2004 TT₃₅₇: A Potential Contact Binary in the Trans-Neptunian Belt

Separated trans-Neptunian binaries have a large variety of properties, from tiny satellites around large primaries to nearly equal-sized systems with primaries and secondaries having comparable sizes, and from short to long orbital periods (Noll et al. 2008). The discovery of binary systems in the trans-Neptunian belt is subject to observational limitations. Only widely separated and nearly equal-sized binaries are detected from the ground (Veillet et al. 2002; Noll et al. 2008; Parker et al. 2011; Sheppard et al. 2012).

The most prolific tool for detecting binary or multiple systems is the Hubble Space Telescope (HST; Noll et al. 2008). However, contact binaries and binaries with tight orbits are impossible to resolve and identify with HST because of the small separation between the system's components. Only detailed lightcurves with a characteristic V-/U-shape at the minimum/maximum of brightness and a large amplitude can identify close or contact binaries.

In 2004 October, using the 4 m Mayall telescope (Kitt Peak, Arizona, USA), Buie et al. (2004) discovered 2004 TT₃₅₇. With a semimajor axis⁴ of 55.17 au, an inclination of 899, and an eccentricity of 0.43, 2004 TT₃₅₇ is a trans-Neptunian object (TNO) trapped in the 5:2 mean motion resonance with Neptune.⁵

2004 TT₃₅₇ is a moderately red object with a slope S = 14.3 ± 2, and its optical colors are: g'–r' = 0.74 ± 0.03 mag, r'–i' = 0.27 ± 0.04 mag, and g'–i' = 0.99 ± 0.04 mag (Sheppard 2012). With an absolute magnitude of ${H}_{r^{\prime} }$ = 7.42 ± 0.07 mag, the estimated diameter of 2004 TT₃₅₇ is 218 ± 7 km (87 ± 3 km), assuming an albedo of 0.04 (0.25) (Sheppard 2012).

We report photometric observations of 2004 TT₃₅₇ obtained in 2015 and 2017 using the 4.3 m Lowell's Discovery Channel Telescope. The lightcurve of 2004 TT₃₅₇ presents an extreme variability that can be explained by a very elongated single object or by a contact/close binary. This paper is divided into six sections. In the next section, we present the fraction of contact binaries among the Solar System. Section 3 describes the observations and the data set analyzed. In Sections 4 and 5, we present and discuss our main results. Section 6 will present the search for companions around 2004 TT₃₅₇ with the HST. Finally, Section 7 is dedicated to the summary and the conclusions of this work.

The extended definition of a contact/close binary system is an object consisting of two lobes in contact (bi-lobed object with a peanut/bone shape), and a system of two separated objects almost in or in contact. This kind of peculiar system/object is found across the small body populations, from the Near-Earth Objects population to the trans-Neptunian belt (Sheppard & Jewitt 2004; Mann et al. 2007; Benner et al. 2015). The expected fraction of contact binaries is high in all of the small body populations, with estimates up to 20%. In the case of the Trojans larger than ∼12 km, the estimate is 14%–23%; it is 30%–51% for Hildas larger than about 4 km based on preliminary estimates from Sonnett et al. (2015). Finally, Ryan et al. (2017) found that 6%–36% of the Trojans are contact binaries. Several studies suggest that between 10% and 30% of the TNOs could be contact binaries (Sheppard & Jewitt 2004; Lacerda 2011). Sheppard & Jewitt (2004) discovered the first contact binary in the trans-Neptunian belt: (139775) 2001 QG₂₉₈. Recently, Lacerda et al. (2014) suggested that the large lightcurve amplitude of the TNO 2003 SQ₃₁₇ could be explained by a contact binary, but they could not totally discard the option of a single, very elongated object. Therefore, 2003 SQ₃₁₇ is a potential contact binary (see Lacerda et al. 2014 for more details).

