THE HUBBLE WIDE FIELD CAMERA 3 TEST OF SURFACES IN THE OUTER SOLAR SYSTEM: THE COMPOSITIONAL CLASSES OF THE KUIPER BELT

The primary goal of this survey was to gain optical and NIR spectroscopic information on KBOs too faint to be observed from the ground. Past NIR spectroscopic surveys have demonstrated an approximate ground-based magnitude limit of V  ∼  21 (Barkume et al. 2008; Guilbert et al. 2009; Barucci et al. 2011). As such, with only a few exceptions, we restrict ourselves to objects with brightnesses below this level. Signal-to-noise estimates suggested that good-quality photometry could be acquired for objects as faint as V  ∼  24, and we used this to bound our target list.

Effort was made to observe as diverse a range of KBOs as possible. Targets were selected from the Minor Planet Center (MPC; Bernstein 2008) based on their orbital quality to maximize the chances that the object would fall in the WFC3 field of view during Cycle 17. The result was a selection of 120 targets spanning the full range of orbital element space occupied by the Kuiper Belt. The observed targets are presented in Table 1. We present the orbital elements of our targets in Figure 1.

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For completeness and historical reasons, we include orbital classifications for the observed objects. As shall be seen, however, the adopted orbital classification scheme has little bearing on the results of this work. We adopt an orbital classification scheme inspired by the system of Lykawka & Mukai (2007). We define Centaurs as those objects having semi-major axes a  <  30 AU or perihelia q  <  25 AU. We also define resonant objects as those objects in the 1:2, 2:3, 3:5, or 4:7 mean-motion resonances with Neptune.

It is well accepted that the non-resonant KBOs with semi-major axes bounded roughly by the 2:3 and 1:2 mean-motion resonances divide in inclination, i, into two populations (Brown 2001). Historically, these two populations, the hot and cold classical objects (CCOs), are defined as those objects with inclinations above and below i = 5°, respectively (Elliot et al. 2005). The CCOs, which all exhibit similar red surfaces, are on orbits with moderate eccentricities e  ≲  0.15, while the hot classical objects (HCOs) exhibit a more diverse range of colors and eccentricities (see, for example, Peixinho et al. 2008). From a color standpoint, the inclination dividing these two populations is ambiguous. Dynamically, however, the inclination division is clear. Analysis of Figure 1 reveals a tight clump of objects with i  <  4° and 42  ≲  a  ≲  46. For i  <  4°, very few known non-resonant objects fall outside of this range in semi-major axis; none of these were observed in our survey. Thus, we adopt a definition for the CCOs, as those objects with i  <  4 and 42  <  a  <  46. We define HCOs as non-resonant objects with a bounded by the 1:2 and 2:3 mean-motion resonances, i  >  4°, and q  >  37 AU.

Those remaining objects not defined as Centaurs, resonant, CCOs, or HCOs are classified as scattered objects. It is worth noting that in some other works the scattered population is divided into groups: those objects on orbits that allow them to have interactions with Neptune, and those that are now well isolated from Neptune (see Gladman et al. 2008). Only two of our survey targets, which we classify as scattered, are not on interaction orbits. Therefore, we avoid this additional sub-classification as an unnecessary complication for the purposes of this manuscript. Modifications to our classifications or the adoption of dynamically motivated and more complicated schemes such as that presented by Gladman et al. (2008) do not affect our conclusions.

The primary scientific purpose of H/WTSOSS was to determine optical slopes and amount of water-ice absorption on faint KBOs. The excellent photometric stability of HST along with the imaging capabilities and filter selection of WFC3 made this new camera the ideal instrument for the job.

Each target was observed in exactly the same way. During the observations, the telescope was slewed at the apparent rate of motion of the target. Each target was visited only once and monitored for the entire visibility window of a single orbit. This ensured that no significant rotational variability would affect our photometry between different filters. Pairs of images were taken in the F606w, F814w, F139m, and F153m bandpasses with exposure times of 129 s and 453 s in each of the optical and NIR filters, respectively. Dithers of 3'' were included between each image of a pair to ensure that the photometry was not affected by cosmic rays or bad regions of a detector. The detectors were windowed to minimize overheads and to ensure the data could be transferred from the telescope during Earth occultation. This resulted in small square fields of view of 205 and 131'' on a side for the optical and NIR images. As a result, eight objects fell outside the optical windows and were only seen in the NIR images. In six cases, the objects were not seen in the optical or NIR images entirely. In addition, six objects fell near enough to bright background sources to prevent reliable photometry in at least a few images. These images were excluded from our analysis (see Table 1).

Images were first processed through the standard WFC3 data processing pipeline, CalWF3 (Rajan et al. 2010). As of publication, all data presented here were processed using version 2.3 of this pipeline. Images were then visually inspected, and bad pixels and cosmic-ray strikes not identified during the initial processing were flagged.

Analysis of the Tiny Tim version 7.1 (Krist 1993) simulated point-spread functions (PSFs) revealed that the simulated PSFs did an adequate job of reproducing the outermost features of the observed PSFs (first airy ring, diffraction spikes, etc.) but failed to reproduce the image cores. As the majority of source flux is contained within the PSF core, photometry derived from matching Tiny Tim PSFs to the observations was deemed unreliable.

