Takayuki TanigawaIchinoseki College, National Institute of Technology, Japan

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Retrograde flow around a low-mass planet is possible.

Retrograde flow affects planet migration.

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Kley 1999Tanigawa & Watanabe 2002

Szulágyi et al. 2014

Lots of simulations showed that gas motion around a planet is prograde. Miki 1982 (2D, local) Sekiya et al. 1987 (3D, global, SPH, #3 × 104) Kley 1999 (2D, global) D’Angelo et al. 2002 (2D, global, nested) Tanigawa & Watanabe 2002 (2D, local) Szulágyi et al. 2014 (3D, global, nested)

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Miki 1982

Colioris force (or equivalently, angular momentum conservation)

◦ Converging flow in a rotating frame Similar to tropical cyclone

en.wikipedia.org

Geostrophic windAccretion flow

−𝛻𝛻𝑃𝑃/𝜌𝜌−𝛻𝛻𝛻

D’Angelo et al. 20024

Prograde as long as the gas moving inward◦ = gas accretion phase

How about low-mass planets?◦ No significant gas accretion◦ No converging flow◦ => not necessarily prograde?

Is retrograde flow impossible?◦ Possible! Lambrechts & Lega 2017 Cimerman 2018 (private communication yesterday)

Lambrechts & Lega 2017

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I would like to share our retrograde flow Done in 1998! Unpublished...

◦ How is the flow look like?◦ Recipe

I would like to discuss ◦ Feasibility of retrograde flow around a planet◦ Effects on the planet formation scenario

Notice in advance...◦ I cannot answer all the details of the simulation because.. The calculation data was lost, and the source code as well ...

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Numerical setup◦ 2D, local (shearing sheet approximation)◦ ZEUS-2D code◦ Isothermal equation of state◦ Cartesian coordinate

Conditions◦ Low-mass (a few tens of Earth masses)

𝑐𝑐𝑟𝑟𝐻𝐻Ω𝐾𝐾

~ 1.8, 2.4◦ No sink at the planet◦ Special initial condition

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Retrograde flowPrograde flow

Rotating beyond the Hill sphere No notable horse-shoe region Wide high-density region

Rotating in the Hill sphere Typical horse-shoe flow Typical density wave

𝑐𝑐𝑟𝑟𝐻𝐻Ω𝐾𝐾

~ 1.8

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“Special” initial conditionInitial condition “Usual” initial condition

• Pure Keplerian shear• Uniform surface density• Not artificial?

• x10 higher density in the Hill radius• Retrograde rotation• Looks very artificial

cf.

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Recycling?◦ This would affect the recycling manner of the

atmosphere. Migration of low-mass planets◦ Structure of the spiral arms are totally different Gravitational torque on the planet from the arms should be

different Migration velocity should also be different

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Natural initial conditions?

Stability?◦ Stable for, at least, a few tens of orbits. Stabilized by the diffusive code (ZEUS-2D)?

◦ Global effect? We did not find the retrograde flow by our

preliminary global test simulation

3D effect?◦ Gas inflow from the pole and outflow

through the midplane tends to produce retrograde motion? more feasible?

Kurokawa & Tanigawa 2018, submittedCimerman et al. 2017 11

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Lambrechts & Lega found!◦ Although the density profile is different...

Recent 3D simulations◦ Outflow in the midplane

Viscosity with the Keplerian shear Giant impacts◦ Heat the atmosphere suddenly, which may provide a

similar initial condition? Epicyclic motion of the planet in a protoplanetary

disk makes retrograde flow?◦ When the planet is in an eccentric orbit.

Similar motion in particle orbits

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The flow becomes prograde easily.

timesink start

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Particle orbit Gas flow

• Much larger than the Hill sphere • About the Hill radius in x-direction

Suetsugu, Ohtsuki & Tanigawa 2011

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Temporary capture of planetesimals◦ 4 types of orbits Type A: prograde Type R: prograde Type H: prograde Type E: retrograde Rotating beyond the

Hill sphere

Prograde Prograde

Prograde Retrograde

Suetsugu, Ohtsuki & Tanigawa 2011

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Vortices in disks by Rossby wave instability?

17rx

Li et al. 2001