Astronomy:Vanth (moon)

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Short description: Moon of 90482 Orcus
Vanth
Orcus-Vanth discovery brightened.png
Vanth (top of Orcus) imaged by the Hubble Space Telescope in November 2005
Discovery[2]
Discovered by
Discovery date13 November 2005
Designations
Designation
(90482) Orcus I[3](p350)
Pronunciation/ˈvænθ/
S/2005 (90482) 1[4]
AdjectivesVanthian
Orbital characteristics[5](p67)
Epoch 21.5 September 2006 (JD 2454000.0)
8999.8±9.1 km
Eccentricity0.00091±0.00053
Orbital period9.539154±0.000020 d
Inclination105.03°±0.18° (to celestial equator)
90.54°±0.17° (to ecliptic)[lower-alpha 1]
Longitude of ascending node53.49°±0.33°
274.51°[lower-alpha 2]
Satellite ofOrcus
Physical characteristics
Mean diameter442.5±10.2 km (occultation)[6](p663)
475±75 km (thermal)[7](p1)[8](p2)
Mass(8.7±0.8)×1019 kg[8](p4)
Mean density1.9±0.3 g/cm3 (occultation)[lower-alpha 3]
1.5+1.0
−0.5 g/cm3 (thermal)[8](p4)
Rotation periodsynchronous[9](p6)[10]
Albedo0.08±0.02[7]
Spectral type
moderately red[11](p2702)
V–I = 1.03±0.05[11](p2702)
Apparent magnitude21.8[12]
Absolute magnitude (H)4.88±0.05[11](p2702)


Vanth (formal designation (90482) Orcus I; provisional designation S/2005 (90482) 1) is a natural satellite or moon of the trans-Neptunian dwarf planet 90482 Orcus. It was discovered by Michael Brown and Terry-Ann Suer using images taken by the Hubble Space Telescope on 13 November 2005. The moon has a diameter of 443 km (275 mi), making it about half the size of Orcus and the third-largest moon of a trans-Neptunian object. Vanth is massive enough that it shifts the barycenter outside of Orcus, forming a binary system in which the two bodies revolve around the barycenter, much like the Pluto–Charon system. It is hypothesized that both systems formed similarly, most likely by a giant impact early in the Solar System's history.[8] In contrast to Orcus, Vanth has a darker and slightly redder surface that apparently lacks exposed water ice, resembling primordial Kuiper belt objects.[11](p2702)

Discovery

Vanth was discovered in Hubble Space Telescope images taken on 13 November 2005, during Michael Brown's survey for satellites around large trans-Neptunian objects (TNOs) using Hubble's high-resolution Advanced Camera for Surveys.[2][13] After Brown's Hubble survey concluded in late 2006, he and his colleague Terry-Ann Suer reported their newly discovered TNO satellites to the Central Bureau for Astronomical Telegrams, which announced their discovery of Vanth alongside three other TNO satellites on 22 February 2007.[13][2] Brown continued observing the Orcus–Vanth system with Hubble in October–December 2006 and November–December 2007 to better determine the moon's orbit.[14][15][12]

Name

Before Vanth was named, it had the provisional designation S/2005 (90482) 1.[4][lower-alpha 4] On 23 March 2009, Brown asked readers of his blog to suggest possible names for the satellite, with the best one to be submitted to the International Astronomical Union (IAU) on 5 April.[16] The name Vanth, the winged Etruscan psychopomp who guides the souls of the dead to the underworld, was first suggested by writer Sonya Taaffe and became the most popular name among the large pool of suggestions.[17][18]

Vanth and Persipnei were among the few names that both matched the Etruscan origin and chthonic theme of Orcus's name, though Vanth was ultimately chosen because its relationship to Orcus in Etruscan mythology strongly parallels the relationship between Pluto and Charon in Greek mythology.[17] In Etruscan iconography, Vanth is frequently portrayed in the company of Charun (the Etruscan counterpart of the Greek Charon), which alludes to the similar properties of the Pluto and Orcus systems (the latter being nicknamed the "anti-Pluto" because its orbital resonance with Neptune keeps it on the opposite side of the Sun from Pluto).[17] Brown quoted Taaffe as saying that if Vanth "accompanies dead souls from the moment of death to the underworld itself, then of course her face is turned always toward Orcus", a reference to the likely synchronous orbit of Vanth about Orcus.[17][18]

