solar system: formationtechniques: photometricTHE ASTRONOMICAL JOURNAL, 124:2279-2296, 2002 October
© 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A.
In 1997 we began the Meudon Multicolor Survey of Outer Solar System Objects with the aim of collecting a large and homogeneous set of color data for trans-Neptunian objects (TNOs) and Centaurs. Here we present our latest B-V, V-R, and R-I color measurements obtained with the CFH12K mosaic camera of the 3.6 m Canada-France-Hawaii Telescope. With the colors of 30 objects reported in this work, we have a combined sample of 52 B-R color measurements for eight Centaurs, 22 classical TNOs, 13 Plutinos, eight scattered objects, and one object of unidentified dynamical class. This is the largest single and homogeneous data set published to date, and it is large enough to search for compositional structures, interrelations between dynamical classes of objects, and correlations with physical and orbital parameters. The color-color diagrams show that all the classes of objects share the same wide color diversity. No significant correlations are seen for the whole population of TNOs and Centaurs, or for individual subpopulations, except for the classical objects. Indeed, we found a significant and strong correlation of the colors of classical TNOs with inclination, eccentricity, and perihelion, but nothing with semimajor axis and absolute magnitude. Most of these results are common to previous works and do not seem to be due to sampling bias. Moreover, a strong correlation with mean excitation velocity [VK(e2 + i2)1/2] points toward a space weathering or impact origin for the color diversity. However, thorough modeling of the collisional/dynamical environment in the Edgeworth-Kuiper belt needs to be done in order to confirm this scenario. We found also that the classical TNOs are made up of a superposition of two distinct populations: the dynamically cold classical TNOs (red colors, low i, small sizes) and the dynamically hot classical TNOs (diverse colors, moderate and high i, larger sizes). Furthermore, the latter population displays a strong correlation between color and mean excitation velocity. The dynamically cold classical TNOs may be primordial, while the dynamically hot classical TNOs, whose surface colors may be the result of space weathering and/or impact processes, have possibly been injected from the inner regions of the disk. Our specific observation strategy to repeat color measurements with no rotation artifacts have permitted us to highlight a few objects suspected to have true compositional and/or texture variation on their surfaces. These TNOs are 1998 HK151, 1999 DF9, 1999 OY3, 2000 GP183, 2000 OK67, and 2001 KA77, and they should be prime targets for further observations in order to study and confirm the color variation with the rotation. Finally, our survey has also highlighted some peculiar objects, such as 1998 SN165, whose colors and dynamical properties put this object in a new dynamical class distinct from the classical TNOs, its previously assigned dynamical class.
Key words: Kuiper beltsolar system: formationtechniques: photometric
1 Based on observations carried out at the Canada-France-Hawaii Telescope (CFHT), operated by the National Research Council of Canada, the Centre National de la Recherche Scientifique of France, and the University of Hawaii. Correspondence and requests for materials should be addressed to A. Doressoundiram, LESIA, Observatoire de Paris, 92195 Meudon Principal Cedex, France; Alain.Doressoundiram@obspm.fr.
2 LESIA, Observatoire de Paris, F-92195 Meudon Principal Cedex, France.
3 Centro de Astronomia e Astrofisica de Universidade de Lisboa, PT-1349-018 Lisboa, Portugal.
4 Dipartimento di Astronomia, vicolo dell'Osservatorio 5, I-35122 Padova, Italy.
5 Canada-France-Hawaii Telescope Corporation, P.O. Box 1597, Kamuela, HI 96743.
The studies of the newly discovered population of the trans-Neptunian objects (TNOs) carried out since 1992 (when the first such object was discovered; see Jewitt & Luu 1993) have led to several surprises. First, the dynamical structure of the Edgeworth-Kuiper belt appears to be much more complex than expected. One can distinguish three main categories of objects: the resonant objects, the scattered disk objects, and the classical objects. Most of the resonant objects are in the 2 : 3 resonance with Neptune, as is Pluto, and have been called Plutinos. The scattered disk objects have highly eccentric and inclined orbits. Most of them have perihelion close to Neptune's orbit. Classical objects have semimajor axes mainly between 40 and 48 AU, and, although these objects are far from Neptune's gravitational influence, many of them have relatively high orbital eccentricities and inclinations. From the set of orbits determined so far, it is clear that objects in the belt have been subjected to a complex dynamical evolution.
According to Duncan, Levison, & Budd (1995), the gravitational influence of Neptune and, to a lesser extent, of Uranus and the other giant planets, cannot explain the observed dynamical structure. Other effects have been considered, such as planetary migration, the temporary presence of large remnant bodies of giant-planet formation that went through the belt before being ejected from the solar system, a star that came very close at some point of the evolution of the solar system, and others. None of the explanations considered so far offers a satisfactory explanation of the observations on its own. Attempts to combine some of these effects or to consider others are underway (see, e.g., Gladman et al. 2001 for a review).
In addition, it is now generally believed that what we presently see in the Edgeworth-Kuiper belt is only a very small fraction of the material originally present. A large part of the mass has been lost (see Stern & Colwell 1997). With a much more massive belt in the past, collisions must have played a very important role, creating small bodies, bringing some "fresh" (i.e., protected from radiation) material from inside, modifying orbits, and eventually facilitating the expulsion of bodies outside the belt.
Another major surprise is the large diversity in the colors of the objects (see Barucci et al. 2001). Colors vary from slightly blue to very red. Since it is believed that the TNOs were formed more or less at the same time and in the same cold region of the outer solar system, this important color variation may be mainly due to different degrees of surface alteration.
