Limits on the number of primordial Scattered Disk 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 respectively. They are believed to be the last remnants of a population of planetesimals that has been reduced by >99% 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 (~1e-3 Earth masses), 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 1e-5 and 1e-3 Earth masses. We compare these limits to the predicted mass-number distribution of various planetesimal and proto-planet growth models. The limits derived here provide a test for future models of planetesimal formation.