> Nuno Peixinho. > Alain Doressoundiram >>> CORRELATIONS BETWEEN COLORS AND ORBITAL PARAMETERS

Transcription

1 >>> CORRELATIONS BETWEEN COLORS AND ORBITAL PARAMETERS > Nuno Peixinho > Alain Doressoundiram Grupo de Astrofísica U. C. Observatório Astronómico U. C. Universidade de Coimbra

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3 Multicolor Photometry of Centaurs and TNOs Born in Deceased in 2006

4 >>> Why do we look for correlations? > Those who find through chance do not deserve the findings. (Nietzsche) > Identifying interconnections between variables is a starting point to understand the reasons of their variability. > The most fundamental analysis of interconnection between two or more variables is the analysis of correlations. > Correlations may be confronted with theoretical predictions and lead to new theoretical and observational/experimental works. > For the moment multicolor photometry the only statistically relevant characterization of surface properties of TNOs.

5 >>> A bit of theory: > There are many different ways to measure a correlation. >> Pearson correlation > It is the most common coefficient used in statistics (Pearson, 1900), but: > It assumes that the parent population distribution is normal; > It tests only for linear correlations; > It is difficult to asses for its significancy.

6 >> Spearman correlation > It ranks the data-values (1st highest, 2nd highest, etc.) and performs the test on those ranks (Spearman, 1904). > It is valid for any continuous parent distribution; > It tests for any monotonic correlation; > It is less sensitive to outliers; > It is easy to asses for its significancy; > Nevertheless, it looses some data information.

7 >> How significant is significance? > Hypothesis testing is a process of rejection, at some level of significance, rather than a process of acceptance. > The confidence level, or significance level, at which one may reject the null hypothesis (H0) is a convention somewhat controversial. > Certainly, we do not wish to conclude for H1 when it is not true and CL should be the highest possible. > However, by increasing CL we are also increasing the risk of failing to conclude for H1 when actually it is true. CL > 95% (p < 0.05) reasonably strong evidence against H 0 CL > 97.5% (p < 0.025) strong evidence against H 0 CL > 99% (p < 0.01) very strong evidence against H 0

8 >> How strong is a correlation? > Like for confidence levels (significance), it is also a rough convention. > The following ratings give a general idea of levels of intensity of ρ: 0.0 ρ < 0.3 absent/negligible correlation 0.3 ρ < 0.6 weak/moderate correlation 0.6 ρ 1.0 strong correlation

9 > The coefficients of correlation ignore error bars! >> How about error bars? > We may include them with simulations (Peixinho et al. 2004), but do we need to? > It gives only the confidence interval of the estimated mean correlation. > The confidence interval of the correlation itself must be computed with parametric bootstrap (Efron & Tibshirani, 1993). -σmean ρmean +σmean -σρ +σρ

10 >> So... do we really need to account for error bars? > NO! For our practical purposes the CI of the correlation is much greater than the CI of its estimated mean value when accounting for error bars.

11 >> So... do we really need to account for error bars? > NO! For our practical purposes the CI of the correlation is much greater than the CI of its estimated mean value when accounting for error bars.

12 >> So... do we really need to account for error bars? For ρ error bars may be important. > NO! For our practical purposes the CI of the correlation is much greater than the CI of its estimated mean value when accounting for error bars.

13 >>> Photometric surveys > Meudon Multicolor Survey (2MS) Using 3.6 m CFHT 71 objects (e.g. Barucci et al. 1999; Doressoundiram et al. 2005) > ESO Large Program on Centaurs and TNOs (LP) Using 3.5 m NTT and 8 m VLT 72 objects (e.g. Boehnhardt et al. 2001; Peixinho et al. 2004) > LP + 2MS = 120 > Tegler and Romanishin s (TR) Using 10 m Keck, 2.3 Stewart and 1.8 Vatican 91 objects (e.g. Tegler & Romanishin, 1998; Tegler, Romanishin & Consolmagno, 2003)

