2007 TY430: A COLD CLASSICAL KUIPER BELT TYPE BINARY IN THE PLUTINO POPULATION

Table 1 shows the heliocentric orbital elements for 2007 TY430 from the minor planet center. The semi-major axis and eccentricity are easily recognized as a 3:2 resonance object or Plutino. Figure 1 shows that 2007 TY430 is near the outer edge of the 3:2 resonance. In order to determine the stability of 2007 TY430's orbit, 10 clones were made using the orbital elements and full covariance matrix of the orbital elements from the AstDys Web site (http://hamilton.dm.unipi.it/astdys/) including observations spanning a more than 3 year arc. Using the Swift integrator program (Levison & Duncan 2000) with the four giant planets and relatively short time steps of about 40 days, the clones were numerically integrated backward in time for the age of the solar system. All ten clones are stable in the 3:2 resonance for the first 1 Myr. Eight of the ten clones remained in the 3:2 resonance for at least 10 Myr, which based on the classification method of Gladman et al. (2008) suggests that it is acceptable to call 2007 TY430 a Plutino, but likely an unstable one. Four of the ten remain in the 3:2 resonance for the age of the solar system with some interactions with the Kozai resonance.

The loss of some of the 2007 TY430 clones is not surprising since objects in the 3:2 resonance can be unstable over the age of the solar system (de Elia et al. 2008; Almeida et al. 2009; di Sisto et al. 2010). 2007 TY430 has a large libration amplitude of ∼120 deg (see also orbit calculations from Marc Buie's Web site at www.boulder.swri.edu/buie/kbo/astrom that has up to date information first published in Elliot et al. 2005). For the eccentricity and inclination of 2007 TY430, this libration amplitude puts it in the unstable part of the Plutino resonance (Tiscareno & Malhotra 2009), so it is not surprising that the orbital integrations showed a lack of long-term stability.

Since the backward numerical integrations did not show 2007 TY430 to be a strongly stable object, its past history cannot be reliably constructed. There are two major possibilities for the origin of 2007 TY430. The first is that 2007 TY430 was swept up into the 3:2 resonance, which is the likely case for most of the Plutinos (Hahn & Malhotra 2005). These Plutinos likely formed closer to the Sun than their current locations. Based on the Brouwer's constant as described in Murray-Clay & Schlichting (2011), the current relatively large heliocentric orbital eccentricity of 2007 TY430 (Table 1) suggests that if it was captured into the 3:2 resonance by an outward, smooth, slowly migrating Neptune, 2007 TY430 would originally have had a semi-major axis of about 31 AU if initially in a circular orbit. Over time, chaotic diffusion could have caused 2007 TY430 to move to higher and higher libration amplitudes until reaching its current situation of being near the outer "edge" of the 3:2 resonance. The second possibility is that 2007 TY430 used to be in a different region of the Kuiper Belt (e.g., the low-inclination "cold" classical region) and escaped into the scattered disk. While in the scattered disk, 2007 TY430 could have entered into the outskirts of the 3:2 resonance in the common phenomenon of resonance sticking (Lykawka & Mukai 2007), as the 3:2 resonance is known to catch scattered-disk objects (Lykawka & Mukai 2006). Resonance sticking naturally explains the large libration amplitude at the present epoch and thus, dynamically, the second scenario above seems the most likely. If scenario two is correct, it is unknown if 2007 TY430 came from an inner extension of what is now the cold classical belt or from what we see as the classical belt today before being pushed into the resonance. How long 2007 TY430 has been in the Plutino resonance and how long ago it left the cold classical region also cannot be determined.

Using a two-body version of the code developed in Ragozzine & Brown (2009), the best-fit orbital properties of 2007 TY430 were found using thousands of individual Powell and Levenberg–Marquardt minimizations (Table 3). The combination of these minimizations provides a strong quadratic locus of points in chi-squared (χ²) versus parameter space, as expected, with clear evidence that the global minimum was found. A single Keplerian orbit provides an excellent fit (reduced chi-squared (χ²_red) = 0.74 with 46 degrees of freedom) and thus no non-Keplerian parameters were included (Figure 6). The residuals to the fit follow a Gaussian distribution. The data span a large enough range in time and viewing angle that the mirror degeneracy (which has χ²_red ≃ 2) is strongly broken and the mirror orbital solution is clearly rejected. The season of potential mutual events ended several years ago.

