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Simulations of Planetesimal Accretion at Short Orbital Periods

Lynn Nguyen and Sarah Kahle

Spencer Wallace

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Formation of Planets

Size

Time

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Start with planetesimals, end with embryos

~100km

~1000km

process is pretty involved, but we simplified by just looking at the stages where planetesimals grow into embryos
base premise of our simulation = started with all planetesimals at same mass, watched as they grew, as they became larger and cleared orbits of other particles, mass became unevenly distributed, led to creation of larger embryos
one quick note: did not include gas drag, assumed it is more important in earlier stages. instead, assumed gravity = most important force governing planetesimal interactions

Sarah

starting with planetesimals, forming planetary embryos
quick stage in relation to rest of planet formation process
gravity is significant; gas is not
as planetesimals grow, some become larger and clear their orbits of other particles

uneven distribution of masses

efficient accretion

Notes from spencer:

Mention that gas drag is more important early on, before our simulation starts

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TRAPPIST-1 = case study

Our solar system vs. TRAPPIST-1’s system

TRAPPIST-1’s planets has shorter orbital periods
We are forming TRAPPIST-1 planets in place

What we want to know: The effects and reasoning as to how TRAPPIST-1 evolved differently to the solar system.

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The Simulation

Analyzed planetary accretion with n-body code ChaNGa

Vary the surface density of disk

Increased collision cross section

Speeds up growth for our purposes

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TRAPPIST-1 Embryos don’t settle into low-eccentricity orbits

Sun

TRAPPIST-1

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Earth: as embryos form, eccentricity decreases
TRAPPIST: as embryos form, eccentricity stays large
TRAPPIST planets have higher orbital velocity, so dynamical friction has less of an affect (vs. Earth)

Dynamical friction should cause embryos to cool

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Formation Time

Constant Final Eccentricity

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Embryo spacing is larger than expected

Hill radius = Gravitational influence

lynn

hill radius = gravitational influence

We are interested in the spacing in the embryos in units of the hill radius.
The hill radius is the little circle around the planet on the right side of the sun, the planet’s gravity is larger than the sun’s gravity.

Plot

Spacing between the embryos in units of the hill radius.
The H dash line is spacing of what everyone would be using; by 10 radi.
less surface density = more spaced out

Best fit slope eq on right: we have a more shallow slope usually it would be e^-1.

There’s some other dynamics going on that we don’t know about and should find and understand.

Notes from spencer:

Explain why we care about the spacing - this sets the initial conditions for late-stage accretion simulations

Q’s: why would we assume that is would be a flat line of 10?: this is what happens when embryos end up on the circular orbit is when you get the constant spacing. There’s an effect called orbital repulsion that effects on the spacing.

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A more massive disk makes more massive embryos

For reference, TRAPPIST-1 planets fall between 10^27 & 10^28 g on this plot

We don’t know what size embryos will form a planet.

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Conclusions

Ran set of planetary accretion simulations at low orbital periods around low mass star

Ineffective dynamical friction might be causing increased eccentricities
Hill radii spacing of embryos is larger than others assume of terrestrial exoplanets

Gas drag might be important
Fragmentation might be important
What is setting the spacing between embryos?