In conclusion, to date only one contact binary and one potential contact binary have been found in the trans-Neptunian belt despite their expected high abundance estimate.

We present data obtained with the Lowell Observatory's 4.3 m Discovery Channel Telescope (DCT). Images were obtained using the Large Monolithic Imager (LMI), which is a 6144 × 6160 pixels CCD (Levine et al. 2012). The total field of view is 125 × 125 with a pixel scale of 012/pixel (unbinned). Images were obtained using the 3 × 3 binning mode. Observations were carried out in situ.

We always tracked the telescope at sidereal speed. Exposure times of 600–700 s and the VR-filter (broadband filter to maximize the signal-to-noise ratio of the object) were used. The visual magnitudes⁶ of 2004 TT₃₅₇ were 22.6 mag and 23 mag during our runs in 2015 and 2017, respectively. All relevant geometric information about the observed object at the date of observation, and the number of images, are summarized in Table 1.

We used the standard data calibration and reduction techniques described in Thirouin et al. (2012, 2014, 2016). The time-series photometry of each target was inspected for periodicities by means of the Lomb periodogram technique (Lomb 1976) as implemented in Press et al. (1992). We also verified our results by using the phase dispersion minimization (PDM; Stellingwerf 1978).

Our data set is composed of two observing runs, one in 2015 and one in 2017. During our observations in 2015, 2004 TT₃₅₇ was close to opposition and thus its phase angle was 01, whereas the 2017 data set was obtained at higher phase angle, 16. Observing one maximum and one minimum over a single night in 2015 allowed us to constrain the rotational period (P > 7.5 hr, assuming a double-peaked lightcurve) and the lightcurve amplitude (Δm > 0.7 mag). The 2017 partial lightcurve confirms these estimates. There is no significant change in the lightcurve amplitude between the two data sets. Our photometry is available in Table 2.

Light–time correction has been applied in order to merge our two observing runs. Our merged data set has been inspected for periodicity by means of the Lomb periodogram (Figure 1). The Lomb periodogram presents several peaks above the 99.9% confidence level. The highest peak is located at 6.16 cycles/day (3.89 hr), and the main aliases are at 5.78 cycles/day (4.15 hr), and 6.48 cycles/day (3.70 hr). The PDM method confirms the main peak at 3.89 hr. For the rest of our study, we will consider the main peak as the rotational period of the target and will not consider the aliases. Once the period has been identified, we have to choose between the single-peaked lightcurve with a rotational period of 3.89 hr and the double-peaked lightcurve with a rotational period of 2 × 3.89 = 7.79 hr.

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Assuming a triaxial ellipsoid, we have to expect a lightcurve with two maxima and two minima, corresponding to a full rotation of the object. However, if the object is a spheroid with albedo variation(s) on its surface, we have to expect a lightcurve with one maximum and one minimum (Thirouin et al. 2014). A single-peaked lightcurve with a variability of about 0.75 mag would require very strong albedo variation(s) on the object's surface, which is unlikely. On the other hand, assuming a fast rotation of 3.89 hr, the object would be deformed due to its rotation and thus its elongated shape would produce a double-peaked lightcurve (as is the case for Haumea Lacerda et al. 2008; Thirouin et al. 2010). Assuming that 2004 TT₃₅₇ is a strengthless spherical object with a rotational period of 3.89 hr, its density is about 0.7 g cm⁻³. Finally, by plotting the double-peaked lightcurve (Figure 1), we note that the lightcurve is asymmetric by about 0.05–0.1 mag. For all of these reasons, we favor the double-peaked lightcurve for 2004 TT₃₅₇. The lightcurve has a rotational period of 7.79 ± 0.01 hr⁷ and a peak-to-peak amplitude of 0.76 ± 0.03 mag (Figure 1). The lightcurve is plotted over two cycles (i.e., rotational phase between 0 and 2). Error bars are not plotted for clarity.