Photometry was derived using standard aperture photometry techniques. Aperture radii were chosen as a function of source brightness and wavelength to minimize measurement scatter. To minimize the effects of bad pixels and cosmic rays, Tiny Tim PSFs were used to interpolate over any bad pixels identified in the CalWF3 processing. Typically, only 1 pixel per aperture was flagged as bad. In addition, the simulated PSFs were used to derive infinite aperture corrections for each object. As the aperture radii were kept larger than the radius of the first airy ring, any errors introduced from the simulated PSF cores were negligible.

In a few cases, partially resolved binary sources were identified. In those cases, an aperture large enough to encompass both sources was used, and the combined photometry of both sources is reported. The adopted photometric system is the STMAG system. The STMAG system defines an equivalent flux density for a source with a spectrum that is flat as a function of wavelength that would produce the observed count rate. The magnitude in this system is just STMAG = −2.5log f_λ − Z, where Z is the filter zero point and f_λ is the flux density expressed in erg cm⁻² s⁻¹ Å⁻¹. The resultant photometry is presented in Table 1, along with object colors in Table 2.

Object 2000 EE173 (60608) fell within the IR field of view but outside the UVIS field of view during observations. Optical data from Benecchi et al. (2011) in the F675w and F814w filters were available for this, from which a reliable estimate of the F606w and (F606w–F814w) color could be made. Conversion was done using an analog solar star and the synphot routine. We note that by estimating the F606w flux of 2000 EE173 in this way may introduce errors due to rotational variability. Duffard et al. (2009) have shown that the majority of non-Centaur KBOs have peak-to-peak light-curve amplitudes of ≲ 0.1 mag. As such, the photometric errors reported by Benecchi et al. (2011) were set to 0.1 mag to roughly account for any errors in estimating the F606w flux. This result is presented along with our other photometry in Table 2. No IR observations in the literature could be used to accurately determine F139m and F153m photometry of those objects that fell outside the IR field of view.

In the case of photometry in either the flux- or background-limited regimes, the uncertainty in the observed magnitude, m, of a source can be well approximated by

$$\begin{equation} \Delta m \sim \gamma 10^{\frac{m-Z}{2.5}}, \end{equation} \tag{ 1 }$$

where Z is the photometric zero point of the passband in question. Theoretically, the proportionality constant γ is a function of the telescope and detector parameters such as gain, read noise, and data reduction parameters such as aperture size. In practice, this parameter is a factor of a few larger than the theoretical expectation (see, for instance, Newberry 1991; Fraser et al. 2008). In addition, theory underestimates the photometric scatter in repeated measurements of bright objects (see Figure 2). As a result, we consider an additional constant, C, and represent our photometric uncertainty by

$$\begin{equation} \Delta m = C + \gamma 10^{\frac{m-Z}{2.5}}. \end{equation} \tag{ 2 }$$

This equation is fit to the observed scatter from the dithered images of each source and each passband. The results of this procedure along with the best-fit parameters are presented in Figure 2. As can be seen, Equation (2) provides an adequate description of the measurement scatter in the photometry. It can also be seen that approximately 1% of measurements deviate significantly away from the curves given by Equation (2), primarily as a result of cosmic-ray strikes affecting one of the measurements of a pair. Thus, if the difference in pairs of observed magnitudes for a given filter was larger than 1.4 times the direct sum of errors of the pair of measurements, then it was assumed that the brighter of the two measurements was affected by a nearby cosmic-ray strike and was subsequently rejected.

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The photometries presented here are average values from the pairs in each filter, or the single value when a measurement was deemed bad, along with photometric uncertainties determined from the best-fit values of Equation (2) added in quadrature; the quoted photometric uncertainties represent 1σ errors.

In Figures 3 and 4, we present the observed (F606w–F814w), (F814w–F193m), and (F139m–F154m) colors of the Centaurs. The well-known bifurcation of the optical colors of the Centaurs can be seen with the two color groups bifurcating about an optical color of (F606w–F814w) ∼ − 0.15. This bifurcation does not extend into the NIR in agreement with previous results (Tegler et al. 2008). It is interesting to note that the observed separation between the two groups is only ∼0.1 mag, much smaller than that found in previous surveys. Rather, we observe a few moderately colored Centaurs that have never before been detected in previous surveys of the Centaur population (Tegler et al. 2008; Benecchi et al. 2011).

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Unlike the blue Centaurs, which exhibit a tight cluster, the red Centaurs span a broad swath of colors. This suggests that the red Centaurs exhibit a more diverse range of surfaces than do the blue Centaurs.

