The color-magnitude distribution of small Jupiter Trojans

We present an analysis of survey observations targeting the leading L4 Jupiter Trojan cloud near opposition using the wide-field Suprime-Cam CCD camera on the 8.2 m Subaru Telescope. The survey covered about 38 deg$^2$ of sky and imaged 147 fields spread across a wide region of the L4 cloud. Each field was imaged in both the $g'$ and the $i'$ band, allowing for the measurement of $g-i$ color. We detected 557 Trojans in the observed fields, ranging in absolute magnitude from $H=10.0$ to $H = 20.3$. We fit the total magnitude distribution to a broken power law and show that the power-law slope rolls over from $0.45\pm 0.05$ to $0.36^{+0.05}_{-0.09}$ at a break magnitude of $H_{b}=14.93^{+0.73}_{-0.88}$. Combining the best-fit magnitude distribution of faint objects from our survey with an analysis of the magnitude distribution of bright objects listed in the Minor Planet Center catalog, we obtain the absolute magnitude distribution of Trojans over the entire range from $H=7.2$ to $H=16.4$. We show that the $g-i$ color of Trojans decreases with increasing magnitude. In the context of the less-red and red color populations, as classified in Wong et al. 2014 using photometric and spectroscopic data, we demonstrate that the observed trend in color for the faint Trojans is consistent with the expected trend derived from extrapolation of the best-fit color population magnitude distributions for bright catalogued Trojans. This indicates a steady increase in the relative number of less-red objects with decreasing size. Finally, we interpret our results using collisional modeling and propose several hypotheses for the color evolution of the Jupiter Trojan population.