14 >>> Colors and colors > Too much color distracts the spectator. (Jacques Tati) > Ten years ago we did not have evidence for any correlations among Centaurs and TNOs, but: > The large color variability was identified > The collisional resurfacing model was proposed (Luu & Jewitt, 1996) > Luu & Jewitt (1996)

15 >> Collisional resurfacing > Blue origin Origin Reddening Collison > Reddening by space weathering versus blueing resurfacing by burried unradiated material due to collisons. > Adapted from Delsanti (2004)

16 >> Intrinsic differences > Tegler & Romanishin (1998) originate the debate on the two separate color groups versus one continuous group that lasted for about 5 years. > Such would imply probable intrinsic differences > But, between 30 and 50 AU: ΔT ~10 K. Not suficient to explain such diversity > Unless... they did not formed in situ. > And migration models are there now!!!

17 >> Centaurs bimodality > Bimodality for all groups!? (Tegler & Romanishin, 1998, 2000, 2003) > Inexistence of bimodality!? (e.g.:hainaut & Delsanti, 2002; Jewitt & Luu, 2001) > Bimodality only for Centaurs (Peixinho et al.,2003)

18 >> Centaurs bimodality 99.7% > Bimodality for all groups!? (Tegler & Romanishin, 1998, 2000, 2003) > Inexistence of bimodality!? (e.g.:hainaut & Delsanti, 2002; Jewitt & Luu, 2001) > Bimodality only for Centaurs (Peixinho et al.,2003)

19 >> Centaurs bimodality 55% > Bimodality for all groups!? (Tegler & Romanishin, 1998, 2000, 2003) > Inexistence of bimodality!? (e.g.:hainaut & Delsanti, 2002; Jewitt & Luu, 2001) > Bimodality only for Centaurs (Peixinho et al.,2003)

20 >>> Colors and colors > Visible colors correlate with decreasing intensity for higher wavelengths. > Usually interpreted as one single agent acting on all colors.

21 >>> Colors and colors > Near-IR colors do not correlate. > Does it mean existence of additional coloring agents?

22 >>> Colors and colors > Delsanti et al. (2006) found that Centaurs are not bimodal in JHK, but: > Red Centaurs possess the lowest HK colors: > Large water ice bands?

23 >>> Colors and colors > Delsanti et al. (2006) found that Centaurs are not bimodal in JHK, but: > Red Centaurs possess the lowest HK colors: > Large water ice bands?

24 >>> Color, inclination and size > Tegler & Romanishin (2000) found a cluster of red Classical objects at low i. > Trujillo & Brown (2002) found, explicitly, the color-i correlation.

25 >>> Color, inclination and size > Tegler & Romanishin (2000) found a cluster of red Classical objects at low i. > Trujillo & Brown (2002) found, explicitly, the color-i correlation. > Trujillo & Brown (2002): ρ=-0.62 > Hainaut & Delsanti (2002): rs=-0.76 > Doressoundiram et al. (2002): ρ=-0.72 > Peixinho et al. (2004): ρ=-0.62

26 >> Modeling the collisions > The correlation between color and collisional velocity is considered as evidence for a collisional mechanism affecting the colors of TNOs (Hainaut & Delsanti, 2002; Doressoundiram et al., 2002; Stern, 2002).

27 >> Modeling the collisions > But, Vrms gives only partial information on the collisional behavior of a given TNO and modeling of the entire Kuiper Belt collisional environment is required (Thébault & Doressoundiram, 2003; Thébault, 2004). > Obtains stronger correlations with e than with i. > All Plutinos should be highly impacted, hence blue.