Analysis of ground-based colors suggests that the bifurcation exhibited by the Centaurs extends into the low-perihelion scattered disk and resonant objects. This can be seen in Figure 5, where we present the (B − R) colors of objects with q  <  35 AU taken from the MBOSS data set (Hainaut & Delsanti 2002). The H/WTSOSS photometry supports this finding. In Figure 6, we present the observed colors of all objects with perihelia q  <  35 AU. This includes Centaurs and scattered, resonant, and HCOs. It can clearly be seen that most of the low-perihelia objects, which include resonant and scattered disk objects, occupy nearly the same range of colors as the Centaurs and exhibit the same bifurcation into two groups based on optical color. Only two H/WTSOSS targets, Elatus (1999 UG5) and 1999 XX143 (121725), are found to have optical colors between that of the blue and red Centaur groups. The ground-based colors of non-Centaur objects, on the other hand, have a higher fraction of objects with intermediate colors. These moderately colored objects, however, are predominately of objects with larger absolute magnitudes than in the Centaurs, suggesting that the larger objects do not exhibit the color bifurcation. Indeed, when only considering ground-based observations of objects with H  ≳  6 in the R band, in the same range as the Centaur H/WTSOSS targets, the bifurcation is more pronounced, suggesting that the largest objects occupy a different color range than the smaller bodies.

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A clear outlier, 2007 OR10 is the reddest and largest object in the H/WTSOSS sample and is likely methane bearing (Brown et al. 2011a). As 2007 OR10 falls in a different class of object than the smaller methaneless objects, it is unsurprising that it appears as an outlier in Figure 6.

When considered together, the blue, (F606w–F814w) <−0.15 low-q objects appear as two distinct groups of objects, each of which exhibits highly correlated optical and NIR colors. The Spearman rank correlation test (Press 2002) suggests that for the blue group the (F606w–F814w) color correlates positively with the (F814w–F139m) color and negatively with the (F139m–F154m) color at the 99.8% and 99% significance levels, respectively (see Figure 6). Despite the wider range of colors, like their blue counterparts, the red low-q objects also exhibit correlated optical and NIR colors that have a 99% significance and correlate in a positive sense between (F606w–F814w) and (F814w–F139m) and in a negative sense between the (F606w–F814w) and (F139m–F154m) colors.

3.1.1. Mixing Models

A two-component mixing model can readily explain the range of observed colors of each color group of the low-q objects. We demonstrate the effectiveness of a compositional mixture with the use of a simple Hapke surface model. Here, we present a derivation showing only the necessary equations for our modeling. For a more thorough and complete derivation, see Hapke (2002).

We start with the wavelength-dependent particle single scattering albedo w(λ). In the two-stream approximation, and under the assumption of irregular particles, the diffusive reflectance of the surface is given by

$$\begin{equation} r_o = \frac{1-\gamma ^*}{1+\gamma ^*}, \end{equation} \tag{ 3 }$$

where γ* is the bulk albedo factor and is given by

$$\begin{equation} \gamma ^* =\sqrt{1-w\left(\lambda \right)}. \end{equation} \tag{ 4 }$$

This equation is valid for an infinitely thick layer. Then, for a spherical object, covered by isotropically scattering particles, and ignoring the opposition effect, the geometric albedo can be approximated by

$$\begin{equation} A\left(\lambda \right) \sim 0.49 r_o + 0.196 r_o^2. \end{equation} \tag{ 5 }$$

Consider a mixture model of two components i and j. Each component will have a unique single scattering albedo, which we denote w(λ)_i and w(λ)_j. These components can be mixed in two separate ways. The first, a geographic mixture, is one in which each component exists as discrete independent units on the surface. In this case, the effective albedo is just the fractional sum of albedos of each component given by Equation (5), or

$$\begin{equation} A\left(\lambda \right)_{{\rm geo}} = f_{{\rm geo}}A\left(\lambda \right)_i + (1-f_{{\rm geo}})A\left(\lambda \right)_j, \end{equation} \tag{ 6 }$$

where f_geo is the fraction of the surface occupied by component i.

Alternatively, the two components could exist as an intimate mixture, e.g., mineral material in an icy matrix. In this case, the effective single scattering albedo is the fractional sum of the single scattering albedos of each component and is given by

$$\begin{equation} w\left(\lambda \right)_{{\rm int}}=f_{{\rm int}} w\left(\lambda \right)_i + (1-f_{{\rm int}})w\left(\lambda \right)_j \end{equation} \tag{ 7 }$$

where f_int is the fraction of the surface occupied by component i. Thus, with a choice in w_i and w_j, Equations (6) and (7) and (5) produce not only a range of colors but also geometric albedos.

Analysis of Figure 6 suggests that the correlated colors of the blue and red groups of low-q objects might be explained by two separate mixing models that differ in their red components but share a common neutral component whose colors are nearly solar. We tested this possibility by fitting both the geographic and intimate mixture models to the observations. We assume two separate branches of a mixing model of the same type (geographic or intimate). In our model, each branch has a different red component, and we assume that both mixtures share the same nearly neutral component.

The geographic mixture requires nine parameters to describe all three observed colors simultaneously. These parameters are essentially the ratios of the single scattering albedos in each filter with respect to the F606w filter, three for each of the three components in our model. The intimate mixture requires two additional parameters describing the difference in single scattering albedos between each of the two red components and the neutral component. A change in these additional parameters results in a change in curvature of the resultant color curve.

