Discovery of a Satellite of the Large Trans-Neptunian Object (225088) 2007 OR₁₀

2007 OR₁₀ was observed with the Hubble Space Telescope at two epochs, on 2009 November 6 (proposal ID: 11644, PI: M. Brown) and on 2010 September 18 (proposal ID: 12234, PI: W. Fraser). Both proposals used similar strategies, observing the target with a set of visual range and near-infrared filters of the WFC3/UVIS and IR cameras. Due to the better spatial resolution, visual range observations are preferred in identifying unknown satellites, and we used the WFC3/UVIS observations to look for potential moons of 2007 OR₁₀ in these series of measurements.

At the first epoch (2009 November 6, 17:08:36 start time) 2007 OR₁₀ was observed with the WFC3/UVIS camera system using the 512-pixel sub-array mode with the UVIS1-C512A-SUB aperture, in a series of four measurements with the F606W–F814W–F606W–F814W filters. Each measurement lasted for 129 s. A similar strategy was followed at the second epoch (2010 September 18, 15:54:12 start time), now taking four measurements with the UVIS2-C512C-SUB aperture and using the F606W–F775W–F606W–F775W filter combination. The F606W measurements lasted for 128 s, while the length of the F775W measurements were 114 s (see also Table 1).

There is a faint source in the vicinity of 2007 OR₁₀ that appears in both epochs and in all images and at the same location with respect to 2007 OR₁₀ at each epoch (see Table 1 and Figure 1).

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We used the drizzle images and routines built on the DAOPHOT-based APER function in IDL⁷ to obtain aperture photometry and astrometry of the photocenters of both 2007 OR₁₀ and the suspected satellite. In the 2009 November 6 images, aperture photometry could be performed for both targets separately, in both bands (F606W and F814W). In the case of the 2010 September 18 images, however, the satellite was too close to 2007 OR₁₀ and reliable photometry of the moon could only be performed after the subtraction of 2007 OR₁₀'s point-spread function (PSF). This was modeled using the TinyTim (Krist et al. 2010) software, using specific setups of date, camera system, target's pixel position, focal length, and spectral energy distribution of the target (blackbody of 5800 K). The TinyTim-created drizzle model images were adequate to subtract the contribution of 2007 OR₁₀ from the original drizzle images. The best-fit parameters of the model PSF were determined using Levenberg–Marquardt nonlinear least-squares fitting. The extracted relative positions of the satellite are listed in Table 1.

At the first observational epoch, 2007 OR₁₀ moved with an average apparent velocity of v_λ = −033 h⁻¹ and v_β = −047 h⁻¹ in Ecliptic longitude and latitude. The total motion observed in the sequence of exposures was 010 (2.5 pixels). At the second epoch, the apparent velocities were v_λ = −186 h⁻¹ and v_β = 001 h⁻¹, and the total observed motion was ∼033 (8 pixels). Within each epoch, the position of the secondary source relative to 2007 OR₁₀ was constant to within the measurement errors of our astrometry (see Figure 1). Since those astrometric errors (∼004) are much smaller than the observed motion of 2007 OR₁₀, we confirm that the secondary source was co-moving at both epochs.

We also determined the brightness difference between 2007 OR₁₀ and its moon for each measurement (see Table 1). As in the case of relative astrometry, proper photometry was only possible after subtracting the PSF of the primary in the second epoch images.

The uncertainties in the relative brightness determination reflect the low signal-to-noise ratio of the satellite detection, especially at the first epoch, when we detected it at the 3–4σ significance level. There is a notable change in the brightness (∼03) of the satellite relative to 2007 OR₁₀ between the two epochs. As the light curve of 2007 OR₁₀ is shallow (Pál et al. 2016), only a maximum of ∼009 difference can be attributed to the rotation of the primary. However, shape and/or albedo variegations on the surface of the satellite can easily account for the remaining flux difference. The mean brightness differences are found to be Δm(F606W) = 423 ± 024, Δm(F775W) = 443 ± 030, and Δm(F814W) = 435 ± 025. As these are nearly equal in all bands, 2007 OR₁₀ and its satellite have very similar colors from the V to the I bands, roughly covered by the three HST/WFC3 filters used. We find it very unlikely that two independent, co-moving sources with similar brightness and both having the same color as 2007 OR₁₀ would be found in the vicinity of 2007 OR₁₀ at two epochs. Therefore, we hypothesize that the two sources we found at the two epochs are two appearances of the same satellite.

With these colors, both 2007 OR₁₀ and the satellite are among the reddest objects known in the trans-Neptunian region.

In general, red TNOs are seen to have higher albedos than gray objects (see Lacerda et al. 2014). Since both 2007 OR₁₀ and the satellite are extremely red, our data suggest that they are likely to have similar albedos, and that the albedo of 2007 OR₁₀ (p_V = 0.089) probably applies to the satellite as well.

