The formation of planets, brown dwarfs and low-mass stars by disc fragmentation

1. Dimitris Stamatellos School of Physics & Astronomy Cardiff University, Wales, UK 3rd April 2008, KIAA/PKU The formation of planets, brown dwarfs and low-mass stars by disc fragmentation

2. Dimitris Stamatellos School of Physics & Astronomy Cardiff University, Wales, UK 3rd April 2008, KIAA/PKU Anthony Whitworth (Cardiff) Thomas Bisbas (Cardiff) David Hubber (Norway) Simon Goodwin (Sheffield) The formation of planets, brown dwarfs and low-mass stars by disc fragmentation

3. Low-mass H-burning stars, brown dwarfs, & planets 1 MJ= 0.01 M 13 MJ 80 MJ Planets Mayor & Queloz 1995 Brown dwarfs Rebolo et al. 1995 Stars

5. Low-mass H-burning stars, brown dwarfs, & planets 1 MJ= 0.01 M 13 MJ 80 MJ Planets Mayor & Queloz 1995 Brown dwarfs Rebolo et al. 1995 Stars

6. Giant planet formation • Core accretion model  a solid core forms first, and subsequently accretes an envelope of gas • planet formation in a few Myr but discs may not be that long lived Perri & Cameron 1974; Mizuno 1980; Lissauer 1993; Rafikov 2004; Goldreich et al. 2004 • Disc fragmentation • planets form in a dynamical timescale (a few thousand years) • doubts whether real discs can fragment Cameron 1978; Boss 1997, 2000; Rice et al. 2003, 2004; Mayer et al. 2002, 2006

7. Brown dwarf formation • turbulent fragmentation of molecular clouds (Padoan & Nordland 2002; Bate et al. 2003) • premature ejection of protostellar embryos (Clarke & Reipurth , Bate et al. 2003; Goodwin et al. 2003 ) • disc fragmentation (Stamatellos, Hubber & Whitworth 2007) 5000 AU 600 AU

8. The formation of low-mass objects by disc fragmentation

9. Edge-on discs

10. Face-on discs

12. Criteria for disc fragmentation (i) Toomre criterion (Toomre 1964) Disc must be massive enough (ii) Gammie criterion (Gammie 2001; Rice et al. 2003) Disc must cool on a dynamical timescale

13. Can real discs fragment to form giant planets?

14. Isothermal discs: snapshots after 1000 yr of disc evolution GASOLINE (SPH) GADGET2 (SPH) Durisen et al. 2007 Wengen comparison test 40 AU FLASH (AMR CARTESIAN-GRID) INDIANA U (CYLIDRICAL-GRID)

15. GASOLINE (SPH) GADGET2 (SPH) t=1.5 ORPS there is still hope ! t=2.5 ORPS Mayer et al. 2007

16. Can real discs fragment to form giant planets?

17. Monte Carlo Radiative Transfer (Multi-frequency/3D) Density | x-z plane | Temperature Density | x-y plane | Temperature Stamatellos, Whitworth, Boyd & Goodwin 2005, A&A

18. Smoothed particle hydrodynamics with radiative transfer 3D multi-frequency radiative transfer + hydrodynamics Computationally prohibitive! SPH + radiative transfer: approximations • Whitehouse & Bate 2004, 2006 • Mayer et al. 2006 Diffusion approximation • Viau et al. 2005 • Oxley & Woolfson 2003 Monte Carlo approach

19. Pseudo-cloud SPH particle Ri Mi Smoothed Particle Hydrodynamics (with radiative transfer) A new method to treat the energy equation in SPH simulations Use the gravitational potential and the density of each SPH particle to define a pseudo-cloud around the particle, which determines how the particle cools/heats. SPH particle potential SPH particle density Particle’s column density Particle’s optical depth Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007

20. Pseudo-cloud SPH particle Mi Calculating the particle’s optical depth using a polytropic pseudo-cloud Use the gravitational potential and the density of each SPH particle to define a pseudo-cloud around the particle, which determines how the particle cools/heats SPH particle potential SPH particle density Particle’s column density Particle’s optical depth Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007

21. Radiative cooling/heating rate Compressional heating/cooling Viscous heating Thermalization timescale Time-stepping Energy equation in Smoothed Particle Hydrodynamics

