Table 1
Observational, physical, and orbital parameters of Varda.
| Quantity | Value | Ref. | Comments |
|---|---|---|---|
| Radius (km) |  |
V14 | Varda radius |
 |
V14 | Effective radius(a) from radiometric modelling (Herschel data) | |
 |
G15 | Assuming that Varda and Ilmarë have spherical shapes and the same albedo, | |
| with brightness difference of Δmag = 1.734 ± 0.042, | |||
| using photometric data of HST, Keck II, and Gemini North Telescopes, | |||
resulting in  km and  km. |
|||
| Mass (1020 kg) | 2.664 ± 0.064 | G15 | System mass |
| Geometric albedo | 0.102 |
V14 | Radiometric modelling, Herschel data (“TNOs are Cool" programme) |
| Absolute magnitude (HV) | 3.61 ± 0.05 | V14 | |
| 3.988 ± 0.048 | A16 | with a phase coefficient(b) β = −0.455 ± 0.071 | |
| Rotational period (h) | 5.9/7.87 | T10 | Single-peaked light-curve with an amplitude of 0.06 ± 0.01 mag |
| 5.91 | T14 | Other possible solutions (aliases) are mentioned: 4.76 h and 7.87 h | |
| Spectral slope (%/100 nm) | 19.2 ± 0.6 | F09 | |
| Density ρ (g cm−3) | 1.12/0.63 | T10 | Associated with the periods (5.9 and 7.87 h) and sizes, respectively |
| Bulk density of the system |  |
V14 | Assuming that Varda and Ilmarë have equal albedo and density values |
| Varda-Ilmarë (g cm−3) |  |
G15 | Using the mass and radius described above |
| Ecliptic orbital elements of Varda | |||
| a (AU) | 46.046 | LS | NIMA ephemeris, see text |
| e | 0.140 | LS | |
| i (deg) | 21.498 | LS | |
| Orbital elements of Ilmarë (ref:G15) | |||
| solution 1 | solution 2 | ||
| a (km) | 4812 ± 35 | 4805 ± 35 | |
| e | 0.0181 ± 0.0045 | 0.0247 ± 0.0048 | |
| Orbital pole (J2000) | |||
| αp (deg) | 273.0 ± 1.5 | 229.5 ± 1.5 | |
| δp (deg) | − 11.0 ± 1.9 | 4.9 ± 1.8 | |
Notes. (a) Vilenius et al. (2014) defined the radiometric (area-equivalent) effective diameter of a binary system as
, where D1 and D2 are the primary and secondary diameters, respectively. (b)This assumes a linear trend of the phase curves and considers a magnitude variability that is due to the rotational light-curve.
References. T10: Thirouin et al. (2010), T14: Thirouin et al. (2014), F09: Fornasier et al. (2009), V14: Vilenius et al. (2014), G15: Grundy et al. (2015), A16: Alvarez-Candal et al. (2016), LS : NIMA ephemerides (https://lesia.obspm.fr/lucky-star/obj.php?p=426).
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