The submission for Vanth's name was assessed and approved by the IAU's Committee for Small Body Nomenclature,[lower-alpha 5] in accordance with the naming procedures for minor planets and satellites.[19] The official naming citation was announced by the Minor Planet Center in a notice published on 30 March 2010.[3](p350)

Observability

Visual

From Earth, Vanth appears very close to Orcus with an angular separation of up to 0.25 arcseconds. For this reason, Vanth could only be visually resolved in high-resolution imaging, which requires the use of large-aperture space telescopes or ground-based telescopes aided by adaptive optics or interferometry.[20](p2) In visible light, Vanth is 2.61 magnitudes fainter than Orcus, or about 9% of Orcus's brightness.[20](p5) Vanth's visible apparent magnitude was 21.8 in 2022, and will gradually brighten alongside Orcus as the system draws closer to the Sun until perihelion in 2142.[12]

Occultations

Stellar occultations are a useful way of directly measuring an object's position, size, and shape, and can be planned when the object's orbital trajectory is well-known.[6](p657) The first successful detection of a stellar occultation by Vanth was made by a single observatory in Hokkaido, Japan on 1 March 2014, which detected the occultation lasting 3 seconds.[21][22](p16) Because this was only a single detection of the occulted star's chord across Vanth, the occultation did not provide a meaningful constraint on Vanth's diameter and shape.[6](p665) On 7 March 2017, another stellar occultation by Vanth was predicted and observed in the Americas and the Pacific Ocean.[6](p657) Of the five observatories that participated in observing the 2017 occultation by Vanth, two of them made positive detections.[6](p660) The remaining observatories that did not detect the occultation, alongside the fact that the occulted star was a double star, tightly constrained the range of Vanth's possible diameters to 432–453 km (268–281 mi), with the assumption that Vanth had a spherical shape.[6](p663) The 2017 occultation did not show signs of an atmosphere on Vanth down to 1–4 microbars, nor rings within 10,000 km (6,200 mi) from Vanth or beyond 8,010 km (4,980 mi) from Orcus.[6](p657)

Orbit

Diagram of Vanth's orbit as viewed face-on from Earth. Vanth appears to revolve counterclockwise because its orbital north pole is pointed toward Earth's line of sight.

Vanth forms a binary system with Orcus, in which the two bodies revolve around the barycenter between them. Orcus and Vanth are separated 9,000 km (5,600 mi) apart from each other's centers and revolve around their barycenter in nearly circular orbits with a period of 9.54 days.[5](p67)[8] Vanth is less massive than Orcus, so it is the secondary component of the binary system and it orbits farther out from the barycenter at an orbital radius of 7,770 km (4,830 mi; 86.3% of the Orcus–Vanth separation distance). The more massive primary component, Orcus, orbits closer to the barycenter at an orbital radius of 1,230 km (760 mi; 13.7% of the separation distance).[lower-alpha 6][8](p4)

Vanth's orbit is inclined perpendicularly (90°) with respect to the plane of the Solar System, such that it is currently being viewed face-on, or toward the Orcus–Vanth system's north pole, from the perspective of Earth.[11](pp2700–2701) The perspective of Vanth's orbital plane shifts very slowly as the Orcus–Vanth system travels along its 247-year orbit around the Sun.[4] Because of this slow shift in perspective, astronomers were not able determine Vanth's actual orbital inclination until 2015.[5](p67) Vanth's orbit will eventually shift from a face-on to an edge-on perspective by the year 2082, after which the Orcus–Vanth system begins its season of mutual events where Orcus and Vanth take turns eclipsing and transiting each other.[5](p67)

Origin

The circular orbits and relative component sizes of the Orcus–Vanth system resembles the Pluto–Charon binary system, which implies that these two systems formed and evolved similarly.[11](p2705)[8](p5) As hypothesized for Charon, Vanth is believed to be a captured fragment of a large body that impacted Orcus likely before the outward migration of Neptune 700 million years after the formation of the Solar System (about 4 billion years ago).[8](p5)[23](p805) According to hydrodynamic simulations for this scenario, the impactor impacted Orcus obliquely at an angle greater than 45° while traveling at near Orcus's escape velocity, which left a large, intact fragment of the impactor (Vanth) in an eccentric orbit around Orcus.[8](p5)[23](p804) Both Orcus and the newly-formed Vanth remained molten for at least 10,000 years after the impact, allowing for tidal interactions to expand and circularize Vanth's orbit as well as tidally lock both components before the present day.[23](p804, 806) Calculations suggest that it took 150–400 million years for both components of the Orcus–Vanth system to migrate out to their current separation distance and become tidally locked.[11](p2704)