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Following the method of Brown et al. (2005) from Press et al. (1992), a Monte Carlo suite of 29 random realizations of the data was created and the global minimum for each was determined for each data set. The best fit for each fit parameter and ancillary value are computed and then the standard deviation of the results is reported as the error in Table 3. Investigation of the distributions of the parameters showed that all the errors were nearly Gaussian. The mean and median of the parameters retrieved from the Monte Carlo simulation were not significantly different from the best-fit value, therefore the best fit on the nominal data set is listed as the central estimate of each parameter as shown in Table 3.

From the parameters in Table 3, the current obliquity is 25  ±  0.5 deg. With the range of heliocentric inclinations observed from the stable clones (7–18 deg), the mutual inclination never reaches above about 30 deg, suggesting that the 2007 TY430 binary in its current heliocentric orbit would not be subject to Kozai oscillations (Perets & Naoz 2009; Ragozzine 2009).

The colors of 2007 TY430 are shown in Table 4. 2007 TY430 is one of the reddest known objects ever observed (g − i = 1.49 ± 0.01 mag) and is well above the ultra-red color cutoff (g − i > 1.2 mag) defined in Sheppard (2010). The term ultra-red objects was coined by Jewitt (2002) and has become associated with the low-inclination classical Kuiper Belt (Tegler & Romanishin 2000; Trujillo & Brown 2002; Peixinho et al. 2008) or Oort Cloud objects (Sheppard 2010) because most objects in these regions appear to have ultra-red surface colors. The composition of the ultra-red material is unknown, but spectral synthesis analysis suggests that the ultra-red color may be associated with organic material (Doressoundiram et al. 2008; Barucci et al. 2008; Fulchignoni et al. 2008).

Because of the near linearity in the optical colors of most KBOs (Doressoundiram et al. 2008), the spectral gradient, S, of an object can be found using two unique optical broadband filters. The spectral gradient is basically a very low resolution spectrum of an object and is usually expressed in percent of reddening per 100 nm in wavelength. Following Sheppard (2010), the spectral gradient for 2007 TY430 was found to be S = 36 ± 2, putting 2007 TY430 within the low-inclination "cold" classical Kuiper Belt color population shown in Table 5 of Sheppard (2010).

Both components of the 2007 TY430 binary have indistinguishable ultra-red colors (Table 4). Like 2007 TY430, the colors of each component of other TNO binary pairs are similar to each other, though the colors of each binary system as a whole span a wide range of colors from near neutral to ultra-red. This suggests the formation of each TNO binary in a specific location within a homogeneous disk during the formation of the solar system (Benecchi et al. 2009). Infrared observations of 2007 TY430 using the Gemini NIRI instrument with the narrowband water and methane filters (Trujillo et al. 2011) show that 2007 TY430 does not have any significant amounts of water or methane ice on its surface (Table 4).

Similar to the moderate to high albedos found for low-inclination cold classical objects (Brucker et al. 2009), the equal-sized, wide, ultra-red binary 2007 TY430 requires a moderate to high albedo and very low density structure to obtain the total mass found for the pair (Figure 7). For a likely absolute minimum density of 0.5 g cm⁻³, the albedo of 2007 TY430 would be greater than 0.17. For reasonable densities, the radii of either component should be less than 60 km, and thus the relatively low eccentricity of the binary is interesting since no tides should be operating on the bodies at their large distances from each other. For instance, assuming a realistic density of 0.75 g cm⁻³, results in an albedo of about 0.23, and radii of the individual components of about 50 km.

