Col-OSSOS: The Distribution of Surface Classes in Neptune's Resonances

The distribution of surface classes of resonant trans-Neptunian objects (TNOs) provides constraints on the protoplanetesimal disk and giant planet migration. To better understand the surfaces of TNOs, the Colours of the Outer Solar System Origins Survey acquired multiband photometry of 102 TNOs and found that the surfaces of TNOs can be well described by two surface classifications: BrightIR and FaintIR. These classifications both include optically red members and are differentiated predominantly based on whether their near-infrared spectral slope is similar to their optical spectral slope. The vast majority of cold classical TNOs, with dynamically quiescent orbits, have the FaintIR surface classification, and we infer that TNOs in other dynamical classifications with FaintIR surfaces share a common origin with the cold classical TNOs. Comparison between the resonant populations and the possible parent populations of cold classical and dynamically excited TNOs reveal that the 3:2 has minimal contributions from the FaintIR class, which could be explained by the ν 8 secular resonance clearing the region near the 3:2 before any sweeping capture occurred. Conversely, the fraction of FaintIR objects in the 4:3 resonance, 2:1 resonance, and the resonances within the cold classical belt suggest that the FaintIR surface formed in the protoplanetary disk between ≳34.6 and ≲47 au, though the outer bound depends on the degree of resonance sweeping during migration. The presence and absence of the FaintIR surfaces in Neptune’s resonances provides critical constraints for the history of Neptune’s migration, the evolution of the ν 8, and the surface class distribution in the initial planetesimal disk.


INTRODUCTION
The surface colors of Trans-Neptunian Objects (TNOs) in a variety of optical and near-infrared wavelengths have been used to classify TNOs into different surface classifications.Small TNOs, with diameters 500 km, typically do not retain volatile ices on their surfaces (Schaller & Brown 2007;Brown et al. 2011), and their reflectance spectra can be well described by a single slope in the optical (Fornasier et al. 2009) and a single slope in the near-infrared (Barucci et al. 2011).This single optical slope is also seen in the correlation between g − r and g − i colors, (e.g.Sheppard 2012;Ofek 2012;Seccull et al. 2021).Based on the optical and near-infrared surface colors of TNOs, a variety of different surface classification schemes have been discussed (e.g.Fraser & Brown 2012;Peixinho et al. 2012;Dalle Ore et al. 2013;Peixinho et al. 2015;Pike et al. 2017b;Fraser et al. 2022).These include two TNO surface classifications (Fraser et al. 2022), three surface types (e.g Fraser & Brown 2012;Pike et al. 2017b), and significantly more surface classifications (Dalle Ore et al. 2013).The model of two TNO surface classifications proposed by Fraser et al. (2022) based on the Colours of the Outer Solar System Origins Survey (Col-OSSOS) photometry reproduces the range of TNO surface colors in both the optical and near-infrared.
The Col-OSSOS project has acquired near-simultaneous multi-band observations of 92 TNOs.For all of the TNOs, photometry was acquired at Gemini Observatory in g and r bands, using the Gemini Multi-Object Spectrograph (GMOS, Hook et al. 2004) and J band using the Near Infrared Imager (NIRI, Hodapp et al. 2003).The data acquisition, reduction, and trailed image photometry methods (Fraser et al. 2016) are described in detail in Schwamb et al. (2019) and summarized, including improvements since the previous publication, in Fraser et al. (2022).The photometry used in this work uses the values in Fraser et al. (2022), which presents the results of the six years of the Col-OSSOS photometry observations, including g − r, r − J, and some u − g and r − z photometry.Utilizing this full sample, Fraser et al. (2022) determined that the surfaces of TNOs fall into two surface classes.Because the optical and near infrared (NIR) colors of TNOs broadly follow the reddening line, or line of constant spectral slope, Fraser et al. (2022) recommends a re-projection of the colors into a principal component space, where one component is the distance along the reddening line (PC 1 ), and the second component is the distance away from the reddening line (PC 2 ).In this projection, the division between the two surface classifications, FaintIR and BrightIR, is a statistically significant linear gap in one of the principle component axes (Fraser et al. 2022).Fraser et al. (2022) found similar results for other color data using different optical and NIR bands, including additional Col-OSSOS bands and Hubble/WFC3 Test of Surfaces in the Outer Solar System (Fraser & Brown 2012).At low values of PC 1 < 0.4, the gap is less apparent and the spectral slopes of these objects more closely resemble the BrightIR surface type even for the few objects with PC 2 < −0.13 and PC 1 < 0.4.The FaintIR surface classification has a limited range of optical colors in the red, and includes the vast majority of the objects typically referred to as cold classical TNOs, which have low eccentricity and low inclination orbits.The BrightIR surface classification is closer to the reddening curve and explores the full range of optical and NIR surfaces.The range of surface colors in the two classifications can be reproduced using a mixture with one neutral and two different red materials, see Fraser et al. (2022) for details, which would be expected if the two surface classifications formed in different regions of the proto-planetesimal disk.The two surface classifications of Fraser et al. (2022) provides a powerful diagnostic tool for determining the current orbital distribution of the two surface classifications and the implications of this distribution on the formation and evolution of the outer Solar System.
The presence or absence of the FaintIR surface classification in various dynamically excited orbits, particularly in the mean motion resonances of Neptune, can be diagnostic of different modes of planetary migration and different initial disk distributions.The resonances include objects which are long-term stable as well as objects which stick into resonance (e.g.Lykawka & Mukai 2007).If Neptune migrated smoothly outward (e.g.Malhotra 1995), it would sweep across the cold classical region and deeply trap a significant number of stable FaintIR objects into the mean motion resonances near the cold classical belt.TNOs which scattered during planetary migration (e.g.Gomes et al. 2005;Levison et al. 2008;Nesvorný 2018) or currently stick in the resonances are captured from the bulk dynamically excited population of TNOs, which may include FaintIR and BrightIR surfaces.The surface classifications of resonant TNOs constrain the capture methods that populated the mean motion resonances of Neptune, and constrains the locations of these source populations.
