The mass and density of the dwarf planet (225088) 2007 OR10
Introduction
Satellites are very important in studying the formation and evolution of Kuiper belt objects (see Noll et al., 2008, for a summary). The orbit of a satellite allows us to obtain accurate system mass and also density when the size of the main body is known (typically from radiometry or occultation measurements). Densities are also indicative of the internal structure, and are important constraints for satellite formation theories. It is possible that systems with small and large moons formed by different processes. Systems with large moons may have formed in low-velocity grazing collisions, both bodies retaining their original compositions and also the primordial densities.
Systems with small moons may have formed in collisions when low-density icy material is lost, increasing the bulk density of the primary (Barr and Schwamb, 2016).
The satellite orbits of most large KBO binaries are nearly circular. An exception is (50000) Quaoar, where the orbit of Weywot is moderately eccentric (ϵ = 0.14), an orbital state that is likely not the consequence of a tidal evolution from an initially circular orbit. The long orbit evolution timescale obtained for Weywot indicates instead that it may have formed with a non-negligible eccentricity (Fraser et al., 2013).
The satellite of (225088) 2007 OR10 (hereafter shortened to 2007 OR10) was discovered on archival images obtained with the WFC3 camera of the Hubble Space Telescope (Kiss et al., 2017). This discovery completes the list of outer solar system dwarf planets with known satellites: now all bodies larger than ∼1000 km in diameter are known to harbor moons (Pluto-Charon, Eris, Haumea, Makemake, Quaoar, Orcus). The existence of a satellite was originally suspected from the long rotation period (∼44.8 h) derived from a Kepler-K2 multi-day light curve (Pál et al., 2016). The initial discovery was based on observations at two epochs only, therefore the orbit of the satellite could not be derived unambiguously from these data alone.
Here, we report on successful recovery observations of the satellite of 2007 OR10, taken with the WFC3 camera of the Hubble Space Telescope (HST) in 2017. The observations allow us to determine the orbit sufficiently well to obtain system mass and estimate the density of the primary. We also give a short assessment of possible orbital evolution and the consequences for both the primary and the satellite.
Section snippets
Observations and data analysis
New observations of 2007 OR10 were obtained with HST in the framework of the proposal “The Moons of Kuiper Belt Dwarf Planets Makemake and 2007 OR10” (proposal ID: 15207, PI: A.H. Parker) at four epochs in October and December 2017 (see Table 1). The WFC3/UVIS camera system with the UVIS2-C512C-SUB aperture was used to take multiple exposures, alternating between the F350LP and either the F606W or the F814W filters. We created co-added images in the co-moving frame of 2007 OR10 using images
Orbit fitting
After the October 2017 observations, we generated a collection of thousands of orbits consistent with the ensemble of astrometric data, using Monte Carlo procedures (Grundy et al., 2008). This cloud of orbits provided a representation of the probability distribution in orbital element space. It contained a number of dense clumps corresponding to distinct orbit solutions differing in their orbital periods, eccentricities, semi-major axes, etc. Each clump was used to provide initial parameters
Photometry results and colors
Based on the differential photometry of 2007 OR10 and the satellite (see Table 1) we obtained average brightness differences of Δ(F606W) = 4.m68±0.m11 (observations on October 3, 18, and December 5) and Δ(F814W) = 5.m01 ±0.m30 (October 11). We use a system-integrated absolute brightness of HV = 2.34 ± 0.01 and the color V–I = 1.65 ± 0.03 (Boehnhardt et al., 2014) to obtain absolute brightness values for the satellite from the relative photometry. When transforming the HST/WFC3 photometry to the
Radiometric size estimates
The thermal emission of 2007 OR10 was observed with the PACS camera of the Herschel Space Observatory, and these data were analysed in detail in Pál et al. (2016). Both the Near-Earth Thermal Asteroid Model and the thermophysical model (TPM) pointed to a same best-fit size of 1535−225+75 km. In that paper, two TPM configurations were tested: a pole-on and an equator-on, and the latter one gave the best fit to the observed flux densities. Although the recent HST observations do not constrain the
The density of 2007 OR10
To calculate the density from the mass of 1.75±0.07·1021 kg, we first used Deff = 1535−225+75 km, derived from radiometric models by Pál et al. (2016), corresponding to our best-fit, Case-1 (equator-on) TPM solution. This provides an average density estimate of 0.92−0.14+0.46 g cm−3, assuming a spherical body. Using the effective diameters from the Case-3a-d TPM solutions (satellite orbit in equatorial plane), the density is ρ = 1.74±0.16 g cm−3. The highest density, ρ = 2.15±0.17 g cm−3, is
Formation and tidal evolution
To investigate the possible formation scenarios and the dependence of the tidal evolution on the basic properties of the system we considered a large number of configurations covering the possible size, density and structural properties of both the primary and the satellite, and estimated the tidal time scales and other parameters in a Monte-Carlo manner.
Variables with known values are assumed to have a normal distribution with expectation value and standard deviation equal to their obtained
Conclusions
In most of the calculations above, 2007 OR10's satellite must be small in order to keep the satellite orbit from circularization during the lifetime of the solar system. While other mechanisms may play a role and increase the eccentricity from a small value to the presently observed one, a small satellite (Rs< 50 km) with a relatively bright surface (pV>0.2) would be consistent with all possible evolutionary scenarios. Among the largest Kuiper belt objects, Quaoar and Haumea have similarly
Acknowledgements
Data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. This work is based in part on NASA/ESA Hubble Space Telescope program 15207. Support for this program was provided by NASA through grants from the Space Telescope Science Institute (STScI). Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant
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