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Through an ultra-deep survey for Neptune Trojans using the Subaru and Magellan telescopes (Sheppard & Trujillo 2010a, 2010b), only one object, 2007 TY430, was found to be a binary. The Neptune Trojan ultra-deep survey detected about 900 faint KBOs. Interestingly, the brightest and likely one of the largest objects detected in the ultra-deep survey was 2007 TY430 (m_R = 20.94 ± 0.01). The vast majority of the objects found in the Neptune Trojan survey were very faint (m_R ∼ 24–25 mag) KBOs with expected radii of only a few tens of kilometers. These discoveries were all checked by eye for binarity at discovery, like 2007 TY430. Most were not followed up to obtain orbits, but the survey was conducted within a few degrees of the ecliptic with most KBOs found to be between 40 and 50 AU, in the heart of the cold classical belt. Adding in the hundred or so KBOs detected in a similar ultra-deep survey for satellites of Saturn, Uranus, and Neptune (Sheppard et al. 2005, 2006) puts the number of KBOs detected in excellent seeing conditions at about one thousand with only one binary detection (0.1^+0.1_−0.07%). The vast majority of the KBOs discovered in the Neptune Trojan survey were in excellent seeing ranging between 0.45 and 0.8 arcsec, allowing easy detection of any found widely separated binaries. Only the brightest KBO found showed a binary nature. Nesvorný et al. (2011) demonstrated that binaries that may have formed through gravitational collapse with radii of less than or equal to 2007 TY430's are less likely to survive because collisions should be able to disrupt the pair over time. This is consistent with the non-detection of any binaries for the thousand smaller KBOs imaged in very good seeing conditions, though observational biases must be taken into account (Naoz et al. 2010).

Previous ground-based surveys have estimated about 1% of TNOs to be widely separated equal-sized binaries. These surveys detected significantly brighter and thus likely larger objects. The Deep Ecliptic Survey (DES), with an average photometric depth of only 22.5 mag in the R band (Elliot et al. 2005), found 4 out of 634 objects to be binaries from the ground, of which only about 212 were found in good seeing with a fine pixel scale using the Magellan telescope (Osip et al. 2003; Kern & Elliot 2006a). An unpublished Keck survey targeted 150 known KBOs and found no obvious binaries from the ground, but it is unknown the brightness distribution of the objects observed (Schaller & Brown 2003). Lin et al. (2010) found two nearly equal mass binaries in the Canada–France ecliptic plane survey and from this suggest that over 1.5% of low-inclination classical KBOs likely have large separation equal-sized binaries (>0.4 arcsec separation). Thus surveys of brighter KBOs show that about 1%–2% are binaries with separations detectable from the ground, while this work shows that there is likely significantly less than this for fainter and smaller objects.

There are observational biases against detecting binaries at smaller sizes. For instance, the Hill spheres (see Section 4.1) of the fainter and thus smaller objects are smaller, making any stable binaries closer to each other. This work went over 2 mag fainter than the DES, thus it was sensitive to objects that were a factor of 2.5 smaller, with a factor of 2.5 smaller Hill radius. This smaller Hill radius would have made the 2007 TY430 binary undetectable from the ground at discovery, but it would still have been an obvious binary if imaged when the components were their furthest distance from each other, which is the configuration in which eccentric binaries spend most of their time. From Table 5, four wide binaries would still have been detected from the ground even if their separations were halved, as their separations at discovery would have been about 0.6 arcsec or greater, similar to the separation of 2007 TY430 at discovery. Observing many very faint KBOs with HST, in a serendipitous (such as Fuentes et al. 2010) as well as a direct targeted search, would help eliminate this selection effect and help determine if smaller objects really do have fewer satellites than larger objects.

The Hill sphere of an object orbiting the Sun is the region where satellites are generally stable around the object, given by

$$\begin{equation} r_{H} = a_{p} \left[\frac{(m_{p1}+m_{p2})}{3\,M_{\odot }}\right]^{1/3}, \end{equation} \tag{ 1 }$$

where a_p is the heliocentric distance of the object in AU, M_☉ is the mass of the Sun, and m_p1 and m_p2 are the mass of the first and second components of the binary, respectively. The Hill radius for 2007 TY430 is about 3.015 × 10⁵ km.