Recent work has attempted to reproduce the color distribution of TNOs, assuming that the different surface classifications formed in different regions of the proto-planetesimal disk.These works have typically assumed that the cold classical TNOs have a distinct surface type, different from the dynamically excited TNOs, and often classifies dynamically excited TNO surface types purely based on optical colors (frequently referred to as 'red' and 'very red').Utilizing only optical colors replicates the bulk of the BrightIR and FaintIR groups, but results in some contamination, particularly the inclusion of optically very red BrightIR objects in the FaintIR group.The distribution of red and very red TNO surfaces has been reported to have a correlation between inclination (Marsset et al. 2019) and eccentricity (Ali-Dib et al. 2021) on surface color, is inferred to be related to differences of formation location and the effects of planetary migration on the populations.The correlation between inclination and surface classification holds when the FaintIR/BrightIR classification system is used (Marsset et al. 2022).Marsset et al. (2019) also identified a dependence between the final inclinations of TNOs and their formation distances has also been found.A dependence between color, inclination, and eccentricity has been reproduced in some inward and outward planet migration scenario simulations (Pirani et al. 2021).Nesvorný et al. (2020) used an N-body integration of several Neptune migration scenarios (Nesvorný & Morbidelli 2012) with a large disk of test particles, and compared the final orbital and color distributions of test particles for various assumptions about the initial surface density profile of the planetesimal disk and the location in that disk that separates where the red and very red TNOs formed.Nesvorný et al. (2020) compared the red and very red population distributions from these simulations to the then-available observational constraints, and they determined that the observed distribution was consistent with a transition in the initial planetesimal disk from an inner red population to an outer very red population occurring between 30-40 au.Buchanan et al. (2022) tested initial particle distributions of red and very red TNOs distributed within 30 au, and found both combinations (red or very red as the inner type, and the other as the outer type) to provide an acceptable match to the observed current color distribution, with inner/outer color transitions at 27-28 au.These analyses all utilized optical colors to differentiate between red and very red surfaces instead of a combination of optical and near-infrared slopes, however, a significant fraction of the objects can be properly classified with only the optical slope.As a result, we expect that with a proper classification into FaintIR and BrightIR surfaces these results can be further refined.
In this work we utilize the FaintIR/BrightIR surface classifications to examine the TNOs trapped in mean motion resonances with Neptune, as the presence of different surface classifications in the resonances provide constraints on the specifics of planetary migration and the initial proto-planetesimal disk.We explore the characteristics of the resonant Col-OSSOS TNOs (Section 2), the FaintIR and BrightIR surface classification-distribution within the different resonances (Section 3), and the implications of this surface-classification distribution for the formation and evolution of the outer Solar System (Section 4).

COL-OSSOS TNO SAMPLE
The Col-OSSOS sample of g − r and r − J photometry of 92 TNOs includes 36 resonant TNOs in a variety of different resonant orbits.This work utilizes the same g − r and r − J colors of the Col-OSSOS objects as Fraser et al. (2022).The photometry and orbital classifications of these targets are listed in Table 1, which is sorted by semi-major axis so that the members of each resonance are listed together.Col-OSSOS attempted to measure a magnitude complete sub-sample of the Outer Solar System Origins Survey (OSSOS) discoveries brighter than m r < 23.6 in the OSSOS E, H, L, O, S, and T blocks (Bannister et al. 2018).There are currently 9 TNOs and two Centaurs which meet the Col-OSSOS selection criteria, but do not have Col-OSSOS g − r and r − J colors measured.The objects without current photometry are included in Table 1 with '-' indicated for their Surface Class, and are primarily classical objects, but include one distant resonant TNOs, in the 17:9 resonance.We do not expect the small number of objects without color observations to significantly affect the interpretation of our sample, as the objects were not observed due to time loss as a result of poor weather, and an effort was made to observe the target list randomly.This should not introduce any significant selection biases that could impact the apparent color distribution of the Col-OSSOS targets.In Table 1, there are no clear trends in the unobserved targets (they span a range of discovery magnitudes, absolute magnitudes, and dynamical classes).
