Col-OSSOS: The Distinct Colour Distribution of Single and Binary Cold Classical KBOs

The cold classical Kuiper Belt Objects (KBOs) possess a high, $\gtrsim30\%$ binary fraction. Widely separated and dynamically fragile, these binary systems have been useful in tracing the origins of KBOs. A new class of binaries was recently identified by their colours. The so-called blue binaries are unanimously members of the less red compositional class, and exhibit a 100% binary fraction. They appear to be push-out survivors, emplaced in the classical region during Neptune's phases of outward migration. The presence of these binary systems implies that the majority of objects that formed near the cold classical region formed as binaries. Here we present new optical colour measurements of cold classical KBOs from the Colours of the Outer Solar System Origins Survey, including colours of a blue binary discovered by the Solar System Origins Legacy Survey -- 2015 RJ277. The increased size of the colours sample has resulted in order-of-magnitude decrease in the probability that the binaries and singles sample share the same colour distribution. From the Anderson-Darling statistic, this probability is only a 0.3%, while it is only 0.002% when utilizing the difference of means statistic. We find a hint that the blue binaries have inflated free inclinations compared to their red counterparts, consistent with the push-out origin for these bodies.


INTRODUCTION
The low inclination component of the classical Kuiper Belt is thought to be the most dynamically pristine planetesimal population in the trans-Neptunian region. In particular, the low-i objects with semi-major axes between the 3:2 and 2:1 mean-motion resonances with Neptune, often referred to as the cold classical Kuiper Belt Objects (CCKBOs) are dynamically isolated from Neptune, and are frequently found in dynamically fragile, widely separated binary pairs (Petit & Mousis 2004;Parker & Kavelaars 2012). It is for these two reasons that the CCKBOs are thought to be the only population of trans-Neptunian Objects that formed mainly insitu, rather than having been emplaced on their current orbits through scattering by Neptune (Parker & Kavelaars 2010;Nesvorný & Vokrouhlický 2019), as many scattering and resonant objects have.

arXiv:2104.00028v1 [astro-ph.EP] 31 Mar 2021
While the majority of objects within the CCKBO population are distinctly red, there is a growing sample of bluer objects in the CCKBO region. The blue binary CCKBOs have been identified via their distinct surface colours . Named for their surfaces with bluer spectral slopes than found for most CCKBOs (eg. Gulbis et al. 2006;Doressoundiram et al. 2007) the so-called blue binaries have optical colours that overlap those of the less red (LR; Wong & Brown 2017;Schwamb et al. 2019) compositional class of all trans-Neptunian Objects (TNOs). Those colours are unlike all other known CCKBOs that all have colours consistent with the very-red (VR) class (Fraser & Brown 2012;Peixinho et al. 2015).
Based on early results from the Colours of the Outer Solar System Origins Survey (Col-OSSOS), in Fraser et al. (2017) we hypothesized that the blue binaries are contaminants to the cold classical region, having been pushed out from a region only slightly interior to the current location of the 3:2 resonance during a phase of Neptune's smooth outward migration in one of the strong mean-motion resonances. The hypothesis that the blue binaries are push-out survivors comes with the startling expectation that the majority of objects in the cold classical region formed in binary pairs . Evidence for this has been building since the discovery of wide binaries. From a dynamical analysis of objects like 2001 QW322 -now recognized as a blue binary -Petit & Mousis (2004) pointed out that in the early Solar System, binaries must have been an order of magnitude more numerous than currently observed, though only 10-30% of CCKBOs are resolved binary systems (Noll et al. 2020). One formation route in which such a scenario is possible is if the binary KBOs are the products of the gravitational collapse of a self-gravitating pebble cloud. During gravitational collapse, due to the conservation of angular momentum, pebble clouds will preferentially produce bound planetesimal systems of high multiplicity with masses and orbital properties comparable to observed KBO binary systems (Nesvorný et al. 2010;Parker et al. 2011;Grundy et al. 2019;Robinson et al. 2020).
