#55 Formation of close-in super-Earths in evolving protoplanetary disks via disk winds Masahiro Ogihara 1 , Eiichiro Kokubo 1 , Takeru K. Suzuki 2 , Alessandro Morbidelli 3 1 National Astronomical Observatory of Japan, 2 University of Tokyo, 3 Observatoire de la Côte d’Azur 3. Disk evolution 4. In situ formation from embryos in a disk evolving via disk winds (Suzuki, Ogihara, et al. 2016) 5. Resonant chain 6. A limit on gas accretion onto cores 7. Summary • We focus on the period-ratio distribution of close-in super-Earths (SEs) • Close-in SEs are generally not in mean- motion resonances (MMRs), which should be reproduced by simulation ❏ Results of N-body simulation • We perform N-body simulations in a power-law disk based on MMSN • Accretion of SEs is quite rapid in the close-in region because of high solid surface density • SEs undergo rapid migration in a power-law disk • SEs form in a compact configuration captured in MMRs • The system is stable even after gas depletion • Period-ratio distribution is not matched to observed distribution @ ⌃ @ t = 1 r @ @ r ⇢ 2 r ⌦ @ @ r (r 2 ⌃↵c 2 s )+ r 2 ↵ w ⌃ p ⇡ H c 2 s + C w ⌃ p ⇡ H c s • Magnetically driven disk winds are observed in 3D-MHD simulations (e.g., Suzuki & Inutsuka 2009, Fromang et al. 2013) • Disk winds cause wind mass loss and wind-driven accretion • Suzuki et al. (2016) derived global viscous disk evolution including disk winds by solving the diffusion equation • Disk profiles can be altered from the power-law disk ❏ Results of N-body simulation • We perform N-body simulations from embryos in disk evolving via disk winds • Type I migration is significantly suppressed owing to small gas density and flat slope in the close-in region • No pileup near the disk inner edge is observed • Planets are captured in MMRs before the disk depletion, which is destroyed by the late orbital instability • Final orbits are not in MMRs, which is consistent with observed period-ratio distribution • Some systems do not undergo late orbital instability • Resonant chain can also form • SE cores should undergo runaway gas accretion based on evolution models of a planetary atmosphere (e.g., Ikoma & Hori 2012) • We propose that rapid radial accretion near the surface due to wind- driven accretion slips out of the core and regulates the gas supply onto the core • Planets undergo rapid inward migration in a power-law disk • Type I migration can be suppressed in a disk evolving via disk winds • Close-in SEs form in a non-resonant configuration after late orbital instability • Observed period-ratio distribution can be reproduced • The gas accretion onto cores can be limited depending on the vertical structure of the radial gas accretion (Ogihara et al. 2018) Schematic picture of disk evolution MHD simulation by Suzuki & Inutsuka (2009) Evolution of gas surface density Comparison of period-ratio distribution Examples of systems with MMRs Comparison of period-ratio distribution 0.01 0.1 1 10 10 3 100 10 1 0.1 Semi-Major Axis [Astronomical Units (AU)] Planet Mass [Earth Mass] exoplanets.org | 6/27/2018 0 5 10 15 20 25 30 Number Period ratio (Pout/Pin) of adjacent pair 2:1 3:2 4:3 5:4 6:5 7:6 1 10 2 3 5 0 0.2 0.4 0.6 0.8 1 1 10 Cumulative distribution 2:1 3:2 4:3 5:4 6:5 7:6 2 3 5 Period ratio (Pout/Pin) of adjacent pair 0.1 1 10 3 10 4 10 5 10 6 10 7 10 8 Semimajor axis (au) Time (yr) -2 -1.5 -1 -0.5 0 0.5 1 log(M/M⊕) 5 0 0.2 0.4 0.6 0.8 1 1 10 Cumulative distribution 2:1 3:2 4:3 5:4 6:5 7:6 2 3 5 Period ratio (Pout/Pin) of adjacent pair 10 -3 10 -2 10 -1 1000 yr 0.1 Myr 1 Myr 0.1 1 10 Myr 0.05 Radial distance (au) Eccentricity Gas surface density (g cm -2 ) 10 3 10 4 10 5 10 -3 10 -2 10 -1 10 3 10 4 10 5 10 -3 10 -2 10 -1 10 3 10 4 10 5 10 -3 10 -2 10 -1 10 3 10 4 10 5 Radial distance (au) Eccentricity Gas surface density (g cm -2 ) 100 Myr 1 Myr 100 yr 10 -3 10 -2 10 -1 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 -3 10 -2 10 -1 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 -3 10 -2 10 -1 0.1 1 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 viscous accretion wind-driven accretion viscous accretion wind-driven accretion wind mass loss wind mass loss 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 0.01 0.1 1 10 100 Gas surface density (g cm -2 ) Radial distance (au) initial 1Myr 10Myr 1.60 1.67 1.50(3:2) 1.50(3:2) 1.34(4:3) 1.25(5:4) 1.33(4:3) 1.33(4:3) 1.50(3:2) 1.33(4:3) 1.67 3:2 3:2 3:2 4:3 3:2 4:3 5:4 observation simulation 1 10 P/P innermost TRAPPIST-1 Kepler-60 Kepler-223 model5-1 model6-1 model6-2 4:3 7:6 3:2 5:4 5:4 7:6 5:4 4:3 r z Rapid gas flow due to wind-driven accretion may slips out of the core close-in super-Earths rapid migration MMRs stable after gas depletion observation 10 runs of simulation MMSN late orbital instability late orbital instability results with M total = 80 M ⊕ results with M total = 40 M ⊕ results with M total = 20 M ⊕ blended results of 3 sets of simulations 1. Close-in super-Earths 2. In situ formation in a power-law disk (Ogihara, Morbidelli, Guillot 2015)