For the 2007 OR₁₀ system we adopt the absolute magnitudes and colors found in Boehnhardt et al. (2014), i.e., H_V = 234, H_R = 149, $B-V$ = 138, $V-R$ = 086, and $R-I$ = 079. Consideration of the contribution of the satellite to the total brightness of the system increases the absolute brightness magnitude of 2007 OR₁₀ by ∼003, while the colors are nearly unchanged. This results in H_V = 657 ∼ 026 for the satellite. We use this value in the size and thermal emission calculations below.

The two set of observations allowed us to set some constraints on the orbit of the satellite around 2007 OR₁₀. We assume that the orbit of the satellite is circular as circularization times are typically significantly shorter than the age of these systems (Noll et al. 2008). Then, the apparent ellipse of the orbit is a projection of the circular orbit, with 2007 OR₁₀ in the center in a co-moving frame. The two orbital positions defined by the two set of observations do not determine the orbit unambiguously, but allow a family of ellipses to be fitted, as presented in Figure 2. In our case, the possible position angles of the ellipses range from 1° to 51° (from north to east in Ecliptic coordinates). The semimajor and semiminor axes of the smallest ellipse are 046 and 022 (29,300 and 13,600 km) with 21° position angle. For smaller and larger values within the 1°–51° range the semimajor axes increase quickly and get infinitely large at the limiting position angles.

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A reliable estimate for the mass of 2007 OR₁₀ can be obtained using the size limits of the thermophysical model calculations (Pál et al. 2016), D_eff = 1310–1610 km. As 2007 OR₁₀ is a fairly large object, internal porosity is likely negligible and a lower limit for the density can be set to 1.2 g cm⁻³, a typical value for medium size TNOs (Brown 2013; Barr & Schwamb 2016; Kovalenko et al. 2017). For an upper limit we use the densities of the largest dwarf planets Pluto and Eris and adopt 2.5 g cm⁻³. With these assumptions, the mass of 2007 OR₁₀ would be 1.5–5.8·10²¹ kg. Then, with the smallest possible semimajor axis the orbital periods would be 185–364, depending on the system mass assumed.

The two observed positions also define the orbital phases for a specific orbit (ellipse), and the phase difference can be used to find those orbital periods that are compatible with the observed positions, considering the time spent between the two set of observations (31595). The semimajor axis and the orbital period also defines the system mass according to Kepler's third law. We applied this scheme to all ellipses fitted to the two satellite positions, determined the compatible orbital periods, and calculated the related systems mass values. The results are presented in Figure 3. The shortest orbital periods compatible with the phase differences for any of the fitted ellipses are 1905 for prograde (black dots) and 1923 for retrograde (red dots) sense of revolution. Shorter orbital periods would require a mass too high for our upper limits (upper left corner in Figure 3). Although only some well-defined orbital periods are allowed there, there are several of these possible orbital period groups in the 20–100 day range. This means that neither the orbital period nor the system mass can be constrained further by the two existing HST observations. Although they cannot be fully excluded, orbital periods longer than ∼100 day become increasingly unlikely as the satellite would spend most of the time at large apparent distances. We have found three groups of possible periods at ∼126, ∼210, and ∼630 days, but no additional orbital periods were identified for >1000 days.

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The expected orbital period of a satellite can be estimated using the formalism in Murray & Dermott (1999), assuming tidal dissipation and requiring that the current semimajor axis is significantly different from the initial one. In this case, the orbital period is $P\,\propto \,{k}^{3/13}{Q}^{-3/13}{q}^{-3/13}{m}_{p}^{-5/13}$, where k is the tidal Love number, Q is the quality factor of the primary, q is the ratio of the primary to the satellite mass, and m_p is the mass of the primary. With some reasonable assumptions for these parameters (see also Brown & Schaller 2007; Brown et al. 2005), and assuming an evolution of 4.5 Gyr, we can estimate the possible orbital periods. In the equal albedo and equal density case, the mass ratio is q ≈ 350, and the high and low mass limits for the primary gives orbital periods between 45 and 76 days. Orbital periods around 35 days require a significant (>2.5×) internal density difference between the primary and the moon. This is, however, reasonable concerning the known higher densities of the largest and the mid-sized TNOs (see, e.g., Brown 2013; Kovalenko et al. 2017). In the case of a low albedo moon (p_V ≈ 5%) and a low-mass primary, the orbital period would be P ≈ 100 days. These calculations show that the preferred orbital periods are in the range of 35–100 days, and that the orbits with the smallest semimajor axes and shortest periods (P ≈ 20 days) may not be the most likely ones.