22. SPH-RT: Equation of state & dust/gas opacities Equation of state  Vibrational & rotational degrees of freedom of H2  H2 dissociation  H ionisation  Helium first and second ionisation Dust & gas opacities  Ice mantle melting  Dust sublimation  Molecular opacity  H- absorption  B-F/F-F transitions Black & Bodenheimer 1975 Bell & Lin 1994

23. SPH with radiative transfer • Realistic EOS • Realistic dust opacities • Realistic cooling + heating • Capture thermal inertia effects • Modest computational cost (+3%)

24. The collapse of a 1-M molecular cloud • 200,000 SPH particles (UKAFF) 16 orders of magnitude in density 4 orders of magnitude in temperature Stamatellos et al. 2007 Masunaga & Inutsuka 2000 (1D) Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007

25. The collapse of a 1-M molecular cloud Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007

26. The collapse of a 1-M molecular cloud • 200,000 SPH particles (UKAFF)  16 orders of magnitude in density  4 orders of magnitude in temperature Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007

27. Disc vertical temperature structure - Hubeny (1990) Stamatellos & Whitworth, 2008, A&A in press

28. 1: The "inner" disc region (<40 AU) 2: The "outer" disc region (>40 AU)

29. Exploring the inner disc region (2-40 AU) • Most of the exoplanets observed are “hot Jupiters”, i.e. relative massive planets orbiting very close to the parent star. [ Initial conditions of the Indiana Group (Durisen, Mejia, Pickett, Cai, Boley) ] Case 1 Ambient heating: Text=10K Case 2 Stellar heating: Text~R-1

30. Ambient heating: Text=10K- Inner disc (2-40 AU)

31. Inner disc (2-40 AU) - Stellar heating: Text~R-1

32. Simulations of disc evolution - Inner disc (2-40 AU) Ambient heating: Text=10K Stellar heating: Text~R-1 The disc does not fragment because it it is too hot (Q>1) The disc does not fragment because it cannot cool fast enough (tcool>3Ω-1) Stamatellos & Whitworth, 2008, A&A in press

33. Ambient heating: Text=10K- Inner disc (2-40 AU) - Stellar heating: Text~R-1 The disc does not fragment because it cannot cool fast enough (tcool>3Ω-1) The disc does not fragment because it it is too hot (Q>1) Stamatellos & Whitworth, 2008, A&A in press

34. Planet formation by gravitational instabilities in discs? Radiative-SPH simulations of circumstellar discs with realistic opacities, cooling+heating, and EOS Formation of giant planets close to the star (R<50 AU) by disc fragmentation is unlikely.

35. Gas column density … BUT Gravitational instabilities may accelerate the core accretion scenario ! Rice et al. 2006

36. Exploring the outer disc region (40-400 AU) • Massive, extended discs are rare, but they do exist (e.g. Eisner et al. 2005; Eisner & Carpenter 2006; Rodriguez et al. 2005). • We argue that they could be more common but they quickly fragment (within a few thousand years). Stamatellos, Hubber, & Whitworth, A&A, 2007

37. Simulations of disc evolution - Outer disc (40-400 AU)

38. Simulations of disc evolution - Outer disc (40-400 AU)

39. Simulations of disc evolution - Outer disc (40-400 AU)

40. Simulations of disc evolution - Outer disc (40-400 AU) ρ=10-2 g cm-3 Browndwarf M=58 MJ

41. Simulations of disc evolution - Outer disc (40-400 AU)

42. 300 AU 100 AU Brown dwarf desert ? Simulations of disc evolution - Outer disc (40-400 AU)

43. SPH simulation (gas included)

44. N-BODY simulation (no gas)

45. Simulations of disc evolution - Outer disc (40-400 AU)

46. Simulations of disc evolution - Outer disc (40-400 AU) - with star irradiation

47. Simulations of disc evolution - Outer disc (40-400 AU) - with star irradiation

48. Simulations of disc evolution - Outer disc (40-400 AU) - with star irradiation

49. Statistical properties of objects produced by disc fragmentation: Radial distribution

50. Statistical properties of objects produced by disc fragmentation: Radial distribution