The three component geographic and intimate mixture models were fit to the observations in a least-squares sense. We chose (F606w–F814w) = −0.15 to separate the objects belonging to the blue and red groups during our fits. It was also necessary to ensure that the resultant range of model colors was restricted to the range of observed colors of our targets. This action was taken to prevent runaway during the least-squares minimization. It should be emphasized that it cannot be determined whether the true colors are beyond this range by the observed colors alone.

The results of the model fitting to the 55 low-q objects in the H/WTSOSS sample are shown in Figures 7 and 8. As can be seen, the colors of the neutral and red components for both models are very similar. Both the intimate and geographic mixture models do an adequate job of describing the observations.

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2007 JG43, 2004 EW95, and 2004 TV357, all blue low-q objects, along with red low-q objects Elatus (1999 UG5), Crantor (2002 GO9) and 2007 OR10, were all identified as outliers responsible for the vast majority of the fit residuals. Crantor has optical color very near but just redward of the (F606w–F814w) = −0.15 color chosen to separate the blue and red Centaurs. Given its NIR colors, however, Crantor is roughly equally consistent with either the red or blue branches of the mixing model. As discussed above, 2007 OR10 possesses a surface unique to the large volatile bearing KBOs, and it is therefore no surprise that it stands out from the majority. It is not unreasonable to expect other outliers as our simple mixing models do not consider other processes such as collisions that can alter surface colors. When the outliers are not considered in the fit, the resultant chi-squared values were reduced by nearly half compared to when the outliers were considered.

A similar finding as for Crantor exists for a few of the blue low-q objects. That is, objects placed in the blue group by our selected division are better described by the blue end of the red mixing curve. It is not clear, however, if this is a result of the limitations of our chi-squared fits. This possibility should be further studied with more observations, however, as the result would imply that the red Centaur population is not uniquely red, but rather occupies a range of optical colors that sparsely samples the blue end of the red mixing curve.

After excluding the six outliers, the model best fits had reduced chi-squared values of χ²_ν, geo = 2.87 and χ²_ν, int = 3.13 with 38 and 40 degrees of freedom for each model, respectively. The geographic model resulted in a reduction of the variance in the data of only 13%, while a reduction of 40% was found for the intimate mixture model. In addition, though the best-fit intimate mixture could account for the colors of 2006 QP160, the best-fit geographic model could not and rejected it as an additional outlier. Despite the two extra parameters, the intimate mixture model provides a better description of the data over the geographic model. These results suggest that intimate mixtures are a better model of the surfaces of the objects we observed compared to the geographic mixtures.

Typically, inference of KBO compositional makeup has been made through extensive spectral modeling of not only deep spectral lines diagnostic of particular materials but also the general spectroscopic shape not attributable to any one material (see Barucci et al. 2008, for a review). Materials required to successfully model featureless spectra of KBOs typically include organic materials such as tholins or other irradiated hydrocarbons, mineral components such as olivine, water-ice, and neutral darkening agents such as carbon (Cruikshank et al. 1998; Alvarez-Candal et al. 2008; Merlin et al. 2010; Barucci et al. 2011). The range of colors required by the components of our mixing model is compatible with many of these materials.

The red components require a material that is blue from ∼1.3 to 1.5 μm. It is tempting to attribute this color to water-ice absorption. The red colors of each material for wavelengths ≲ 1.3 are compatible with the irradiated organic ices and tholins often attributed to the spectral shapes of other KBOs (Cruikshank et al. 1991; Brunetto et al. 2006). While no unique identification can be made from these observations, it seems plausible that the red components are different combinations of organic and water ices.

The range of colors of the neutral component requires a material that is virtually neutral across all four filters used in our observations. Due to the large absorption at ∼1.55 μm, water-ice is not a candidate. Rather, a plausible candidate for the neutral component appears to be silicates. The colors of various minerals taken from the USGS Spectral Library (Clark et al. 2007) are shown in Figures 7 and 8, along with their albedos in Figure 9. Minerals consistent in color with the inferred neutral component include olivines similar to those inferred from previous spectral modeling of KBOs (Merlin et al. 2010). Other compatible minerals include serpentines and aqueously altered phyllosilicates, the latter of which provide the best match to our fitted colors. The albedos of all of these silicate materials, however, are all too high to be consistent with the low ρ  ∼  5% albedos of the blue Centaurs. Rather, some additional neutral darkening agent such as amorphous carbon is needed, as has been found in previous spectral modeling efforts (see, for instance, Cruikshank et al. 1998).

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The candidate silicate materials we and others have presented are similar to the iron-rich minerals and hydrated silicates that have been suggested to exist on the largest, outermost Saturnian irregular satellite, Phoebe (Clark et al. 2005). Phoebe and the other irregular satellites are captured objects that likely originated from the same primordial population as the observed KBOs (Nesvorný et al. 2007). Thus, while no claim from our observations can be made as to what the neutral component may be, the apparent compositional similarity between Phoebe and the observed KBOs suggests that indeed these objects share a genetic link, and that the minerals we present are good candidates for the neutral material. If confirmed, this result would suggest that despite the large formation distances of KBOs and irregular satellites, aqueous alteration and therefore liquid water were prevalent in the outer solar system.

