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 [Hahn J. Malhotra R."Neptune's migration into a stirred-up Kuiper Belt" The Astronomical Journal, 130, pp.2392-2414, Nov.2005. [http://arxiv.org/abs/astro-ph/0507319 Full text on arXiv] . ] .

Distribution

The diagram illustrates the distribution of the known trans-Neptunian objects (up to 70 AU) in relation to the orbits of the planets together with Centaurs for reference. 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 Neptune Trojans), 2:3 marks the orbit of Pluto and plutinos, 1:2, 2:5 etc. a number of smaller families).

^†The designation "2:3" or "3:2" refer both to the same resonance for TNOs. There’s no confusion possible as TNO, by definition, have periods longer than Neptune. The usage depends on the author and the field of research. The statement "Pluto is in 2:3 resonance to Neptune" appears to better capture the meaning: Pluto completes 2 orbits for every 3 orbits of Neptune.

Origin

Detailed analytical and numerical studiesMalhotra, Renu "The Phase Space Structure Near Neptune Resonances in the Kuiper Belt". Astronomical Journal v.111, p.504 [http://arxiv.org/abs/astro-ph/9509141 preprint] ] E. I. Chiang and A. B. Jordan, "On the Plutinos and Twotinos of the Kuiper Belt", The Astronomical Journal, 124 (2002), pp.3430–3444. [http://www.iop.org/EJ/article/1538-3881/124/6/3430/202320.html (html)] ] of the Neptune’s resonances have shown that they are quite narrow i.e. the objects must have a relatively precise range of energy (i.e. semi-major axes). If the object semi-major axis is outside these narrow ranges, the orbit becomes chaotic (widely changing orbital elements).Curiously, substantial numbers^† of TNO being discovered appeared to be in 2:3 resonances, the proportion far from random distribution.It is now believed that the objects have been "collected" from wider distances by the sweeping resonances during the migration of NeptuneRenu Malhotra, "The Origin of Pluto's Orbit: Implications for the Solar System Beyond Neptune", The Astronomical Journal, 110 (1995), p. 420 [http://arxiv.org/abs/astro-ph/9504036 Preprint] .] .Well before the discovery of the first TNO, it was suggested that interaction between giant planets and a massive disk of small particles would, via momentum transfer, make Jupiter migrate inwards and while Saturn, Uranus and especially Neptune would migrate outwards. During this relatively short period of time, Neptune’s resonances, would be "sweeping" the space, trapping objects on initially varying heliocentric orbits into resonance.Malhotra, R.; Duncan, M. J.; Levison, H. F. "Dynamics of the Kuiper Belt". Protostars and Planets IV, University of Arizona Press, p. 1231 [http://arxiv.org/abs/astro-ph/9901155 preprint] ]

^†More than 10% are classified or suspected plutinos

Known populations

2:3 resonance (plutinos)

The 2:3 resonance at 39.4 AU is by far the dominant category among the resonant objects, with 92 confirmed and 104 possible member bodies. [ [http://www.johnstonsarchive.net/astro/tnos.html Trans-Neptunian objects ] ] The objects following orbits in this resonance are named plutinos, after Pluto which has the first known orbit of this type. Large, numbered plutinos include:List of the classified orbits [http://cfa-www.harvard.edu/iau/mpec/K06/K06X45.html from MPC] ]
*90482 Orcus
*28978 Ixion
*mpl|(84922) 2003 VS|2
*38628 Huya

1:2 resonance (twotinos)

This resonance at 47.8 AU is often considered as the outer "edge" of the Kuiper Belt and the objects in this resonance are sometimes referred to as "twotinos". There are far fewer objects in this resonance (a total of 14 as of September 27, 2006) [ [http://www.johnstonsarchive.net/astro/tnos.html Trans-Neptunian objects ] ] than plutinos. Objects with well established orbits include:

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*mpl|(119979) 2002 WC|19
*mpl|(130391) 2000 JG|81

2:5 resonance

Objects with well established orbits at 55.4 AU include:
*mpl|(84522) 2002 TC|302, the largest
*mpl|(26375) 1999 DE|9
*mpl|(38084) 1999 HB|12
*mp|(60621) 2000 FE|8
*mpl|(69988) 1998 WA|31
*mpl|(119068) 2001 KC|77

