1997, only a dozen had been known, including Phoebe, the largest irregular satellite of Saturn, and Himalia, the largest irregular satellite of Jupiter. It is currently thought that the irregular satellites were captured from heliocentric orbits near their current locations, early after the formation of their parent planet. An altenative theory, that they orginated further out in the Kuiper Belt, is not supported by current observations.

Definition

planet	rH[Gm]
Jupiter	51
Saturn	69
Uranus	73
Neptune	116

There is no widely accepted precise definition of an irregular satellite. Informally, satellites are considered irregular if they are far enough from the planet that the precession of their orbital plane is primarily controlled by the Sun.

In practice, the satellite's semi-major axis is compared with the planet's Hill sphere (that is, the sphere of its gravitational influence) $r_{H}$. Irregular satellites have semi-major axes greater than 0.05 $r_{H}$ with apoapses extending as far as to 0.65 $r_{H}$. The radius of the Hill sphere is given the table.

Orbits

Current distribution

Irregular satellites of Jupiter (red), Saturn (yellow), Uranus (green) and Neptune (blue). The horizontal axis shows their distance from the planet (semi-major axis) expressed as a fraction of the planet’s Hill sphere's radius. The vertical axis shows their orbital inclination. Points or circles represent their relative sizes.

The diagram illustrates the orbits and relative sizes of the irregular satellites of the giant planets. The satellites above the horizontal axis are prograde, the satellites beneath are retrograde. Retrograde satellites appear more common. No satellites are known with inclinations higher than 55° (smaller than 130° for retrograde). Some groupings can be identified, with a single large and a few smaller satellites following similar orbits.

Origin

Irregular satellites are belived to have been captured from heliocentric orbits. For this to occur, one of three things needs to have happened:

• energy dissipation (e.g. in interaction with the primordial gas cloud)
• a substantial (40%) extension of the planet's Hill sphere in a brief period of time (thousands of years)
• a transfer of energy in a three-body interaction.

The last mechanism involving a collision (or a close encounter) of two satellites could result in one of them losing energy and be captured.

After the capture, some of the satellites could break up leading to groupings of smaller moons following similar orbits. Resonances could further modify the orbits making these groupings less recognizable.

Long-term stability

Remarkably, the current orbits prove stable in numerical simulations, in spite of substantial perturbations near the apocenter . The cause of this stability in a number of irregulars is the fact that they orbit with a secular or Kozai resonance. In addition, simulations indicate the following conclusions:

• Orbits with inclinations higher than 50° (or 130° for retrograde orbits) are very unstable: their eccentricity increases quickly resulting in the satellite being lost
• Retrograde orbits are more stable than prograde (stable retrograde orbits can be found further from the planet)

Increasing eccentricity results in smaller pericenters and large apocenters. The satellites enter the zone of the regular (larger) moons and are lost or ejected via collision and close encounters. Alternatively, the increasing the perturbations by the Sun at the growing apocenters push them beyond the Hill sphere.

Retrograde satellites can be found further from the planet the prograde. Detailed numerical integrations proved this asymmetry. The limits are a complex function of the inclination and eccentricity but in general, the prograde satellites with semi-major axis up to 0.47 r_H (Hill sphere) can be stable, while the prograde can extend up to 0.67 r_H.

The difference can be explained very intuitively by the Coriolis acceleration in the frame rotating with the planet. For the prograde satellites the acceleration points outward and for the retrograde it points inward, stabilising the satellite.

Physical characteristics

Size

Illustration of the power law. The number of objects depends on theirs size.

Given the varying distances from Earth, the known population of the irregulars of Uranus and Neptune are understandably poorer than that of Jupiter and Saturn. With this observational bias in mind, the size distribution is similar for all four giant planets.

Typically, the relation expressing the number $N\,\!$ of objects of the diameter smaller or equal to $D\,\!$ is approximated by a power law:

${\frac {dN}{dD}}\sim D^{-q}$ with q defining the slope.

Shallow power law (q~2) is observed for sizes 10 - 100km ¹ but steeper (q~3.5) for objects smaller than 10km² .

For comparison, the distribution of Kuiper Belt objects is much steeper (q~4) i.e. for one object of 1000km there’s 1000 objects with diameter of 100km. The size distribution provides insights into the posiible origin (capture, collision/break-up or accretion)

¹For every object of 100km, ten objects of 10km can be found

²For one object of 10km, some 140 objects of 1km can be found

Colours

Colours of irregular satellites of Jupiter (red labels), Saturn (yellow) and Uranus (green).