Looking at the surfaces of objects belonging to the different populations can help us in retracing their dynamical evolution and environmental and collisional history, as well as in eventually identifying objects that have not undergone any collisional processing (i.e., whose surfaces have been affected only by aging). From the photometric studies carried out so far, some trends have been noted in initial works (Tegler & Romanishin 2000; Doressoundiram et al. 2001, hereafter DOR01) and subsequent papers (Trujillo & Brown 2002; Hainaut & Delsanti 2002). The primary finding is an excess of red objects for perihelion distances greater than 40 AU, indicating that highly inclined classical objects are preferentially gray, and a wider range of colors for Plutinos than for the other classes of objects. However, there is a clear need for more data in each individual class of objects to confirm these trends and eventually look for other correlations.
We have engaged in an important observational program aimed at collecting a set of high-accuracy photometric data that is as homogeneous and as large as possible and includes not only objects in the different dynamical classes of trans-Neptunians, but also Centaurs. Centaurs probably constitute a population intermediate between the trans-Neptunians and the Jupiter-family comets. In this paper we discuss our observations of 30 objects, which have been carried out at the 3.6 m Canada-France-Hawaii Telescope in 2000 and 2001. We have combined this new data set with results from previous observations (29 objects) by our group (Barucci et al. 1999, 2000; DOR01) made with similar observational and reduction techniques. We thus have at our disposal a combined data set of 52 B-R colors (rather than 59, because of duplicated measurements of the same object or, in a few cases, missing B-V measurements) to look for correlations with various parameters.
This photometric program was part of a large program on the Canada-France-Hawaii Telescope dedicated to the discovery, recovery, and photometry of TNOs. This multifaceted program was aimed at a dynamical and compositional characterization of the Edgeworth-Kuiper belt, while optimizing the use of the large field of view of the CFH12K camera.
Visible observations were performed during three runs: 2000 December 21
24, 2001 June 2628, and 2001 August 1214. We used the 3.6 m Canada-France-Hawaii Telescope (CFHT; Mauna Kea, Hawaii) equipped with the CFH12K panoramic CCD camera, which is a mosaic of 12 2K × 4K CCD devices, covering a field of view of 42 × 28 arcmin2 with 0
2 pixel-1. Frames were taken through Mould BVRI broadband filters. Two nights (2001 June 28 and 2001 August 13) were not clear, so no photometry was done. All the other nights were photometric, under good seeing conditions.
Objects were selected from their observability, their brightness (MV < 22.5 as estimated by the Minor Planet Center ephemeris service6), their positional accuracy (e.g., multiopposition objects), the need to have a new or improved color measurement, and the absence of bright field stars in the vicinity of the object that would compromise the photometric measurement. In addition, newly discovered objects with large orbital uncertainties that were first observed in the recovery part of the large program have been targeted for photometric measurements. The selected objects and their observational circumstances are reported in Table 1. The telescope and instrument characteristics are described in Table 2.
 | TABLE 1 OBSERVATIONAL CIRCUMSTANCES |
 | TABLE 2 TELESCOPE/INSTRUMENT CHARACTERISTICS |
We adopted a specific observation strategy adapted to the variable and faint nature of the trans-Neptunian and Centaur objects. All target objects and standard stars were placed within CCD No. 3 (HiRho-type CCD of the mosaic), because it was found to be the best in terms of quantum efficiency, charge transfer efficiency, and cosmetics. Futhermore, this CCD part exhibits a very low fringing of 0.5% in the I band because of its higher thickness (Cuillandre et al. 2000). The exposure times did not exceed 600 s, in order to minimize trailing of the TNOs relative to the stars. At opposition, TNOs' motions at 50 AU are roughly 26 hr-1, thus producing a trail of 
04 in 600 s, which is small compared with the 0812 FWHM seeing for most of our observations. The telescope was tracked at sidereal rate. Since we aimed at a signal-to-noise ratio (S/N) between 20 and 30 in all filters, for the faintest objects we co-added images to achieve sufficient S/N. To eliminate systematic errors in the colors (i.e., B-V, V-R, V-I) caused by rotational light-curve variation, we adopted the following photometric sequence: R-V-B-I-V. This sequence was repeated two times during the night in order to (1) secure the measurement and then reduce the uncertainty in the color indexes and (2) eventually monitor any color variation on the TNO's surface. We think that the issue of the color variability is an important one, which is not well addressed in the literature. Indeed, the resurfacing hypothesis (Jewitt & Luu 2001) predicts such azimuthal color variation on individual objects. Finally, we gave great attention to the photometric calibration of our data in order to maintain a low level of uncertainty in the final color indexes. This goal was achieved by observing a large number of Landolt standard fields (Landolt 1992) over a wide range of air masses and colors. Transformation equations were solved for zero point, extinction, and color terms, leading to a total calibration error typically around 0.010.02 mag.