The best fits of the intimate mixture to the colors of the blue objects have a preference to models in which the red component shares a similar single scattering albedo to the blue component. The red objects, however, are better matched if the red component albedo of the red branch is significantly larger than that of the neutral component. Despite the poor availability of albedo measurements, many of which are thermal model dependent, our findings are in agreement with the observed trend in KBO albedo with color. We present measured albedos of KBOs (see Stansberry et al. 2008) versus their F606w–F814w color calculated from their observed colors taken from the MBOSS data set in Figure 9. This suggests that the reddest objects have higher albedos than the bluest objects. The observed colors and albedos are well reproduced by the intimate mixture model if the red components of the blue and red branches have albedos a factor of ∼2 and ∼4 times larger than that of the neutral component (assumed to be 3% in Figure 9). The geographic mixture model can also reproduce the albedo color trend but predicts that the reddest objects will have albedos ≳ 25%, a factor of ∼3 higher than that predicted for the intimate model. Further observations are required to determine if such high albedos exist for reddest KBOs.

The chi-squared fits of the mixture models we present here have a few potential weaknesses. As stated above, the colors of the two components were restricted to prevent runaway during the minimization. As such, the true colors of the neutral and red components might be beyond the range of colors inferred from the fits. In addition, the model we present is rather simple and does not account for many processes that may affect the surfaces of KBOs. As such, the fits we present are best used as a guide to understanding the primary surface properties of objects in the Kuiper Belt rather than an exact description. Despite the model's simplicity, it is clear that two separate branches of a mixing model that shares a common—and neutral—component can account for the major trends in the observed colors of the low-perihelion KBOs. In addition, a model in which the components are mixed intimately appears to be favored over one in which the mixture is geographic.

The observed colors of the hot classical, scattered, and resonant objects with q  >  35 AU are shown in Figure 10. Other than the two identified Haumea family members, 2003 UZ117 and 2003 SQ317 (Schaller & Brown 2008; Snodgrass et al. 2010), much of the distant excited population is consistent in color with the intimate mixture model fit to the low-q population. The distant population, however, has a higher fraction of objects with moderate optical color, −0.2 ≲ (F606w–F814w) ≲ 0.0, and suggests that the colors of the distant objects are not consistent with the intimate mixture model. No obvious hints of a bimodal population are apparent for the high-q objects.

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We tested whether or not the non-Haumea family, high-q objects could be drawn from the mixture model of the low-q objects with a Monte Carlo technique. This involved drawing from the dual intimate mixture model, a sample of objects equal in number to the high-q population with the same ratio of red to blue objects. Gaussian scatter was added to the random colors with standard deviations equal to the observed uncertainties. Then, by adopting the observed uncertainty distribution, the intimate mixing model that was used to describe the low-q objects was refit to the random sample. This process was repeated 100 times, and the distribution of chi-squared values was recorded. In 90% of cases, the simulated chi-squared values were lower than the observed value, demonstrating that the model that describes the low-q objects does not match the observed high-q population.

As discussed above for 2007 OR10, the largest objects have a different color distribution than smaller objects. Using the observed absolute magnitude as a proxy for size, the observed high-q population contains objects with absolute magnitudes 4  ≲  H₆₀₆  ≲  8, while the low-q population, ignoring 2007 OR10, only has objects with H₆₀₆  >  6. Indeed, the largest objects in our sample are the most discrepant. After rejecting the eight intermediate-sized objects with high-q objects with H₆₀₆ < 5.6, the Monte Carlo test suggests that the probability of drawing a random chi-squared equal to or greater than the observed value for the remaining 20 objects is 35%; the colors of the small, high-q objects are consistent with being drawn from the intimate mixture model that describes the colors of the low-q objects. It should be noted that object 2001 CZ31 appears as an outlier. Indeed, when this object is rejected, the probability of drawing a random chi-squared equal to or greater than the observed value becomes 50%. However, rejection of this object as an outlier is not formally required by the model.

The colors of the small, excited, high-q population are shown in Figure 11. No bifurcation of the optical colors is apparent in this figure. It should be noted that this sample has uncertainties that are ≳ 50% larger than the low-q sample. Thus, we should not expect to see the bimodality exhibited by the low-q objects. The observations we present here are not of sufficient quality to show the existence of such a bimodality. The colors of the small, excited, high-q objects, however, are consistent with the bimodal low-q population.

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Our results suggest that only the largest objects in our high-q sample are inconsistent with the low-q population. The larger uncertainties could mask small changes in color between the two samples. If it is true that the small high-q objects possess the same color distribution as the low-q objects, this would suggest that little to no color evolution occurs when high-q objects are scattered into the Centaur region. Even if color evolution does occur, as typical color uncertainties are only of order 5%, the changes must be small.

