A carefully characterised and tracked Trans-Neptunian survey, the size-distribution of the Plutinos and the number of Neptunian Trojans

The Trans-Neptunian Objects (TNOs) may preserve evidence of planet building in their orbital and size-distributions. While all populations show steep size-distributions for large objects, recently relative deficit of Neptunian Trojans and scattering objects with diameters $D<100\,\mathrm{km}$ were detected. We have investigated this deficit with a 32 square degree survey, detecting 77 TNOs to a limiting $r$-band magnitude of 24.6. Our Plutinos sample (18 objects in 3:2 mean motion resonance with Neptune) also shows a deficit of $D<100\,\mathrm{km}$ objects. We reject a single power-law size-distribution and find that the Plutinos favour a divot. The Plutinos are thus added the list of populations with a deficit of $D<100\,\mathrm{km}$ objects. The fact that three independent samples of three different populations show this trend suggests that it is a real feature, possibly shared by all hot TNO populations as a remnant of "born big" planetesimal formation processes. We surmise the existence of $9000\pm3000$ Plutinos with $H_r\leq8.66$ and $37000^{+12000}_{-10000}$ Plutinos with $H_r\leq10.0$. Our survey also discovered one temporary Uranian Trojan, one temporary Neptunian Trojans and one stable Neptunian Trojan, from which we derive populations of $110^{+500}_{-100}$, $210^{+900}_{-200}$ and $150^{+600}_{-140}$ , respectively, with $H_r\leq10.0$. The Neptunian Trojans are thus less numerous than the main belt asteroids, which has over 700 asteroids with $H_r\leq10.0$. With such numbers, the temporary Neptunian Trojans cannot be previously stable Trojans that happen to be escaping the resonance now; they must be captured from another reservoir. With three 3:1 and one 4:1 resonators, we add to the growing evidence that the high-order resonances are more populated than expected.