Table 1.Col-OSSOS Resonant TNOs.The Minor Planet Center (MPC) identification and OSSOS internal name are both provided for all targets.The Discovery magnitude is the magnitude calculated by the OSSOS project for the discovery images, and solar system absolute magnitude Hr was calculated from the discovery magnitude, and uncertainty is dependent on the uncertainty in discovery magnitude.The orbital fit parameters (semi-major axis a, eccentricity e, and inclination i) and the object Dynamical Classification are from the OSSOS orbital fits (Bannister et al. 2018), and all digits printed are significant.Insecure resonance classification, where one or more of the variant orbits does not show the resonant behavior seen in the nominal clone, is indicated by a '*'.The free inclination ifree is calculated by Huang et al. (2022 and Van Laerhoven et al. (2019, VL2019) in that order; the free inclination is used to separate classical TNOs into 'cold' and 'hot' classes according to Van Laerhoven et al. (2019)'s results (see main text).The Surface Class column indicates whether the object is BrightIR or FaintIR based on their PC values (FaintIR: PC 2 grJ > −0.13 and PC 1 grJ > 0.4).The g − r and r − J colors are in the Sloan Digital Sky Survey (SDSS) filters Fraser et al. (2022).The object indicated with '**' was not on the initial target selection list, but with the revised and improved OSSOS photometry, this object meets the Col-OSSOS selection criteria and is included here for completeness.The TNOs were classified into different dynamical groups utilizing the Gladman et al. (2008) scheme as described in the OSSOS data release publications (Bannister et al. 2016(Bannister et al. , 2018)).The resonant TNO classifications are determined by numerically integrating the OSSOS orbits (including clones representing the orbital uncertainty) of each TNO and examining the time histories for libration of any resonant angles (see, e.g.Volk et al. 2016Volk et al. , 2018)).We use these resonant classifications exactly as identified by OSSOS.Insecure classifications (where not all of the orbital clones agree with the nominal) are indicated by a '*' in Table 1.We consider the samples of 4:3, 3:2, and 2:1 resonant TNOs individually.Because of the small number of Col-OSSOS targets in some of Neptune's resonances, in this work we combine all of the resonant TNOs with semi-major axes between the 3:2 and 2:1 resonances into a single group, which we refer to as "resonant within the classical belt", and we combine all of the resonant TNOs beyond the 2:1 resonance (at 47 au) into a group which we refer to as "resonant a > 49 au."For the remainder of the Col-OSSOS sample, we divide the objects into two groups based on their orbital dynamics: "cold classical" and "dynamically excited" objects.The number of TNOs in each category is given in the legend of Figure 1. W utilize a classification scheme for cold classical TNOs and dynamically excited objects based on Van Laerhoven et al. ( 2019)'s analysis of the inclination distributions of the TNO populations and similar work by Huang et al. (2022).Van Laerhoven et al. ( 2019) computed the free inclination (i.e., the orbit's inclination relative to a locally dynamically meaningful reference plane) for classical OSSOS TNOs, PIKE ET AL. and found that the free inclination i f ree is a much more robust criteria for evaluating the degree of dynamical stirring which the object has experienced (see, e.g., Gladman & Volk 2021 for a review of both the concept of free inclinations and the motivation for using i f ree to separate cold and excited TNOs).As a result, i f ree is a much more effective criteria for classifying objects as dynamically cold than the current osculating ecliptic orbital inclination.The criteria used to classify cold classical TNOs, or those objects which are most likely to have formed in their current location, are semi-major axes 42.5 < a < 45 au and i f ree < 4 • or 45 < a < 47 au with i f ree < 6 • , as the more distant portion of the classical belt is thought to have experienced slightly more stirring.We use the i f ree values, given in Table 1, to identify cold classical TNOs, and all of the remaining Col-OSSOS objects are grouped into the category of "non-Resonant Dynamically Excited" TNOs.These dynamically excited (DE) TNOs include all objects described in the Table 1 as Centaurs, hot classical, detached, scattering, and Jupiter coupled.Figure 1 shows the orbital distribution of the resonant and non-resonant Col-OSSOS TNOs that have g − r and r − J colors.The significant number of Plutinos is immediately apparent, as is the motivation for combining the resonant objects within the classical belt into one group and the resonant TNOs beyond the 2:1 resonance into another.We combine these dynamical classifications with the FaintIR and BrightIR surface classification from Fraser et al. (2022)

THE SURFACES OF RESONANT TNOS
In the projection color space, the Col-OSSOS sample of TNOs shows only a single bifurcation and gap, into the two surface types BrightIR and FaintIR (Fraser et al. 2022).For the resonant sub-sample discussed in this work, we utilize the same reprojection into the principal components along and away from the reddening line (PC 1 and PC 2 respectively, Fraser et al. 2022) to classify the objects into FaintIR and BrightIR surface classifications.We find that the colors of resonant TNOs span the full range of color-color space in g − r and r − J and in the re-projection.As we are utilizing the g − r and r − J colors, we refer to the re-projected values as PC 1 grJ and PC 2 grJ .In the re-projection, the FaintIR and BrightIR are divided primarily based on PC 2 grJ = −0.13, the dashed line in the right panel of Figure 2, with the small sub-sample which are PC 2 grJ = −0.13classified as BrightIR, as these are beyond the statistically significant gap and their spectral slopes more closely resemble that group.To better demonstrate the different surfaces between the different populations, Figure 3 shows the cumulative fraction of TNOs in each group with particular PC 1 grJ and PC 2 grJ values.The cumulative PC 2 grJ plot highlights the differences between the different populations, and also shows that small changes in the precise location of the cut between FaintIR and BrightIR (PC 2 grJ = −0.13)would change the classification of a few objects right near the division, but would not affect the overall PC 2 grJ distribution of each dynamical classification.
The distribution of PC 1 grJ values on the left in Figure 3 does show different distributions for the dynamically excited objects and cold classical objects, but is less useful for diagnostic purposes.The value of PC 1 grJ is related to the spectral slope an object would have if it was directly on the reddening line, so the cumulative value of PC 1 grJ is similar to the spectral gradient plots in previous work (e.g.Sheppard 2012).The resonant object outliers in the color-color plot, particularly the 4:3 and 2:1 deep in the cold classical clump, are not at all obvious in the cumulative PC 1 grJ distributions.Figure 2. Left: The r − J vs. g − r color distribution of Col-OSSOS TNOs.The black arc is the redding line, or line of constant spectral slope.The same symbol colors are used here as in Figure 1: non-resonant Dynamically excited objects (black circles), cold classical objects (pink squares), 4:3 resonators (orange triangles), 3:2 resonators (yellow squares), resonant objects within the classical region (green wide 'x's), 2:1 resonators (cyan diamonds), and resonant objects with semi-major axes a > 49 au (blue hexagons).The Plutinos are the largest resonant sample, and are found with all of the surface colors seen in the sample.The objects below the gap feature are primarily cold classical and resonant TNOs.Right: The color-color plot re-projected into the PC 1 and PC 2 components, the distance along the reddening line and from the reddening line respectively.In this re-projection, the gap feature is indicated by the dashed line at PC 2 grJ = −0.13.The FaintIR surface classification below this line is dominated by cold classical objects and resonant TNOs.It includes one 4:3, one 2:1, and several 3:2 resonators, as well as a few dynamically excited objects and a distant a > 49 au resonator.