An impact origin of the Orcus–Vanth system would imply that both components should have similar densities, surface compositions, and colors.[11](p2702) While Vanth does have a similar density to Orcus (albeit with a large uncertainty),[8](p5) the color and water ice abundance of Vanth appears different from Orcus for unknown reasons.[11](p2702)[20](p5) The inconsistent surface properties of Orcus and Vanth does not necessarily refute the impact hypothesis however, especially since measurements of Vanth's surface composition are still uncertain.[11](p2705)[20](p5) Astronomers have proposed alternative hypotheses for Vanth's origin to explain this color difference, such as the gravitational capture of another Kuiper belt object, but these hypotheses have since fallen out of favor as Vanth's physical properties and formation mechanisms of dwarf planet satellites became better understood.[7](p1)[8]

Physical characteristics

Size, mass, and density

Diagram of three binary trans-Neptunian dwarf planets and their satellites with true colors, diameters, and distances to scale. Each system's barycenter position marked is in red crosshairs.

(As of 2023), the most accurate estimate for Vanth's diameter is 443 ± 10 km (275 ± 6 mi), determined from a stellar occultation in 2017.[6](pp663, 665)[8](p2) This estimate is consistent with the previous estimate of 475 ± 75 km (295 ± 47 mi) from thermal emission measurements by the Atacama Large Millimeter Array (ALMA) in 2016.[6](p664)[7](p2) Both estimates show that Vanth is roughly half of Orcus's diameter and is the third-largest known moon of a trans-Neptunian object, after Charon and Dysnomia.[7](p3)[8](p2)

Vanth is massive enough that it gravitationally forces Orcus into orbit around the system's barycenter. High-resolution imaging by ALMA resolved Orcus's barycentric orbital motion in 2016, which showed that the barycenter lay 13.7%±1.3% along the separation distance from Orcus to Vanth.[8](p4) This indicates Vanth has a mass of (8.7±0.8)×1019 kg.[lower-alpha 6][8](p4) Of all known planet and dwarf planet satellite systems, Vanth is the most massive satellite relative to its primary: the ratio of Vanth's mass to Orcus's mass is 16%±2%, which is greater than the Pluto–Charon binary's mass ratio of 12%.[8](p5)

Vanth appears to have a similar density as Orcus, despite there being large uncertainties in current estimates for Vanth's density.[8](p5) According to ALMA measurements for Vanth's diameter and mass, Vanth's density is 1.5+0.5
−1.0 g/cm3.[8](p4) Using the occultation estimate for Vanth's diameter instead of ALMA yields a higher density of 1.9±0.3 g/cm3.[lower-alpha 3] If Vanth's density is indeed similar to Orcus's, this would support an impact origin for the system.[8](p5) Nevertheless, additional observations of the Orcus–Vanth system are needed to refine Vanth's mass and density before any conclusions could be made about Vanth's origin and interior structure.[8](p5)

Surface

Visible and near-infrared Hubble observations of Vanth from 2007–2008 showed that the moon's surface appears moderately red, being increasingly more reflective over longer and redder wavelengths.[11](p2702) Vanth's surface is expected to be devoid of volatile ices such as ammonia and methane, since Vanth is too small for its gravity to prevent gases from escaping into space.[24](p8) Near-infrared spectroscopy by the Very Large Telescope in 2010 confirmed Vanth's reddish color, but did not conclusively detect signs of water ice in Vanth's spectrum due to the low resolution of the observations.[20](p5) Nevertheless, Vanth's spectrum appears consistent with a low water ice abundance on its surface, which would make it resemble primordial, tholin-covered Kuiper belt objects more than Orcus, whose surface has a neutral (gray) color and is abundant in exposed water ice by contrast.[11](p2702)[20](p5) The difference between the colors and water ice abundances of Orcus and Vanth challenges the common assumption that impact-formed satellites should have a similar color and composition as its primary, although it is uncertain whether this assumption is true or whether the Orcus–Vanth system did form by an impact.[11](p2702)[20](p5) Vanth's reddish color and apparent lack of exposed water ice hinted that it should have a dark surface with a geometric albedo lower than that of Orcus;[11](p2704)[9](p6) this was confirmed in ALMA observations from 2016, which determined a geometric albedo of 0.08 for Vanth based on its thermal emission.[7](p3)