Neptune trojans

A few objects have been discovered following orbits with semi-major axes similar to that of Neptune, near Lagrangian points L₄ and L₅. These Neptune Trojans, named by analogy to the Trojan asteroids, are in 1:1 resonance with Neptune. Six are known as of December 2007:List of Neptune Trojans [http://cfa-www.harvard.edu/iau/lists/NeptuneTrojans.html from MPC] ]
*mpl|2001 QR|322
*mpl|2004 UP|10
*mpl|2005 TN|53
*mpl|2005 TO|74
*mpl|2006 RJ|103
*mpl|2007 VL|305

Other resonances

So called higher-order resonances are known for a limited number of objects, including the following numbered objects
*3:4 mp|(15836) 1995 DA|2
*3:5 mp|(126154) 2001 YH|140
*4:7 mpl|(119070) 2001 KP|77, mp|(118698) 2000 OY|51
*3:7 mp|(95625) 2002 GX|32
*5:17 dp|Eris

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 Deep Ecliptic Survey introduced formally defined dynamical classes based on long-term forward integration of orbits under the combined perturbations from all four giant planets. (see also formal definition of classical KBO)

It should be noted that in general, the mean motion resonance can involve not only orbital periods of the form :$m\; pcdotlambda\; -\; m\; qcdotlambda\_\{\; m\; N\}$

where p and q are small integers, λ and λ_N are respectively the mean longitudes of the object and Neptune but can also involve the longitude of the perihelion and the longitudes of the nodes (see orbital resonance, for elementary examples)

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)J. L. Elliot, S. D. Kern, K. B. Clancy, A. A. S. Gulbis, R. L. Millis, M. W. Buie, L. H. Wasserman, E. I. Chiang, A. B. Jordan, D. E. Trilling, and K. J. Meech"The Deep Ecliptic Survey: A Search for Kuiper Belt Objects and Centaurs. II. Dynamical Classification, the Kuiper Belt Plane, and the Core Population."The Astronomical Journal, 129 (2006), pp. [http://alpaca.as.arizona.edu/~trilling/des2.pdf preprint] ]

:$phi\; =\; m\; pcdotlambda\; -\; m\; qcdotlambda\_\{\; m\; N\}\; -\; m\; mcdotvarpi\; -\; m\; ncdotOmega\; -\; m\; rcdotvarpi\_\{\; m\; N\}\; -\; m\; scdotOmega\_\{\; m\; N\}$ where the $varpi$ are the longitudes of perihelia and the $Omega$ are the longitudes of the ascending nodes, for Neptune (with subscripts "N") and the resonant object (no subscripts).

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 $phi$ librates around 180° with an amplitude of around 82° degrees, ie. the angle changes periodically from 180°-82° to 180°+82°.

All new plutinos discovered during the Deep Ecliptic Survey proved to be of the type:$phi\; =\; m\; 3cdotlambda\; -\; m\; 2cdotlambda\_\{\; m\; N\}\; -\; varpi$similar or Pluto's mean motion resonance.

More generally, this 2:3 resonance is an example of the resonances p:(p+1) (example 1:2, 2:3, 3:4 etc.) that have proved to lead to stable orbits. Their resonant angle is:$phi\; =\; m\; pcdotlambda\; -\; m\; qcdotlambda\_\{\; m\; N\}\; -\; (\; m\; p-\; m\; q)cdotvarpi$In this case, the importance of the resonant angle $phi,$ can be understood by noting that when the object is at perihelion i.e. $lambda\; =\; varpi$ then :$phi\; =\; qcdot\; (\; varpi\; -\; lambda\_\{\; m\; N\})$i.e. $phi,$ gives a measure of the distance of the object's perihelion from Neptune.Renu Malhotra, "The Origin of Pluto's Orbit: Implications for the Solar System Beyond Neptune", The Astronomical Journal, 110 (1995), p. 420 [http://arxiv.org/abs/astro-ph/9504036 Preprint] ] The object is protected from the perturbation by keeping its perihelion far from Neptune provided $phi,$ librates around an angle far from 0°.

^†Capital R is used to refer to this formally defined class as opposed to common meaning of resonant

References

Further reading

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* ( [http://www.lpl.arizona.edu/faculty/malhotra_preprints/ISP_Nov04.html as HTML] )