As in Fraser et al. (2022), we note that the FaintIR group (with PC 2 grJ < −0.13) contains the vast majority of the dynamically cold classical TNOs, with the exception of three outliers.(There are four outliers if the low PC 1 grJ cold classical is also included.)The presence of three to four objects identified as cold classicals based on their free inclinations within the BrightIR group may simply represent the low-i tail of the hotter inclination distribution of the 33 dynamically excited objects.We tested whether this misclassification was consistent with the sample by using models of the TNO populations and the survey simulator.For an unbiased sample with an inclination width of 14.5 • , which has been found to be the best fit for the hot classical region (Petit et al. 2017), approximately 4% (or 1.5 objects) of the dynamically excited sample would have i < 4 • .We used a survey simulator (Lawler et al. 2018) to model the pointing and depth biases of our sample, and an input model distribution of cold and dynamically excited TNOs, generated by modifying the Canada-France Ecliptic Plane Survey L7 model of the hot and cold classical populations (Petit et al. 2011) to match the inclination widths of 14.5 • (Petit et al. 2017) for the hot population and 1.75 • (Van Laerhoven et al. 2019) for the cold population.Importantly, we modeled these inclination widths as free inclination widths rather than widths relative to the invariable plane, which is a comparatively poor match to the plane of the classical Kuiper belt.We input these modified L7 model objects until the survey simulator detected 10,000 objects, then sub-selected the sample brighter than m r ≤23.6, to imitate the brightness limit of Col-OSSOS, which gave a sample of ∼1,000 simulated detections.When we examine the simulated observations of the intrinsically hot classical population, we find that 15 ± 2% of grJ values.The non-resonant dynamically excited objects (black 'x's), dynamically cold classical objects (pink squares), 4:3 resonators (orange triangles), 3:2 resonators (yellow squares), resonant objects within the classical region (green wide 'x's), 2:1 resonators (cyan diamonds), and resonant objects with semi-major axes a > 49 au (blue hexagons) are all shown separately.The gray dashed line indicates the divide between the FaintIR (left) and BrightIR (right) surface classifications at PC 2 grJ = −0.13.The cold classical TNOs are dominated by the FaintIR surface classification, but this surface classification is also found in the resonances, including the 4:3 resonance which is sunward of the current cold classical belt.The non-resonant dynamically excited objects are dominated by the BrightIR surface classification, and their PC 2 value distribution is similar to the resonant a > 49 au surfaces.the detected hot sample would have free inclinations low enough to be mis-classified as cold.There are 19 hot classical TNOs in our sample.Postulating that the three to four BrightIR "cold" classical TNOs are actually the low-i tail of this hot population is completely consistent with our estimate of the mis-classification rate (3/22 or 4/23 is ∼ 14 − 17%).On the other hand, our simulated observations imply that only 1.5 ± 0.5% of the intrinsically cold classical population have inclinations large enough to be misclassified as hot.There are 19 FaintIR cold classical TNOs in our sample.To postulate that the 4 FaintIR hot classical TNOs really belong to the intrinsically cold population, that would imply an inconsistently high mis-classification rate of ∼ 17%.Additionally, several of the FaintIR hot classicals have free inclinations far too large to be considered the high-i tail of the cold population.While these simple survey simulations based on the L7 model do not account for the full complexity of the hot and cold populations, they strongly suggest that the BrightIR interlopers in our apparently cold population are simply the low-i tail of the hot population but that the FaintIR objects in the hot population are not simply the result of overlapping inclination distributions.
The dynamically excited TNOs and the resonant TNOs within the FaintIR group are likely to represent objects which formed in the FaintIR region and were scattered or captured into other populations during planetary migration.The FaintIR objects labeled dynamically excited objects are not consistent with being the high-inclination tail of the cold population (21% +13 −14 compared to 5±1%).For the resonant TNOs, in the cumulative PC 2 grJ shown on the right in Figure 3, these populations show different enhancements of FaintIR surfaces relative to the dynamically excited population.It is clear that a higher fraction of the resonant TNOs in the 4:3, and within the classical belt have more surfaces similar to the cold classical TNOs, which have the FaintIR surface classification.The 3:2 resonance and a > 49 resonances show a PC 2 grJ distribution similar to the dynamically excited TNOs.The Plutinos are the largest sub-sample, 15 objects, and are also found with the full range of surface colors.This remains consistent with the possibility of capture from the bulk dynamically excited population, however, as that population includes ∼ 20% FaintIR surfaces.The inclusion of several resonant TNOs that are coincident with the bulk of the cold classical TNOs is immediately apparent, and includes a 4:3, a 2:1, and a 3:2 resonator.
The TNOs currently in Neptune's resonances include objects with a variety of origins.Some resonant objects were captured during the era of planet migration via sweeping (resonances picking up objects as the resonances move through a population already exterior to Neptune) and scattering (objects dynamically perturbed outward from the giant planet region that end up in Neptune's resonances); there are also objects from the current scattering population that temporarily stick in the resonances.
Depending on the specifics of planetary migration, different resonances may have preferentially captured objects from different primordial planetesimal populations (we expand upon this in Section 4).It is generally thought that the dynamically excited populations originate from a portion of the planetesimal disk closer to the giant planets than the cold classical TNOs thought to have formed in situ (see review by Gladman & Volk 2021), which is motivated by, and consistent with, the idea of a color transition in the planetesimal disk, as discussed above.In this scenario, we expect the resonances that are dominated by capture of scattering objects (either in the early solar system or from the current scattering population) to have surface properties similar to the dynamically excited population; while resonances dominated by sweeping capture of cold disk objects should share surface properties with the cold classical population.
