Revisiting equilibrium condensation and rocky planet compositions

Introducing the ECCOPLANETS code

¹ Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
e-mail: t.timmermann@stud.uni-goettingen.de
² Geowissenschaftliches Zentrum Abteilung Geochemie und Isotopengeologie, Goldschmidtstraße 1, 37077 Göttingen, Germany
³ Centre for Earth Evolution and Dynamics, University of Oslo, Sem Salands vei 2A ZEB-bygget 0371 Oslo, Norway

Received: 31 August 2022
Accepted: 13 June 2023

Abstract

Context. The bulk composition of exoplanets cannot yet be directly observed. Equilibrium condensation simulations help us better understand the composition of the planets’ building blocks and their relation to the composition of their host star.

Aims. We introduce ECCOPLANETS, an open-source Python code that simulates condensation in the protoplanetary disk. Our aim is to analyse how well a simplistic model can reproduce the main characteristics of rocky planet formation. For this purpose, we revisited condensation temperatures (T_c) as a means to study disk chemistry, and explored their sensitivity to variations in pressure (p) and elemental abundance pattern. We also examined the bulk compositions of rocky planets around chemically diverse stars.

Methods. Our T-p-dependent chemical equilibrium model is based on a Gibbs free energy minimisation. We derived condensation temperatures for Solar System parameters with a simulation limited to the most common chemical species. We assessed their change (∆T_c) as a result of p-variation between 10⁻⁶ and 0.1 bar. To analyse the influence of the abundance pattern, key element ratios were varied, and the results were validated using solar neighbourhood stars. To derive the bulk compositions of planets, we explored three different planetary feeding-zone (FZ) models and compared their output to an external n-body simulation.

Results. Our model reproduces the external results well in all tests. For common planet-building elements, we derive a T_c that is within ±5 K of literature values, taking a wider spectrum of components into account. The T_c is sensitive to variations in p and the abundance pattern. For most elements, it rises with p and metallicity. The tested pressure range (10⁻⁶ − 0.1 bar) corresponds to ∆T_c ≈ +350 K, and for −0.3 ≤ [M/H] ≤ 0.4 we find ∆T_c ≈ +100 K. An increase in C/O from 0.1 to 0.7 results in a decrease of ∆T_c ≈ −100 K. Other element ratios are less influential. Dynamic planetary accretion can be emulated well with any FZ model. Their width can be adapted to reproduce gradual changes in planetary composition.