Forming Gas-Giants Through Gravitational Instability: 3D Radiation Hydrodynamics Simulations and the Hill Criterion

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1 Forming Gas-Giants Through Gravitational Instability: 3D Radiation Hydrodynamics Simulations and the Hill Criterion Patrick D Rogers & James Wadsley June 15, 2012

2 Forming Gas-Giants Through Gravitational Instability: 3D Radiation Hydrodynamics Simulations and the Hill Criterion Patrick D Rogers & James Wadsley June 15, 2012

3 Gas-Giant Formation Formation of gas-giant planets and brown dwarfs Fragmentation via GI - Formation in ~10 3 years hubblesite.org Standard Core-accretion - Formation in ~10 6 years (at 5 AU) - Outer limit of ~35 AU? (Dodson-Robertson+, 2009) - Scattering/formation farther out? Mayer+ (2004)

4 Gas-Giant Formation via GI The Standard Criteria: (Toomre 1964, Gammie 2001, Rice+ 2005) Low Toomre Q: Short cooling time:

5 Gas-Giant Formation via GI The Standard Criteria: (Toomre 1964, Gammie 2001, Rice+ 2005) Low Toomre Q: Short cooling time: - from suite of numerical experiments, each with constant - Convergence of? crit - Meru & Bate (2011) cool =

6 Gas-Giant Formation via GI The Standard Criteria: (Toomre 1964, Gammie 2001, Rice+ 2005) Low Toomre Q: Short cooling time: Rafikov (2007) - Fragmentation unlikely at small radii (10 AU) - Fragmentation likely at large radii (100 AU)

7 Radiative Transfer in Gasoline Rogers & Wadsley (2011) - Grey flux-limited diffusion in SPH - Photosphere boundary condition

8 Radiative Transfer in Gasoline Rogers & Wadsley (2011) - Grey flux-limited diffusion in SPH - Photosphere boundary condition edge (photosphere) particles

9 Radiative Transfer in Gasoline Rogers & Wadsley (2011) - Grey flux-limited diffusion in SPH - Photosphere boundary condition

10 Fragmentation In the Outer Regions Rogers & Wadsley (2012)! /3 apple! 3apple 400 AU 3D Radiation Hydrodynamics simulations Gasoline TreeSPH code with flux-limited diffusion Extended, gravitationally unstable, irradiated disc Irradiation from Chiang & Goldreich (1997) model (Kratter+ 2010) 1.35 M sun central star Also (1/10, 1, 10)

11 Fragmentation In the Outer Regions Rogers & Wadsley (2012)! /3! /3 apple! 3apple apple! 3apple 400 AU 3D Radiation Hydrodynamics simulations Gasoline TreeSPH code with flux-limited diffusion Extended, gravitationally unstable, irradiated disc Irradiation from Chiang & Goldreich (1997) model (Kratter+ 2010) 1.35 M sun central star Also (1/10, 1, 10)

12 Fragmentation In the Outer Regions Rogers & Wadsley (2012)! /3 apple! 3apple 400 AU low Q -> spirals Lower opacity -> faster cooling -> fragmentation low Q -> spirals Higher opacity -> slower cooling -> no fragmentation

13 Fragmentation In the Outer Regions Rogers & Wadsley (2012)! /3 apple! 3apple 400 AU low Q -> spirals Lower opacity -> faster cooling -> thinner spiral arms -> fragmentation low Q -> spirals Higher opacity -> slower cooling -> thicker spiral arms -> no fragmentation

14 Spiral Arm Formation Taking the Toomre Instability Into the Non-linear Regime compression

15 The Hill Criterion for Spiral Arm Fragmentation l 1 > 2H Hill non-fragmenting l 1 < 2H Hill is set by balance of heating & cooling fragmenting

16 The Hill Criterion for Spiral Arm Fragmentation Consistent with simulations! /3 apple! 3apple

17 The Hill Criterion for Spiral Arm Fragmentation Consistent with simulations! /3 apple! 3apple

18 The Hill Criterion for Spiral Arm Fragmentation Consistent with simulations! /3 fragmenting apple! 3apple non-fragmenting

19 Disc Stability From our Model Analytic model of disc stability - Spiral arms form from linear instability - Spiral arms have a width determined by heating and cooling - Spiral arms fragment if they satisfy the Hill criterion Heating from spiral arms (Cossins+ 2009) M M 2 Q + = c 2 s 2 Consider stability of IC for different forms of cooling

