Rocks Go Wild: How to Make a Solar System

Title:  Constraining the Formation of the Four Terrestrial Planets in the Solar System

Authors: Patryk Sofia Lykawka and Takashi Ito

First Author’s Institution: School of Interdisciplinary Social and Human Sciences, Kindai University

Status: Published in ApJ, open access on ArXiv

Our Solar System is really unique. As far as we can tell after our first ~decade of exoplanet hunting and planet formation observations and theory, it’s quite the special snowflake . In order to answer one of the biggest questions in astronomy — “How did the Earth form?” — we first need to ask how our solar system formed. Our moon, Jupiter and Saturn, the asteroid belt, our Sun’s solar activity all provide hints as to how one can possibly form this incredibly habitable planet that we live on. Inspired by this, today’s bite answers the question: how did the terrestrial planets form? The authors argue that in order to fully understand the formation of one planet, we really should be thinking of its formation as one member of a system.

Simulating the Formation of Our Terrestrial Planets

The authors explore terrestrial planet formation through the medium of N-body simulations. They start with a number of embryos and planetesimals in a simulated solar environment. The embryos and planetesimals represent the large and small rocky bodies that are left over after gas dissipation of a protoplanetary disk, which is a remnant of stellar formation. We believe that our rocky/terrestrial planets are born out of collisions of these objects. The authors allow their simulated rocks to collide and interact with each other for a series of timesteps that equate to 400 million years. By that time, all of the planets will have formed and a stable system should be established. The authors create different initial distributions of the embryos and planetesimals that are inspired by different planet formation models, for example the Grand Tack model, Empty Asteroid Belt, and pebble accretion. They explore the mass ratios of embryos to planetesimals— i.e. which type of pre-solar body will carry the most mass. Is it mostly in the smaller pebble sided objects, or in the bolder sized objects?

Figure 1: The embryo (large circle) and planetesimal (small circle) mass and radial distribution derived to represent three different planet formation models: A normal distribution (top), Empty Asteroid Belt Model (middle), and pebble accretion (bottom). This figure is altered from Figure 1 in the original paper.

The authors also have different configurations of the gas giant planets which we believe should have mostly formed by the time terrestrial planets started to form. Their location and eccentricities would affect the movements of bodies within 2AU.  They run 540 different combinations of these initial contentions and let the rocks go wild. In addition to the final mass and location of the planets that form, they also keep track of the water mass fraction, which is the fraction of mass that water makes up on each planet. Water is transported to these planets via collisions. We know generally the water mass fraction of Mars and Venus, we know the value pretty darn well for Earth, and we really have no idea for Mercury. And finally they keep track of the giant impacts that each planet experiences. We believe our Moon came from a giant impact that happened early in the Earth’s formation. So for a simulated solar system to be an analog of our system, the planets should have similar water mass fractions and the correct number and timing of giant impacts.

Do you have what it takes to be a planet in the solar system??

Out of these 540 different solar systems, it’s time to find the systems that are most like our solar system. There are a few criteria  to narrow them down. They define the region within 2 AU of the star [where 1 AU is the distance of the Earth to the sun, today] as the planetary region, and outside of that is the asteroid belt. Are there at least three planets in the planetary region? Yes? Good. Moving on. Are there at least two that are Venus/Earth massed? Yeah? Fantastic. Next, you identify which planet-analog is Venus and Earth. Once that is determined we now have defined the Mercury and Mars regions inside of Venus and outside of the Earth locations, respectively. Next, are there planets in these regions that correspond to Mercury and Mars mass? Maybe there are multiple! If so, we determine which is going to be the planet analog by using its radial location from the sun. This team created the above checklist to begin to determine which planet systems were most like ours. In the end, they found only seventeen systems that were similar to our terrestrial planet system.

Figure 2: The 17 terrestrial systems that were deemed solar-system analogs. The simulation system 0 is our solar system. Green dots are Mercury, pink is Venus, blue is Earth, red is Mars, and black is the dwarf planet Ceres. The size of each dot corresponds to a mass, and the arrow represents inclination.

So what does all this tell us about how our solar system formed? Right away, it’s clear that it is difficult to form Mercury. Only 38 total Mercury analogs were formed, and most of them were still over two times the mass of Mercury. The disk models that formed the most Mercury-analogs typically had an ‘inner region,’ which meant there were embryos and planetesimals located very close to the sun at the beginning of their model run. They also saw that Mercury always formed too close to Venus.  The models did a pretty good job creating Venus and Earth— yay! However, they did not get enough water to Earth. In most of their simulations, Earth had a giant impact within 10 Myr, which is consistent with when we think our Moon was formed. Go moon! Mars analogs typically formed more massive than Mars really is, and often there were multiple Mars-like planets that formed nearby. 

The Ingredients to Make a Solar System

After synthesizing their results, the authors came down to five crucial criteria that are necessary to form the terrestrial planets:

  1. Disks need to start out with a concentration of total disk mass between ~0.7-1.2 AU — it helps form Venus AND Earth.
  2. Disks need an inner region ~0.3-0.4 AU in order to form my favorite planet: Mercury.
  3. Beyond 1.2 AU up to the asteroid belt  (~2AU), there needs to be significantly less mass. This aided in the production of dwarf planets in the asteroid belt and helped with the mass ratio between Venus and Earth
  4. The embryos (large boulder-y rocks) need to carry most of the mass of the disk, as opposed to planetesimals.
  5. Jupiter and Saturn need to be on eccentric orbits. This keeps the Mars-analog planet from getting too massive and chucks out any planets that meander over to the asteroid belt.

This paper aids our understanding of terrestrial planet formation and tests how well current planet formation theories can recreate Mercury, Venus, Earth, and Mars analogs. Some aspects, like the excess water we have on Earth, the orbital spacing, and inclination of the planets are still a mystery, but the authors do take us one step closer to understanding the uniqueness of our solar system.

About Jenny Calahan

Hi! I am a third year graduate student at the University of Michigan. I study protoplanetary disks, which set the stage for planet formation. For the past few years I've been using high resolution ALMA data to pull out the 2D thermal structure of different types of disks using thermo-chemical modeling. Outside of astronomy, I love belting showtunes, eating Thai food, I enjoy crafting, and I love to travel and explore new places. Check out my website: https://sites.google.com/umich.edu/jcalahan

1 Comment

  1. It’s a long, lonnng time ago, but I remember Icarus, then openly available on our city library shelves, reporting a brave simulation of planetary formation. Its algorithms were deprecated for producing scant few solar systems like ours, but a surprising number with gas-giants real-close to star. Now, we call such ‘Hot Jupiters’…

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