The dynamical evolution of transiting planetary systems including a realistic collision prescription

The dynamical evolution of transiting planetary systems including a realistic collision prescription Alexander James Mustill Melvyn B. Davies Anders Johansen MNRAS submitted, arxiv.org/abs/1708.08939

Alexander Mustill PLATO Mission Conference 2017-09-07 The Kepler Dichotomy: an excess of systems with a single transiting candidate Contribution to single-, double- and triple-candidate systems Reconstructed intrinsic multiplicities at different mutual inclinations Johansen et al 2012; see also Fang & Margot 2012, Ballard & Johnson 2016

The Kepler Dichotomy: explanations Alexander Mustill PLATO Mission Conference 2017-09-07

Alexander Mustill PLATO Mission Conference 2017-09-07 The Kepler Dichotomy: explanations Grinding down Unstable non-resonant systems (Pu & Wu 2015, Volk & Gladman 2015) Unstable resonant systems (Izidoro et al. 2017) Secular resonance sweeping (Spalding & Batygin 2016) Destabilisation by outer systems (Mustill et al 2017, Huang et al 2017)

Alexander Mustill PLATO Mission Conference 2017-09-07 The Kepler Dichotomy: explanations Grinding down Building up Unstable non-resonant systems (Pu & Wu 2015, Volk & Gladman 2015) Unstable resonant systems (Izidoro et al. 2017) Secular resonance sweeping (Spalding & Batygin 2016) Destabilisation by outer systems (Mustill et al 2017, Huang et al 2017) In situ embryo accretion (Hansen & Murray 2013, Moriarty & Ballard 2016) Other formation effects (number of cores/seeds, &c.)

Alexander Mustill PLATO Mission Conference 2017-09-07 What are the encounter velocities in unstable planetary systems? 10 0 = 10r H,mut, 10M 100 80 a2 [au] 10 1 60 40 v1 [km s 1 ] Pericentre velocity of outer planet Keplerian velocity of inner planet 10 2 10 2 10 1 10 0 a 1 [au] 20 0 This is a minimum: will be higher including z-components of velocity and gravitational focusing

Improving the collision treatment in the MERCURY N-body integrator

Improving the collision treatment in the MERCURY N-body integrator Improve the algorithm for detecting collisions: if close encounter detected, iteratively halve timestep. Need accurate impact parameter and velocity to know collision outcome. Improve the algorithm for resolving collisions: Low collision velocity: retain perfect merging. Large impact parameter, moderate velocity: hit-and-run impact. Geometrical approximation for mass shaved off. High velocity: disruptive or super-catastrophic impact. Scaling laws from Leinhardt & Stewart (2012). Modifications to allow for disparate densities. Treatment of collision fragments: two approximations: Instantaneous removal: mass lost in collision is removed from integration. Represents mass lost as small grains, removed by radiation forces Full retention: mass is distributed into super-particles. Fragment velocity distribution from Jackson & Wyatt (2012), scaled to planetary escape velocity. Represents mass lost as larger chunks.

Improving the collision treatment in the MERCURY N-body integrator Improve the algorithm for detecting collisions: if close encounter detected, iteratively halve timestep. Need accurate impact parameter and velocity to know collision outcome. Improve the algorithm for resolving collisions: Low collision velocity: retain perfect merging. Large impact parameter, moderate velocity: hit-and-run impact. Geometrical approximation for mass shaved off. High velocity: disruptive or super-catastrophic impact. Scaling laws from Leinhardt & Stewart (2012). Modifications to allow for disparate densities. Treatment of collision fragments: two approximations: Use this as most extreme case Instantaneous removal: mass lost in collision is removed from integration. Represents mass lost as small grains, removed by radiation forces Full retention: mass is distributed into super-particles. Fragment velocity distribution from Jackson & Wyatt (2012), scaled to planetary escape velocity. Represents mass lost as larger chunks.

Alexander Mustill PLATO Mission Conference 2017-09-07 Begin b < bcrit? N Grazing impact Small body hits big body? Y Y Head-on impact vcoll < verosive? Y Hit-andrun collision N vcoll < vʹesc? Y Perfect merging Disruptive impact N Supercatastrophic disruption N vcoll < vsupercat? Y Regular disruption

Collision outcomes in unstable super-earth systems

Collision outcomes in unstable super-earth systems 70% Collision outcomes as function of inner planet's semimajor axes 60% 50% Decreasing vkep, constant vesc 40% 30% 20% 10% 0% 0.1au 0.3au 0.5au 0.7au Perfect r Imperfect accretion Erosion