The lightcurve presents the typical V-/U-shape at the minimum/maximum of brightness characteristic of a contact binary system (Sheppard & Jewitt 2004). However, the lightcurve amplitude is below the 0.9 mag amplitude threshold⁸ needed to infer that this object is a contact binary (Weidenschilling 1980; Leone et al. 1984). With a lightcurve amplitude of 0.76 mag, 2004 TT₃₅₇ is between the Roche and Jacobi sequences, and thus its lightcurve can be explained by a very elongated object or by a contact binary, assuming that the variability is due to the object's shape (more details in Section 5), although a non-equal-sized contact binary may never reach the 0.9 mag amplitude threshold, even when viewed equator-on.

The lightcurve of a rotating small body can be produced by: (i) albedo variation(s), (ii) non-spherical shape, and/or (iii) contact/close binary. In this section, we present the arguments in favor of a single, very elongated object, a contact binary configuration, and an object with an extreme albedo variation for interpreting the lightcurve of 2004 TT₃₅₇.

5.1. Albedo Variation(s)

5.2. Elongated Shape: Jacobi Ellipsoid

If 2004 TT₃₅₇ is a single elongated object (i.e., Jacobi ellipsoid), its lightcurve amplitude can constrain its elongation and density.

According to Binzel et al. (1989), if a minor body is a triaxial ellipsoid with axes a > b > c and rotating along its shortest axis (c-axis), the lightcurve amplitude (Δm) varies as a function of the observational (or viewing) angle ξ as:

$$\begin{eqnarray}&&{\rm{\Delta }}m=2.5\mathrm{log}\left(\displaystyle \frac{a}{b}\right)-1.25\mathrm{log}\left(\displaystyle \frac{{a}^{2}{\cos }^{2}\xi +{c}^{2}{\sin }^{2}\xi }{{b}^{2}{\cos }^{2}\xi +{c}^{2}{\sin }^{2}\xi }\right).\end{eqnarray} \tag{ 1 }$$

The lower limit for the object elongation (a/b) is obtained assuming an equatorial view (ξ = 90°). Considering a viewing angle of ξ = 90°, we estimate an elongation of a/b = 2.01, and an axis ratio⁹ c/a = 0.38. This corresponds¹⁰ to a = 204 km (a = 82 km), b = 102 km (b = 41 km), and c = 78 km (c = 31 km) for an albedo of 0.04 (0.25) and an equatorial view.

However, for a random distribution of spin vectors, the probability of viewing an object on the angle range [ξ, ξ+dξ] is proportional to sin(ξ)dξ, and the average viewing angle is ξ = 60° (Sheppard 2004). Using a viewing angle of 60°, we derive an axis ratio a/b > 2.31. However, ellipsoids with a/b > 2.31 are unstable to rotational fission (Jeans 1919). Therefore, assuming that 2004 TT₃₅₇ is stable to rotational fission (i.e., a/b < 2.31), its viewing angle must be larger than 75°.

If 2004 TT₃₅₇ is a triaxial ellipsoid in hydrostatic equilibrium, we can compute its lower density limit based on Chandrasekhar (1987). Considering an equatorial view, we estimate a density ρ ≥ 0.78 g cm⁻³. This density is typical in the trans-Neptunian belt, and suggests an icy composition for this object (Sheppard et al. 2008; Grundy et al. 2012; Thirouin et al. 2014).

We fitted our data with a second-order Fourier series. This kind of fit is generally used to reproduce lightcurves due to Jacobi ellipsoid (Thirouin et al. 2014, 2016). But the fit failed to reproduce the lightcurve, especially the V-shape of the curve (Figure 1). Therefore, the lightcurve cannot be reproduced if 2004 TT₃₅₇ is assumed to be a Jacobi ellipsoid. One may invoke the fact that strong albedo variations on the object's surface can match the part of the curve that the fit is not able to reproduce (Lacerda et al. 2014). However, such strong variations are unlikely and would have to be located exactly at the maximum and the minimum of brightness of the object.

