Hydrodynamic Outcomes. Transitional Discs. of Planet Scattering in. Nick Moeckel IoA. Phil Armitage Colorado

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1 Hydrodynamic Outcomes of Planet Scattering in Transitional Discs Nick Moeckel IoA Phil Armitage Colorado

2 Messy Transitional Dynamics Hydro to Gravitational transition HR 8799 Marois+ HST imaging of Orion

3 Messy Dynamics Question: what happens planet-planet to scattering outcomes in a Mon. Not. R. Astron. Soc. (211) doi:1.1111/j x Hydrodynamic outcomes of planet scattering in transitional discs Nickolas Moeckel 1 and Philip J. Armitage 2,3 1 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 HA 2 JILA, 44 UCB, University of Colorado, Boulder, CO , USA 3 Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 839, USA Accepted 211 August 25. Received 211 August 24; in original form 211 August 1 ABSTRACT Asignificantfractionofunstablemultipleplanetsystemsarelikelytoscatterduringthe transitional disc phase as gas damping becomes ineffectual. Using a large ensemble of FARGO hydrodynamic simulations and MERCURY N-body integrations, we directly follow the dynamics of planet disc and planet planet interactions through the clearing phase and through 5 Myr of planetary system evolution. Disc clearing is assumed to occur as a result of X-ray-driven photoevaporation. We find that the hydrodynamic evolution of individual scattering systems is complex, and can involve phases in which massive planets orbit within eccentric gaps, or accrete directly from the disc without a gap. Comparing the results to a reference gas-free model, we find that the N-body dynamics and hydrodynamics of scattering into one- and two-planet final states are almost identical. The eccentricity distributions in these channels are almost unaltered by the presence of gas. The hydrodynamic simulations, however, also form a population of low-eccentricity three-planet systems in long-term stable configurations, which are not found in N-body runs. The admixture of these systems results in modestly lower eccentricities in hydrodynamic as opposed to gas-free simulations. The precise incidence of these three-planet systems is likely a function of the initial conditions; different planet setups (number or spacing) may change the quantitative character of this result. We analyse the properties of surviving multiple planet systems, and show that only a small fraction (a few per cent) enter mean motion resonances after scattering, while a larger fraction form stable resonant chains and avoid scattering entirely. Our results remain consistent with the hypothesis that exoplanet eccentricity results from scattering, though the detailed agreement between observations and gas-free simulation results is likely coincidental. We discuss the prospects for further tests of scattering models by observing planets or non-axisymmetric gas structure in transitional discs. Key words: hydrodynamics scattering planets and satellites: dynamical evolution and stability planet disc interactions protoplanetary discs planetary systems. gas disk? 1 INTRODUCTION Prior to gap opening, gravitational interactions between planets and their surrounding gas discs act to efficiently damp planetary ec- 1996; Lin & Ida 1997). Extensive N-body experiments have shown that with realistic mass functions, the dynamics of unstable twoplanet (Ford & Rasio 28), three-planet (Chatterjee et al. 28) or richer systems (Jurić&Tremaine 28)can successfullyreproduce

4 exoplanets in a and e Semi-major axis [AU] Eccentricity from Hanno Rein s ios app Semi-major axis [AU] 1 cumulative fraction eccentricity

5 dynamical origin of eccentricities Instability in multi-planet systems yields ejection, mergers, eccentricity Rasio & Ford 1996 Weidenschilling & Marzari 1996 Lin & Ida 1997 with realistic mass spectrum, excellent agreement to observations n = 2 n = 3 n = 1+ Ford & Rasio 28 Chatterjee+ 28 Juric & Tremaine 28

6 what about the disc? 1D 1 5 Log (Density) at t = 5133yrs 2D Marzari+ 21 y -5 Moeckel x 3D Matsumura+ 21, Chatterjee+ 28

7 hydro X-ray photoevaporation prescription (Owen+) to gravity FARGO (Masset) with modifications MERCURY (Chambers)

8 disc and au 5 MJ Owen+ 211 planet setup Surface Density [g cm ] g cm -2.2 g cm -2 ~1 5 yr Radius [AU].3 5. MJ, f(m) ~ m -1.1 aj = ai + 4 RHij RHij = ( mi + mj) 3Mo 1/3 ai + aj 2

9 disc mass evolution 5 disc mass M J time yr

10 collision example

11 1 15 yr yr 2 another collision example 15 yr a AU 1 mass M J eccentricity disk mass M J time years time years

12 instability outcomes disc lifetime after 5 Myr N N tot disc no disc not stable n p 3 n p 2 n p log t i yr disc no disc

13 eccentricity distributions significant differences triple when systems included cumulative fraction cumulative fraction 1..5 single and Hill stable double systems.3 disc no disc observed pks=.1 pad=.37 eccentricity N N tot.2.1 all scattered systems.3 pks<1-3 pad<1-3 disc no disc observed eccentricity N N tot eccentricity eccentricity

14 scattered and circularized not stable n p n p disc no disc n p x x a AU a AU

15 1 135 yr yr 2 scattered and circularized 57 yr a AU 1 mass M J eccentricity disk mass M J time years time years

16 φ 1, φ 2, ϖ 2 ϖ 1 2 Π Π 2 Π Π 6:3:2 middle inner: 3: Π Π outer middle: 2:1 outer inner: 3: triple resonance example 27 out of 1 never scattered 6 of these have two planets in MMR 12 are in triple resonance 2 Π 2Λ 1 4Λ 2 2Λ 3 φ L Π time years

17 conclusions modestly lower eccentricities when gas included ICs that yield good observational agreement with no gas no longer work as well. 1 and 2 planet outcomes similar to gas-free case- addition of 3 planet outcomes is the difference. however: difference comparable to what you see using different mass functions. IC tuning to reach agreement seems likely. resonance outcomes may be a more sensitive probe fewer 2 body resonances than in previous work, lots of 3 body chains. uncertainties in resonance disruption need to be resolved

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