In order to determine whether the surface classifications of resonant TNOs are consistent with capture from the current dynamically excited population, we used the Anderson-Darling (AD, Anderson & Darling 1952) statistical test, which is similar in concept to the often used Kolmogorov-Smirnov (KS) test.The AD test statistic is a measure of the difference between the cumulative distributions of a parameter from two populations and can be used to assess the probability that the two populations are sub-samples drawn from the same parent population.The significance of the AD statistic is computed with a bootstrapping method, which re-samples the assumed parent population distribution to compare against itself to compute the expected distribution of the AD statistic for the case where we know the two samples are related.For the resonant objects, we consider the possibility that the parent population is either: (1) the dynamically excited TNOs, (2) the cold classical TNOs, or (3) a mixture of the two.
To determine what source population is consistent with the resonant TNO PC 2 grJ values, we compared each of the resonant PC 2 grJ distributions with: the PC 2 grJ distribution of the dynamically excited TNOs; the PC 2 grJ distribution of the cold classical TNOs, and source populations which are a mixture of the cold classical and dynamically excited TNOs.We created possible parent populations by combing the two possible parent populations (dynamically excited and cold classical TNOs) with different relative contributions of the two components, ranging from 0-100% in steps of 5%.We cloned the full list of PC 2 grJ values for each of components until they reached the desired total ratio.Possible parent populations for the resonant TNOs include the 100% dynamically excited TNOs, 95% dynamically excited TNOs with 5% cold classical TNOs, etc.In Figure 4, the results of the comparisons between the different resonant populations and possible source populations are given.The values within the 2σ limits are parent population models which are not rejectable, indicated by small diamonds.We find, unsurprisingly given the known optical color distribution, that all of the resonances reject at > 3σ a scenario where their source population is made up entirely of the cold classical population.However, a wide range of mixed contributions from the two populations were nonrejectable.Note that the acceptable ratios reflect the apparent and not the intrinsic population ratios-due to the differences between the size and albedos of the different surface types, the apparent fraction of neutral/BrightIR surfaces is much lower than the intrinsic fraction of these surfaces (Schwamb et al. 2019).
We also investigated two additional variations on the parent populations: excluding the Centaurs and moving the three dynamically cold classical objects with high PC 2 grJ values (which we argue in previously are consistent with the low-i tail of the dynamically excited population) into the dynamically excited population.There are several Centaurs in the Col-OSSOS sample, which are classified as dynamically excited TNOs.Because the surface properties of Centaurs with small perihelion distances can potentially have been altered since formation by thermal modification in the Centaur region (e.g.Jewitt 2009), we also tested the sub-population of dynamically excited TNOs with pericenter q > 22; the exclusion of these objects did not significantly affect the results.We also repeated the AD tests with the three PC 2 grJ >-0.13 BrightIR objects with cold classical orbits moved to the dynamically excited objects lists.All three scenarios: (1) exactly as classified in Figure 1 and Table 1; (2) dynamically excited objects limited to q > 22; and (3) low-i tail of dynamically excited objects moved to dynamically excited sample; are included in Figure 4 for comparison.
The lower-a resonances with the exception of the 3:2 resonators do show some trends toward larger contributions from the cold classical population.The 'least rejectable' parent populations for the 4:3 (interior to the classical belt at 36.4 au), 2:1 (beyond the classical belt at 47.7 au), and resonances within the classical belt include a significant contribution from the cold classical population (30-40%).Additionally, the PC 2 grJ values of the objects in the 4:3 resonance and the resonant within the classical belt population reject the hypothesis that they are sourced exclusively from the dynamically excited population.

DISCUSSION
The resonant populations preserve a record of the capture events that occurred during planetary migration.As Neptune migrated, its resonances trapped outwardly scattered objects (e.g.Gomes 2003) as well as dynamically colder objects that the resonances swept (e.g.Malhotra 1995) during migration.Present-day scattering objects can also become transiently stuck to resonances as their orbits evolve (Lykawka & Mukai 2007).These different capture mechanisms have different source regions in the  , with different percentages of each of the two groups, from 0-100% calculated in steps of 5%.The distance between the distribution of resonant PC 2 grJ values and parent population PC 2 grJ values is computed with the AD test, then the significance of that result is obtained by bootstrapping using the input parent population.The large diamonds indicate the least rejectable D-statistic parent population fraction, and the small diamonds indicate the 2σ limits based on the D-statistic.The width of each bar is proportional to the D-statistic value at each 5% step.The three different bars for each resonance show the results for slightly different assumptions in the parent populations.The green (left) bar uses the DE and CC populations exactly as defined in Table 1.The teal (middle) bar uses the CC objects as defined in Table 1, but for the DE objects uses only the DE objects with pericenter q > 22.The purple (right) bar uses the CC and DE objects as classified in Table 1 except that the 3 cold classicals with PC 2 grJ >-0.13 BrightIR surfaces are moved from the CC group to the DE group, as 3 low-i objects is consistent with being the low-i tail of the DE inclination distribution, see Section 3 for details.Note that the Parent Population used here is to reproduce the apparent surface distribution and not the intrinsic population ratios of the dynamically excited and cold classical objects-due to detection biases and albedo differences, the intrinsic fraction of BrightIR objects is much larger than the apparent fraction.original planetesimal disk.The scattering capture which occurs