174567 Varda

174567 Varda (provisional designation ) is a binary trans-Neptunian planetoid of the resonant hot classical population of the Kuiper belt, located in the outermost region of the Solar System. Its moon, Ilmarë, was discovered in 2009.

Astronomer Michael Brown estimates that, with an absolute magnitude of 3.5 and a calculated diameter of approximately 700 –, it is likely a dwarf planet. However, William M. Grundy et al. argue that objects in the size range of 400–1000 km, with albedos less than ≈0.2 and densities of ≈1.2 g/cm3 or less, have likely never compressed into fully solid bodies, let alone differentiated, and so are highly unlikely to be dwarf planets. It is not clear if Varda has a low or a high density.

Discovery and orbit
Varda was discovered in March 2006, using imagery dated from 21 June 2003, by Jeffrey A. Larsen with the Spacewatch telescope as part of a United States Naval Academy Trident Scholar project.

It orbits the Sun at a distance of 39.5–52.7 AU once every 313.1 years (over 114,000 days; semi-major axis of 46.1 AU). Its orbit has an eccentricity of 0.14 and an inclination of 21.5° with respect to the ecliptic. , Varda is 47.5 AU from the Sun. It will come to perihelion around November 2096. It has been observed 321 times over 23 oppositions, with precovery images back to 1980.

Name
The names for Varda and its moon were announced by the Minor Planets Center on 16 January 2014. Varda is the queen of the Valar, creator of the stars, one of the most powerful servants of almighty Eru Ilúvatar in J. R. R. Tolkien's fictional mythology. Ilmarë is a chief of the Maiar and Varda's handmaiden.

The use of planetary symbols is discouraged in astronomy, so Varda never received a symbol in the astronomical literature. There is no standard symbol for Varda used by astrologers either. Zane Stein proposed a gleaming star as the symbol.

Satellite
Varda has one known satellite, Ilmarë (or Varda I), which was discovered in 2009. It is estimated to be about 350 km in diameter (about 50% that of its primary), constituting 8% of the system mass, or $0.08$, assuming its density and albedo are the same as that of Varda.

The Varda–Ilmarë system is tightly bound, with a semimajor axis of $0.235$ (about 12 Varda radii) and an orbital period of 5.75 days.

Physical properties
Based on its apparent brightness and assumed albedo, the estimated combined size of the Varda–Ilmarë system is $740 km$, with the size of the primary estimated at $722 km$. The total mass of the binary system is approximately $2.45 kg$. The density of both the primary and the satellite is estimated at $2.664 kg$, assuming that they have equal density. On the other hand, if the density or albedo of the satellite is lower than that of primary then the density of Varda will be higher up to $1.23 g/cm3$.

On 10 September 2018, Varda's projected diameter was measured to be $1.78 g/cm3$ via a stellar occultation, with a projected oblateness of $5.61 h$. The equivalent diameter is 740 km, consistent with previous measurements. Given Varda's equivalent diameter derived from the occultation, its geometric albedo is measured at 0.099, making it as dark as the large plutino.

The rotation period of Varda is unknown; it has been estimated at 5.61 hours in 2015, and more recently (in 2020) as either 4.76, 5.91 (the most likely value), 7.87 hours, or twice those values. The large uncertainty in Varda's rotation period yields various solutions for its density and true oblateness; given a most likely rotation period of 5.91 or 11.82 hours, its bulk density and true oblateness could be either $5.91 h$ and 0.235 or $11.82 h$ and 0.080, respectively.

The surfaces of both the primary and the satellite appear to be red in the visible and near-infrared parts of the spectrum (spectral class IR), with Ilmarë being slightly redder than Varda. The spectrum of the system does not show water absorption but shows evidence of methanol ice.