J/A+A/577/A35 Visible colors of Centaurs and KBOs (Peixinho+, 2015)
Reanalyzing the visible colors of Centaurs and KBOs:
what is there and what we might be missing.
Peixinho N., Delsanti A., Doressoundiram A.
<Astron. Astrophys. 577, A35 (2015)>
=2015A&A...577A..35P 2015A&A...577A..35P
ADC_Keywords: Solar system ; Minor planets ; Colors
Keywords: Kuiper belt: general - methods: data analysis - methods: statistical -
techniques: photometric
Abstract:
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.
Description:
Table 2: significant Spearman-rho correlations detected between all
colors and all orbital parameters of Centaurs, scattered disk objects,
scattered or detached objects, Plutinos, other resonants, classical
KBOs, binary or multiple KBOs, KBOs (without Haumea family and
retrograde orbits), all objects (also without Haumea family and
retrograde orbits), and KBOs except classical KBOs (also without
Haumea family and retrograde orbits). First and second columns
indicate the variables, third column the number of objects with both
variables measured, forth column indicate the correlation value and its
68.2% error interval, fifth column indicates the p-value of the
correlation, sixth column indicate the equivalent confidence level of
the p-value in Gaussian sigmas, columns seven to nine indicate the
detail of the False Discovery Correction for confidence levels of
2.5σ and 3σ (see Sect. 3.4), tenth column indicates the
maximum detectable rho at a 2.5σ confidence level with a 10%
risk of missing it, eleventh column indicates the maximum detectable
rho at a 3σ confidence level with a 10% risk of missing it (see
Sect. 3.2)
Table 5: Compilation of R-band absolute magnitude, not corrected for
the phase-angle, of Spectral gradient, B-V, V-R, R-I, V-I, B-I, B-R,
and corresponding orbital and orbital related parameters of 366
Centaurs and KBOs. For each object/observation, we computed the
reflectance spectrum using equation (3) from Delsanti et al.
(2001A&A...380..347D 2001A&A...380..347D), when 2 or more filters were available. The
resulting spectra were manually checked, and obviously deviant data
from a given filter were removed from the dataset. Color indexes are
computed within one given epoch, leading to colors obtained from
"simultaneous" photometry (the different bands were observed over a
maximum timespan of 2 hours). Then the average colors indexes and
their one σ errors from different papers and epochs are computed
for each object using equations (1) and (2) from Hainaut and Delsanti
(2002A&A...389..641H 2002A&A...389..641H), providing more accurate estimates when multiple
measurements are available. Absolute magnitude in R band (HR) are
computed for each object/epoch whenever a R-band magnitude is
available, using: HR=R-5log(rΔ), where R is the R-band
magnitude, r and Δ the helio- and geocentric distances at the
time of observations, respectively.Different values for a given object
were also averaged using the aforementioned equations (1) and (2). We
did not correct for any phase effect.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
table4.dat 131 326 *Significant Spearman-rho correlations detected
table4.tex 437 445 LaTeX version of table4
table5.dat 254 366 Compilation of R-band absolute magnitude, spectral
gradient, colours and corresponding orbital and
orbital related parameters of 366 Centaurs and KBOs
table5.tex 678 454 LaTeX version of table5
refs.dat 100 50 References
--------------------------------------------------------------------------------
Note on table4.dat: between all colors and all orbital parameters of Centaurs
scattered disk objects, scattered or detached objects, Plutinos, other
resonants, classical KBOs, binary or multiple KBOs, KBOs (without Haumea
family and retrograde orbits), all objects (also without Haumea family and
retrograde orbits), and KBOs except classical KBOs (also without Haumea family
and retrograde orbits).
