Here we measure the absolute magnitude distributions ( H-distribution ) of the dynamically excited and quiescent ( hot and cold ) Kuiper Belt objects ( KBOs ) , and test if they share the same H-distribution as the Jupiter Trojans .
From a compilation of all useable ecliptic surveys , we find that the KBO H-distributions are well described by broken power-laws .
The cold population has a bright-end slope , \alpha _ { \textrm { 1 } } = 1.5 _ { -0.2 } ^ { +0.4 } , and break magnitude , H _ { \textrm { B } } = 6.9 _ { -0.2 } ^ { +0.1 } ( r ’ -band ) .
The hot population has a shallower bright-end slope of , \alpha _ { \textrm { 1 } } = 0.87 _ { -0.2 } ^ { +0.07 } , and break magnitude H _ { \textrm { B } } = 7.7 _ { -0.5 } ^ { +1.0 } .
Both populations share similar faint end slopes of \alpha _ { 2 } \sim 0.2 .
We estimate the masses of the hot and cold populations are \sim 0.01 and \sim 3 \times 10 ^ { -4 } \mbox { M$ { } _ { \bigoplus } $ } .
The broken power-law fit to the Trojan H-distribution has \alpha _ { \textrm { 1 } } = 1.0 \pm 0.2 , \alpha _ { \textrm { 2 } } = 0.36 \pm 0.01 , and H _ { \textrm { B } } = 8.3 .
The KS test reveals that the probability that the Trojans and cold KBOs share the same parent H-distribution is less than 1 in 1000 .
When the bimodal albedo distribution of the hot objects is accounted for , there is no evidence that the H-distributions of the Trojans and hot KBOs differ .
Our findings are in agreement with the predictions of the Nice model in terms of both mass and H-distribution of the hot and Trojan populations .
Wide field survey data suggest that the brightest few hot objects , with H _ { \textrm { r' } } \lesssim 3 , do not fall on the steep power-law slope of fainter hot objects .
Under the standard hierarchical model of planetesimal formation , it is difficult to account for the similar break diameters of the hot and cold populations given the low mass of the cold belt .