Light curve, rotation, and shape

Due to the pole-on perspective of the Orcus–Vanth system from Earth, a large portion of the components' surfaces stay in view as they rotate, resulting in minuscule changes in brightness that make it difficult for astronomers to study the system's light curve.[11](p2704) In addition, Orcus and Vanth orbit so close to each other that most telescopes on Earth cannot resolve them individually, so the light curves from each component are combined as a single light curve.[9](p2) Continuous photometric observations of the unresolved Orcus–Vanth system in 2009–2010 showed that its overall brightness varies with a small light curve amplitude of 0.06±0.04 magnitudes and a period of 9.7±0.3 days.[9](p3) This roughly coincides with Vanth's 9.54-day orbital period, which indicates there is synchronous rotation in one or both of the system's components.[9](p3) At least one of these synchronously rotating components must have either an elongated shape or surface albedo variations to cause these brightness variations.[9](p3) Researchers J. L. Ortiz et al. suggested in 2011 that at least Vanth must be synchronously rotating according to the Orcus–Vanth system's light curve,[9](p3) whereas D. L. Rabinowitz and Y. Owainati argued in 2014 that the system's variability should most likely come from both components, meaning the Orcus–Vanth system should be doubly synchronous.[10] Considering that the Orcus–Vanth system formed and tidally evolved similarly to the doubly synchronous Pluto–Charon system, it is more likely that the Orcus–Vanth system is doubly synchronous.[8](p5)

No individually-resolved light curve for Vanth has been measured yet, so its shape is unknown.[6](p663) Vanth's diameter lies close to the ~400 km (250 mi) threshold for hydrostatic equilibrium in icy trans-Neptunian objects, so Vanth would probably not be massive enough to gravitationally compress itself into a sphere, especially in the cold temperatures of the Kuiper belt where ice and rock is more rigid.[25](p75)[26](p176)

Notes

  1. ↑ Given Vanth's orbit pole ecliptic latitude of −0.54°±0.17°,[5](p67) subtracting this angle from the ecliptic north pole of +90° gives the inclination with respect to the ecliptic: i = +90° – (–0.54°) = +90.54°.
  2. ↑ Grundy et al. (2019) only give the longitude of periapsis for Vanth's orbit, which is 328°±51°.[5](p67) The longitude of periapsis is the sum of the ascending node and argument of periapsis, so subtracting Vanth's ascending node of 53.49°±0.33° from its longitude of periapsis gives 274.51° for its argument of periapsis.
  3. ↑ 3.0 3.1 Brown and Butler (2023) did not calculate Vanth's density for its occultation-derived diameter of 442.5±10.2 km.[8](p2) Using correct units, dividing Vanth's estimated mass of (8.7±0.8)×1019 kg by the spherical volume of the occultation-derived diameter gives a density of approximately 1.9±0.3 g/cm3.
  4. ↑ In his blog posts, Michael Brown wrote Vanth's provisional designation as S/1 90482 (2005), which is a not a standard way of writing satellite provisional designations.[16][17]
  5. ↑ The IAU's Committee for Small Body Nomenclature is now known as the Working Group Small Body Nomenclature.
  6. ↑ 6.0 6.1 In a two-body binary system, the ratio of the primary body's (Orcus) orbital radius (r1) from the barycenter to the system's separation distance (a) is equivalent to the ratio of the secondary's (Vanth) mass (m2) to the system's total mass (m1 + m2): [math]\displaystyle{ \frac{r_1}{a} = \frac{m_2}{m_1 + m_2} }[/math]

