Paper Abstract (abridged):  

This study aims to identify the profile of a typical system that harbours an ELP by investigating the architecture of systems and the properties of their innermost detectable planets. Here, we introduce a novel method for determining the architecture of planetary systems and categorising them into four distinct classes. We then conduct a statistical study to identify the most favourable arrangements for the presence of an ELP. Methods. Using three populations of synthetic planetary systems generated using the Bern model around three different types of stars, we studied the 'theoretical' architecture (the architecture of a complete planetary system) and the 'biased' architecture (the architecture of a system in which only detectable planets are taken into account after applying an observation bias) of the synthetic systems. To describe a typical system hosting an ELP, we initially examined the distribution of ELPs across different categories of architectures, highlighting the strong link between planetary system architecture and the presence of an ELP. A more detailed analysis was then conducted, linking the biased architecture of a system with the physical properties of its innermost observable planet to establish the most favourable conditions for the presence or absence of an ELP in a system.

We show in this paper that the detections of ELPs can be predicted thanks to the already known properties of their systems, and we present a list of the properties of the systems most likely to host such a planet.

Paper Abstract: In the first paper of this series (see below), we proposed a model-independent framework for characterising the architecture of planetary systems at the system level. There are four classes of planetary system architecture: similar, mixed, anti-ordered, and ordered. In this paper, we investigate the formation pathways leading to these four architecture classes. To understand the role of nature versus nurture in sculpting the final (mass) architecture of a system, we apply our architecture framework to synthetic planetary systems - formed via core-accretion - using the Bern model. General patterns emerge in the formation pathways of the four architecture classes. Almost all planetary systems emerging from protoplanetary disks whose initial solid mass was less than one Jupiter mass are similar. Systems emerging from heavier disks may become mixed, anti-ordered, or ordered. Increasing dynamical interactions (planet-planet, planet-disk) tends to shift a system's architecture from mixed to anti-ordered to ordered. Our model predicts the existence of a new metallicity-architecture correlation. Similar systems have very high occurrence around low-metallicity stars. The occurrence of the anti-ordered and ordered classes increases with increasing metallicity. The occurrence of mixed architecture first increases and then decreases with increasing metallicity. In our synthetic planetary systems, the role of nature is disentangled from the role of nurture. Nature (or initial conditions) pre-determines whether the architecture of a system becomes similar; otherwise nurture influences whether a system becomes mixed, anti-ordered, or ordered. We propose the `Aryabhata formation scenario' to explain some planetary systems which host only water-rich worlds. We finish this paper with a discussion of future observational and theoretical works that may support or refute the results of this paper.

Paper Abstract: We present a novel, model-independent framework for studying the architecture of an exoplanetary system at the system level. This framework allows us to characterise, quantify, and classify the architecture of an individual planetary system. Our aim in this endeavour is to generate a systematic method to study the arrangement and distribution of various planetary quantities within a single planetary system. We propose that the space of planetary system architectures be partitioned into four classes: similar, mixed, anti-ordered, and ordered. We applied our framework to observed and synthetic multi-planetary systems, thereby studying their architectures of mass, radius, density, core mass, and the core water mass fraction. We explored the relationships between a system's (mass) architecture and other properties. Our work suggests that: (a) similar architectures are the most common outcome of planet formation; (b) internal structure and composition of planets shows a strong link with their system architecture; (c) most systems inherit their mass architecture from their core mass architecture; (d) most planets that started inside the ice line and formed in-situ are found in systems with a similar architecture; and (e) most anti-ordered systems are expected to be rich in wet planets, while most observed mass ordered systems are expected to have many dry planets. We find, in good agreement with theory, that observations are generally biased towards the discovery of systems whose density architectures are similar, mixed, or anti-ordered. This study probes novel questions and new parameter spaces for understanding theory and observations. Future studies may utilise our framework to not only constrain the knowledge of individual planets, but also the multi-faceted architecture of an entire planetary system. We also speculate on the role of system architectures in hosting habitable worlds.

Paper Abstract: Planet formation models now often consider the formation of planetary systems with more than one planet per system. This raises the question of how to represent planetary systems in a convenient way (e.g. for visualisation purpose) and how to define the similarity between two planetary systems, for example to compare models and observations.
We define a new metric to infer the similarity between two planetary systems, based on the properties of planets that belong to these systems. We then compare the similarity of planetary systems with the similarity of protoplanetary discs in which they form.

We first define a new metric based on mixture of Gaussians, and then use this metric to apply a dimensionality reduction technique in order to represent planetary systems (which should be represented in a high-dimensional space) in a two-dimensional space. This allows us study the structure of a population of planetary systems and its relation with the characteristics of protoplanetary discs in which planetary systems form.
We show that the new metric can help to find the underlying structure of populations of planetary systems. In addition, the similarity between planetary systems, as defined in this paper, is correlated with the similarity between the protoplanetary discs in which these systems form. We finally compare the distribution of inter-system distances for a set of observed exoplanets with the distributions obtained from two models: a population synthesis model and a model where planetary systems are constructed by randomly picking synthetic planets. The observed distribution is shown to be closer to the one derived from the population synthesis model than from the random systems.
The new metric can be used in a variety of unsupervised machine learning techniques, such as dimensionality reduction and clustering, to understand the results of simulations and compare them with the properties of observed planetary systems.