--------------------------------------------------------------------------------
See also:
J/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)
Byte-by-byte Description of file: table4.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 31 A31 --- Class Dynamical class or type of objects
32- 34 F3.1 --- FDRs [2.5/3] Confidence level threshold after the
False Discovery Correction (in σ)
35- 39 A5 --- --- [sigma]
42- 46 A5 --- Xvar X variable on the correlation (G1)
49- 55 A7 --- Yvar Y variable on the correlation (G1)
57- 59 I3 --- n [18/328] Number of (X,Y) data points
61- 65 F5.2 --- rho [-1/1] Spearman-rank correlation value ρ
68- 71 F4.2 --- E_rho [0.04/0.3] Upper error of the 68.2% confidence
interval of rho
74- 78 F5.2 --- e_rho [0.04/0.4] Lower error of the 68.2% confidence
interval of rho
81- 88 F8.6 --- p-rho [1.e-6/0.036] P-value of rho
91- 94 F4.2 --- CLs [2/8] Confidence level of rho
98- 99 I2 --- i [1/60] Rank of the correlation after ordering
by increasing P-values
102-109 F8.6 --- p2.5 [1.e-4/0.009] FDR-corrected P-value as a
function of the number of tests for 2.5σ
of confidence level (see Sect. 3.4)
112-119 F8.6 --- p3 [2.e-5/0.002] FDR-corrected P-value as a
function of the number of tests for 3σ
of confidence level (see Sect. 3.4)
122-125 F4.2 --- rho2.5 [0.2/0.8] Maximum detectable rho at a 2.5σ
confidence with a beta risk of 10% of
missing it (see Sect. 3.2)
128-131 F4.2 --- rho3 [0.2/0.9] Maximum detectable rho at a 3σ
confidence with a beta risk of 10% of missing
it (see Sect. 3.2)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table5.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 24 A24 --- Object Object number/name/designation
27- 36 A10 --- Class Dynamical class (1)
39- 43 F5.2 mag HR [-1.6/12.4]?=- R-band HR (G1)
46- 49 F4.2 mag e_HR [0.01/0.51]?=- 1-σ error bar of HR
52- 57 F6.2 10+5m-1 Grt [-4.2/75]?=- Spectral gradient (G1)
60- 64 F5.2 10+5m-1 e_Grt [0.8/30]?=- 1-σ error bar of Grt
67- 70 F4.2 mag B-V ?=- B-V color index
73- 76 F4.2 mag e_B-V ?=- 1-σ error bar of B-V color index
79- 82 F4.2 mag V-R ?=- V-R color index
85- 88 F4.2 mag e_V-R ?=- 1-σ error bar of V-R color index
91- 94 F4.2 mag R-I ?=- R-I color index
97-100 F4.2 mag e_R-I ?=- 1-σ error bar of R-I color index
103-106 F4.2 mag V-I ?=- V-I color index
109-112 F4.2 mag e_V-I ?=- 1-σ error bar of V-I color index
115-118 F4.2 mag B-I ?=- B-I color index
121-124 F4.2 mag e_B-I ?=- 1-σ error bar of B-I color index
127-130 F4.2 mag B-R ?=- B-R color index
133-136 F4.2 mag e_B-R ?=- 1-σ error bar of B-R color index
139-144 F6.3 AU q [5.7/77] Perihelion distance
146-153 F8.3 AU Q [10.8/1603] Aphelion distance
155-159 F5.1 deg i [0/105] Orbital inclination
162-167 F6.4 --- e [0/1] Orbital eccentricity
170-176 F7.3 AU a [8/814] Semimajor axis
178-182 F5.2 km/s Vc [0.1/17] Collisional velocity (G1)
185-193 F9.7 --- psi [0/0.1] Oepik's ψ parameter (G1)
196-200 F5.3 --- eps [0.02/1.2] Orbital excitation ε (G1)
203-207 F5.3 --- TN Tisserand Parameter relative to Neptune (G1)
210-215 F6.3 --- TJ Tisserand Parameter relative to Jupiter (G1)
218-254 A37 --- Refs Pointer for bibliographic references of
measurements that have been used, in refs.dat
--------------------------------------------------------------------------------
Note (1): Dynamical classes are explained in Sec.2 of the paper.
Binary/multiple objects are indicated with (b);
retrograde orbits with (r);
and "Haumea collisional family" objects with (h).
--------------------------------------------------------------------------------
Byte-by-byte Description of file: refs.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 2 I2 --- Ref Reference number
4- 22 A19 --- BibCode BibCode
24- 45 A22 --- Aut Author's name
47-100 A54 --- Com Comments
--------------------------------------------------------------------------------
Global Notes:
Note (G1): the parameters are:
* colors: (B-V), (B-R), (B-I), (V-R), (V-I), (R-I);
* Grt, the spectral grandient (reddening), defined as the reflectivity
spectrum variation in percent of reddening per 100nm (1000Å)
* HR, the absolute R-band magnitude HR not corrected for phase effects
* orbital parameters: a (semi-major axis), e (eccentricity), i (inclination
to the Ecliptic), q (perihelion)
* epsilon, the orbital excitation (ε = sqrt(e2+sin2i)) (Sec.5.6.2)
* psi, Oepik's ψ = [(5/8)e2+sin2i]/a (Sec.5.6.2)
* TN, Tisserand parameter TN relative to Neptune (Sec.5.6.2)
* TJ, Tisserand parameter TJ relative to Jupiter (Sec.5.6.2)
* Vc, collisional velocity (Sec.5.6.2)
--------------------------------------------------------------------------------
Acknowledgements:
Nuno Peixinho, nuno.peixinho(at)uantof.cl,
Unidad de Astronomia, Universidad Antofagasta, Chile
History:
* 28-Apr-2015 : on-line version
* 14-May-2015 : table2 renamed table4
(End) Nuno Peixinho [U. Antofagasta], Patricia Vannier [CDS] 17-Feb-2015