5.3. Contact Binary: Roche System

If 2004 TT₃₅₇ is a contact binary (i.e., Roche system), we can constrain the mass ratio, the separation, the density, and the axis ratios of the components.

Leone et al. (1984) studied the sequences of equilibrium of these binaries with a mass ratio between 0.01 and 1 (see Leone et al. 1984 for more details about the model¹¹ ). Using the network of Roche sequences in the plane lightcurve amplitude-rotational frequency, we can estimate the mass ratio and the density of 2004 TT₃₅₇ (Figure 2, adapted from Figure 2 of Leone et al. 1984). We derive two main options: (i) a system with a mass ratio of q_max = 0.8 ± 0.05 and a density of ρ_max = 5 g cm⁻³, or (ii) a system with a mass ratio of q_min = 0.45 ± 0.05 and a density of ρ_min = 2 g cm⁻³. We derive q_min and q_max by taking into account the error bar of the lightcurve amplitude. Based on the fact that we only have one lightcurve of this object and the number of assumptions made by Leone et al. (1984), we will use conservative mass ratios of q_min = 0.4, and q_max = 0.8. Using Leone et al. (1984), we are only able to derive the extreme cases (min and max); a combination of values in between are also possible. Only a careful modeling of the system using several lightcurves at different epochs will allow us to improve the mass ratio, density, and geometry of the system. The parameter¹² ω²/(πGρ) is 0.048 with a mass ratio of 0.8, and is 0.120 with a mass ratio of 0.4 (Figure 2). Using Table 1 of Leone et al. (1984), we derive the axis ratios and the separation between the components.

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If 2004 TT₃₅₇ is a binary system with a mass ratio of 0.8 and a density of 5 g cm⁻³, we derive the axis ratios of the primary as b/a = 0.93, c/a = 0.89; the axis ratios of the secondary are b_sat/a_sat = 0.91, c_sat/a_sat = 0.88. The parameter D is defined as (a+a_sat)/d, where d is the orbital separation, and a and a_sat are the longest axes of the primary and the secondary, respectively. The components are in contact when D = 1. We calculate that D = 0.56, thus d = (a+a_sat)/0.56.

If 2004 TT₃₅₇ is a binary system with a mass ratio of 0.4 and a density of 2 g cm⁻³, we derive the axis ratios of the primary as b/a = 0.85, c/a = 0.77 (a = 75/30 km, b = 63/25 km, and c = 57/22 km assuming an albedo of 0.04/0.25); the axis ratios of the secondary are b_sat/a_sat = 0.40, c_sat/a_sat = 0.37 (a = 89/37 km, b = 75/31 km, and c = 68/28 km assuming an albedo of 0.04/0.25). The parameter D is 1, suggesting that the components are in contact.

The largest TNOs have higher densities than the smaller ones (Sheppard et al. 2008; Grundy et al. 2012; Brown 2013; Thirouin 2013; Vilenius et al. 2014). Considering only the binary/multiple systems with true densities derived from their mutual orbits, the largest objects have a mean density of around 2 g cm⁻³, and the intermediate-sized objects have a mean density of about 1.5 g cm⁻³, whereas the smallest ones have a mean density of ∼0.5 g cm⁻³ (Thirouin 2013). Therefore, a density of 5 g cm⁻³ is unlikely in the trans-Neptunian belt, especially for as small an object as 2004 TT₃₅₇. Therefore, we consider that explaining the lightcurve from a contact binary system with a mass ratio of 0.8 and a density of 5 g cm⁻³ is unrealistic. Even if a density of 2 g cm⁻³ seems more reasonable for a TNO, it is important to point out that such a density will make 2004 TT₃₅₇ one of the densest objects in its size range. Some TNOs have a density of around 2 g cm⁻³, and thus such a high value is not uncommon (Thirouin et al. 2016). The densities of 2004 TT₃₅₄, and 2003 SQ₃₅₇ are comparable, whereas the density of 2001 QG₂₉₈ is less than 1 g cm⁻³. This high density suggests a rocky composition.

