2.5 Analysis
2.5.2 Trends with Inclination
This principal component may now be compared to other physical and orbital parameters associated with these objects in order to explore potential trends that might explain the origin and evolution of the swarms. Roig et al. (2008) found a correlation of inclination, absolute magnitude, and spectral slope among Jupiter Trojans in the SDSS MOC. They claim that both swarms trend towards redder objects being larger and having higher orbital inclinations. As all of the objects in this survey are relatively large compared to most of the objects in the MOC, we examine if this trend holds true for inclination. Figure 2.12shows
a˚
T as a function of inclination for both the L4 Greeks presented here and the MOC4 sample.
Only known L4 Jupiter Trojans with qualitygriz photometric data were used for the MOC4 sample, resulting in 167 objects. Figure 2.13 shows the same, but for the L5 camp and with 232 objects from the MOC4. The Lupton (2005) conversion equations (Equation 2.3through
Equation 2.6) from the SDSS website6
were used to calculate a˚ T. B “g`0.3130˚ pg´rq `0.2271 (2.3) V “g´0.5784˚ pg´rq ´0.0038 (2.4) R “r´0.2936˚ pr´iq ´0.1439 (2.5) 6 http://classic.sdss.org/dr4/algorithms/sdssUBVRITransform.html#Lupton2005
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-0.2
-0.1
0.0
0.1
0.2
0.3
a*
T0
10
20
30
40
Inclination (
o)
L4
Figure 2.12: Principal component a˚
T (Equation 2.2) plotted for converted SDSS MOC4
L4 Greeks (small black points) as well as the photometric data presented for L4 Greeks in this work (larger dots with blue error bars) against the orbital inclination in degrees for these objects. Unlike the L5 data shown inFigure 2.13, high inclination, less-red X-type and C-type objects with a˚
T less than 0 are not seen in the Greek camp.
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-0.2
-0.1
0.0
0.1
0.2
0.3
a*
T0
10
20
30
40
Inclination (
o)
L5
Figure 2.13: Principal component a˚
T (Equation 2.2) plotted for converted SDSS MOC4
L5 Trojans (small black points) as well as the photometric data presented for L5 Trojans in this work (larger dots with red error bars) against the orbital inclination in degrees for these objects. Fewer high inclination, less-red X-type and C-type objects with a˚
T less than 0 are
seen among the MOC4 objects than among the Trojans observed here.
The lack of high inclination, less-red7
objects apparent in the MOC4 sample appears to be present in our L4 Greek population, but is not obvious in the larger L5 objects used for this survey. As can be seen from Figure 2.14, when the two camps are combined less-red
7
Here we use the terms “less-red” in the style ofEmery et al.(2011) to describe the bluer X- and C-type Jupiter Trojans as none of these objects are truly blue and are indeed quite red compared to many other Solar System objects.
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X- and C-type objects seem to be lacking in our sample at all inclinations compared to the MOC4 sample (SDSS Trojans inFigure 2.14). A cutoff of 11˝ was used to separate high
inclination objects from low inclination objects because this value cuts the population roughly in half. The two-sample Kolmogorov-Smirnov test (KS test) gives the probability that two samples could be randomly drawn from the same parent sample by evaluating the maximum difference between the cumulative distribution functions of each sample and accounting for sample size. This statistic indicates a small probability8
(5.4%) that the high and low inclination populations in the L5 MOC4 data are drawn from the same underlying color distribution. We find an even smaller probability for the L4 MOC4 data. However, the same statistical test finds no such distinction for the sample provided in this work (labelled “Large Trojans” inFigure 2.14). Not only is no statistical difference found between the high and low inclination Large Trojan populations, but also there is not any significant difference between the high inclination Large Trojans and the equivalent population from the MOC4 sample. However, when both camps were combined, there is a significant difference (6.2% probability of being drawn from like samples) between the profiles of the MOC4 and Large Trojans at inclinations below 11˝. In other words, we show no significant difference between the entire
sample of Large Trojans presented here and the high inclination population of somewhat smaller objects in MOC4, but we do see a significant probability that this population of large objects is distinct from the low inclination objects found in MOC4. This might imply two different populations, one that is very red, at high inclinations, and containing most of
8
The two sample KS test results in a P value representative of the similarity between the two samples. By convention P values less than 0.05 are considered “significant”, but there is no quantitative reason for this convention. Since high numbers (here considered to be significantly larger than 5%) are nondiagnostic, we only report P values less than 10%.
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the largest objects in the camps, as well as a second, less-red population of smaller objects that is less scattered at low inclinations.
Both Roig et al. (2008) and Wong et al. (2014) tentatively hypothesize that the redder
D-types that dominate the higher inclinations in the MOC4 sample are older and therefore less likely to have experienced collisions than the more recently resurfaced or disrupted less- red, X- and C-type objects in the lower inclination Trojan orbits. Szab´o et al.(2007) suggest that a dynamical effect could increase weathering effects on the higher inclination objects. The similar color distributions for large high and low inclination Trojans from both camps shown here could support these hypotheses if a lack of disruptive events is what allows these large objects to survive and redden over time. This hypothesis is also supported by fact that more large Jupiter Trojans exist at high inclinations.
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-0.2
-0.1
0.0
0.1
0.2
0.3
a*
T0
10
20
30
Number (Inc. < 11
o)
0
10
20
30
Number (Inc. > 11
o)
SDSS Trojans
Large Trojans (H < 10.1)
Figure 2.14: Histograms of the SDSS MOC4 Jupiter Trojans (SDSS Trojans) and the larger
objects from both camps observed for this work (Large Trojans), both shown inFigure 2.12
and Figure 2.13, divided into roughly equal populations at an inclination of 11˝. The SDSS
population (black, dashed line) is clearly differentiated, with low inclination objects in the lower frame having a significantly disparate color distribution to that of high inclination objects (upper frame). The low and high inclination Large Trojan populations (solid, red line) are statistically indistinguishable from each other, but we find only a 6.2% probability that the low inclination Large Trojan and SDSS populations are sourced from the same parent population.
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