28 >>> The Complexity of Classical Objects >> Hot and Cold, true compositional diversity? > Two different inclination distributions (Brown, 2001). > High i objects are larger than low i objects (Levison & Stern, 2001) > Best cutoff between cold population (red cluster) and hot population (diverse colors): > Using Squared Ranks Test: i=4.5 (Peixinho et al. 2004)

29 >>> The Complexity of Classical Objects >> Hot and Cold, true compositional diversity? Hot > Two different inclination distributions (Brown, 2001). > High i objects are larger than low i objects (Levison & Stern, 2001) > Best cutoff between cold population (red cluster) and hot population (diverse colors): Cold > Using Squared Ranks Test: i=4.5 (Peixinho et al. 2004)

30 >>> The Complexity of Classical Objects >> Hot and Cold, true compositional diversity? Real continuous trend? > Two different inclination distributions (Brown, 2001). > High i objects are larger than low i objects (Levison & Stern, 2001) > Best cutoff between cold population (red cluster) and hot population (diverse colors): > Using Squared Ranks Test: i=4.5 (Peixinho et al. 2004)

31 >>> The Complexity of Classical Objects >> Hot and Cold, true compositional diversity? Two continuous blocks? > Two different inclination distributions (Brown, 2001). > High i objects are larger than low i objects (Levison & Stern, 2001) > Best cutoff between cold population (red cluster) and hot population (diverse colors): > Using Squared Ranks Test: i=4.5 (Peixinho et al. 2004)

32 >> Color, perihelion and size > Cluster of red Classical objects at q> 40 AU (Tegler & Romanishin, 2000).

33 >> Color, perihelion and size > Cluster of red Classical objects at q> 40 AU (Tegler & Romanishin, 2000).

34 >> Color, perihelion and size > Color-q correlation for Classical objects: > Peixinho et al. (2004): ρ=0.55 (CL>99.9%) > Doressoundiram et al. (2005): ρ=0.65 (CL>99.9%)

35 >> Large and small: two different behaviors? Small Large > The color-q correlation seems size dependent (Peixinho et al. 2004): > HR<6.2 (>220 km, pr=0.09) ρ=0.83 (CL>99.9%) > HR>6.2 (<220 km pr=0.09) ρ=0.48 (CL=98.4%)

36 >> The return of the Collisional resurfacing > Collisional resurfacing with triggered cometary activity (Delsanti et al. 2004) Origin Reddening Collision Activity Resurfacing > Adapted from Delsanti (2004)

37 >> The return of the Collisional Resurfacing > It considers the heliocentric distances for sublimations of several ices and, crust thickness as activity inhibitor and collisions. > It accounts for critical radius to maintain bound comae leading to homogeneous resurfacing. Objects larger than km can maintain bound comae at 50 AU. > Delsanti et al. (2004) Heliocentric Distance [AU]

38 >> Large and small: two different behaviors revisited Small Large

39 >> Large and small: two different behaviors revisited > The size dependence of the color-q correlation was not due to larger error bars for smaller objects at a CL= 99.0%. However: > HR<6.2 (N=14) ρ=0.83 ; σρ=0.35 CI=[0.48:1] > HR>6.2 (N=28) ρ=0.48 ; σρ=0.21 CI=[0.27:0.69] > The confidence level of difference between these ρs is only 39% > Consequently, there is no mathematical evidence for such difference.

40 >> Large and small: two different behaviors revisited > Data points to a color-h (size) frontier (Doressoundiram et al. 2006). For objects brighter than 7.5 maximum colors allowed decrease with decreasing H magnitude. > Note that the 6 plutinos with H>7 do not violate the bimodality: > is bimodality related with sized and with cis-neptunian orbits?

41 >> Large and small: two different behaviors revisited Frontier Frontier Bimodality Gap > Data points to a color-h (size) frontier (Doressoundiram et al. 2006). For objects brighter than 7.5 maximum colors allowed decrease with decreasing H magnitude. > Note that the 6 plutinos with H>7 do not violate the bimodality: > is bimodality related with sized and with cis-neptunian orbits?

42 >> Large and small: two different behaviors revisited Frontier Frontier Bimodality Gap > Data points to a color-h (size) frontier (Doressoundiram et al. 2006). For objects brighter than 7.5 maximum colors allowed decrease with decreasing H magnitude. > Note that the 6 plutinos with H>7 do not violate the bimodality: > is bimodality related with sized and with cis-neptunian orbits?

