Circumplanetary Disk Formation Ward & Canup 2010.

Patricio Cubillos Abril 21st, 2011. Introduction:

Giant planet satellites suggest a formation from a circumplanetary disk.

Early giant planet formation studies employed a canonical MMSN model.

The authors develop a planet + disk + inflow evolution model. Outline: 1 - Disk Formation: ‣ Inviscid disk ‣ Viscous disk 2 - Accreting Disk: ‣ Inflow stages: - Flux { - Couple ‣ Planet contraction: - Stable rotation { - Critical rotation 3 - Angular Momentum Inflow 4 - Planet-Disk Model: ‣ Inflow - Regimes ‣ Polytropic planet model ‣ Collapse phase 5 - Results: ‣ Final mass ‣ Contraction phase ‣ Disk profile ‣ Collapse phase 6 - Conclusions 1-Disk Formation: Average angular momentum delivered to the planet: - Inviscid - Viscous 2-Accreting Disk: uncertain! - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow As the planet contracts, it spins up: 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile Define a critical Radius: Rrot - Collapse phase 6- Conclusions 1-Disk Formation: Contraction of an accreted planet: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: No stress ⇒ Shed material stays in orbit. - Flux - Couple Mass and angular momentum conservation: - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow - Planet For a Jupiter like planet: Mdisk ∼0.56 MJ. - Collapse 5- Results: - Too large. - Final mass - Probably unstable. - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: - Inviscid The source and magnitude is still debated. - Viscous 2-Accreting Disk: - Inflow stages: Use alpha model: ν =αch. - Flux - Couple - Planet contraction: The shear due to viscosity generates a torque on the disk: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow and drives a in-plane radial mass flux in the disk: - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: We conserve angular momentum again, but considering the - Inviscid viscous torque. - Viscous 2-Accreting Disk: - Inflow stages: The mass of the disk: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow Less than 5% of the total mass. 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: The centrifugal radius: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: Inflow rate of material F is accreted in range: 1/4 rc, 9/4 rc - Stable rotation - Critical rotation 3- Angular Momentum Two conditions determine the overall behavior: Inflow 1.- Is the planet in stable or critical rotation? 4- Planet-Disk Model: 2.- Where is the material falling? - Inflow - Planet - Collapse In equations, the in-plane flux is determined by: 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: ri , ro ∝ RH - Inviscid - Viscous S: no disk F = const. ≥ 0 2-Accreting Disk: - Inflow stages: C: shed - Flux material - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: S: Fp ≤ 0 F = const. - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile F = const. - Collapse phase F = const. 6- Conclusions S: Fp ≤ 0 1-Disk Formation: They managed to write the flux in a general form: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation To determine Fd, its necessary to know the variation in the - Critical rotation couple: 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow - Planet ... ⇒ - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: They are in position of developing a model for the planet - Inviscid and the disk as a function of time: - Viscous 2-Accreting Disk: - Inflow stages: - Flux Known the inflow mass rate, the planet’s growth rate is: - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow And also: 4- Planet-Disk Model: - Inflow - Planet - Collapse Next, consider two cases: 5- Results: Stable rotation: gp = 0 - Final mass - Contraction phase Critical rotation: ω = ωc - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: Solve equations of flux and couple: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: Solve equations again: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow I believe that these last equations are among the main contributions of the paper. 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: Three possible growth phases: - Inviscid - Viscous •Shear-limited 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation Diffusion-limited - Critical rotation • 3- Angular Momentum Inflow •Torque-limited 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: Model the planet as a polytrope: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux Pressure, density, temperature and energy are defined. - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum ⇒ Inflow 4- Planet-Disk Model: - Inflow - Planet Expect molecular Hydrogen be predominant: - Collapse ⇒ n = 2.5 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: - Inviscid Planet contraction rises the central temperature. - Viscous • 2-Accreting Disk: - Inflow stages: •Above 3500 K Hydrogen dissociation occur. - Flux - Couple •Enables the body to contract very fast. - Planet contraction: - Stable rotation Past collapse, little change in radius. - Critical rotation • 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: Mass versus time dependence: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple Torque - Planet contraction: limited - Stable rotation }growth - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: Diffusion - Inflow limited - Planet growth - Collapse } 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: F - Inflow - Planet Ṁ - Collapse

5- Results: Fd - Final mass - Contraction phase - Disk profile Fp - Collapse phase 6- Conclusions 1-Disk Formation: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: - Inviscid - Viscous 2-Accreting Disk: - Inflow stages: - Flux - Couple - Planet contraction: - Stable rotation - Critical rotation 3- Angular Momentum Inflow 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions 1-Disk Formation: 1.- Circumplanetary disks form via spin-out from planet - Inviscid and inflow, then transitions to accretion. - Viscous 2-Accreting Disk: 2 3 2 - Inflow stages: 2.- Peak gas surface densities are ∼ 10 -10 g/cm - Flux - Couple 3.- Temperatures in the disk are low enough to condense - Planet contraction: - Stable rotation ices. - Critical rotation 3- Angular Momentum 4.- During the evolution there might be a brief collapse Inflow phase. 4- Planet-Disk Model: - Inflow - Planet - Collapse 5- Results: - Final mass - Contraction phase - Disk profile - Collapse phase 6- Conclusions