References

  1. ↑ Suer, Terry-Ann. "Publications". https://sites.google.com/view/terryannsuer/publications. Retrieved 11 July 2023. 
  2. ↑ 2.0 2.1 2.2 Green, Daniel W. E. (22 February 2007). "Satellites of 2003 AZ_84, (50000), (55637), and (90482)". IAU Circular (Central Bureau for Astronomical Telegrams) 8812: 1. Bibcode: 2007IAUC.8812....1B. http://www.cbat.eps.harvard.edu/iauc/08800/08812.html#Item1. Retrieved 4 July 2011. 
  3. ↑ 3.0 3.1 "M. P. C. 69496". Minor Planet Circulars (Minor Planet Center) (69496): 350. 30 March 2010. http://www.minorplanetcenter.org/iau/ECS/MPCArchive/2010/MPC_20100330.pdf. Retrieved 8 August 2010. 
  4. ↑ 4.0 4.1 4.2 "JPL Small-Body Database Browser: 90482 Orcus (2004 DW)". Jet Propulsion Laboratory. https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=90482&view=S. Retrieved 14 July 2023. 
  5. ↑ 5.0 5.1 5.2 5.3 5.4 5.5 Grundy, W. M.Expression error: Unrecognized word "etal". (December 2019). "Mutual Orbit Orientations of Transneptunian Binaries". Icarus 334: 62–78. doi:10.1016/j.icarus.2019.03.035. Bibcode: 2019Icar..334...62G. http://www2.lowell.edu/users/grundy/abstracts/preprints/2019.TNB_orbits.pdf. 
  6. ↑ 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Sickafoose, A. A.Expression error: Unrecognized word "etal". (February 2019). "A stellar occultation by Vanth, a satellite of (90482) Orcus". Icarus 319: 657–668. doi:10.1016/j.icarus.2018.10.016. Bibcode: 2019Icar..319..657S. 
  7. ↑ 7.0 7.1 7.2 7.3 7.4 7.5 Brown, Michael E.; Butler, Bryan J. (October 2018). "Medium-sized satellites of large Kuiper belt objects". The Astronomical Journal 156 (4): 6. doi:10.3847/1538-3881/aad9f2. 164. Bibcode: 2018AJ....156..164B. 
  8. ↑ 8.00 8.01 8.02 8.03 8.04 8.05 8.06 8.07 8.08 8.09 8.10 8.11 8.12 8.13 8.14 8.15 8.16 8.17 8.18 8.19 8.20 8.21 Brown, Michael E.; Butler, Bryan (October 2023). "Masses and densities of dwarf planet satellites measured with ALMA". The Planetary Science Journal 4 (10): 6. doi:10.3847/PSJ/ace52a. 193. Bibcode: 2023PSJ.....4..193B. 
  9. ↑ 9.0 9.1 9.2 9.3 9.4 9.5 9.6 Ortiz, J. L.Expression error: Unrecognized word "etal". (January 2011). "A mid-term astrometric and photometric study of trans-Neptunian object (90482) Orcus". Astronomy & Astrophysics 525: 12. doi:10.1051/0004-6361/201015309. A31. Bibcode: 2011A&A...525A..31O. 
  10. ↑ 10.0 10.1 Rabinowitz, David L.; Owainati, Yasi (November 2014). "The synchronous rotations of Eris/Dysnomia and Orcus/Vanth binary systems". 46th DPS Meeting. American Astronomical Society. 510.07. Bibcode: 2014DPS....4651007R. 
  11. ↑ 11.00 11.01 11.02 11.03 11.04 11.05 11.06 11.07 11.08 11.09 11.10 11.11 11.12 11.13 11.14 Brown, M. E.; Ragozzine, D.; Stansberry, Bryan J.; Fraser, W. C. (June 2010). "The size, density, and formation of the Orcus-Vanth system in the Kuiper belt". The Astronomical Journal 139 (6): 2700–2705. doi:10.1088/0004-6256/139/6/2700. Bibcode: 2010AJ....139.2700B. 
  12. ↑ 12.0 12.1 12.2 Grundy, Will (21 March 2022). "Orcus and Vanth (90482 2004 DW)". Lowell Observatory. http://www2.lowell.edu/users/grundy/tnbs/90482_2004_DW_Orcus.html. Retrieved 11 July 2023. 
  13. ↑ 13.0 13.1 Brown, Michael (July 2005). "Icy planetoids of the outer solar system". Mikulski Archive for Space Telescopes (Space Telescope Science Institute) (10545): 10545. Cycle 14. Bibcode: 2005hst..prop10545B. https://archive.stsci.edu/proposal_search.php?id=10545&mission=hst. Retrieved 11 February 2023. 