Using the heliocentric semi-major axis of 2007 TY430 from Table 1 and a total mass of 7.90 ± 0.21 × 10¹⁷ kg for the binary gives a_bin/r_H of about 0.07 for 2007 TY430. While this is still well within the stable region of orbital phase space, it is among the widest known binaries (Nesvorný et al. 2003; Nicholson et al. 2008; Noll et al. 2008a).

Widely separated binaries were probably much more common in the past as they are unstable over the age of the solar system from dynamical perturbations (Petit & Mousis 2004; Noll et al. 2006, 2008a; Petit et al. 2008; Parker & Kavelaars 2010). It is possible that the cold classical KBOs have had lower numbers of collisions or fewer planet interactions allowing the largest population of surviving wide, equal-sized binaries in the Kuiper Belt. 2007 TY430 has similar separation and component sizes as the cold classical KBOs 1998 WW31 and 2000 CF105 (Table 5). Petit & Mousis (2004) determined that these two binary KBOs were only stable for about 1–2 Gyr. The Petit & Mousis (2004) result is likely a lower limit on the binary lifetimes since they used a steeper size frequency distribution for the smaller KBOs than currently believed to exist, allowing for more small impactors to disrupt the binaries than is currently likely (Fraser et al. 2008; Fuentes & Holman 2008; Fuentes et al. 2009; Fraser 2009). The 2007 TY430 binary probably has a similar timescale of stability, though 2007 TY430 is in the Plutino population and not the low-inclination classical belt. The timescales of destruction for wide binary TNOs by Parker & Kavelaars (2010) also suggest 2007 TY430 would not have a high probability for surviving for the age of the solar system, and thus 2007 TY430 could just be one of a few binaries left of a once much larger population of binaries.

4.1.1. 2007 TY430: The Case for a Primordial Binary Orbit

The inclinations of many TNO binary components are generally high (Naoz et al. 2010). The Kuiper Belt binary 2001 QW322 was found to have a fairly low eccentricity (e < 0.4) yet a very large inclination (i ∼ 125 deg) and semi-major axis (∼120, 000 km; Petit et al. 2008). Because of 2001 QW322's large inclination, its relatively low eccentricity and large semi-major axis can be explained by the Kozai mechanism (Perets & Naoz 2009). Most binary minor planets do not appear to have primordial orbits as they could have been affected by either tidal forces or have high eccentricities or high inclinations at which the Kozai mechanism may operate (Ragozzine 2009; Naoz et al. 2010).

The binary orbit of 2007 TY430 is compared to other known equal-sized binary orbits in Figures 8 and 9. 2007 TY430 does not have orbital elements similar to other TNO binaries shown in a similar Figure 3 of Naoz et al. (2010), which compares the normalized separations of the binary components to their eccentricities. The log (a_bin/r) for 2007 TY430 is slightly greater than 2.5, but still in a stable region of Naoz et al.'s Figure 3. Interestingly, when including recent results from Parker et al. (2011), it appears most of the equal-sized binaries with very large semi-major axes appear to have moderate to low eccentricities and low inclinations, making them unsusceptible to the Kozai resonance and tides. This is in contrast to many of the lower semi-major axis, equal-sized binaries that appear susceptible to the Kozai mechanism because of their large mutual inclinations and higher eccentricities. This result is likely because the large semi-major axis objects would become unstable to perturbations if their eccentricities or inclinations were too large.

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2007 TY430 is the lowest eccentricity, wide-component, equal-sized binary known. Because the mutual orbital elements of the 2007 TY430 binary have low inclination, low eccentricity, and large semi-major axis (Figures 8 and 9), the Kozai mechanism and tidal interactions have not likely modified the primordial orbit of 2007 TY430 (Chyba et al. 1989; Murray & Dermott 1999; Perets & Naoz 2009). Modification of the 2007 TY430 binary could have occurred over the age of the solar system from direct collisions on either of the two components, from relatively massive bodies passing within the Hill sphere of the two components or interactions with the giant planets (Petit & Mousis 2004; Nesvorný et al. 2011).