Collision outcomes in unstable super-earth systems Collision outcomes as function of inner planet's semimajor axes Collision outcomes as function of planetary mass range 70% 60% 70% 60% Increasing vesc, constant vkep 50% Decreasing vkep, constant vesc 50% 40% 40% 30% 30% 20% 20% 10% 10% 0% 0.1au 0.3au 0.5au 0.7au 0% 0.1-1 M 0.3-3M 1-10M Perfect r Imperfect accretion Erosion Perfect r Imperfect accretion Erosion Collision outcomes as function of planetary spacing in mutual Hill radii 70% 60% Constant vkep, constant vesc 50% 40% 30% 20% 10% 0% 4-6rH 6-8rH 7-9rH 8-10rH Perfect r Imperfect accretion Erosion

Collision outcomes in unstable super-earth systems Collision outcomes as function of inner planet's semimajor axes Collision outcomes as function of planetary mass range 70% 60% 70% 60% Increasing vesc, constant vkep 50% Decreasing vkep, constant vesc 50% 40% 40% 30% 30% 20% 20% 10% 10% 0% 0.1au 0.3au 0.5au 0.7au 0% 0.1-1 M 0.3-3M 1-10M Perfect r Imperfect accretion Erosion Perfect r Imperfect accretion Erosion Collision outcomes as function of planetary spacing in mutual Hill radii Collision outcomes as function of system configuration 70% 70% 60% Constant vkep, constant vesc 60% Stronger eccentricity excitation 50% 50% 40% 40% 30% 30% 20% 20% 10% 10% 0% 4-6rH 6-8rH 7-9rH 8-10rH 0% 5p 3p+3J 3p+J+B Perfect r Imperfect accretion Erosion Perfect r Imperfect accretion Erosion

Alexander Mustill PLATO Mission Conference 2017-09-07 At 0.1 au most collisions are not perfect rs. But erosive collisions do not result in much mass loss Large number of collisions resulting in little mass loss: these are mostly hit-and-run

Alexander Mustill PLATO Mission Conference 2017-09-07 Little impact on final multiplicity after instability 100 Hard to grind a system down to one or zero detectable planets 90 80 70 60 50 40 30 20 10 0 a=0.1au,big a=0.3au,big a=0.5au,big a=0.7au,big 0.1-1M, big,big 0.3-3M, big,big 6-8rH,big 7-9rH,big 8-10rH,big 0pl 1pl 2pl 3pl 4pl 5pl

Alexander Mustill PLATO Mission Conference 2017-09-07 Exception: when starting from smaller planets 100 90 80 70 60 50 40 30 20 10 0 a=0.1au,big a=0.3au,big a=0.5au,big a=0.7au,big 0.1-1M, big,big 0.3-3M, big,big 6-8rH,big 7-9rH,big 8-10rH,big 0pl 1pl 2pl 3pl 4pl 5pl

Alexander Mustill PLATO Mission Conference 2017-09-07 Observed multiplicities: still not enough singles Observed multiplicities: around 6 singles for every 1 double (depending slightly on selection criteria), e.g. Johansen et al (2012), Lissauer et al (2014) Our unstable multiples reduce to ~3:1 observed singles:doubles Still need extra source of singles (see also Izidoro et al 2017 for initially resonant systems, perfect merging assumed) 464 147

Alexander Mustill PLATO Mission Conference 2017-09-07 Effects on in-situ formation from embryos Always perfect merging: highmultiplicity systems formed Realistic collision algorithm: few high multiplicity, many singles and zeros Caveat: fragments removed (no reaccretion)

Alexander Mustill PLATO Mission Conference 2017-09-07 Conclusions Collisions between planets or embryos at ~0.1 au usually do not result in perfect rs. Fewer perfect rs when planets are smaller, or high eccentricities are excited by outer system dynamics. Many collisions are grazing impacts resulting in little mass loss. Little effect on final mass distribution or multiplicity when starting from large planets. In-situ formation from embryos is strongly affected by the collision prescription. If collision debris is efficiently removed, many single- or zero-planet systems form. Contribution to the Kepler dichotomy for rocky planets. See arxiv.org/abs/1708.08939 for further details.

At small orbital distances, Keplerian velocity can significantly exceed surface escape velocity

At small orbital distances, Keplerian velocity can significantly exceed surface escape velocity Known exoplanets with mass and radius measurements

At small orbital distances, Keplerian velocity can significantly exceed surface escape velocity Known exoplanets with mass and radius measurements Solar System planets

At small orbital distances, Keplerian velocity can significantly exceed surface escape velocity Solar System planets at 0.1au Known exoplanets with mass and radius measurements Solar System planets

Final mass distributions in unstable super-earth systems

Abandoning the perfect merging algorithm results in more widely-spaced systems Empirical Kepler distribution (Weiss et al 2017)