Observed colours vary from neutral to reddish but not as red as the colours of some Kuiper Belt objects (KBO).

albedo	neutral	reddish	red
low	C 3-8%	P 2-6%	D 2-5%
medium		M 10-18%	A13-35%
high		E 25-60%

Each planet's system displays slightly different characteristics. Jupiter's irregulars are grey to slightly red, consistent with C, P and D-type asteroids . Groupings with similar colours can be identified (see later sections). Saturn's irregulars are slightly redder than that of Jupiter. The very red colours typical for classical KBOs are rare among the irregulars.

Colour indices are simple measures of differences of the apparent magnitude of an object through blue (B), visible (V) i.e. green-yellow and red (R) filters. The diagram illustrates these differences (in slightly enhanced colour) for the irregulars with known colour indices. For reference, the Centaur Pholus and three classical Kuiper Belt objects are plotted (grey labels, size not to scale). For comparison, see colours of centaurs and KBOs.

Spectra

With the current resolution, the visible and near-infrared spectra of most satellites appear featureless. So far, water ice has been inferred on Phoebe and Nereid and features attributed to aqueous alteration were found on Himalia.

Rotation

Typically, the rotation of the regular moons is synchronous with their orbital rotation (tidal locking). For the irregular satellites, given the distance from the planet, the tidal forces are negligible and rotation periods in the range of 10 hours have been measured for the biggest moons Himalia, Phoebe and Nereid (to compare with their orbital periods of hundreds of days).

Families with a common origin

Given very similar orbital parameters of some satellites, a possible common origin has been investigated.

Dynamic groupings

Simple collision models can be used to estimate the possible dispersion of the orbital parameters given a velocity impulse δV. Applying these models to the known orbital parameters makes possible to estimate the δV necessary to create the observed dispersion. It is believed that δV of tens of meters per seconds (5-50m/s) could result from a break-up. Dynamical groupings of irregular satellites can be identified using these criteria and the likelihood of the common origin from a break-up evaluated.

When the dispersion of the orbits is too wide (i.e. it would require δV in the order of hundreds of m/s)

• either more than one collision must be assumed, i.e. the cluster should be further subdivided into groups
• or significant post-collision changes, for example resulting from resonances, must be postulated.

Colour groupings

When the colours and spectra of the satellites are known, the homogeneity of these data for all the members of a given grouping is a substantial argument for the common origin. However, the precision of the available data makes often difficult to draw statistically significant conclusions. In addition, the observed colours are not necessarily representative for the bulk composition of the satellite.

Observed groupings

Irregular satellites of Jupiter

Irregular satellites of Jupiter.

Typically, the following groupings are listed (dynamically tight groups displaying homogenous colours are listed in bold)

• Prograde satellites
  • Himalia group (inclination 28° cluster): confined dynamically (δV~150m/s); very homogenous n visible (neutral colours similar to C-type asteroids) and near infrared spectrum.
  • Themisto (isolated so far)
  • Carpo (isolated so far)
• Retrograde satellites
  • Carme group (165° cluster): dynamically tight (5<δV<50m/s) and very homogenous, displaying light-red colours consistent with a D-type progenitor
  • Ananke group (148° cluster): little dispersion of orbital parameters (15<δV<80m/s); Ananke itself appears light-red while the satellites following similar orbits are grey
  • Pasiphae group: dispersed; Pasiphae appears to be grey while other members are light-red ¹.

¹Sinope, sometimes included into Pasiphae group, is thought to be independent, trapped in a secular resonance with Pasiphae

Irregular satellites of Saturn

Irregular satellites of Saturn.

Typically, the following groupings are listed

• Prograde satellites
  • Gallic group (inclination 34° cluster): tight dynamically (δV~50m/s), homogenous in both visible (light-red colours) and near IR
  • Inuit group (34° cluster): dispersed (δV~350 m/s) but physically homogenous (light-red colours)
• Retrograde satellites
  • Norse group is defined mostly for naming purposes; the orbital parameter’s dispersion is large and different sub-divisions have been investigated, including
    • Phoebe group (174° cluster); large dispersion suggesting at least two sub-groupings
    • Skathi sub-group

Irregulars of Uranus and Neptune

Irregular satellites of Uranus and NEPTUNE.

planet	rmin[km]
Jupiter	1.5
Saturn	3
Uranus	7
Neptune	16

It is believed that the relatively poorer (known) populations of the irregulars of Uranus and Neptune are due to the varying observational limits (the table on the left; the albedo of 0.04 is assumed). Statistically significant conclusions about the groupings are difficult. Single origin for the retrograde irregulars of Uranus seems unlikely given the dispersion of the orbital parameters that would require high impulse (~300 km) implying a large diameter of the impactor (395km), incompatible in turn with the size distribution of the fragments. Instead, the existence of two groupings is speculated

• Caliban group
• Sycorax group

The two groups have been found distinct (with 3σ confidence) in axis/eccentricity space.

For Neptune, a possible common origin of Psamathe and S/2002 N 4 was noted .