The high eccentricities and inclinations of other TNO binary components suggest formation in a dense collisional environment. In this environment, gravitational encounters can create these high eccentricities and inclinations along with secular Kozai effects and tidal evolution (Naoz et al. 2010). Other binaries observed to date could have formed in a similar manner as 2007 TY430, but later three-body encounters or direct collisions after binary formation changed the binary components' orbits to be highly inclined and eccentric. It is thus possible that 2007 TY430 simply has escaped any significant collisions or gravitational encounters while other known binaries have not or formed in a different collisional environment. This could be because 2007 TY430 diffused out of the low-inclination classical belt early on and the Plutino orbit made it less susceptible to collisions. Thus, 2007 TY430's binary orbit could be more primordial than many of the other known equal-sized wide binary objects observed to date.

The proposed binary formation by Funato et al. (2004) from exchanged binaries is unlikely since TNOs appear to lack the many high-eccentricity binaries suggested by this mechanism (Naoz et al. 2010), of which 2007 TY430 is another example of a low-eccentricity binary. Weidenschilling (2002) proposed a hybrid mechanism of a direct collision between two bodies while in the Hill sphere of a third body, which can directly form large separation binaries. This mechanism would only be likely to occur during the formation of the Kuiper Belt, as many more large bodies than currently observed are required as well as low velocities are needed. A similar mechanism, the L³ mechanism proposed by Goldreich et al. (2002), has a third body strongly interacting with two other bodies while they each are within the other body's Hill sphere. The L³ mechanism should dominate over the Weidenschilling (2002) mechanism because strong gravitational interactions should occur much more frequently than the actual collisions of objects. Chaos-assisted capture (Astakhov et al. 2005; Lee et al. 2007) is effectively the same as the L³ mechanism; in chaos-assisted capture, two bodies are temporarily trapped in their mutual Hill spheres and can become permanently trapped when a third "intruder" body is scattered by the pair. This mechanism would create wide separation binaries with equal size and moderate eccentricity.

A second binary formation mechanism proposed by Goldreich et al. (2002), the L²s mechanism, involves two objects forming an unbound transient binary that becomes bound with the aid of the dynamical friction from a sea of small objects. Any binary formation that involves dissipation of energy in a smooth and gradual manner, like the L²s mechanism, will likely form retrograde binaries (Schlichting & Sari 2008b).

Because of 2007 TY430's prograde orbit, it is unlikely to have formed by the L²s mechanism. Unlike the L²s mechanism, the L³ mechanism of Goldreich et al. (2002) should form equal populations of prograde and retrograde binaries (Schlichting & Sari 2008b). So 2007 TY430 could have formed through the L³ mechanism which would only be likely if the KBOs had relatively large velocities, called super-Hill velocities (Schlichting & Sari 2008a, 2008b).

The Hill velocity (Rafikov 2003; Goldreich et al. 2004; Murray-Clay & Chiang 2006; Lee et al. 2007) is defined as

$$\begin{equation} v_H = \left[\frac{G(m_{p1}+m_{p2})}{r_{H}}\right]^{1/2}, \end{equation} \tag{ 2 }$$

where G is the gravitational constant. For 2007 TY430, the Hill velocity is about 0.4 m s⁻¹, which is much less than the Keplerian velocity of its Plutino-type orbit that is about 4 km s⁻¹.

Formation through the L³ mechanism would require large velocities between KBOs that several authors do not think were prevalent in the early Kuiper Belt (Goldreich et al. 2002; Schlichting & Sari 2008b; Murray-Clay & Schlichting 2011). Goldreich et al. (2002) suggest that the velocities of KBOs were about one-third of the Hill velocity, which would make retrograde orbits through the L²s mechanism the dominant binary formation mechanism. This is because binary formation efficiency from gravitational encounters decreases significantly with higher relative velocities since the sphere of influence or time an object affects another is decreased (Noll et al. 2008a; Schlichting & Sari 2008b). Murray-Clay & Schlichting (2011) argue that sub-Hill velocities and the binary formation from dynamical friction (L²s mechanism) is the best mechanism for the equal-sized binary formations. 2007 TY430 does not fall in along these formation lines because it is not retrograde, meaning large velocities during formation were likely and thus dynamical friction unlikely to be the capture mechanism. A weakness to the high-velocity scenario is that Schlichting & Sari (2008b) suggest that the velocity would need to be finely tuned and stay in such a state for a considerable amount of time in order for a high velocity regime to form these prograde, equal-sized binaries.