  14. ↑ Brown, Michael (July 2006). "The largest Kuiper belt objects". Mikulski Archive for Space Telescopes (Space Telescope Science Institute) (10860): 10860. Cycle 15. Bibcode: 2006hst..prop10860B. https://archive.stsci.edu/proposal_search.php?id=10860&mission=hst. 
  15. ↑ Brown, Michael (July 2007). "Collisions in the Kuiper belt". Mikulski Archive for Space Telescopes (Space Telescope Science Institute) (11169): 11169. Cycle 16. Bibcode: 2007hst..prop11169B. https://archive.stsci.edu/proposal_search.php?id=11169&mission=hst. 
  16. ↑ 16.0 16.1 Brown, Michael E. (23 March 2009). "S/1 90482 (2005) needs your help". Mike Brown's Planets (blog). http://www.mikebrownsplanets.com/2009/03/s1-90482-2005-needs-your-help.html. Retrieved 25 March 2009. 
  17. ↑ 17.0 17.1 17.2 17.3 17.4 Brown, Michael E. (6 April 2009). "Orcus Porcus". Mike Brown's Planets (blog). http://www.mikebrownsplanets.com/2009/04/orcus-porcus.html. Retrieved 6 April 2009. 
  18. ↑ 18.0 18.1 Taaffe, Sonya. "Vanth – The Naming of Vanth". https://sonyataaffe.com/vanth. Retrieved 15 January 2024. 
  19. ↑ "Committee on Small Body Nomenclature: Names of Minor Planets". International Astronomical Union. 25 March 1999. http://www.ss.astro.umd.edu/IAU/csbn/mpnames.shtml. Retrieved 8 April 2009. 
  20. ↑ 20.0 20.1 20.2 20.3 20.4 20.5 20.6 Carry, B.Expression error: Unrecognized word "etal". (October 2011). "Integral-field spectroscopy of (90482) Orcus-Vanth". Astronomy & Astrophysics 534: 9. doi:10.1051/0004-6361/201117486. A115. Bibcode: 2011A&A...534A.115C. 
  21. ↑ "Occultation of TYC_5476-00882-1 by 90482 Orcus – 2014 March 01". Trans Tasman Occultation Alliance. Royal Astronomical Society of New Zealand. https://www.occultations.org.nz/planet/2014/results/20140301_90482_Orcus.htm. Retrieved 19 August 2023. 
  22. ↑ Guhl, Konrad (September 2017). "Beyond Jupiter: (90482) Orcus". Journal for Occultation Astronomy 7 (3): 15–16. https://iota-es.de/JOA/JOA2017_3.pdf. Retrieved 18 July 2023. 
  23. ↑ 23.0 23.1 23.2 Arakawa, Sota; Hyodo, Ryuki; Genda, Hidenori (June 2019). "Early formation of moons around large trans-Neptunian objects via giant impacts". Nature Astronomy 3 (9): 802–807. doi:10.1038/s41550-019-0797-9. Bibcode: 2019NatAs...3..802A. 
  24. ↑ Delsanti, A.; Merlin, F.; Guilbert-Lepoutre, A.; Bauer, J.; Yang, B.; Meech, K. J. (September 2010). "Methane, ammonia, and their irradiation products at the surface of an intermediate-size KBO?. A portrait of Plutino (90482) Orcus". Astronomy & Astrophysics 520: 15. doi:10.1051/0004-6361/201014296. A40. Bibcode: 2010A&A...520A..40D. 
  25. ↑ Lineweaver, Charles H.; Norman, Marc (28–30 September 2009). "The Potato Radius: a Lower Minimum Size for Dwarf Planets". Proceedings of the 9th Australian Space Science Conference. National Space Society of Australia (published 2010). pp. 67–78. ISBN 9780977574032. Bibcode: 2010arXiv1004.1091L. https://www.mso.anu.edu.au/~charley/papers/Potato%20Radiusv8.pdf. 
  26. ↑ Tancredi, G. (April 2010). "Physical and dynamical characteristics of icy "dwarf planets" (plutoids)". Proceedings of the International Astronomical Union 5 (S263): 173–185. doi:10.1017/S1743921310001717. Bibcode: 2010IAUS..263..173T. 

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