during planetary migration would likely have caught objects from the primordial disk which were scattered outward from the region currently occupied by the giant planets (e.g.Gomes et al. 2005;Levison et al. 2008); see also review by Nesvorný 2018.This differs from modern transient resonance sticking from the scattering population in that the still on-going migration allowed these objects to evolve into more stable regions of the resonances.The precise efficiency of this capture depends on the initial conditions of the disk and the specifics of the planetary migration scenario (e.g.Murray-Clay & Chiang 2006;Nesvorný 2015a;Volk & Malhotra 2019).These objects scattered and captured into resonance during planetary migration are likely to have similar origins to the bulk dynamically excited Kuiper belt region (e.g.Levison et al. 2008), which include TNOs currently in the hot classical, detached, and scattering populations.The current, transiently sticking resonant objects represent captures from the reservoir of currently scattering TNOs; while not all transient resonant captures are particularly recent (residency timescales are roughly evenly distributed in log time; Yu et al. 2018), they are sourced from the post-migration scattering population and thus share an origin with the dynamically excited population.Thus resonant objects should have the same surface distribution as the dynamically excited TNOs, i.e. dominated by BrightIR surface classifications, if all of the resonant objects are captured through scattering capture during migration and present-day transient resonance sticking.However, if Neptune's migration included a phase of smooth migration, it may have swept TNOs from the current cold classical region, thought to be a preserved remnant of the in situ primordial disk, into some of the resonances.Sweeping capture into the resonances during migration is orders of magnitude more efficient than scattering implantation (e.g.Volk & Malhotra 2019), so if sweeping capture occurred for a resonance, a large population of FaintIR surfaces is expected.While smooth migration alone does not adequately explain all of the observed TNO population, Neptune might have smoothly migrated outward at the end of its migration (see, e.In this work, we find some FaintIR surface classifications in all dynamically excited orbital classifications, at varying degrees of representation.The distribution of FaintIR and BrightIR surfaces based on their orbital parameters is shown in Figure 5. Arguably the most dynamically interesting FaintIR surface is found in the 4:3 resonance.This object, 2013 US 15 is optically very red and falls conclusively within the FaintIR surface classification group.2013 US 15 has a semi-major axis of 36.38 au, sunward of the current cold classical region.2013 US 15 is also the least dynamically excited 4:3 resonator in the sample, with e = 0.07 and i = 2.02 • , similar to the cold classical orbits, but at smaller semi-major axis.The inclusion of this object into the 4:3 resonance requires further investigation.A straightforward explanation for the presence of a FaintIR 4:3 resonator is that the primordial FaintIR surface type extended sunward of the current cold classical belt to at least 36 au, and some resonance sweeping occurred to trap this object into the 4:3 resonance.The low excitation of its current orbit (low e and low i) implies it could not have been carried very far from its original location by the resonance.To test the stability of this object, we integrated 250 clones sampled from the orbital uncertainties for >3 Gyr.The orbits of the clones were all stable for the duration of the integration, and the libration amplitude of the resonator was also stable at 94 • ±3 • (comparable to it's current libration amplitude of 95 • ±1 • determined from a 10 Myr integration).Resonance sticking with similar libration amplitudes is possible, but not common (Yu et al. 2018), and the long-term stability of the entire orbital cloud supports a formation in-situ and a deep, primordial capture into the 4:3 resonance.Currently, the FaintIR surface of 2013 US 15 accounts for one third of the sample of 4:3 resonators, so the fraction of the 4:3 resonators with FaintIR surfaces may be quite significant.However, the intrinsic FaintIR/BrightIR surface ratio is difficult to constrain with this small sample, and additional optical and near-infrared observations of 4:3 resonators would be extremely helpful for understanding the intrinsic frequency of FaintIR surfaces in this resonance.
Just sunward of the cold classical belt, the 3:2 resonance includes some FaintIR objects.However, the fraction of FaintIR surfaces within the 3:2 resonance is more similar to the non-resonant dynamically excited TNOs than other resonances near and inside the cold classical belt.In Figure 4, it is clear that the 3:2 resonance strongly rejects a significant contribution from the cold classical population, and favors a higher contribution from the Dynamically Excited population, 90 +5 −40 %.In other resonances, the FaintIR objects were predominantly those with lower-i orbits, whereas the OSSOS sample of 3:2 objects examined here have moderate-to large-i, i 5 • .Low-inclination 3:2s are not common, but have been found in other surveys (e.g.Alexandersen et al. 2016), so these objects warrant additional observations to determine whether their surfaces fall into the FaintIR category.We note, however, that resonant sweeping (if it occurred) might have been less effective near the 3:2 resonance if the intrinsically cold population sunward of the 3:2 was cleared by secular resonances during planetary migration before the 3:2 could sweep it.The inner edge of the modern-day cold classical population is sculpted by the ν 8 eccentricity secular resonance which destabilize low-inclination orbits in the 40-42 au region adjacent to the 3:2 resonance (see, e.g., Gladman & Volk 2021); there is also an inclination secular resonance in the same region that could excite the inclinations of initially cold objects (e.g.Chiang & Choi 2008).The locations and strengths of these secular resonances during planet migration could have significantly affected capture probabilities for cold objects into the 3:2 and their final inclinations if captured (see discussion in Volk & Malhotra 2019).Based on the 3:2 sample here, we do not find evidence of resonant sweeping capture into the 3:2, but the complex dynamics near this resonance and the mid-to high-inclinations of the observed sample do not provide conclusive evidence against sweeping having occurred.
