Oort Cloud and sednoid formation in an embedded cluster, I: Populations and size distributions

In this paper we report on massive computer simulations aimed to clarify the formation of an Oort Cloud and the adjoining sednoid population during the earliest times of the solar system due to the perturbing effects of the Sun's birth aggregate, for which we use different embedded cluster models. We define the sednoid population to have semi -major axes between 100 and 1600 astronomical units, and it can be seen as the innermost extension of the Oort Cloud. By also restricting the orbits to perihelion distances exceeding 60 astronomical units, the sednoid population can be regarded as dynamically inert with respect to both planetary and Galactic influences. It includes the objects (90377) Sedna, 2012 VP 113 and (541132) Lele & aacute;ku<overline>honua. We start by creating 12 cluster models, using the NBODY6++GPU code, with three random realisations of four physically different models. In each of these we select six random solar template stars and equip those with a planetary system composed of Jupiter, Saturn and 4000 massless planetesimals representing a population of stray planetesimals in the Jupiter-Saturn zone with a total mass assumed to be about 20 Earth masses. From dynamical simulations of all these 72 variants of the early solar system including the cluster perturbations, we derive the total numbers and orbital characteristics of the sednoid and Oort Cloud populations, including the size distributions resulting from the limiting effects of solar nebula gas drag on extraction efficiency. We find that the predicted number of sednoids varies dramatically depending on the orbital evolution of the solar template star in the cluster. In general, numbers consistent with the existence of the observed sednoids is an expected outcome only for a birth aggregate with a strong central condensation and a relatively long lifetime of the residual gas, whereas other cluster models tend to fail to explain this. In the most successful, concentrated cluster models, we predict the existence of an as yet unseen population of at least 10 8 km -sized sednoids. However, we note that these cluster models produce an overheated inclination distribution at variance with the observed inclinations. Hence, we conclude that our study points to a possible, severe problem of the embedded cluster scenario in explaining the origin of the sednoids. The Oort Cloud predicted to originate in local, Jupiter-Saturn planetesimals by our simulations amounts to similar to 10 % of the estimated, current size of the entire Oort Cloud. This shows that such comets, likely characterised by Earth -like D/H ratios, may be a minority though a significant one. In an accompanying paper we discuss the extraction dynamics in some detail, based on the same simulations as here.