43 >>> Comparing Families > The question of the origins of the several dynamical groups of TNOs and their presumably related populations is still an open debate. > Identifying the color distribution compatibilities/incompatibilities between each population is a step forward to establish their genetic links.

44 >>> Comparing Families >> The dynamical classification problem > No clear separation between Classical and SDOs > Classif. I: q sep =35 AU [Torbett & Smoluchowski (1990)] > Classif. II: q sep =39 AU [Kuchner et al. (2002) : simplified]

45 >>> Comparing Families >> The dynamical classification problem > No clear separation between Classical and SDOs Classif. I > Classif. I: q sep =35 AU [Torbett & Smoluchowski (1990)] > Classif. II: q sep =39 AU [Kuchner et al. (2002) : simplified]

46 >>> Comparing Families >> The dynamical classification problem > No clear separation between Classical and SDOs Classif. I > Classif. I: q sep =35 AU [Torbett & Smoluchowski (1990)] > Classif. II: q sep =39 AU [Kuchner et al. (2002) : simplified]

47 >>> Comparing Families >> The dynamical classification problem > No clear separation between Classical and SDOs Classif. I Classif. II > Classif. I: q sep =35 AU [Torbett & Smoluchowski (1990)] > Classif. II: q sep =39 AU [Kuchner et al. (2002) : simplified]

48 >>> Comparing Families > Doressoundiram et al. (2005), using Kruskal-Wallis tests compared V-R colors of: > Irregular satellites, SPCs, SDOs, Classical, Plutinos.

49 >>> Comparing Families > Doressoundiram et al. (2005), using Kruskal-Wallis tests compared V-R colors of: > Irregular satellites, SPCs, SDOs, Classical, Plutinos.

50 >>> Comparing Families > Doressoundiram et al. (2005), using Kruskal-Wallis tests compared V-R colors of: > Irregular satellites, SPCs, SDOs, Classical, Plutinos.

51 >>> Comparing Families > Doressoundiram et al. (2005), using Kruskal-Wallis tests compared V-R colors of: > Irregular satellites, SPCs, SDOs, Classical, Plutinos.

52 >>> Comparing Families > Obtaining: > Irregular satellites compatible with SPCs and SDOs > SPCs marginally compatible with SDOs > All others are mutually compatible

53 >>> Some open questions > How to explain the color diversity? > Primordial differences? > Surface alteration models? > Both combined? > Why are Centaurs bimodal? > Dual origin? > Surface processing effects? > Classical separate in two distinct populations: > Is the color-i correlation a continuous trend or an effect of two different blocks? > Can a different classification scheme erase all correlations?

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57 >> Why is everything so controversial? > Critical Rationalism: > Karl Raimund Popper ( ): > Scientific theories are universal in nature, and can be tested only indirectly, by reference to their implications.

58 >> Why is everything so controversial? > Critical Rationalism: > Karl Raimund Popper ( ): > Scientific theories are universal in nature, and can be tested only indirectly, by reference to their implications. > Anarchist view of science: > Paul Karl Feyerabend ( ): > No interesting theory is ever consistent with all the relevant facts. > New theories came to be accepted not because of their accord with scientific method, but because their supporters made use of any trick rational, rhetorical or ribald in order to advance their cause.

59 >> Why is everything so controversial? > Critical Rationalism: > Karl Raimund Popper ( ): > Scientific theories are universal in nature, and can be tested only indirectly, by reference to their implications. > Anarchist view of science: > Paul Karl Feyerabend ( ): > No interesting theory is ever consistent with all the relevant facts. > New theories came to be accepted not because of their accord with scientific method, but because their supporters made use of any trick rational, rhetorical or ribald in order to advance their cause. > Postmoderns: > The true seat of power is wherever the knowledge is being controlled. > All knowledge is merely a discourse, no knowledge is different from any other as they are all legitimized by the same processes.