6 See http://cfa-www.harvard.edu/iau/MPEph/MPEph.html.
The images were processed using both MIDAS and IRAF data reduction packages. Data were reduced in the usual manner. First, the frames were bias-subtracted and flat-fielded by a median of the twilight flats. Each image was visually inspected for cosmic rays or bad pixels, and the photometry of the objects was performed using, in parallel, both aperture correction and a large aperture (aperture size of 6 FWHM). All of the details of the photometric reduction steps have been described in previous papers (Barucci et al. 2000; DOR01), and the interested reader may find all the details about the aperture correction method used. The basis of this method is that we made the photometric measurements by using a small aperture of the order of the size of the seeing disk. Then, to correct for the missing light, we used a mean point-spread function (PSF) built from an average of the field stars of the frame. Several small apertures were used to check for consistency. For all the photometry, the sky value was computed as the mode of sky areas surrounding the object. The advantages in the use of a small aperture are (1) a decrease in the contribution of the sky, which could be important and critical for faint objects, and (2) a minimization of the probability of contamination from unseen background sources. We see two main limitations to this method: first, each imaging instrument has image distortion across the field that is modulated by seeing and is color dependent. We overcame this problem by analyzing in the image as many bright isolated stars as possible, and preferentially stars in the vicinity of the object. Stars with PSFs that deviated too far (i.e., resolved galaxies or saturated/contaminated stars) were automatically rejected. This results in a final mean PSF calculated with several tens of stars, which serves for the correction of small aperture measurements. The distortion effect is thus reflected in the standard deviation of the fit, which in turn contributes to the photometric error. Secondly, the TNO and stars do not have exactly the same PSF, since our images usually are slightly trailed for the TNOs. However, depending on the seeing and trailing conditions, one can choose an aperture large enough to minimize this error (<0.01 mag). Of course, excessive trailing of objects will make the aperture correction technique inapplicable. In conclusion, performing the photometry with the aperture correction technique offers large improvements in the accuracy and in the reliability of the measurement, provided that one checks and takes into account the limitations of the method.
For each individual B, V, R, or I magnitude obtained, 1 
uncertainties are based on the combination of several uncertainties. The photometric uncertainly (pho) is based on photon statistics and sky noise. The uncertainty on the aperture correction (ap) is determined from the dispersion among measurements of the different field stars. The final uncertainty in the magnitude is derived from
where cal is the calibration error.
A mean V magnitude is listed in Tables 3 and 4, column (2). It is an average of several single V (generally four) measurements made through the photometric sequence R-V-B-I-V. Geometric effects were removed by reducing the photometry to H magnitudes following Bowell et al. (1989). A canonical value of G = 0.15 was assumed throughout. G is the slope parameter, indicative of the gradient of the phase curve. We have also computed, from the derived H magnitude, the estimated diameter of the objects (col. [8] of Table 4), assuming an albedo of 0.04 in common for dark objects and cometary nuclei. One should be aware that the sizes are purely indicative and largely uncertain. For instance, if we used instead an albedo of 0.14 (i.e., the albedo of the Centaur 2060 Chiron), all these size estimates would have to be divided by about 2. B-V, V-R, and V-I color indexes were computed using V magnitude measurement closest in time in the photometric sequence. When repeated color indexes were obtained for the same object, they were found for the vast majority to be consistent within the error bars. However, there were some exceptions, which will be discussed below. Thus a weighted mean has been computed, which is listed in Table 3, for each color index (shaded line). Table 4 summarizes the combined color indexes for each object, as well as the absolute magnitude (Hv) and size.
 | TABLE 3 INDIVIDUAL COLOR MEASUREMENTS |
 | TABLE 4 MEAN COLORS AND ESTIMATED SIZE OF CENTAURS AND TNOS |
By performing two (in most of our observations) photometric sequences over a significant time span, thus obtaining color indexes corresponding to different parts of the surface of the rotating object, we could monitor any possible color variation. This occurred a few times, where the differences between the measurements were significant in comparison with the uncertainties. We checked that these differences were not due to reduction or observational (contamination) problems. Indeed, in some cases, the differences were larger (0.10.2 mag) than expected from unseen background sources. However, although improbable, we could not exclude fast rotation of elongated TNOs that would introduce rotational effects within a single photometric sequence. The objects that show color variations are 1998 HK151, 1999 DF9, 1999 OY3, 2000 GP183, 2000 OK67, and 2001 KA77. The color variation could originate from true compositional and/or textural variation on the surface of the object. Here are the details for each object for which color variations have been found.
1998 HK151: This Plutino is pointed out as a possible variable object because we obtain a B-V color different from a previous measurement (DOR01). In DOR01 the authors noted the unusual bluish B-V color of this object (B-V = 0.51 ± 0.09, V-R = 0.43 ± 0.08, R-I = 0.36 ± 0.07) and pointed out the need to confirm this measurement. One year later Boehnhardt et al. (2001) confirmed the V-R and R-I color measurements but unfortunately did not make a B-V color measurement. In this paper we report new BVRI colors. The V-R and R-I colors are in good agreement with our previous measurements, while the B-V is much higher (B-V = 0.72 ± 0.05). We believe that this last measurement corresponds to the true physical nature of 1998 HK151.
1999 DF9: We report the first color measurements for this object. This classical object had a variable V-I color (3 difference) over a 40 minute time span, while the other colors were constant. The time line is relatively short. This V-I color needs to be confirmed before any tentative interpretation can be made.
1999 OY3: This classical object had both V-R and V-I color variations (>3 ) over a nearly 1 hr time span. On the other hand, the two B-V colors are the same. The colors vary between slightly blue to almost solar. This variation at longer wavelengths appears real. The B-V and V-R colors reported by Tegler & Romanishin (2000) are similar to the second set of measurements. Also, Hainaut & Delsanti (2002) suggest that this object may host intrinsic activity.
2000 GP183: This Plutino had only a variable V-I color (>2 ) over a nearly 1 hr time span. This is the first color measurement published for this object. This suspicious marginal variation needs further confirmation.
2000 OK67: This classical object had a variable B-V color (>2 ) over 45 minutes. Another color measurement for this object has been reported by Delsanti et al. (2001). Their B-V color are very close to one of our two measurements. Their V-R color is in good agreement within the error bars with our measurements. The B-V color needs to be measured again in order to confirm any true variability.
2001 KA77: We report the first color measurements for this object. This classical object had all B-V, V-R, V-I colors being variable (23 ) over a relatively short time span (23 minutes). If true, this variation may indicate relatively fast rotation of an elongated object.
