J/A+A/577/A35ivo://CDS.VizieR/J/A+A/577/A35doi:10.26093/cds/vizier.35770035CDSPeixinho N.Delsanti A.Doressoundiram A.2015-09-04T15:04:45Z2015-04-28T08:57:36ZCDS support team

CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France

cds-question@unistra.frsolar-systemasteroidstwo-color-diagramsSince 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.2015A&A...577A..35Phttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/577/A35CatalogResearchIsServedByTAP VizieR generic servicerelated-toJ/A+A/380/347 : BVRI photometry of 27 Kuiper Belt Objects (Delsanti+, 2001)J/AJ/133/26 : Solar phase curves of distant icy bodies (Rabinowitz+, 2007)J/A+A/546/A86 : R absolute magnitudes of Kuiper Belt objects (Peixinho+, 2012)https://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/A+A/577/A35https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/A+A/577/A35http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/A+A/577/A35https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/A+A/577/A35https://vizier.iucaa.in/viz-bin/votable?-source=J/A+A/577/A35http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/A+A/577/A35GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapdefaultJ/A+A/577/A35/table5Compilation of R-band absolute magnitude, spectral gradient, colours and corresponding orbital and orbital related parameters of 366 Centaurs and KBOse_B-I? 1-{sigma} error bar of B-I color indexmagstat.error;phot.color;em.opt.BfloatnullablerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintObjectObject number/name/designationmeta.id;meta.maincharClassDynamical class (1)src.classcharHR[-1.6/12.4]? R-band H_R_ (G1)magphys.magAbsfloatnullablee_HR[0.01/0.51]? 1-{sigma} error bar of HRmagstat.errorfloatnullableGrt[-4.2/75]? Spectral gradient (G1)100000m**-1arith.gradfloatnullablee_Grt[0.8/30]? 1-{sigma} error bar of Grt100000m**-1stat.errorfloatnullableB-V? B-V color indexmagphot.color;em.opt.B;em.opt.Vfloatnullablee_B-V? 1-{sigma} error bar of B-V color indexmagstat.error;phot.color;em.opt.BfloatnullableV-R? V-R color indexmagphot.color;em.opt.V;em.opt.Rfloatnullablee_V-R? 1-{sigma} error bar of V-R color indexmagstat.error;phot.color;em.opt.VfloatnullableR-I? R-I color indexmagphot.color;em.opt.R;em.opt.Ifloatnullablee_R-I? 1-{sigma} error bar of R-I color indexmagstat.error;phot.color;em.opt.RfloatnullableV-I? V-I color indexmagphot.color;em.opt.V;em.opt.Ifloatnullablee_V-I? 1-{sigma} error bar of V-I color indexmagstat.error;phot.color;em.opt.VfloatnullableB-I? B-I color indexmagphot.color;em.opt.B;em.opt.IfloatnullableB-R? B-R color indexmagphot.color;em.opt.B;em.opt.Rfloatnullablee_B-R? 1-{sigma} error bar of B-R color indexmagstat.error;phot.color;em.opt.Bfloatnullableq[5.7/77] Perihelion distanceAUpos.distance;src.orbital.periastronfloatQ[10.8/1603] Aphelion distanceAUpos.distance;src.orbitaldoublei[0/105] Orbital inclinationdegsrc.orbital.inclinationfloate[0/1] Orbital eccentricitysrc.orbital.eccentricityfloata[8/814] Semimajor axisAUphys.size.smajAxisfloatVc[0.1/17] Collisional velocity (G1)km/sphys.velocfloatpsi[0/0.1] Oepik's {psi} parameter (G1)src.orbitaldoubleeps[0.02/1.2] Orbital excitation {epsilon} (G1)src.orbitalfloatTNTisserand Parameter relative to Neptune (G1)src.orbitalfloatTJTisserand Parameter relative to Jupiter (G1)src.orbitalfloatRefsPointer for bibliographic references of measurements that have been used, in refs.datmeta.ref;pos.framecharJ/A+A/577/A35/refsReferencesrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintRefReference numbermeta.id;meta.mainintBibCodeBibCodemeta.bib.bibcodecharAutAuthor's namemeta.bib.authorcharComCommentsmeta.notecharJ/A+A/577/A35/table4*Significant Spearman-rho correlations detectedrecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintClassDynamical class or type of objectssrc.classcharFDRs[2.5/3] Confidence level threshold after the False Discovery Correction (in {sigma})stat.fit.goodnessfloatXvarX variable on the correlation (G1)stat.correlationcharYvarY variable on the correlation (G1)stat.correlationcharn[18/328] Number of (X,Y) data pointsmeta.numberintrho[-1/1] Spearman-rank correlation value {rho}stat.correlationfloatE_rho[0.04/0.3] Upper error of the 68.2% confidence interval of rhostat.error;stat.maxfloate_rho[0.04/0.4] Lower error of the 68.2% confidence interval of rhostat.errorfloatp-rho[1.e-6/0.036] P-value of rhostat.fit.goodnessdoubleCLs[2/8] Confidence level of rhostat.fit.goodnessfloati[1/60] Rank of the correlation after ordering by increasing P-valuesstat.correlationintp2.5[1.e-4/0.009] FDR-corrected P-value as a function of the number of tests for 2.5{sigma} of confidence level (see Sect. 3.4)stat.fit.goodnessdoublep3[2.e-5/0.002] FDR-corrected P-value as a function of the number of tests for 3{sigma} of confidence level (see Sect. 3.4)stat.fit.goodnessdoublerho2.5[0.2/0.8] Maximum detectable rho at a 2.5{sigma} confidence with a beta risk of 10% of missing it (see Sect. 3.2)stat.correlationfloatrho3[0.2/0.9] Maximum detectable rho at a 3{sigma} confidence with a beta risk of 10% of missing it (see Sect. 3.2)stat.correlationfloat