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Description
Since the discovery of the Kuiper Belt, broadband surface colors were thoroughly studied as a first approximation to the objects reflectivity spectra. Visible colors (BVRI) have proven to be a reasonable proxy for real spectra, which are rather linear in this range. On the contrary, near-IR colors (JHK bands) could be misleading when absorption features of ices are present in the spectra. Although the physical and chemical information provided by colors are rather limited, broadband photometry remains the best tool for establishing the bulk surface properties of KBOs and Centaurs. In this work, we explore for the first time general, recurrent effects in the study of visible colors that could affect the interpretation of the scientific results: i) how a correlation could be missed or weaken due to the data error bars, ii) the "risk" of missing-out an existing trend due to low sampling, and the possibility to make quantified predictions on the sample size needed to detect a trend at a given significance level, assuming the sample is unbiased, iii) the use of partial correlations to disentangle the mutual effect of two or more (physical) parameters, iv) the sensitivity of the "reddening line" tool to the central wavelength of the filters used. To illustrate and apply these new tools, we have compiled the visible colors and orbital parameters of about 370 objects available in the literature, assumed, by default, as unbiased samples, and carried-out the "traditional" analysis per dynamical family. Our results show in particular how: a) data error-bars impose a limit on the detectable correlations regardless of sample size and, therefore, once that limit is achieved it is important to diminish the error-bars but pointless to enlarge the sampling with the same or larger errors; b) almost all dynamical families still require larger samplings to "ensure" the detection of correlations stronger than +/-0.5, i.e. correlations that may "explain" ~25% or more of the color variability; c) the correlation strength between (V-R) vs. (R-I) is systematically lower than the one between (B-V) vs. (V-R) and not related with error-bar differences between these colors; d) it is statistically equivalent to use any of the different "flavors" of orbital excitation or collisional velocity parameters regarding the famous color-inclination correlation among Classical KBOs --- which no longer evidences to be a strong correlation --- whereas the inclination and Tisserand parameter relative to Neptune cannot be separated from one another; and e) Classical KBOs are the only dynamical family which evidences for neither (B-V) vs. (V-R) nor (V-R) vs. (R-I) correlations, being, therefore, the family with the most unpredictable visible surface reflectivities.
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