In Figure 1 we plot our new data in the now classical B-V versus V-R color diagram, along with all other data published by our group (Barucci et al. 1999, 2000; DOR01; see Table 5). A few objects (e.g., 1998 VG44) were observed again during this last campaign. The colors obtained were very similar to our previous measurements (except 1998 HK151, which was discussed in the previous section). Thus we now have at our disposal a grand total 52 objects, the largest published data set obtained so far by a single team. It is important to note that our analysis is based on a homogeneous data set (the same team using the same observation strategy and data reduction techniques). This has not been the case for recent TNO color analyses, which have used compilations of different data sets. Obviously, with a homogeneous data set it is possible to prevent possible inconsistencies between color measurements of the same object from multiple investigators. The main reasons for these possible inconsistencies are different observation strategies, filter transformations, and data processing methods.
 | FIG. 1. |
 | TABLE 5 ALL OTHER DATA PUBLISHED BY OUR GROUP |
With such a significant contribution the picture of the wide color diversity of TNOs and Centaurs is further outlined. Figure 2 is the same as Figure 1 but instead shows the different populations: eight Centaurs, 22 classical objects, 13 Plutinos, eight scattered objects, and one object of unidentified dynamical class (see discussion on 1998 SN165 below). No distinct behavior is apparent among Centaurs, classical TNOs, Plutinos, or scattered objects. Instead, objects in each population exhibit a wide spread of colors, from gray (solar colors) to very red. This wide range of colors is thought to be the result of concomitant processes acting on the surfaces, including the reddening of surface material by irradiation and resurfacing effects by cratering impacts, and intrinsic activity. However, it must be kept in mind that the weathering/impact resurfacing hypothesis is merely a suggestion that is as yet unsupported by any quantitative and precise modeling.
 | FIG. 2. |
The color diversity of TNOs and Centaurs is also present in the two other color-color diagrams (Figs. 3 and 4). Colors are mutually correlated (e.g., rcorr = 0.79 between B-V and V-R, or rcorr = 0.47 between B-V and R-I), showing that the identical coloring process is responsible for the reddening from the B (0.43 
m) to the I (0.82 m) wavelengths. The lower correlation between B-V and R-I results from the fact that the spectrum of the reddest objects generally flattens toward the infrared. This seems to be in agreement with the hypothesis that the surfaces of TNOs consist of an irradiated icy crust. Indeed, as already noted by Hainaut & Delsanti (2002), following the laboratory work of Thompson et al. (1987) on irradiated frosts, the reddest TNOs are expected to have a spectrum that flattens toward the infrared.
 | FIG. 3. |
 | FIG. 4. |
This wide color diversity is peculiar to the outer solar system bodies and is not observed among asteroids, comet nuclei, or planetary satellites. This color diversity is an observational fact that is widely accepted by the community (e.g., DOR01; Jewitt, Aussel, & Evans 2001; Delsanti et al. 2001, and references therein). Colors range continuously from gray to very red. However, Tegler & Romanishin (1998, 2000) found instead that the color distribution is bimodal. DOR01 showed that differences in color measurements among our data and those of Tegler & Romanishin do not underlie this interpretation: we do have color agreement. The origin of this apparent paradox seems to reside in small number statistics and small error bars from Tegler & Romanishin's colors. We strongly encourage observers to better reduce their uncertainties and target those specific objects that lie between the two hypothetical groups.
Figures 5 and 6 are composite plots showing color, size, and orbital elements of outer solar system objects from our survey. We used the same type of representation as first presented in DOR01. Figures 5 and 6 show B-R colors of TNOs and Centaurs plotted according to orbital eccentricity (e) versus semimajor axis (a) and orbital inclination (i) versus semimajor axis (a), respectively. The B-R color index measures the ratio of the surface reflectance at B (430 nm) and R (660 nm) wavelengths. A color palette has been adopted to scale the color spread for objects of our survey from B-R = 1.01 (dark blue) to B-R = 1.88 (red). In comparison, B-R = 1.03 for the Sun, 1.21.3 on average for a typical short-period comet, and 1.97 for the Centaur 5145 Pholus (the reddest known object in the solar system). The size of the symbols are proportional to the corresponding object's diameter (assuming a constant albedo of 0.04). The advantage of this representation is that it makes it possible to visualize the global color distribution of the Edgeworth-Kuiper belt and may shed light on some singularities and trends in the belt.
 | FIG. 5. |
 | FIG. 6. |
We took the TNO and Centaur orbital elements from the Minor Planet Center (Marsden 2002).7 Before we analyze our results, we wish to caution the reader on the relative uncertainty of TNO's orbital parameters, whose accuracy is routinely improved as more data are collected. As a result of the very long orbital period of TNOs (longer than 250 yr), the orbital elements cannot be reliably determined in less than three oppositions (Petit et al. 2001). For instance, orbital elements may be dramatically wrong if they are determined from short arcs (months). In the framework of this work most of our objects have been observed for at least three oppositions, following our observational strategy (see § 2.1), to securely place the objects within chip No. 3. So we expect that the figures shown will not change drastically (only slight differences in a and e for the most recently discovered objects could occur).
