Formation of terrestrial planets in disks with different surface density profiles

Abstract

We present the results of an extensive study of the final stage of terrestrial planet formation in disks with different surface density profiles and for different orbital configurations of Jupiter and Saturn. We carried out simulations in the context of the classical model with disk surface densities proportional to r −0.5 , r −1 and r −1.5 , and also using partially depleted, non-uniform disks as in the recent model of Mars formation by Izidoro et al (2014). The purpose of our study is to determine how the final assembly of planets and their physical properties are affected by the total mass of the disk and its radial profile. Because as a result of the interactions of giant planets with the protoplanetary disk, secular resonances will also play important roles in the orbital assembly and properties of the final terrestrial planets, we will study the effect of these resonances as well. In that respect, we divide this study into two parts. When using a partially depleted disk (Part 1), we are particularly interested in examining the effect of secular resonances on the formation of Mars and orbital stability of terrestrial planets. When using the disk in the classical model (Part 2), our goal is to determine trends that may exist between the disk surface density profile and the final properties of terrestrial planets. In the context of the depleted disk model, results of our study show that in general, the ν 5 resonance does not have a significant effect on the dynamics of planetesimals and planetary embryos, and the final orbits of terrestrial planets. However, ν 6 and ν 16 resonances play important roles in clearing their affecting areas. While these resonances do not alter the orbits of Mars and other terrestrial planets, they strongly deplete the region of the asteroid belt ensuring that no additional mass will be scattered into the accretion zone of Mars so that it can maintain its mass and orbital stability. In the context of the classical model, the effects of these resonances are stronger in disks with less steep surface density profiles. Our results indicate that when considering the classical model (Part 2), the final planetary systems do not seem to show a trend between the disk surface density profile and the mean number of the final planets, their masses, time of formation, and distances to the central star. Some small correlations were observed where, for instance, in disks with steeper surface density profiles, the final planets were drier, or their water contents decreased when Saturn was added to the simulations. However, in general, the final orbital and physical properties of terrestrial planets seem to vary from one system to another and depend on the mass of the disk, the spatial distribution of protoplanetary bodies (i.e., disk surface density profile), and the initial orbital configuration of giant planets. We present results of our simulations and discuss their implications for the formation of Mars and other terrestrial planets, as well as the physical properties of these objects...

Formation of Terrestrial Planets

“…This has become known as the "small Mars" problem and was first pointed out by Wetherill (1991). The small Mars problem is pervasive in simulations in which a) the giant planets are on low-eccentricity, low-inclination orbits, and b) the disk of terrestrial material follows a simple powerlaw profile with an r −1 to r −2 slope (O'Brien et al 2006;Raymond et al 2006bRaymond et al , 2009Morishima et al 2010;Izidoro et al 2014aIzidoro et al , 2015cFischer and Ciesla 2014;Kaib and Cowan 2015;Haghighipour and Winter 2016;Lykawka and Ito 2017;Bromley and Kenyon 2017).…”

Terrestrial Planet Formation: Dynamical Shake-up and the Low Mass of Mars

“…Jupiter's orbital eccentricity is key to dynamical shake-up. If the gas giant was as-sembled close to its current location, as in "classical" models (see Haghighipour & Winter 2016, and references therein), interactions with the gas disk produce a large enough eccentricity to drive a shake-up (Goldreich & Sari 2003;Duffell & Chiang 2015). In other scenarios, convergent migration leads to resonance trapping between Jupiter and Saturn (Masset & Snellgrove 2001;.…”

“…To illustrate the impact of dynamical shake-up on numerical simulations of planet formation, we consider a representative example designed to remove solid material at a 1.5 AU well before protoplanets reach the mass of Mars. From previous simulations of terrestrial planet formation with little dynamical depletion at 1.5-3 AU (e.g., Kenyon & Bromley 2006;Lunine et al 2011;Chambers 2013;Walsh & Levison 2016;Haghighipour & Winter 2016), giant impacts produce Mars-mass (Earth-mass) objects in 1-10 Myr (10-100 Myr). Radiometric analyses suggest Mars achieved most of its final mass in 3-5 Myr (Dauphas & Chaussidon 2011;Dauphas & Pourmand 2011).…”

“…As the disk's gravity fades, the location of this resonance sweeps inward, pumping the eccentricity of all objects in its path (Nagasawa et al 2005; Thommes et al 2008). This dynamical "shake-up" sculpts the inner solar system, leaving its imprint on Mars and the asteroid belt (O'Brien et al 2007;Nagasawa et al 2007;Haghighipour & Winter 2016).…”

The Mars anomaly

“…Pebble accretion avoids giant planet migration by tweaking the disk. Haghighpour and Othon Winter, from the University of São Paolo, have elaborated yet another explanation for Mars' small size using a model that alters the mass distribution in the initial disk (10).…”