Elaboration of a model for planetary formation in the hydrodynamic magneto code FARGO3D

Author(s)

Luiz Alberto de Paula

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto Astronômico e Geofísico (IAG/SBD)
• Defense date: 2018-09-26

Examining board members

Tatiana Alexandrovna Michtchenko; André Izidoro Ferreira da Costa; Octavio Miguel Guilera; Pablo Benitez Llambay; Eduardo Janot Pacheco; Fernando Virgilio Roig

• Advisor: Tatiana Alexandrovna Michtchenko

Abstract

According to the sequential model of accretion, the giant planets are formed from a solid nucleus by capturing planetesimals. When this nucleus reaches a certain mass, it captures the residual gas of the protoplanetary disc that will constitute its envelope, forming a giant planet (Mizuno, 1980; Pollack et al., 1996). The critical part of this scenario is to adjust the planet formation and migration timescales with the lifetime of the disk (Mordasini et al., 2010). Numerical results show that the time required for the formation of a giant planet is very long compared to the lifetime of the disc, and that planetary migration can be very rapid, causing the planets to fall into the star before their full formation. In general, works on planetary formation use analytical models to deal with the migration of the planets (Fortier et al., 2013). However, these analytical models are limited given that they do not include several effects associated with the thermodynamics of the gas disc (Paardekooper et al., 2010). Indeed, in order to deal with planetary migration of type I, these analytical models use physically simple gas discs and rely on the linearization of the hydrodynamic equations (Meyer-Vernet e Sicardy, 1987; Tanaka et al., 2002). For the type II migration, the situation is even more complicated. This is due to the fact that the large mass of the planet creates a gap around the orbit of the planet, causing nonlinearities (Bryden e Lin, 1999). Thus, the numerical results obtained using hydrodynamic simulators, such as FARGO3D (Masset, 2000; Bentez-Llambay e Masset, 2016), ZEUS (Stone e Norman, 1992), PLUTO (Mignone et al., 2012), among others, are essential for a more robust analysis of the processes of planetary migration considering a wider range of physical conditions for the gas disc. However, in general, hydrodynamic simulators do not have a model for the planetaryformation. In some of them, models for gas accretion are built based of the runaway regime of accretion (Kley, 1999). Furthermore, the accretion of solids and the accretion of gas for low mass planets are not considered in most of the cases. This is mainly due to the fact that the models of planetary formation use N-body simulations that are computationally very expensive. Thus, it is necessary to use alternative models for the planetary formation, that are capable of reproducing the same results of an N-body simulation. Building a complete model that takes into account all these processes is a hard and challenging task. So, this project aims the implementation of a physically plausible scenario for a planetary formation inside the magneto-hydrodynamic code FARGO3D. For the accretion model we use the works by Guilera et al. (2010) and Fortier et al. (2013), which employ an statistical model to determine the accretion rate of planetesimals (Inaba et al., 2001). This model will be implemented for the first time in the FARGO3D code. It is now known that the accretion of peebles (material with size ranging from mm and cm) has a important impact on the planetary formation (Lambrechts e Johansen, 2014; Guilera, 2016; Johansen e Lambrechts, 2017), although cores with a few masses of the Earth have a planetary envelope that could destroy those pebbles, before they reach the nucleus (Venturini et al., 2015). In this thesis, we will only deal with the accretion of planetesimals, leaving the study of pebbles for future work. For the gas accretion, we use a modified model based on Kley (1999). The modifications aim to incorporate the Bondi radius (Bondi, 1952) to determine the accretion zone, the effect of the height of the disc and the frequency of accretion. The implemented modifications are based on the works by Dürmann e Kley (2015), Russell (2011) and Fortier et al. (2013). The adaptation in the gas accretion code to take into account a wider range of planetary masses was achieved using the Kelvin-Helmoltz timescale, according to the works by Ikoma et al. (2000) and Ida e Lin (2004b). To test the planetary formation model in FARGO3D, the standard simulation for the gas disc uses a bi-dimensional thin disc. The discs aspect ratio is h = 0.05 with a curvature factor of = 0.0. These values are consistent with the theory of thin dics and are used in most of the simulations for accretion discs (Bell et al., 1997; Frank et al., 2002). The disc is assumed to be locally isothermal and the viscosity of the disc is driven by the prescription from Shakura e Sunyaev (1973), with = 0.03. The disc model is simplified and important features, such as energy exchanges, may influence the process of planetary formation andmigration. However, it is a good initial model for a consistent test of the implemented model of planetary formation, which has an known analysical result. More complex cases will be explored in future work. With the newly implemented model for planetary formation, it was possible to simul- taneously study the planet formation and the planet migration using the hydrodynamic simulator. That is, we analyzed both the timescale for planetary formation and the timescale for the migration of the planet, and compared them for the parameters of the model. The analysis revealed that, for our disc model, the timescale of the growth rate of the planet remained lower than the migration timescale, even when the planet crossed the ice line, where there is less material available for solid accretion. Thus, for small planetesimals (1km radius) it was possible to obtain planets with masses of approximately 5 Jupiter masses in regions between 0.5 and 1 au, in nearly the same time as the lifetime of the disc. It is worth noting that this thesis presents a detailed description of how to implement the model for planetary formation in the FARGO3D, including an appendix with the commented code. The goal is to allow the reader to use this planet formation model to obtain new results both about the formation of exoplanetary systems and our Solar System, as well as use it in any relevant application. (AU)

• FAPESP's process: 14/00492-3 - Modeling the formation of giant planets
• Grantee: Luiz Alberto de Paula
• Support Opportunities: Scholarships in Brazil - Doctorate