On the other hand, if any trends are apparent in color-orbital parameter distributions, and outliers become obvious, they may be diagnostic of preliminary uncertain orbital elements calculations (see below). In this paragraph we first analyze Figures 5 and 6 visually before moving on to make statistical tests in the next section. Here are some interesting patterns that emerge from these color maps, most of which have already been reported in DOR01 are more pronounced with this larger B-R color sample of 52 objects:
6) is a gray object. The colors are in agreement with other published values. 1998 SN165 is currently classified as a classical object, while we consider it rather as an object with unidentified dynamical class because it is located ahead of the 3 : 2 resonance. As a classical object, 1998 SN165 would look peculiar in Figures 5 and 6 because it is "blue" (e.g., has a gray surface), while it is located at relatively low i and e. Actually its colors are more similar to the "low-excitation" objects located at a < 39 AU (ahead of the 2 : 3 resonance). Perhaps this object is a member of a rather separate dynamical class, as suggested by Gladman (2002) based on dynamical considerations, which is distinct from the classical objects. In fact, several objects have been discovered in that part of the Kuiper belt (a 38 AU, low i), which are thought to be very primitive objects that have been stable in their original location since the early stages of the solar system formation.
Among scattered TNOs two more objects, 1999 DE9 (a = 56.0 AU, e = 0.42, i = 76) and 1999 CC158 (a = 54.4 AU, e = 0.28, i = 187), may be considered marginal, as their colors are moderately red compared with the other six scattered TNOs, which are gray. Their orbits are no more or less excited than the other scattered TNOs, so some other explanation of their color differences must be found. No color variation has been detected on scales less than 1 hr, and our colors are in good agreement with other published values. They are multiopposition objects, so their orbital parameters can be considered as secure. Are these two objects real members of the scattered disk object (SDO) population? Are the scattered TNOs colors gray in general? Obviously more data need to be gathered to improve statistical analysis of the SDO population.
However, these tentative analyses on the outliers must be regarded with care, as always when dealing with small numbers.
All these interesting traits do indeed show up clearly in Figures 5 and 6. But, in order to assess their significance, we need to perform statistical tests. Contrary to our initial TNO surveys, we can now perform robust and simple tests on this large and homogeneous data set in order to determine how reliable any of these results are. Very recently some reliable correlations have been found, such as the inclination-color correlation reported by Trujillo & Brown (2002).
To investigate all the possible relationships between color and physical/orbital characteristics (size, absolute magnitude, orbital elements, etc.), we used the Spearman rank correlation statistics, rcorr (-1 
rcorr < 1), for our data set. The method (Press et al. 1992) is nonparametric. We use a nonparametric test (such as the Kolmogorov-Smirnov test, which we will use in § 6) because such techniques are not dependent upon an underlying assumption of normal distributions for the sampled variables. Heuristically, instead of using the real data values for its computation, the Spearman method ranks the (x, y) data points as a function of the x-values and measures how unranked they will be. One of the advantages of this test is that it makes no assumption about any fitting function to estimate the correlation (as does the Pearson or linear correlation method). The closer to 1 or -1 the rcorr, the stronger the correlation between the two variables, while a value close to zero indicates that they are uncorrelated.
Table 6 summarizes the correlations obtained for a selection of interesting cases. The quantity P(r > rcorr) gives the probability that a correlation coefficient equal to or larger than that measured could be obtained by chance in an uncorrelated sample. The probability P follows the Student's t-test distribution independently of the original distribution of our data sample. The value of 1 - P gives the confidence level of the correlation coefficient found. For instance, P(r > rcorr) = 0.003 indicates a confidence level of 99.7%, which is the nominal 3 criterion for a statistically significant correlation.
 | TABLE 6 CORRELATIONS |
First of all, we did not find any kind of correlation when we considered the TNO and Centaur populations as a whole in our data set (N = 52), as expected from the examination of the color maps. We then looked specifically at each population.
7 See http://cfa-www.harvard.edu/iau/lists/TNOs.html and http://cfa-www.harvard.edu/iau/lists/Centaurs.htm.
We wanted to investigate the trend seen in the color maps (point 1 of the above list), i.e., that the eight Centaurs in our sample seem to have redder colors at higher eccentricity. We indeed found a strong correlation rcorr = 0.62 between B-R and e. However, the significance found is low (1.6 ). Also, we found moderate correlation with a, i, and aphelion (Q), but it was still not statistically significant. Before speculating on the possible origin of this trend, we need to wait for further data. Actually, when increasing our sample with eight additional color data found in the literature, all these correlations vanish.
We found only weak correlations with e. Ultimately, with the extended data set (see below) of Plutinos' colors, we do not see any correlation at all (see Table 6).
We confirmed point 3 of the list. The colors of scattered TNOs are not correlated with any of a, e, i, size, or H. As for the average color, the colors of scattered TNOs are indeed bluer than those of the other populations. However, we have at our disposal only eight colors in our scattered-TNO sample. So, in principle, small number statistics could be responsible for this result. Hainaut & Delsanti's (2002) results from a larger database of 95 objects, put together as the combination of several published data sets, found no systematic color differences between the different TNO populations.
For the rest of the paper we are considering as classical TNOs those objects with semimajor axes between 40.5 AU (thus excluding the Plutinos) and roughly 48 AU. By taking these boundaries, we are automatically rejecting 1998 SN165 (a = 37.9 AU), which we have discussed above as a peculiar object, which may belong to a dynamical class distinct from the classical TNOs. Actually, several TNOs whose orbital parameters are close to those of 1998 SN165 have been discovered in that small region of the Edgeworth-Kuiper belt (a 38 AU, low i) predicted to be stable by Duncan et al. (1995), and obviously there is a nomenclatural problem for the classical objects posed by this population (see Gladman 2002).