The largest objects in our sample have colors inconsistent with the two intimate mixtures that describe the low-q population. As these objects must have formed of the same material as the smaller objects, it must be that some processes that do not readily occur on smaller objects have altered the surfaces of the larger bodies. Our observations suggest that the size transition occurs at H₆₀₆  ∼  5.6. Assuming a 6% albedo, this corresponds to objects with diameters D  ∼  400 km. This also coincides with a transition in albedos; objects smaller than this size have lower albedos than larger objects. The larger, intermediate-sized objects are still too small to retain their primordial volatile budget as the largest known KBOs have. But for these intermediate-sized objects, effects such as the onset of differentiation could modify their surfaces. Whatever the cause might be, the apparent difference in colors between objects with absolute magnitudes smaller and larger than H₆₀₆  ∼  5.6 clearly warrants confirmation.

The observed colors of the CCOs are presented in Figure 12. The well-known unique colors of this population are clear, lacking not only the reddest objects but also the entire blue group of objects observed in other KBO populations. Interestingly, with the exception of object 2003 HG57, the CCOs appear consistent in color with the red branch of the intimate mixture model that describes the low-q population, albeit with a narrower range of colors. Indeed, our Monte Carlo tests suggest that the colors of the CCOs are entirely consistent with the red branch of the mixture model; the probability of a randomly drawn chi-squared value greater than that observed is only 20% when 2003 HG57 is excluded.

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Our observations alone would suggest that the CCOs and the red branch of the Centaurs and small excited KBOs share different mixtures of the same primordial materials. This simple picture is challenged by available albedo observations of these objects. Despite the sparser sampling and larger error bars, Brucker et al. (2009) have shown that the albedos of the CCOs ≳ 0.15, inconsistent with that predicted from the red branch of the mixing model. The excited high-q objects, however, are fully consistent with the model and exhibit the same general trends in albedo as the low-q objects; the red objects appear to have higher and exhibit a wider range of albedos than do the blue objects, which all appear to have low albedos of ∼5%. Thus, while it appears that the small, excited populations of the Kuiper Belt are all drawn from either the red or blue branches of the mixing model, the CCOs are not. Higher quality albedo measurements are required to determine whether or not the CCOs possess a surface unique to this population alone.

In Section 3.1, we identified an apparent bifurcation in the colors of the low-q objects that is consistent with that observed in the ground-based optical colors of the Centaurs (Tegler et al. 2008). While the colors of all small, excited objects appear to exhibit this bifurcation, the significance of this feature and the physical model we put forth to explain it remain untested. We turn to the use of "blind" statistical tests, that is, tests that require no a priori information or user input to test if the data exhibit two separate populations, or are consistent with being drawn from a single population. The first test we turn to is the non-parametric bifurcation test commonly adopted in the literature pertaining to the colors of KBOs, Hartigan's DIP test (Hartigan & Hartigan 1985). The DIP test, however, is only one-dimensional. Thus, when utilizing the DIP test, we must only consider the optical color alone, where the data appear most bifurcated. For the multivariate data we present here, the one-dimensional DIP test is inappropriate.

We also consider multivariate clustering techniques. The first clustering technique we consider is hierarchical clustering using Ward's criterion (Everitt et al. 2011). Ward's criterion uses a sum of squares of cluster member distances from average cluster position as a clustering metric and typically results in same-sized, circular clusters. In addition, we consider the normal mixture model distribution clustering technique, which assumes underlying multivariate Gaussian distributions for each of the identified clusters. In a Bayesian formalism, this technique fits a chosen number of Gaussian components or clusters to the observed distribution, resulting in a best-fit likelihood, L. As such, the corrected Bayes information criterion (BIC), which can be approximated by −2log L + plog ((n − 2)/24), can be evaluated for different cluster numbers to provide subjective information as to the true number of clusters within the data. Here, p is the number of parameters in the fit (12 per Gaussian component in three dimensions), and n is the number of data points. That is, the number of clusters can be increased one at a time such that the resultant increase in the BIC is maximized. This provides the most likely number of clusters. Mixture model maximum likelihood fits to the data were performed with the PyMix package (Georgi et al. 2010). A review of these and other common clustering techniques is available in Everitt et al. (2011).

We also consider the minimum spanning tree (MST) based technique, maximum standard deviation reduction (MSDR), presented by Grygorash et al. (2006). This technique is excellent at identifying clusters in small-sample, multivariate data sets and avoids the chaining effect to which other hierarchical and MST-based techniques are prone (Everitt et al. 2011)

Much like virtually all other clustering methods, however, the three clustering techniques mentioned above, hierarchical, mixture model, and MSDR, provide virtually no information as to the correct number of clusters in the observed data. When this information is available, it is subjective at best—no test of the significance of identified clusters is provided. To overcome this weakness, we introduce the F optimal plane or FOP-test. The FOP-test, which is also based on the MST of the data, uses a separate clustering statistic than MSDR to determine which edge to prune, resulting in two sub-clusters of the data. In addition, the resultant statistic F of the pruned edge provides a means of determining the significance that the two sub-clusters are consistent with the null hypothesis, that the data are consistent with a single population only. Thus, the FOP-test has a major advantage over other multivariate clustering techniques in that it provides quantitative information as to the number of extant clusters in the observed data.

