Resonant trans-Neptunian object

In astronomy, a resonant trans-Neptunian object is a trans-Neptunian object (TNO) in mean-motion orbital resonance with Neptune. The orbital periods of the resonant objects are in a simple integer relations with the period of Neptune, e.g. 1:2, 2:3, etc. Resonant TNOs can be either part of the main Kuiper belt population, or the more distant scattered disc population.^[1]

Distribution

The diagram illustrates the distribution of the known trans-Neptunian objects. Resonant objects are plotted in red. Orbital resonances with Neptune are marked with vertical bars: 1:1 marks the position of Neptune's orbit and its trojans; 2:3 marks the orbit of Pluto and plutinos; and 1:2, 2:5, etc. mark a number of smaller families. The designation 2:3 or 3:2 both refer to the same resonance for TNOs. There is no ambiguity, because TNOs have, by definition, periods longer than Neptune's. The usage depends on the author and the field of research.

Origin

Detailed analytical and numerical studies of Neptune's resonances have shown that the objects must have a relatively precise range of energies.

A few objects have been discovered following orbits with semi-major axes similar to that of Neptune, near the

Leading Trojans at L₄

Following Trojans at L₅

2:3 resonance ("plutinos", period ~247.94 years)

The 2:3 resonance at 39.4 AU is by far the dominant category among the resonant objects. As of February 2020, it includes 383 confirmed and 99 possible member bodies (such as (175113) 2004 PF115).^[6] Of these 383 confirmed plutinos, 338 have their orbits secured in simulations run by the Deep Ecliptic Survey.^[7] The objects following orbits in this resonance are named plutinos after Pluto, the first such body discovered. Large, numbered plutinos include:

3:5 resonance (period ~275 years)

As of February 2020, 47 objects are confirmed to be in a 3:5 orbital resonance with Neptune at 42.5 AU. Among the numbered objects there are:^[7][6]

4:7 resonance (period ~290 years)

Another population of objects is orbiting the Sun at 43.7 AU (in the midst of the classical objects). The objects are rather small (with two exceptions, H>6) and most of them follow orbits close to the ecliptic.^[7] As of February 2020^[update], 55 4:7-resonant objects have had their orbits secured by the Deep Ecliptic Survey.^[6][7] Objects with well established orbits include:^[7]

1:2 resonance ("twotinos", period ~330 years)

This resonance at 47.8 AU is often considered to be the

There are far fewer objects in this resonance than plutinos. Johnston's Archive counts 99 while simulations by the Deep Ecliptic Survey have confirmed 73 as of February 2020.[6]^[7] Long-term orbital integration shows that the 1:2 resonance is less stable than the 2:3 resonance; only 15% of the objects in 1:2 resonance were found to survive 4

Objects with well established orbits include (in order of the absolute magnitude):^[6]

2:5 resonance (period ~410 years)

There are 57 confirmed 2:5-resonant objects as of February 2020.^[6][7]

Objects with well established orbits at 55.4 AU include:

1:3 resonance (period ~500 years)

Johnston's Archive counts 14 1:3-resonant objects as of February 2020 at 62.8 AU.^[6] A dozen of these are secure according to the Deep Ecliptic Survey:^[7]

Other resonances

As of February 2020, the following higher-order resonances are confirmed for a limited number of objects:^[7]

Haumea

rotating frame, with Neptune stationary (see 2 Pallas for an example of non-librating)

The libration angle ${\displaystyle \phi }$ of Haumea's weak 7:12 resonance with Neptune, ${\displaystyle \phi ={\rm {12\cdot \lambda -{\rm {7\cdot \lambda _{\rm {N}}-{\rm {5\cdot \varpi -{\rm {1\cdot \Omega }}}}}}}}}$, over the next 5 million years

${\displaystyle \Omega }$

Coincidental versus true resonances

One of the concerns is that weak resonances may exist and would be difficult to prove due to the current lack of accuracy in the orbits of these distant objects. Many objects have

Simulations by Emel'yanenko and Kiseleva in 2007 show that (131696) 2001 XT254 is librating in a 3:7 resonance with Neptune.^[16] This libration can be stable for less than 100 million to billions of years.^[16]

Emel'yanenko and Kiseleva also show that (48639) 1995 TL8 appears to have less than a 1% probability of being in a 3:7 resonance with Neptune, but it does execute circulations near this resonance.^[16]

Toward a formal definition

The classes of TNO have no universally agreed precise definitions, the boundaries are often unclear and the notion of resonance is not defined precisely. The

In general, the mean-motion resonance may involve not only orbital periods of the form

${\displaystyle {\rm {p\cdot \lambda -{\rm {q\cdot \lambda _{\rm {N}}}}}}}$

where p and q are small integers, λ and λ_N are respectively the

An object is resonant if for some small integers (p,q,n,m,r,s), the argument (angle) defined below is librating (i.e. is bounded):[17]

${\displaystyle \phi ={\rm {p\cdot \lambda -{\rm {q\cdot \lambda _{\rm {N}}-{\rm {m\cdot \varpi -{\rm {n\cdot \Omega -{\rm {r\cdot \varpi _{\rm {N}}-{\rm {s\cdot \Omega _{\rm {N}}}}}}}}}}}}}}}$

where the ${\displaystyle \varpi }$ are the longitudes of perihelia and the ${\displaystyle \Omega }$ are the longitudes of the

The term libration denotes here periodic oscillation of the angle around some value and is opposed to circulation where the angle can take all values from 0 to 360°. For example, in the case of Pluto, the resonant angle ${\displaystyle \phi }$ librates around 180° with an amplitude of around 86.6° degrees, i.e. the angle changes periodically from 93.4° to 266.6°.^[18]

All new plutinos discovered during the Deep Ecliptic Survey proved to be of the type

${\displaystyle \phi ={\rm {3\cdot \lambda -{\rm {2\cdot \lambda _{\rm {N}}-\varpi }}}}}$

similar to Pluto's mean-motion resonance.

More generally, this 2:3 resonance is an example of the resonances p:(p+1) (for example 1:2, 2:3, 3:4) that have proved to lead to stable orbits.^[4] Their resonant angle is

${\displaystyle \phi ={\rm {p\cdot \lambda -{\rm {q\cdot \lambda _{\rm {N}}-({\rm {p-{\rm {q)\cdot \varpi }}}}}}}}}$

In this case, the importance of the resonant angle ${\displaystyle \phi \,}$ can be understood by noting that when the object is at perihelion, i.e. ${\displaystyle \lambda =\varpi }$, then

${\displaystyle \phi =q\cdot (\varpi -\lambda _{\rm {N}})}$

i.e. ${\displaystyle \phi \,}$ gives a measure of the distance of the object's perihelion from Neptune.^[4] The object is protected from the perturbation by keeping its perihelion far from Neptune provided ${\displaystyle \phi \,}$ librates around an angle far from 0°.

Classification methods

As the orbital elements are known with a limited precision, the uncertainties may lead to