The existence of the blue binaries as objects pushed out to their current locations indicates that the conditions needed to produce a high binary fraction must have extended into the ∼ 30 − 40 AU zone of the primordial Solar System. The push-out origin theory for the blue binaries hinges on the idea that the binary CCKBOs possess a different surface colour distribution than do the single (or unresolved) CCKBOs. If the single and binary CCKBOs do not possess distinct colour distributions, then there is no evidence to suggest that the binary CCKBOs possess a population of LR objects that is not present in the singles. It is because the observed binary CCKBO colour distribution extends to bluer surface colours than that observed for the singles, that the presence of the blue binaries has been inferred (see Figure 1).
Here we increase the sample of CCKBO optical colours, and consider recent identifications of binary KBOs made with high spatial resolution observations. Specifically, we make use of observations from the Colours of the Outer Solar System Origins Survey (Col-OSSOS; Schwamb et al. 2019) and the Solar System Origins Legacy Survey (SSOLS; Parker et al. 2020;Benecchi et al. 2020). This significantly increases the sample of binary CCKBOs with which to test whether or not the binary colour distribution differs from that of the singles.
Here we present a more statistically robust demonstration that the binary CCKBOs have a colour distribution that is distinct from the single bodies.
In Section 2 we discuss the increased sample of colours and high resolution observations. In Section 3 we consider the orbital elements of our sample of CCKBOs with colour measurements, and present the possibility that the blue binaries on average, have higher free inclinations (the orbital inclinations measured with respect to the forced orbital plane (Van Laerhoven et al. 2019)) than their red counterparts.

THE COLOURS AND BINARIES SAMPLE
We adopt the usual definition of cold classical (eg. Elliot et al. 2005;Gladman et al. 2008), with the usual orbital element selection typically used to select these objects: non-resonant objects with inclinations i < 6 • , perihelion distances q > 37 AU, and semi-major axes 42 < a < 47.5 AU, the same definition we adopted in Fraser et al. (2017). We also include objects in the 7:4 mean-motion resonance with Neptune, with inclinations i < 6 • . The inclusion of these objects was made because low-i objects in this region can be temporarily resonant. In addition, most of these low-i resonators likely share a common origin with non-resonant CCK-BOs. This is highlighted by the blue binary, 2016 BP81, which has been re-classed from non-resonant (Bannister et al. 2016) to resonant (Bannister et al. 2018). This system appears like all other blue binaries, and differs only in its transient resonant behaviour, due to its chance location near the 7:4, as demonstrated by numerical integration of its heliocentric orbit. We emphasize that even with the exclusion of all resonant and non-resonant objects within ∼ 0.3 AU of the 7:4 resonance we would still draw the same conclusions as presented below.
The aim of Col-OSSOS is to gather a brightness complete, UV-optical-NIR colours sample of objects discovered in certain blocks of the Outer Solar System Origins Survey (Bannister et al. 2018) which has been gathering UV-optical-NIR colours with the Frederick C. Gillett Gemini North Telescope, and the Canada-France-Hawaii Telescope. Details of Col-OSSOS observations, target selection, and data reductions can be found in Schwamb et al. (2019). Here we report newly measured optical colours for 17 CCKBOs along with the complete sample of all CCKBOs measured by Col-OSSOS.
We further consider the binary classifications of the SSOLS project Benecchi et al. 2020) 1 . The SSOLS program is conducting a search for binaries among the complete set of OSSOS and the Canada-France Ecliptic Plane Survey (CFEPS) bright CCKBOs with aim to create a binary sample with well characterized discovery biases. Together, the new colour measurements and binary detections are used to supplement the sample we utilized in Fraser et al. (2017).
We adopt the spectral slopes and methods in determining those slopes that were published in Fraser et al. (2017). Specifically, the synphot tool was used to forward model a Solar spectrum convolved with a linear spectrum to estimate colours in appropriate bands as a function of spectral slope. Reported measurements are the weighted means of all available measures for a given target, and we only consider those mean spectral slope values with uncertainty ∆s < 7%/100 nm. As the phase curves of virtually all objects in our sample are unknown, no effort to correct to 0 • phase angle is made. Though we highlight the near-simultaneous nature of the observations from which the colours were measured, mitigating the need to account for differences in phase angle. The total sample of high quality CCKBO colours is increased from 87 to 113 (a 30% increase), 30 of which have been identified as binaries. We present the full sample of spectral slopes, along with (g-r) colours for the Col-OSSOS targets in Table 1.
