7 Discussion and summary

7.1 Dataset

We compiled the colors of Minor Bodies in the Outer Solar System from 40 references, totaling measurements during 486 epochs of 104 objects, i.e. 13 SP Comets, 14 Centaurs, 9 Scattered TNOs, 20 Plutinos and 48 Cubewanos. For each object, these measurements have been carefully combined, taking care not to introduce rotational artifacts in the colors, and weighting each measurement with its error bar. The final error bar reflects the combined signal/noise ratio and the dispersion between the measurements. The absolute R magnitudes (M(1,1)) and the mean reflectivity slope $\cal S$ have been computed for each object, together with the deviation from a linear spectrum. The color-color diagrams are presented. The mean of each color (and its error) is presented for all the MBOSS classes.

7.2 Individual objects

A small group of objects - 1995 SM₅₅, 1996 TL₆₆, 1999 OY₃, 1996 TO₆₆ and (2060) Chiron - have almost perfectly solar colors, suggesting they are covered with neutrally colored fresh ice. Chiron is known to be cometary active, and 1996 TO₆₆ is suspected to be so too. The other objects from this group therefore deserve a closer study to look for activity and/or fresh ice spectral signature.

Four objects appear as outliers from the general population: 1994 ES₂, 1994 EV₃, 1998 HK₁₅₁ and 1995 DA₂. In all cases, we suspect that they do not correspond to physically distinct objects, but that the colors reported are not accurate.

7.3 Gradient and colors

In the color-color diagram, the objects follow closely the "reddening line'' (which is the locus of objects having a linear reflectivity spectrum). This confirms that most MBOSSes have globally linear reflectivity spectra in the visible. Nevertheless, some systematic effects are visible:

• The diagrams involving the I band indicate that the spectrum of many objects becomes flatter toward the near-IR, which is expected if one considers the laboratory spectra.
• Also, many objects present a bend in the B region. The latter is not matching the laboratory spectra for fresh ices. Maybe they correspond to objects in an evolved state (e.g. covered with extremely irradiated ices, which can have reflectivity spectra bend in the blue region), as opposed to having recently been re-surfaced.

7.4 Correlations with orbital elements

7.4.1 Semi-major axis $\mathsfsl{a}$

There is no correlation between the color (and spectral gradient) of the objects and their orbit semi-major axis. This stands for the whole MBOSS population as well as for the individual families. Therefore, the traditional increasing reddening of asteroids with a that is observed for Main-Belt asteroids and Trojans stands for the MBOSSes as a whole (i.e. they are on average considerably redder than objects closer to the Sun, cf. Table 3), but not within the MBOSSes themselves.

7.4.2 Orbit excitation $\mathsfsl{i}$, $\mathsfsl{e}$ and $\mathsfsl{\cal E}$

For the Plutinos, Centaurs and Scattered TNOS, the correlation between colors (including spectral gradient) and the other orbital parameters is either nonexistent or very weak: no trend is apparent in the different color vs. parameter plots, and this is confirmed by weak correlation coefficients and statistical tests.

One notable exception: the color of the Cubewanos presents a very strong, very significant correlation with the eccentricity, inclination and "excitation'' ($\cal E$ obtained by combining quadratically i and e): Cubewanos with a small excitation are systematically and significantly redder than those with a higher excitation. This confirms the results presented by Trujillo et al. (2001) and Stern (oral comm. at Meudon 2001 workshop), who obtained similar correlations on smaller samples.

In addition, the Cubewanos with large orbital excitation have significantly broader color distributions than the others.

In a more general way, the difference is greater between Cubewanos with a small and large orbital excitation than the difference between the different classes of MBOSSes.

This suggests either that

• objects with higher excitation suffer a more efficient resurfacing, because of more numerous and stronger collisions than those with smaller excitation, or that
• objects with low excitation constitute a different population, possibly covered with a more primordial surface, or of a different nature.

7.5 Absolute magnitude

The tests involving the absolute magnitude of the object (M(1,1), neglecting the solar phase correction, which is unknown but expected to be small) deserve special attention.

Cubewanos with faint M(1,1) tend to be redder than the others (this effect is visible through the correlation coefficients and the t-tests). Plutinos present the opposite trend (faint M(1,1)tend to be bluer), with about the same significance. It is difficult to explain this through a selection effect at discovery. However, the Plutinos extend to fainter M(1,1) than the Cubewanos (a effect of the latter being on average further away from the Sun, therefore fainter than Plutinos of the same absolute magnitude). At this point, these opposite trends are not explained.

The width of the color distributions of the objects with faint M(1,1) is never significantly different than those of the larger objects. The models of collisional resurfacing balancing the reddening (Luu & Jewitt 1996a; Jewitt & Luu 2001) predict that the smaller objects will have a broader range of colors, which is not observed. Therefore, the current database does not support this model. Jewitt & Luu (2001) discuss also that, for that model, the colors of a given object should vary with same amplitude as the variation of colors between objects of the same diameters, which is not the case. However, as this database does not explore the rotational variations, this cannot be further explored.

7.6 Comparison between populations

The color distribution of the Scattered TNOs systematically cover a narrower range than those of the other classes; this is not substantiated by the statistical tests, but possibly because the distributions have fairly different shapes. Nevertheless, if confirmed in the future, this would indicate that they are on average exposed to a narrower range of resurfacing effects - for instance, less collisions because they spend a significant fraction of their time far out of the densely populated regions, or strictly no cometary activity because they are the most distant objects from the Sun. This could give constraints on the conditions to which they are exposed.

We performed a series of statistical tests on the color distributions (f-test, t-test and KS). These tests indicate that the comets' colors are significantly bluer than those of the other MBOSSes. This result is very strong for the Cubewanos and Plutinos (with a probability that the comet are actually similar to these objects of $\sim$10^-3 on individual color indexes), and weaker for the Centaurs and Scattered TNOs (probability of the order of a %).

There is no evidence that the Plutinos, Cubewanos, Centaurs and Scattered TNOs have significantly different color distributions.

Non-physical, arbitrary populations (in which the objects are distributed according to their designation) were used to test the statistical methods; they indicate that probabilities larger than $\sim$5-10% should not be considered as reliable.

7.7 Bimodality of the color distributions

Visually comparing the color CPFs of the various classes, it appears that the Cubewanos and Centaurs tend to have "bimodal'' (2 well separated steps) or "broken'' (2 well separated slopes) distributions, while the Plutinos tend to have very continuous distributions (i.e. uniform CPF slope over the whole range).

However, statistical comparison of the observations with simple 1D and 2D model distributions indicate that, in no case we have enough data to rule out the validity of simple, continuous distributions to represent the data. This does not mean that the distributions are continuous, but that we have to be extremely careful if saying that they are not.

Jewitt & Luu (2001) have performed some statistical tests (bin, dip and interval distribution tests) on a smaller sample; these tests do not provide evidence that the B-V and V-Rof their sample are distributed bimodally.

7.8 Prospects

We plan to maintain and update the observations database and keep it available on the web (at  http://www.sc.eso.org/~ ohainaut/MBOSS). We encourage the observers to send us the tables of their publications electronically. We intend to update this paper when the number objects in the database will have doubled or when the conclusions will have significantly changed.