A detailed discussion of the FOP-test and some examples of its performance versus the MSDR clustering technique are presented in the Appendix. The reader is warned that the FOP-test is an ad hoc combination of two alternative clustering metrics that remains to be mathematically proven. As is shown in the Appendix, however, the FOP-test performs just as well and often even outperforms the mathematically tested MSDR-based clustering technique in both correctly identifying the true number of clusters and correctly assigning cluster membership in various simulated data sets.

In Figures 13 and 14, we present the results of the blind statistical tests applied to the observed colors of the small, excited population, or those non-CCO, non-family member objects with H  >  5.6. For this test, we further reject the data with error in (F6062–F814w) of 0.1 mag or larger to avoid biasing our results with poor-quality data.

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In the (F606w–F814w) color alone, the small, excited sample appears bimodal; the DIP test confirms this with 98.6% chance of bimodality. The application of the hierarchical clustering technique with two clusters results in two clusters that exactly reflect the red and blue compositional classes identified in Sections 3.1 and 3.2. That is, those blue class members are all uniquely identified to one cluster, and those red class members are uniquely identified to the other cluster with no incorrect identifications.

Application of the normal mixture models paints a similar picture. The value of the BIC as the number of clusters is increased from 1 to 5 is a, b, c, d, and e with a maximal increase when the number of clusters is 3. The first two identified clusters are just the red and blue compositional classes. Most of the red objects fall into the first cluster, and most of the blue objects fall into the blue cluster, with only eight objects (six red and two blue) falling into the third cluster, which occupies nearly the full extent of the blue and red clusters combined. Thus, the normal mixture model clustering paints the same picture as we discuss above; the small, excited KBOs appear to exhibit compositional classes with a few outlier objects.

The results of the FOP-test are in agreement with the hierarchical and normal mixture model results. The FOP-test identifies two clusters within the data—exactly the two classes we identified in Sections 3.1 and 3.2. The edge pruned by this method is the only edge of the MST that spans (F606w–F814w) = −0.15, the color that divides the two compositional classes. The results of the FOP-test agree; calibrating the result of the FOP-test by bootstrapping and by sampling from the uniform distribution demonstrates that the probability that the observed data are consistent with a single population is only 5% or 7%, respectively (see the Appendix for a discussion of these calibration methods).

The MSDR technique further strengthens this result. The first two sub-clusters found by this technique are those visually identified in Sections 3.1 and 3.2 and are identical to those found by the FOP-test. The stopping criterion of the MSDR technique is met when four clusters are produced. The FOP-test, however, demonstrates that further divisions beyond the first are insignificant, and only two populations are required.

Upon application of these blind tests to the Centaur and low-q populations, we find the same results, albeit with lower significance. Hartigan's DIP test suggests that the probability of bimodality is 85% and 67% for the Centaurs and low-q samples, respectively. The MSDR clustering and FOP-test both identify identical sub-populations, the same two classes discussed above separated by (F606w–F814w) = −0.15. For the Centaur and low-q subsets, the probability that the sample consists of a single population is 14% and 30%, respectively.

We note that the DIP test was sufficient to reveal the bifurcation in the observed ground-based colors of the Centaurs from their optical data alone with a sample size similar to what we present here. This is most likely a result of the use of the (B − R) color where the bifurcation is most prominent having a width of ∼0.3 mag between the two groups (see Figure 5). Thus, further confirmation of our result could be provided with additional observations at ∼0.5  μm.

The results of all five separate statistics, the DIP test, the FOP-test, and hierarchical, normal mixture model, and MSDR clustering, are all in agreement—the colors of the small, excited KBOs are bifurcated. Indeed, the four separate clustering methods produce nearly identical results, with only the normal mixture model results differing from the other three methods, producing the same two main clusters and a third small cluster of outliers. The results of these blind statistical tests support our assertion above, that these objects fall into two compositional classes, the colors of which are described by two branches of a simple two-component compositional mixing model. This result solves a long-standing issue with the Centaurs, the colors of which appeared different from the other excited populations that are ultimately responsible for replenishing the dynamically short-lived Centaurs. We find the simple idea that all small, excited KBOs fall into one of two compositional classes a pleasing result.

Our observations suggest that the small excited Kuiper Belt populations that include the Centaurs, scattered disk, resonant, and HCOs fall into two separate compositional classes, the colors of which are determined by the relative composition an object has within its class. In addition, our observations suggest that little surface evolution occurs as an object evolves from an excited orbit into the Centaur population. This suggests that both classes of objects must have existed within the primordial planetesimal disk before the occurrence of the scattering event that emplaced these objects in the Kuiper Belt.

One possible explanation for the primordial existence of two classes of objects is presented in Brown et al. (2011b), who have shown that the methanol sublimation line exists at ∼20 AU, roughly within the primordial disk from which the excited KBOs are believed to have originated. They demonstrated that methanol ice could survive on planetesimal surfaces outside of ∼20 AU, while inside this distance, methanol sublimation is rapid enough to deplete all surface methanol before the scattering event occurred. Methanol is an important organic ice, as solar irradiance can drive methanol chemistry to produce longer chain hydrocarbons. Surface processing would produce a red irradiated mantel of complex hydrocarbons on roughly Myr timescales, resulting in a red appearance. Objects that spent most of their time inside of 20 AU were unable to retain methanol, resulting in a neutral surface free of a red irradiation mantel. Despite the attractiveness of this model, alternate explanations for the two unique surfaces are possible.