We consider two samples: those objects reported as binary, and the sample of singles, noting that the latter is likely made up of a combination of truly single bodies, and those with unresolved companions. We present the cumulative spectral slope histograms of the binary and single populations in Figure 1.
2015 RJ277 stands out as the only new CCKBO identified with a slightly redder than Solar optical colour since our 2017 manuscript; its spectral slope is s = 11.9 ± 1.3%/100 nm consistent with the colours of the LR class. RJ277 is the 6th bluest surface in our sample (see Table 1). Hubble Space Telescope observations of this target from SSOLS have revealed this to be a binary system with an apparent separation of ∼ 0.04". This system is indicative of the standout nature of the blue binaries: the 6 bluest objects in our sample of cold classicals are all binaries. Alternatively stated, 100% of objects bluer than the bluest single object in our colours sample are binary.
It is apparent from Figure 1 that the binary sample extends to lower spectral slopes s ∼ 0%/100nm than does the singles sample with the bluest single having spectral slope s = 14%/100nm; the 6 objects with lowest spectral slope are binary. This feature of the binary colours sample is also apparent in the raw colours from which the spectral slopes were estimated (see Figure 2). The bluest objects in (g-r), (V-R), and (F606w-F814w) are binary. The only colour for which this is not true is (V-I). By chance, the (V-I) sample does not include any of the blue binaries. It is worth noting that the majority of blue binaries arise from the Col-OSSOS sample. As the spectra of small KBOs are quite linear (eg. Barucci et al. 2011;Peixinho et al. 2015), this feature of the colours sample is likely nothing more than a sampling fluke and is not indicative of different spectral behaviour in those bands.
Oddly, the singles sample also extends to redder spectral slopes; the 7 reddest targets in our full colours sample are singles. This is likely just an effect of the more populous singles sample, and probably does not reflect anything unusual about the red side of the colour distributions. If samples of size equal to the binary and single samples are drawn from the full colours sample, the probability that the ≥ 7 reddest source belong to the singles population is 7%.
We make use of two statistics to determine the probability that the single and binary samples share the same parent spectral slope distribution. As we did in Fraser et al. (2017), we utilize the difference of means. We also make use of two-sample Anderson-Darling (AD) statistic (Anderson & Darling 1952;Efron & Stein 1981;Scholz & Stephens 1987). To determine the significance of either statistic, we implement bootstrapping with repeats and include additional scattering that matching the uncertainties. That is, from the single colours sample, a random spectral slope sample of size equal to the observed binary sample was bootstrapped, with each sampled point scattered by a gaussian. The widths of each gaussian were also bootstrapped from the distribution of spectral slope uncertainties of the single colours sample. The AD statistic using this random sample was then calculated. This process was repeated 10 6 times, and the simulated statistic values were compared against the statistic evaluated from the observed binary and singles samples. The probability of drawing a simulated AD statistic equal to or larger than the real value was 0.3%. That is to say, the probability that the single and binary samples share the same parent colour distribution is only 0.3%. For the difference of means statistic, the probability of the null hypothesis was only 0.002%. The difference in results from the two statistics reflects their relative sensitivities to differences in the tails of two cumulative distributions, which is exactly where the single and binary distributions differ the most. More compelling than the statistics, however, is the nature of our result. In Fraser et al. (2017) we predicted that the rare blue members of the CCKBO group are all binary. The only new blue member added in the last 4 years is, indeed, binary, consistent with our earlier prediction.