The Col-OSSOS sample has some additional FaintIR objects of note, including objects which are resonant within the cold classical belt (5:3, 7:4, 9:5, and 11:6.These resonances, which overlap in semi-major axis with the current cold classical region, have a significantly enhanced fraction of FaintIR surfaces.The 7:4 and 11:6 resonators are both low-e and low-i(<4 • ), the 5:3 object is low-i but large-e, while the 9:5 resonator has an excited orbit with i =18.3 • .The higher-i orbit of the FaintIR 9:5 may be the result of diffusion within the resonance, as this object is in a mixed e-i resonance.The enhancement in FaintIR surfaces for the resonances within the classical region is seen in Figure 3 and Figure 4, and the preferred source population is 60% dynamically excited TNOs and 40% cold classicals (see Figure 4).The enhancement of the FaintIR surface class in the resonances within the cold classical region also supports the conclusion that there was some amount of resonant sweeping which captured FaintIR surfaces into these resonances.
Just beyond the cold classical belt, the 2:1 resonance includes a FaintIR object.One object, 2013 JE 64 , is firmly within the FaintIR surface classification, and has an excited orbit (e = 0.29 and i =8.34 • ).The larger e and i may suggest a larger distance of resonance sweeping before capture, or that this particular object was captured through scattering/resonance sticking.As with the 4:3 resonance, a larger sample of optical and near-infrared surface colors of 2:1 resonators is needed to better constrain the intrinsic fraction of FaintIR and BrightIR surface classifications.
The distant a > 49 resonances include the smallest fraction of FaintIR surfaces of the resonances, and the surface class distribution is very similar to the non-resonant dynamically excited surfaces.This is consistent with the FaintIR objects in the outer resonances being captured during scattering, during planetary migration and/or current scattering capture.We note that, similar to the 3:2, the sample does not include i < 5 • distant resonators.Significant numbers of low-i resonators are not expected in these distant resonances, which have intrinsically hot inclination distributions (e.g.Volk et al. 2016;Pike et al. 2017a).We also do not necessarily expect these more distant resonances to have had a cold, primordial FaintIR disk population to have swept during any period of smooth migration.The currently known cold population does not extend past the 2:1, so Neptune's end-stage smooth migration would need to have extended for at least 4 au for the next major resonance, the 5:2, to have had any chance of sweeping up objects from the known cold population.If low-i resonators are found in these distant resonances, particularly the 5:2, measuring their surface properties in the optical and near-infrared would be helpful in determining the primordial outer limit of the disk of FaintIR objects.
The objects in this sample come from a large program which attempted to acquire a brightness complete sub-sample of several blocks of the OSSOS discoveries.The overwhelming majority of the targets which met this criteria, 92 of 103, have g − r and r − J surface colors acquired as part of the Col-OSSOS project.The exclusion of some targets (all listed in Table 1) was the result of weather loss during some of the allocated time, and an effort was made to observe the sample randomly.Due to the weather conditions, there was a slight preference for observing the brighter (larger) cold classical objects in the sample, and 6 cold classicals remain un-observed.There are, however, many cold classicals which were observed by Col-OSSOS with similar H r to these skipped targets and included in the sample.The 5 dynamically excited targets which were not observed span a range of H r and apparent magnitudes.No objects were observed but not measured due to poor signal to noise in one band, which could impose a color dependent bias on the sample.As a result, we do not expect significant bias effects to result from the unobserved targets which meet the sample selection criteria.
The Col-OSSOS sample was selected to be brightness-complete based on the r-band discovery magnitude, m r ≤ 23.6, which imposes a specific bias on the sample.Because the cut is made in r-band, the size limit for red and very red objects is differentthe sample would include smaller very red objects, as a similar sized red object would have an r-band magnitude fainter than the cut.The solar system absolute magnitude at discovery is shown in Figure 6 compared to the PC 2 grJ values.Six of the seven smallest objects have the BrightIR surface classification.It is possible that this difference in surface classification is based on size, however, the majority of non-resonant faint dynamically excited objects are also BrightIR surfaces.As we noted in Section 3, excluding the objects with pericenters q < 22 au (whose surfaces may have evolved due to cometary-like activity) did not affect the results of our analysis.We note that the non-resonant dynamically excited TNOs span the range of H r magnitudes seen by the majority of the resonant objects and the cold classicals.grJ values and absolute magnitude in r-band Hr at discovery.The dynamically excited objects span a large range of values, and the fraction above and below the PC 2 grJ division does not obviously depend on Hr.The different dynamical classifications are consistent with previous figures: non-resonant Dynamically excited objects (black circles), dynamically cold classical objects (pink squares), 4:3 resonators (orange triangles), 3:2 resonators (yellow squares), resonant objects within the classical region (green wide 'x's), 2:1 resonators (cyan diamonds), and resonant objects with semi-major axes a > 49 au (blue hexagons).Lower: The distribution PC 2 grJ values compared to object size, assuming albedos of 0.14 for PC 2 grJ < −0.13 and 0.085 for PC 2 grJ > −0.13.The distribution is shifted slightly compared to the Hr panel, and the result is that the Plutinos and cold classicals appear to be more comparable in terms of intrinsic size.
A main prediction of Fraser et al. (2022) was that the FaintIR group would share similar properties, such as higher albedo than the BrightIR group.To understand how this would affect sample characteristics, we calculated the diameter of the objects assuming albedos of 0.14 for BrightIR and 0.085 for FaintIR surfaces (PC 1 grJ > 0.4 and PC 2 grJ > −0.13) based on typical values for hot classical and cold classical TNOs from Vilenius et al. (2018).Using these albedo assumptions we find that the diameter distribution of non-resonant dynamically excited TNOs spans a large range of diameters, D, but there is no obvious dependence between surface classification and size, see Figure 6.The size range of the Plutinos and cold classical TNOs is more similar than their H r -magnitude range.Based on the lack of obvious correlations in the distributions of H r and D, we conclude that it is appropriate to directly compare the distribution of surfaces within the different dynamical classifications.We note, however, that the parent population fractions we calculate for the resonances are apparent fractions and not intrinsic fractions due to the typical size differences between the FaintIR and BrightIR surfaces.