To date, not enough equal-sized binary orbital inclinations are known to draw a strong conclusion. Only 17 equal-sized KBO binaries have known inclinations (Figure 8). Of these, 5 are retrograde and 12 are prograde, but 3 of the prograde objects have ΔMag > 1 mag and thus are not quite equal-sized binaries. Several authors have suggested that the observed inclinations of TNO binaries are consistent with them being randomly distributed (Noll 2003; Chiang et al. 2007; Grundy et al. 2011). This suggests that the Kuiper Belt disk was in the dispersion-dominated (dynamically hot) regime during binary formation (see Stewart & Ida 2000; Collins & Sari 2006; Schlichting & Sari 2008b). Lee et al. (2007) point out that there are more prograde than retrograde binaries and determine this as a sign of how the binaries formed. Schlichting & Sari (2008b) suggest that this sign is showing the velocity regime in which the binaries formed. Schlichting & Sari (2008b) predicted that over 97% of the binaries with comparable masses will have retrograde orbits if the relative velocities of the KBOs were low. Since it appears to be well below 50%, the relative velocities must have been significantly higher, as discussed above for the formation of 2007 TY430.

Binary formation from direct gravitational collapse of an overdensity of concentrated cm- to meter-sized solids was suggested by Nesvorný et al. (2010). This mechanism appears to be able to produce a wide range of distant equal-sized binaries with a large range of eccentricities with most having prograde inclinations. This mechanism could explain 2007 TY430, but may have trouble producing the retrograde binaries found to date.

The Neptune mean motion resonance populations could have been emplaced by one of the two favored mechanisms. (1) The slow migration outward of Neptune by over 10 AU from its formation location from planetesimal scattering would have allowed Neptune to sweep many objects into the resonances we see today (Malhotra 1995; Hahn & Malhotra 2005). This scenario would likely mean that the inner 3:2 resonance would have a significantly different population of objects than the more outer resonances that would have swept through the classical Kuiper Belt population. This scenario would also suggest the resonance populations should have a cold component representative of the cold classicals along with a hot component representing the objects from closer in. (2) The chaotic population of the resonances could have occurred if Neptune was scattered with a relatively large eccentricity out from near the current Saturn region to near its present semi-major axis (Levison & Morbidelli 2003; Tsiganis et al. 2005; Levison et al. 2008). As Neptune circularized its orbit through interactions with planetesimals, objects in the resonance areas would become trapped. In this scenario, the resonance populations would be more uniform and not have a cold component, unlike the slow migration scenario.

The resonance populations should have a cold component if Neptune experienced extensive slow, smooth migration. This cold component should be similar in characteristics to the low-inclination classical Kuiper Belt, that is, equal-sized binaries should be common as well as ultra-red material (Murray-Clay & Schlichting 2011). This cold component should also have lower eccentricities compared to other objects, meaning there could be a correlation between binaries, color, and eccentricity as well as with inclination in the resonance populations. In the Levison et al. (2008) scenario, chaotic scattering of Neptune and then circularization, the resonance populations should match the scattered disk in characteristics.

No obvious cold component is observed in the 3:2 resonance population and the statistics are too low for the other resonance populations to determine if there is a cold component (Murray-Clay & Schlichting 2011). The 3:2 having no cold component is still consistent with slow, smooth migration since the 3:2 does not sweep through the cold classicals (Murray-Clay & Schlichting 2011). Thus the 3:2 resonance is not as strong as a marker as the other resonances, which should have cold components as they swept through the classical region of the Kuiper Belt. It is possible that sweeping of the ν₈ resonance through the 3:2 resonance and inner classical Kuiper Belt cleared out much of these regions (Petit et al. 2011). If this is true, the ν₈ resonance likely did not sweep through until after the formation of any equal-sized binaries since the binaries are unlikely to have formed as the density of such objects would have been too low.