For the classical TNOs the most obvious relationship shown in color maps involves inclination. Indeed, we found a strong correlation between color and inclination (Fig. 7), but only for the subpopulations of classical and scattered disk objects (N = 30). Excluding the scattered objects from the sample gives a better correlation, but it remains statistically tentative given the small number of scattered TNOs in our data set (N = 8). For B-V versus inclination, the Spearman rank correlation coefficient is found to be rcorr = -0.80 (N = 22); the probability of this rcorr or a more significant one occurring in an uncorrelated sample is P = 9 × 10-6 (4.4 significance for Gaussian statistics). For B-R versus inclination, we found rcorr = -0.72 with a probability P = 0.0002 (3.8 significance). We note that the correlation with B-V is stronger than that with B-R and also stronger than that with B-I (rcorr = -0.69). This result is general to all the correlations we have found: the correlation is stronger at shorter color wavelengths. This trend is a consequence of what was already noted in the color-color plots (Figs. 24): most of the reddest TNOs have a spectrum that flattens toward the infrared.
 | FIG. 7. |
The color-inclination correlation has been reported recently by Trujillo & Brown (2002) from their data set of N = 24 B-R colors, including, however, both classical and scattered objects. Their trend corresponded to a 3.1 significance level. On the other hand, Jewitt & Luu (2001) did not find any correlation with color in their sample of 28 B-I color indexes. We attribute this to the high proportion of resonant objects included in their sample, which hid the correlation.
How reliable is the color-inclination correlation regarding the orbital uncertainties? Actually, the inclination is generally the best determined of the six orbital elements because it is uniquely calculated by the motion of the TNO perpendicular to the ecliptic. Even a short arc of observation at opposition (where most TNOs are discovered) is sufficient to obtain i with an accuracy of less than 05.
We also investigated the correlation with eccentricity. We also found a strong one. We obtained a B-R versus eccentricity correlation coefficient rcorr = -0.60, with a probability P = 0.003 (3 ). Thus, the correlation found is statistically reliable. Such a correlation has been only reported by Hainaut & Delsanti (2002).
Looking for other correlations with color, we found only one with perihelion distance (Fig. 8). We obtained a B-R versus perihelion correlation statistic rcorr = 0.76, with a 4.1 significance for the classical objects (N = 22). Trujillo & Brown (2002) also noted this correlation, but they attributed it to a sampling bias. They based this conclusion on the analysis of a constant-i subsample in which they found no correlation between color and perihelion (Fig. 3 of their paper). We performed the same analysis by considering a constant-i subsample consisting of objects in the range 7° < i < 15° (the same boundaries as Trujillo & Brown). We obtained a result opposite to that of Trujillo & Brown: indeed, we found a strong correlation, rcorr = 0.74 (N = 8, 2.1 significance), between color and perihelion. However, more data would be preferable, especially at low q, to increase the significance, though this test indicates that the trend may be real (see Fig. 9). We suspect that the reason the Trujillo & Brown did not find a trend is that they included 1997 SZ10 and 1998 SM165 (q 30 AU) in their subsample, which are likely to be located in the 1 : 2 resonance. These resonant objects, like the Plutinos, might not show any correlation.
 | FIG. 8. |
 | FIG. 9. |
We did not find any correlation between color and absolute magnitude (Fig. 10) or between color and semimajor axis. These results apply to all subpopulations and for all color indexes. The lack of correlation between color and absolute magnitude translates into a lack of correlation between color and size, even if possible differences in albedos between the different objects are taken into account. Indeed, even if we varied the albedo of the objects between 0.04 and 0.14 (the value for Chiron), with the reddest objects having the smallest albedos, as suggested by Fernández, Jewitt, & Sheppard (2002), the main characteristics observed in Figure 10 remained (a large spread of colors for all sizes in each population). It is noteworthy that Hainaut & Delsanti (2002), based on the analysis on their combined data set (N = 95), found a trend for classical objects with faint H to be redder than the others. Moreover, they found the opposite trend for the Plutinos (faint-H tend to be bluer). We did not find any of these trends in our homogeneous but smaller data set. Of course, these opposite trends need to be confirmed by a larger observational data set, and even so their interpretation remains difficult.
 | FIG. 10. |
In order to make sure that relying on a single data set was not responsible for the results, and at the same time to increase the sample size, we repeated this analysis combining our data with all other major BVR data sets previously published (Tegler & Romanishin 1998, 2000; Jewitt & Luu 2001; Delsanti et al. 2001; Trujillo & Brown 2002; Boehnhardt et al. 2001). For multiple measurements of the same object, we took the mean. However, we stress that the combination of many different data sets may introduce artifacts (see § 4.1). Combining these additional data with our data set and selecting only the classical objects, the significance of the inclination and color correlation increases to 4.0 (N = 50). On the other hand, the correlation of color with eccentricity and perihelion is weak and no more significant. Nevertheless, we believe that the strong and significant correlations we have found for the classical TNOs of our survey are real, because they were built up from a homogeneous and large enough data set. And even if some of our measurements may agree within the uncertainties with those of a given observer, we believe that a single and homogeneous data set is better for a statistical analysis. Of course, the correlations with e and particularly with q need to be strengthened with additional data. The correlation between color and perihelion is an interesting and important result, since it may provide some clues to the structure of the Edgeworth-Kuiper belt (structure in a and e, extension of the disk, etc.). Obviously, we will continue to increase our observational data set with additional colors, especially for those TNOs whose orbits lie at small q (30 AU).
The correlation with i and e for classical TNOs points out that dynamically excited objects tend to have less red surfaces. This is observational evidence that some process is more efficient in that part of the belt than in other parts in reworking the surfaces of TNOs.
We present one more color-correlation estimate, that is, with the rms excitation:
where VK is the Keplerian orbital velocity, given by VK = (29.8 km s-1)a1/2, and a is the semimajor axis expressed in AU.