20 Disc Stability From our Model Analytic model of disc stability - Spiral arms form from linear instability - Spiral arms have a width determined by heating and cooling - Spiral arms fragment if they satisfy the Hill criterion Heating from spiral arms (Cossins+ 2009) M M 2 Q + = c 2 s 2 Consider stability of IC for different forms of cooling

21 Disc Stability From our Model Analytic model of disc stability - Spiral arms form from linear instability - Spiral arms have a width determined by heating and cooling - Spiral arms fragment if they satisfy the Hill criterion Heating from spiral arms (Cossins+ 2009) M M 2 Q + = c 2 s 2 Consider stability of IC for different forms of cooling

22 Disc Stability From our Model Analytic model of disc stability - Spiral arms form from linear instability - Spiral arms have a width determined by heating and cooling - Spiral arms fragment if they satisfy the Hill criterion Heating from spiral arms (Cossins+ 2009) M M 2 Q + = c 2 s 2 Consider stability of IC for different forms of cooling

23 First Analytical Estimate of The Critical Cooling Time Simulation IC -prescription cooling:

24 First Analytical Estimate of The Critical Cooling Time Simulation IC -prescription cooling:

25 First Analytical Estimate of The Critical Cooling Time Cossins+ (2009) disc -prescription cooling: Q 1 disc - Use =0.2 - Match 0.4 Result: 4 crit - agrees with simulations of Cossins+ (2009)

26 Stability of Radiative Discs Simulation IC Radiative cooling (Kratter+ 2010): F = 16 3apple T 4 T 4 irrad

27 Stability of Radiative Discs Simulation IC Radiative cooling (Kratter+ 2010): F = 16 3apple T 4 T 4 irrad

28 Stability of Radiative Discs Simulation IC Radiative cooling (Kratter+ 2010): F = 16 3apple T 4 T 4 irrad

29 Stability of Radiative Discs Simulation IC Radiative cooling (Kratter+ 2010): F = 16 3apple T 4 T 4 irrad fragmentation fragmentation

30 Fragment Mass in Radiative Discs Simulation IC Radiative cooling (Kratter+ 2010): F = 16 3apple T 4 T 4 irrad

31 Fragment Mass in Radiative Discs Simulation IC Radiative cooling (Kratter+ 2010): F = 16 3apple T 4 T 4 irrad

32 Conclusions GI can produce gas-giants at large radii (100 AU) - radiative cooling allows for fragmentation

33 Conclusions GI can produce gas-giants at large radii (100 AU) - radiative cooling allows for fragmentation

34 Conclusions GI can produce gas-giants at large radii (100 AU) - radiative cooling allows for fragmentation More detailed physical model for fragmentation via GI - explain link between cooling and fragmentation - first analytic calculation of critical cooling time - stability of radiative discs - initial masses of fragments

35 Conclusions GI can produce gas-giants at large radii (100 AU) - radiative cooling allows for fragmentation More detailed physical model for fragmentation via GI - explain link between cooling and fragmentation - first analytic calculation of critical cooling time - stability of radiative discs - initial masses of fragments Future research: - Improved understanding of model parameters (GI) - What happens to gas-giants? Survival, migration? - Disc formation and fragmentation - Role of accretion, magnetic field

36 THANK YOU

37 Destruction of Diffuse Fragments Fragments can be destroyed by spiral arms.

38 Radiative Transfer in Gasoline Rogers & Wadsley (2011) Boley+ (2007) relaxation test

39 Radiative Transfer in Gasoline Rogers & Wadsley (2011) Boley+ (2007) relaxation test Photosphere cooling g Volume heating Photosphere cooling

40 Radiative Transfer in Gasoline Rogers & Wadsley (2011) Boley+ (2007) relaxation test

41 Gas-Giant Formation via GI The Standard Criteria: (Toomre 1964, Gammie 2001) Low Toomre Q: Short cooling time: Rafikov (2007)

42 Gas-Giant Formation via GI The Standard Criteria: (Toomre 1964, Gammie 2001) Low Toomre Q: Short cooling time: Rafikov (2007) - Fragmentation unlikely at small radii (10 AU)

43 Gas-Giant Formation via GI The Standard Criteria: (Toomre 1964, Gammie 2001) Low Toomre Q: Short cooling time: Rafikov (2007) - Fragmentation unlikely at small radii (10 AU) - Fragmentation likely at large radii (100 AU)