2007 TY430 has a moderately inclined and eccentric heliocentric orbit, and thus would be considered part of the hot component of the 3:2 resonance on dynamical grounds. Although 2007 TY430 could easily have been emplaced recently by dynamical scattering and resonance sticking, it is interesting to speculate on the meaning of this cold-classical-like binary if it was placed in the resonance primordially. As discussed above, if 2007 TY430 was captured from an originally low-eccentricity, low-inclination orbit by slow, smooth migration, it would have originated around 31 AU by conservation of Brouwer's integral. This would suggest that the primordial cold classical region extended much further inward than is seen today, but the observational evidence for a cold region of the 3:2 resonance is insufficient (Murray-Clay & Schlichting 2011). If its dynamical history was well known, the relatively high eccentricity and inclination of 2007 TY430 could have been seen as an indication that the slow, smooth migration model is insufficient. More binary objects need to be discovered in the 3:2, but the existence of 2007 TY430 in the hot region of the 3:2 and no other known equal-sized 3:2 resonance objects would favor chaotic scattering by Neptune over slow smooth migration.

Table 5 shows the other known equal-sized TNO binaries. Here, equal sized is defined as the components having less than 1 mag difference between components. This magnitude difference corresponds to mass ratios less than 4, assuming similar albedos and densities for the two components and the lack of significant rotational brightness variations. As shown in Table 5 and Figures 1–4, the equal-sized binary population is mostly in the low-inclination classical belt. Interestingly, most of the equal-sized binary TNOs not in the low-inclination classical belt appear to be in mean motion resonances. We see no obvious increase in the binary population between the semi-major axes of 43.5 and 44.5 AU, which has been called the "Kernel" area by Petit et al. (2011) as this region appears to be somewhat more dense than the rest of the classical Kuiper Belt (Figures 3 and 4). It does appear that there is an absence of equal-sized binaries around 43.5 AU, which is near the 7:4 resonance, as well as very few with eccentricities greater than 0.10.

The colors of the equal-sized binaries are not all ultra-red, as many are near neutral in color (Tegler & Romanishin 2000; Trujillo & Brown 2002; Gulbis et al. 2006; Peixinho et al. 2008; Petit et al. 2008; Benecchi et al. 2009; Sheppard 2010). As Figure 10 shows, the only equal-sized binary that is ultra-red in color (S ≳ 25 as defined in Sheppard 2010) and not in the classical population is 2007 TY430 (colors are from the database described in Hainaut & Delsanti 2002). In all, only one of six equal-sized binaries with known colors outside of the classical population has an ultra-red color, which is 2007 TY430 (Table 5). In contrast, 13 of 17 equal-sized binaries in the classical population have spectral gradients near or within the ultra-red color region (S > 20).

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Numerically integrating the non-classical equal-sized binaries from Table 5 (2000 QL251, 2000 FE8, 2006 SF369, 1998 WV24, 2000 CM114, and 2001 QC298) with ten clones each for 500 Myr found all but 2000 CM114 were fairly stable. Some of the clones of 2000 QL151 (6/10, 1 a little chaotic) and 2006 SF369 (10/10, 3 a little chaotic) were experiencing Kozai oscillations (not unusual for resonant objects). Thus only 2000 CM114 is likely to have come from the classical region, but its inclination is currently very large and is not ultra-red in color. Since all of the equal-sized binaries outside the classical belt, except for 2007 TY430, do not have ultra-red colors, it suggests that equal-sized binaries are formed in multiple locations and not just in the cold classical belt. As shown in Figure 10, the inner classical Kuiper Belt is likely an extension of the main classical Kuiper Belt as both have low-inclination, ultra-red, equal-sized binaries. If the ultra-red, equal-sized binary of 1999 OJ4 were formed in the inner classical belt, where we see it today, it must have formed before any clearing through the ν₈ resonance sweeping mechanism since the density of KBOs would have been too low for likely equal-sized binary formation after any significant clearing of the region.