We have found that the blue and red mixing models do not describe the colors of objects with H₆₀₆  ≲  5.6. This roughly corresponds to a diameter of D ∼ 300–400 km. Our findings are in agreement with albedo observations that suggest that objects larger than D ∼ 400 km have higher albedos than those smaller objects (Stansberry et al. 2008). These results point to a fundamental difference in the surface properties of objects with diameters D  ≳  400 km. These intermediate-sized objects also exhibit different surfaces than the volatile bearing objects with D  ≳  1000 km. It seems that the surfaces of the intermediate-sized objects are dominated by other processes that have little effect at smaller sizes. These could include the onset of differentiation or cryovolcanic processes, both of which would have the effect of covering or removing non-icy materials from the surface.

The CCOs exhibit a unique surface with different albedos than either class of excited KBO. As these objects most likely formed nearly in situ, it appears that the primordial disk from which all KBOs formed generally consisted of three separate classes of small object. The colors of the CCOs are formally compatible with the red branch of the mixing model. A simple explanation for this is that both populations formed adjacent to one another in the primordial disk. Due to their larger formation distance, however, the classical objects accreted material with a slightly different composition than did the red excited objects. Brown et al. (2011b) suggest that the CCOs may possess a significantly higher fraction of NH₃ compared to the excited populations. While it is not clear what effects variations in NH₃ content might have on an object's appearance, it seems reasonable to think that the existence of primordial ices not likely retained by the red excited objects could result in a different surface.

Little can be said about the red components of each mixing branch from our observations alone. Other spectroscopic studies, however, provide some additional guidance. In modeling observed spectra, the red optical color of KBOs is usually attributed to irradiated organic material and tholins produced in the laboratory and seen on other icy bodies (see, for example, Cruikshank et al. 1991; Brunetto et al. 2006; Filacchione et al. 2007). In addition, absorption at ∼1.5 μm is often attributed to water ice. The range of colors compatible with our data is similar to those produced in spectral modeling of these ices (Cruikshank et al. 1998; Merlin et al. 2010; Barucci et al. 2011). Thus, combinations of irradiated organics and water ice are likely red candidates.

The existence of a common neutral component for both branches implies that this material was prevalent throughout the protoplanetary disk both interior to and exterior to the methanol sublimation line. As discussed above, the best-fit neutral color is consistent with silicate materials inferred to be present on other KBOs (Merlin et al. 2010), including various aqueous altered silicates. Such a result would imply the existence of liquid water in objects in the outer solar system at some point in the past. Our findings are consistent with other works that suggest the existence of aqueous alteration in KBOs (Alvarez-Candal et al. 2008) and comets (Stodolna et al. 2010). This result is surprising as it is expected that only the largest KBOs would have ever possessed large quantities of liquid water at any stage during their histories (McKinnon et al. 2008; Coradini et al. 2008).

One issue still remains with the candidate neutral component, that of albedos. The candidate silicates all have albedos much too high to be compatible with the observed albedos of the small low-q objects. This is consistent with other works that find that to match the low albedos requires the existence of some neutral colored darkening agent (Cruikshank et al. 1998; Barucci et al. 2011). Our results suggest that the relative composition of the darkening agent must not vary significantly compared to the silicate material responsible for the color of the neutral component. Otherwise, two components (neutral and red) would be insufficient to describe the observed colors of either branch.

Our findings suggest that small excited KBOs generally divide into two types. Each type is defined primarily by surface color and can be linked to its formation location within the primordial disk and the mechanism responsible for emplacing that object into the Kuiper Belt. Previous efforts have been made to classify KBOs based on their surface colors. Fulchignoni et al. (2008) present a recent example in which they used G-mode analysis of available ground-based optical and NIR photometry to identify classes of objects. The result was the identification of four separate classes, each with its own unique color. Fulchignoni et al. (2008) attribute the colors of each of their classes to relative amounts of surface evolution experienced by each class's members. The KBO taxons presented in that and other past efforts are fundamentally different from the types we present here, as the objects in both types represent a range of colors rather than one average value. Our interpretations are also different. The mixing models we consider have testable predictions in regard to the spectral shape of objects amongst each class; as one moves redward along a mixing line, the spectra of objects at that color and belonging to that type will vary primarily in a way consistent with an intimate mixture of two component's spectra. Future detailed spectral observations will be able to test this prediction.

The majority of small excited KBOs are consistent with being drawn from two compositional types. The simple compositional model we present, however, has not accounted for a few important effects. The Haumea family demonstrates that collisions can play an important role in modifying the colors of icy bodies. In addition, due to the chaotic nature of the scattering that disrupted the primordial disk, it is possible that a small fraction of KBOs originated from different regions than the primary source populations. While these processes will modify the surfaces in ways not accounted for by our simple picture, their overall effect is not sufficient to hide the existence of the two unique surface types.