Reanalyzing the visible colors of Centaurs and KBOs: what is there and what we might be missing

Since the discovery of the Kuiper belt, broadband surface colors were thoroughly studied as a first approximation to the object reflectivity spectra. Visible colors (BVRI) have proven to be a reasonable proxy for real spectra, which are rather linear in this range. In contrast, 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 Kuiper belt objects (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 weakened as a result of the data error bars; ii) the “risk” of missing an existing trend because of low sampling, and the possibility of making 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 distinguish the mutual effect of two or more (physical) parameters; and 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 a 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 that therefore, once that limit is achieved, it is important to diminish the error bars, but it is 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, that is, 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 is 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 appears to be a strong correlation – whereas th