Limits on the number of primordial Scattered disc objects at Pluto mass and higher from the absence of their dynamical signatures on the present-day trans-Neptunian Populations

Today, Pluto and Eris are the largest and most massive Trans-Neptunian Objects (TNOs), respectively. They are believed to be the last remnants of a population of planetesimals that has been reduced by > 99 per cent since the time of its formation. This reduction implies a primordial population of hundreds or thousands of Pluto-mass objects, and a mass-number distribution that could have extended to hundreds of Lunas, dozens of Mars, and several Earths. Such lost protoplanets would have left signatures in the dynamics of the present-day Trans-Neptunian Populations, and we statistically limit their primordial number by considering the survival of ultra-wide binary TNOs, the Cold Classical Kuiper belt, and the resonant population. We find that if the primordial mass-number distribution extended to masses greater than Pluto (∼ 10^-3M_⊕), it must have turned downwards to be no more top-heavy than roughly equal mass per log size, a significant deviation from the distribution observed between 10^-5M_⊕ and 10^-3M_⊕. We compare these limits to the predicted mass-number distribution of various planetesimal and protoplanet growth models. The limits derived here provide a test for future models of planetesimal formation.