CONSIDERING ORBITAL ELEMENTS
If blue binaries are push-out survivors, it may be that they possess a different orbital element distribution than do the single objects, or even the very red (VR) binaries. The idea that the blue binaries have been pushed out during Neptune's migration suggests that on average, the blue binaries should possess higher free inclinations than do the red CCKBOs, as generally the push-out process acts to inflate an object's inclination (Malhotra 1993;Hahn & Malhotra 2005;Nesvorný 2015a). This is shown in Figure 3, where we plot the element distributions of an example migration simulation from Nesvorný (2015b). This simulation is typical of those that provide a decent match to the observed elements, and uses grainy migration with timescale of τ = 10 Myr, and a disk with exponential profile with eccentricity folding value of 3 AU. From this simulation, it is clear that push-out objects are preferentially found on more excited orbits, with higher eccentricities and inclinations than their non-push-out counterparts (also, see Fraser et al. 2017).
We consider the barycentric orbital elements of our sample of CCKBO with measured colours. We present their orbital elements, cumulatively in Figure 3, and individually in Figure 4. Generally, with the AD statistic, we have found no statistically significant differences in the orbital element distributions between any of the binary samples or that of the singles. The only hint of a difference in orbital elements between the two samples arises from their free inclinations, i f . The values of i f , are the orbital inclinations measured with respect to the forced orbital plane (Van Laerhoven et al. 2019). When considering i f , we have removed all objects with semimajor axes, 43.45 < a < 43.65 AU as they may inter-act with the 7:4 resonance, which would invalidate our calculation of i f . From the cumulative distributions, it seems that the singles and red binaries are preferentially found on orbits with low-i f , with 80% of those objects found with i f 3 • . The blue binaries however, appear to be more commonly found on higher inclination orbits, with half possessing inclinations i f > 3 • . This distinction is not significant however, and is only indicative of what signals might be searched for as sample sizes grow.
The colours sample appears to show a similar preference of higher i f for the blue binaries, compatible with the idea that these objects are push-out survivors. By definition of the cold classical object, the inclination inflation experienced by the blue binaries must be small, which may explain why the difference in cumulative i f distributions between the LR binaries and the CCKBOs in general is not particularly large and is not statistically significant. We applied the AD statistic in the same manner as for the spectral slope distribution and found a 20% chance that the the i f distributions share the same parent distribution.
Increasing the sample size of LR CCKBOs with surveys that involve optical colour measurements, and high resolution observations, is a worthwhile pursuit. If it is shown that the i f (or e) distribution of the LR binaries is different from the VR CCKBOs, it would provide an important lever with which to constrain their initial inclination distributions, and the push-out distance experienced by those bodies. Moreover, the orbital element distributions of the blue binaries have the potential to reveal details of the migratory path experienced by Neptune during push-out of those objects.

ACKNOWLEDGMENTS
The authors acknowledge the sacred nature of Maunakea and appreciate the opportunity to observe from the mountain. This work is based on observations from various programs at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil). This work is also based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. Benecchi acknowledges support from HST program GO-15648 provided from NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.    and binary (dashed) samples, that were used to evaluate mean spectral slopes s presented in Figure 1. Like in Figure 1, we only plot those objects with spectral slope error less than 7%/100 nm. The vertical line shows the colour corresponding to s = 17%/100 nm. The bluest objects are binaries in all but (V-I) which happens to not include any of the blue binary CCKBOs. . Cumulative free inclination, eccentricity, and semi-major axis of the TNO colours sample (top), and from the results of a migration simulation from Nesvorný (2015b) (bottom). The element distributions of the VR binaries, LR binaries, and single objects are shown by the red, blue, and black curves, respectively. From the simulation, the dashed and solid lines present the element distributions of those objects ending as cold classicals, that originated in the cold classical region (initial a > 42 AU; solid curve), and those originating interior to the region (initial 30 < a < 41 AU; dashed curve). We emphasize that a different selection of initial distances for those objects originating interior to the cold classical region makes no appreciable difference on the final orbital element distributions. We do not include the small contribution from objects originating inside 30 AU, as binarity would be disrupted from push-out over such large distances. The overall contribution of these bodies to the cold classical population will be considered in a future work.