The quantity Vrms is the mean excitation velocity. This parameter is of great interest, since it gives a first-order approximation of the collisional encounter velocity for a given TNO. Such information might be useful because one of the proposed explanations for the color diversity within the belt is the effect of collisional resurfacing after mutual impacts among TNOs (e.g., Luu & Jewitt 1996). This scenario is based on the concomitant action of two time-dependent processes: the reddening and darkening of icy surfaces by solar and Galactic irradiation, and the excavation of fresh, primordial ices as the result of collisions. These fresh materials, made of brighter and more neutral ices, will thus make the surface bluer. Of course, the collisional-resurfacing hypothesis requires that both processes have about the same timescale. If this is not the case, we will have either a population uniformly red or a population uniformly gray. More recently, Gil-Hutton (2002) obtained similar results with a different resurfacing model. Furthermore, referring to the laboratory work of Thompson et al. (1987), he takes into account the possibility that, with further irradiation (after about 6 × 108 yr), the red crust would again become gray in color, while retaining its low albedo. This behavior obviously complicates the interpretation of the color distribution in the absence of knowledge of the albedo distribution. Indeed, only the albedo will permit one to distinguish between gray TNOs whose surfaces have been extensively reworked by collisions (high albedo) and gray TNOs whose surfaces possess a dark, thick irradiation mantle (low albedo).
The collisional resurfacing scenario remains hypothetical and is still the subject of much discussion. It nevertheless presents the advantage of making seemingly simple predictions concerning the color correlation within the Edgeworth-Kuiper belt. Basically, the most excited objects should be those most affected by energetic impacts and, thus, the most gray ones. It is thus very tempting to check the correlation between the color index and VK(e2 + i2)1/2, since both i and e should contribute to the average encounter velocity of a TNO. The result of this correlation estimation is presented in Table 6. An obvious result is that the correlation is very good (Fig. 11) for the classical objects. The Spearman rank correlation coefficient is found to be r = -0.77, with a significance of 4.2 (N = 22). This result suggests that collisions may play a role in the color diversity. This tends to confirm the results of Stern (2001) obtained with a smaller object sample made of all subpopulations.
 | FIG. 11. |
One must nevertheless remain very careful when interpreting such correlations. The Vrms parameter gives very partial information indeed. Strictly speaking, it gives only estimates of the TNO proper excitation, which might strongly differ from its average impact velocity. This parameter does not take into account the fact that a collision can occur between bodies originating from different parts of the belt, each having a different excitation contributing to the total impact velocity. Furthermore, the Vrms parameter is a quantity that gives the average impact velocity in a Maxwellian population with average values and e and i. It does not give the average impact velocity for a single object with e and i. Thus the predictions of the collisional resurfacing scenario are not as simple as they might seem. An accurate study of the impact-velocity distribution must be done using more complex tools. This problem is addressed in Thébault & Doressoundiram (2002) using accurate deterministic numerical simulations, which show obvious similarities to, but also clear departures from, the observed color distribution.
LOW INCLINATION CLUSTER: COULD COLOR DIVERSITY BE THE RESULT OF TRUE COMPOSITIONAL VARIEGATION? Levison & Stern (2001) showed that the classical objects are the superposition of two distinct populations. The first population would contain dynamically hot objects with high-inclination orbits and large objects. The second population would contain dynamically cold objects with low-inclination orbits and relatively small TNOs. Independently, Brown (2001), analyzing the unbiased inclination distribution of the Edgeworth-Kuiper belt, similarly concluded in favor of a two-component inclination distribution of the classical TNOs. Based on this bimodal behavior of the classical TNOs in both inclination and size, Levison & Stern (2001) speculated that the hot population originated from the inner regions of the disk, where the size distribution and color varied with heliocentric distance. On the other hand, the cold population (low i, a > 41 AU) should be primordial and dynamically stable over the age of the solar system, according to results of Duncan et al. (1995). Members of this cold population should have very similar physical characteristics because they were formed at the same time and within a relatively small region. The existence of two distinct classical populations appears to be borne out by our results shown in Figure 6, where a red, low-inclination cluster of TNOs is apparent.
In order to check that the two populations are statistically different regarding both their colors and sizes, we apply the two-dimensional Kolmogorov-Smirnov (K-S) statistical test (Peacock 1983). This test computes the probability that two two-dimensional populations are extracted from the same parent population. A zero probability means that the two populations are different, while a unit probability means they are the same. To test this hypothesis, we separate the "hot classical population" from the "cold classical population" of our sample of classical objects by putting an inclination cutoff at i = 5° (see Table 7), following Levison & Stern's assumption. We find that the K-S probability for the two populations, characterized both by their colors and size distribution, is 0.01. Thus, the cold classical population and the hot classical population are most probably different. We check that the K-S result is not affected when varying the sizes, considering that we may have albedo differences. Indeed, the H (absolute magnitude) distributions of the two populations are completely different.
 | TABLE 7 ORBITAL AND PHYSICAL CHARACTERISTICS OF THE DYNAMICALLY COLD AND HOT CLASSICAL TNOS |
If still speculative, this scenario is, however, opposite to the collision-resurfacing hypothesis suggested by the Vrms correlation. In other words, the color diversity could originate from true compositional diversity and not from collisional processes reworking surfaces of TNOs. To test this hypothesis, we analyze the colororbital excitation distribution within the hot classical population. Surprisingly, we still find a 3.3 (N = 13) strong and significant correlation between B-R color and mean excitation velocity [VK(e2 + i2) 1/2)]. This result suggests that the dynamical excitation of TNOs' orbits certainly plays a role in the color diversity seen in the hot classical population. Does this result exclude the hypothesis of an origin in the inner disk? We do not think so, because the temperature gradient across the Uranus-Neptune region is expected to be small. The temperature gradient between 20 and 30 AU is only 12 K, barely enough to induce strong compositional differences among TNOs. Therefore, the color diversity seen among hot classical TNOs could be explained by collisional resurfacing processes as sustained by the color-Vrms correlation found.