The distribution of FaintIR and BrightIR surfaces within Neptune's resonances appears dependent on semi-major axis.The FaintIR and BrightIR classification system is more robust than using purely optical surface colors for classification.The color fractions of the Neptune resonances provide a useful criteria for assessing different models of planetary migration and constraining the initial distribution of surface classifications in the primordial disk and motivates work similar to Nesvorný et al. (2020) and Buchanan et al. (2022), but using the new surface classifications.Our preferred explanation for the inclusion of a FaintIR surface, also seen for the bulk of the cold classicals, in the 4:3 resonance is that the original extent of the FaintIR objects began sunward of the current 4:3 resonance (36.4 au).The higher fraction of FaintIR surfaces in the resonances within the classical belt and the inclusion of a FaintIR object in the 2:1 resonance implies that this primordial FaintIR surface extended through the current cold classical region and at least close to the 2:1 resonance.The high fraction of FaintIR surfaces in these resonances means that at least some small amount of sweeping migration was likely, however, a larger sample of 4:3 and 2:1 surface colors in optical and near-infrared would provide a more robust measurement of the intrinsic color fraction in these resonances.The reduced fraction of FaintIR surfaces in the 3:2 is less clear to interpret due to both the potential influence of secular resonances on capture probabilities during migration (smooth or otherwise) and the lack of low-i 3:2s in the Col-OSSOS sample.The distant resonances (a > 49 au) do not show evidence of an enhancement of FaintIR surfaces compared to the wider dynamically excited population, but a larger sample of surface properties for objects in the 5:2 resonance would provide a useful constraint on the limit of the outer extent of the primordial FaintIR surface objects.The distribution of FaintIR and BrightIR surfaces in the different Neptune resonances provides useful constraints on the original extent and surface distribution within the proto-planetesimal disk.

Figure 1 .
Figure1.The orbital distribution of Col-OSSOS targets in a, e, and i.The semi-major axis is shown with three different scales, as indicated in the x-axis and separated by axis gaps, in order to show the details in the cold classical region as well as the inner and distant objects in the Col-OSSOS sample.The different dynamical classifications are non-resonant Dynamically Excited objects (DE, black circles), cold classical objects (pink squares), 4:3 resonators (orange triangles), 3:2 resonators (yellow squares), resonant objects within the classical region (green wide 'x's, includes all resonant objects within the main classical belt), 2:1 resonators (cyan diamonds), and resonant objects with semi-major axes a > 49 au (blue hexagons).The number of objects in each classification is indicated in parentheses in the legend.All populated resonances are labeled with gray dashed vertical lines.Neptune is indicated with a large blue circle.

Figure 4 .
Figure4.The results are presented for acceptable apparent parent populations for the different resonant populations.The different resonances are indicated along the x-axis.The parent populations are a combination of the dynamically excited TNOs (DE) and cold classical TNOs (CC), with different percentages of each of the two groups, from 0-100% calculated in steps of 5%.The distance between the distribution of resonant PC 2 grJ values and parent population PC 2 grJ values is computed with the AD test, then the significance of that result is obtained by bootstrapping using the input parent population.The large diamonds indicate the least rejectable D-statistic parent population fraction, and the small diamonds indicate the 2σ limits based on the D-statistic.The width of each bar is proportional to the D-statistic value at each 5% step.The three different bars for each resonance show the results for slightly different assumptions in the parent populations.The green (left) bar uses the DE and CC populations exactly as defined in Table1.The teal (middle) bar uses the CC objects as defined in Table1, but for the DE objects uses only the DE objects with pericenter q > 22.The purple (right) bar uses the CC and DE objects as classified in Table1except that the 3 cold classicals with PC 2 grJ >-0.13 BrightIR surfaces are moved from the CC group to the DE group, as 3 low-i objects is consistent with being the low-i tail of the DE inclination distribution, see Section 3 for details.Note that the Parent Population used here is to reproduce the apparent surface distribution and not the intrinsic population ratios of the dynamically excited and cold classical objects-due to detection biases and albedo differences, the intrinsic fraction of BrightIR objects is much larger than the apparent fraction.

Figure 5 .
Figure5.The orbital distribution of Col-OSSOS TNOs, with surface classification indicated.As in Figure1, the semi-major axis is scaled by three different amounts, as indicated in the x-axis and separated by gaps, and the symbol shapes are preserved, but the colors of the points indicate BrightIR classification (black) and FaintIR classification (red).The low-inclination and low-eccentricity 4:3 resonator at 36.4 au is particularly evident, as is the classification-inclination dependence, particularly at large-a, noted byMarsset et al. (2019Marsset et al. ( , 2022)).Neptune is indicated by the large blue circle.

Figure 6 .
Figure 6.Upper: The PC 2grJ values and absolute magnitude in r-band Hr at discovery.The dynamically excited objects span a large range of values, and the fraction above and below the PC 2 grJ division does not obviously depend on Hr.The different dynamical classifications are consistent with previous figures: non-resonant Dynamically excited objects (black circles), dynamically cold classical objects (pink squares), 4:3 resonators (orange triangles), 3:2 resonators (yellow squares), resonant objects within the classical region (green wide 'x's), 2:1 resonators (cyan diamonds), and resonant objects with semi-major axes a > 49 au (blue hexagons).Lower: The distribution PC 2 grJ values compared to object size, assuming albedos of 0.14 for PC 2 grJ < −0.13 and 0.085 for PC 2 grJ > −0.13.The distribution is shifted slightly compared to the Hr panel, and the result is that the Plutinos and cold classicals appear to be more comparable in terms of intrinsic size.
The cumulative fraction of Col-OSSOS targets by PC 2