In conclusion, we have presented arguments in favor of a very elongated single object or a contact binary system to explain the extreme variability of the lightcurve of 2004 TT₃₅₇. Based on the U-/V-shape morphology of the lightcurve, the contact binary explanation seems most likely. More data at different observing angles in the future will allow us to confirm the nature of this object/system (Lacerda 2011).

2004 TT₃₅₇ was observed with the HST in order to search for a binary companion. Images were obtained on 2012 February 21, starting at 09:46 UT in visit 86 of cycle 19 GO snapshot program 12468, How Fast Did Neptune Migrate? A Search for Cold Red Resonant Binaries. Images were obtained using WFC3 with two 350 s exposures in the F606W filter and one 400 s exposure in the F814W. The individual flat-fielded images show a single, compact point-spread function (PSF) with a uniform appearance in all three images. An empirical PSF-fit yields an average full width at half maximum of 1.70 pixels, consistent with an unresolved, single object (Figure 3).

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We have collected photometric data for 2004 TT₃₅₇ using the Lowell's DCT in 2015 and 2017. Our results are summarized here.

• 1.  
  The lightcurve of 2004 TT₃₅₇ presents a V-/U-shape at the minimum/maximum of brightness. 2004 TT₃₅₇ has an asymmetric double-peaked lightcurve with a rotational period of 7.79 hr, and an amplitude of 0.76 mag. Such a large lightcurve amplitude can be explained by a very elongated single object or a contact/close binary.
• 2.  
  In the case of a contact binary, we find two extreme solutions: (i) a system with a mass ratio q_min = 0.45 ± 0.05 and a density ρ_min = 2 g cm⁻³, or (ii) a system with a mass ratio q_max = 0.8 ± 0.05 and a density ρ_max = 5 g cm⁻³. Because a density of ρ = 5 g cm⁻³ is unlikely in the trans-Neptunian belt for an object in the size range of 2004 TT₃₅₇, we favor the solution given by a mass ratio of about 0.4 and a density of ρ = 2 g cm⁻³. This is still a higher-than-normal density for a small TNO.
• 3.  
  Assuming a mass ratio of 0.4 and a density of ρ = 2 g cm⁻³, we estimate the axis ratio of the primary as b/a = 0.85, c/a = 0.77, and b_sat/a_sat = 0.40, c_sat/a_sat = 0.37 for the secondary. We derive a parameter D = 1, suggesting that the components are in contact.
• 4.  
  If 2004 TT₃₅₇ is a Jacobi ellipsoid in hydrostatic equilibrium, its density is ρ ≥ 0.78 g cm⁻³ and its elongation is a/b = 2.01 (assuming a viewing angle ξ = 90°). In order for this object to be rotationally stable, the viewing angle needs to be between 75° and 90°.
• 5.  
  Only changes in the lightcurve in the future can allow us to further confirm the binary nature (or not) of 2004 TT₃₅₇. Lightcurve(s) at different epoch(s) will be needed to model and characterize the system and its geometry (similar work published in Lacerda 2011 for 2001 QG₂₉₈).
• 6.  
  No resolved companion orbiting 2004 TT₃₅₇ has been found based on Hubble Space Telescope data obtained in 2012.

We thank the referee for useful comments. This research is based on data obtained at the Lowell Observatory's Discovery Channel Telescope (DCT). Lowell operates the DCT in partnership with Boston University, Northern Arizona University, the University of Maryland, and the University of Toledo. Partial support of the DCT was provided by Discovery Communications. LMI was built by Lowell Observatory using funds from the National Science Foundation (AST-1005313). We acknowledge the DCT operators: Heidi Larson, Teznie Pugh, and Jason Sanborn. Audrey Thirouin is partly supported by Lowell Observatory funding.