Given these results and the lines of supporting evidence for a two-component inclination distribution of the classical TNOs, reported by the above quoted authors, we speculate on a possible structure of the classical population. We confirm the statistical reality of the two populations. The cold classical objects consist of small objects at low i. Our survey demonstrates that they are also mostly red (except 1999 HR11, which is slightly different with a moderately red colorthis object was fainter than expected, Mv = 23.9, and the uncertainties are consequently very large. Its color measurements need to be refined). The hot classical objects consist of larger members at higher inclination. We found that their colors are very diverse.
We have reported BVRI colors for 30 trans-Neptunian and Centaur objects obtained at the Canada-France-Hawaii Telescope. This observational campaign is part of our ongoing Meudon Multicolor Survey of Outer Solar System Objects. Combining this last data set with our previous published colors, we obtained a unique and homogeneous data set of 52 B-R colors, which is the largest data set obtained so far by a single team. We then analyzed this data set to look for correlations between colors and various parameters, such as heliocentric distance, absolute magnitude, and orbital parameters.
The main results of this analysis are as follows: We confirm the wide and continuous spread of all B-V, V-R, and R-I colors. The different dynamical classes (e.g., Centaurs, Plutinos, and classical and scattered objects) seem to share the same color diversity. We find no correlation between size, colors, or heliocentric distance for the whole TNOs and Centaurs populations of our survey. As a result of our observing procedure of repeating color measurements, we highlighted a few objects for which color variations have been found and thus that may be diagnostic of true compositional and/or texture variation on the surface of the objects. These TNOs are 1998 HK151, 1999 DF9, 1999 OY3, 2000 GP183, 2000 OK67, and 2001 KA77 and should be prime targets for further observations in order to study and confirm the color variation with rotation.
We did not find any kind of correlation for the individual Plutinos, Centaurs, or scattered populations with orbital parameters. The only exception is the classical objects, for which we found a strong and significant correlation of color with orbital eccentricity, orbital inclination, and perihelion distance. We also investigated the correlation between color and mean excitation velocity [VK(e2 + i2) 1/2], and, as previously reported in the literature, we found a significant correlation. This is a strong argument in support of the collisional resurfacing hypothesis (Luu & Jewitt 1996). However, considering only the mean excitation velocity of a given TNO gives only partial information on the object's collisional dynamics. It does not take into account the fact that this body might collisionally interact with impactors from very different regions of the disk. Nevertheless, the correlation found is an encouraging result that led two of us to perform quantitative collisional/dynamical modeling in order to estimate the role of collisions in that region of the Edgeworth-Kuiper belt (Thébault & Doressoundiram 2002).
Instead of showing a continuous color distribution from low- to high-inclination orbits, the classical objects may consist in the superposition of two distinct populations, as suggested by Levison & Stern (2001) and Brown (2001). A supporting line of evidence in our data to this scenario is the presence of a red, low-inclination cluster of classical objects for i < 5°. With a two-dimensional Kolmogorov-Smirnov test we found that the dynamically cold classical TNOs (red colors, low i, small sizes) and the dynamically hot classical TNOs (diverse colors, moderate and high i, larger sizes) are two significantly different populations that could not have been extracted from the same parent population. Furthermore, the hot classical TNOs display a strong correlation between color and mean excitation velocity. Based on these results, we suggest that the cold classical TNOs are a primordial population, that the hot classical TNOs may have been injected from the inner regions of the disk, and that their surfaces' colors may be the result of space weathering and/or impact processes. However, quantitative collisional/dynamical modeling needs to be done, and additional observational data need to be obtained in order to resolve this issue.
An analysis based on visible colors with no albedo measurement available (only one TNO, Varuna, has had its albedo measured) has its limitations. Important differences in the albedos of TNOs with the same visible colors may exist. This would be the case, for instance, for objects that have a gray color because of the presence of fresh ices, as compared with objects with a gray color because of a very long period of irradiation (see § 5). And putting these two categories of objects into the same class would be erroneous. Furthermore, objects with similar colors in the visible may have very different colors in the near-infrared, which would mean different surface compositions. Unfortunately, because of the faintness of the objects, near-infrared colors have been obtained for only a very limited number of objects. The type of classification presented in this paper has the advantage of being the one for which the largest data set can built up. As more albedo measurements become available (in particular with the SIRTF satellite to be launched in 2003), its value will significantly increase.
Finally, from the global trends found with colors and orbital parameters, we highlighted a peculiar object: 1998 SN165 (a = 37.9 AU, e = 0.05, i = 46) is an object with yet unidentified dynamical class. Based on its gray colors, which are atypical for a low-excitation object, and given the fact that its orbit lies in a very stable region of the belt (Duncan et al. 1995), we conclude that 1998 SN165 belongs to a rather new dynamical class, distinct from the classical TNOs. While the origin of its gray color is unknown and still difficult to interpret without knowledge of the albedo, it will be very interesting to see whether other objects from the same class share the same color properties. Also of high interest, the visible spectrum of this object could easily be obtained with an 810 m class telescope. If this object's surface is covered with extremely irradiated ices (e.g., dark gray colors), its spectrum may show a bend in the B region, possibly diagnostic of its evolved state (see Hainaut & Delsanti 2002).
We thank Solenne Blancho for her help in part of the data reduction. We are very grateful to Brett Gladman for helpful discussions and ideas. Many thanks to R. P. Binzel for a careful reading of the manuscript. We would also like to thank M. E. Brown for fruitful refereeing and comments.
. 2000, Nature, 407, 979 First citation in article | Crossref | ADS | PubMed