The Deep Ecliptic Survey ( DES ) was a survey project that discovered hundreds of Kuiper Belt objects from 1998-2005 .
Extensive follow-up observations of these bodies has yielded 304 objects with well-determined orbits and dynamical classifications into one of several categories : Classical , Scattered , Centaur , or 16 mean-motion resonances with Neptune .
The DES search fields are well documented , enabling us to calculate the probability on each frame of detecting an object with its particular orbital parameters and absolute magnitude at a randomized point in its orbit .
The detection probabilities range from a maximum of 0.32 for the 3:2 resonant object 2002 ~ { } GF _ { 32 } to a minimum of 1.5 * 10 ^ { -7 } for the faint Scattered object 2001 ~ { } FU _ { 185 } .
By grouping individual objects together by dynamical classes , we can estimate the distributions of four parameters that define each class : semi-major axis , eccentricity , inclination , and object size .
The orbital element distributions ( a , e , and i ) were fit to the largest three classes ( Classical , 3:2 , and Scattered ) using a maximum likelihood fit .
Using the absolute magnitude ( H -magnitude ) as a proxy for the object size , we fit a power law to the number of objects vs . H magnitude for 8 classes with at least 5 detected members ( 246 objects ) .
The Classical objects are best fit with a power-law slope of \alpha = 1.02 \pm 0.01 ( observed from 5 \leq H \leq 7.2 ) .
Six other dynamical classes ( Scattered plus 5 resonances ) have consistent magnitude distributions slopes with the Classicals , provided that the absolute number of objects is scaled .
Scattered objects are somewhat more numerous than Classical objects , while there are only a quarter as many 3:2 objects as Classicals .
The exception to the power law relation is the Centaurs , which are non-resonant objects with perihelia closer than Neptune and therefore brighter and detectable at smaller sizes .
Centaurs were observed from 7.5 < H < 11 , and that population is best fit by a power law with \alpha = 0.42 \pm 0.02 .
This is consistent with a knee in the H-distribution around H = 7.2 as reported elsewhere ( 2 ; 12 ) .
Based on the Classical-derived magnitude distribution , the total number of objects ( H \leq 7 ) in each class are : Classical ( 2100 \pm 300 objects ) , Scattered ( 2800 \pm 400 ) , 3:2 ( 570 \pm 80 ) , 2:1 ( 400 \pm 50 ) , 5:2 ( 270 \pm 40 ) , 7:4 ( 69 \pm 9 ) , 5:3 ( 60 \pm 8 ) .
The independent estimate for the number of Centaurs in the same H range is 13 \pm 5 .
If instead all objects are divided by inclination into “ Hot ” and “ Cold ” populations , following Fraser et al .
( 12 ) , we find that \alpha _ { Hot } = 0.90 \pm 0.02 , while \alpha _ { Cold } = 1.32 \pm 0.02 , in good agreement with that work .