Disk Instability Models: What Works and What Does Not Work Disk Instability Models: What Works and What Does Not Work The Formation of Planetary Systems Heretic’s Approach to Solar System FormationFForm Alan P. Boss Carnegie Institution of Washington From Protostellar Disks to Planetary Systems University of Western Ontario, London, Ontario, Canada May 18, 2006

Outline:  Recent work on disk instability models: Vertical convective fluxes Survival of virtual protoplanets Disks in binary G dwarf star systems 200-AU-scale disks around G dwarfs Disks around M dwarf stars Formation of super-Earths around M dwarfs 3

Disk Instability ? In order for disk instability to be able to form giant protoplanets, there must be a means of cooling the disk on the time scale of the instability, which is on the order of the orbital period. Radiative cooling in an optically thick disk is too inefficient to cool the disk’s midplane, as its characteristic time scale is of order 30,000 yrs for the solar nebula at 10 AU. The only other possible mechanism for cooling the disk midplane is convective transport – can it do the job?

Vertical scale expanded by 10 Inner edge 4 AU20 AU 2 AU Temperature contours at 339 yrs ^ ^ ^

4 AU20 AU 2 AU Vertical scale expanded by 10 Superadiabatic vertical temperature gradients (Schwarzschild criterion for convection) 339 yrs ^ ^ ^

Velocity vectors at 339 yrs 2 AU 8 AU14 AU ^ ^ ^

Vertical Convective Energy Flux 1. For each hydrodynamical cell, calculate the vertical thermal energy flux: F conv = - v  A E  where v  = vertical velocity, A = cell area perpendicular to the vertical velocity, E = specific internal energy of cell, and  cell density. 2. Sum this flux over nearly horizontal surfaces to find the total vertical convective energy flux as a function of height in the disk.

339 yrs Peak flux is high enough to remove all thermal energy from this ring of gas in 50 yrs.

Rapid Convective Cooling? (Boss 2004) Radiative transfer is unable to cool disk midplanes on the dynamical time scale (a few rotational periods). Convective transport appears to be capable of cooling disk midplanes on the dynamical time scale. Evidence for convective transport includes Schwarzschild criterion for convection, convective cells seen in velocity vector fields, and calculations of the total vertical convective energy flux. Assuming that the surface can radiate away the disk’s heat on a comparable time scale, marginally gravitationally unstable disks should be able to form giant protoplanets.

Mayer et al. (2002) disk instability model after 800 yrs [SPH with simple thermodynamics] time evolution of clump orbits

Virtual protoplanet orbits for at least 1000 years, at least 30 orbits Boss (2005)

Gas Giant Planets in Multiple Star Systems Hierarchical triple star systems (planet orbits the single member of the triple): 16 Cygni B – about 850 AU separation HD B – about 640 AU separation HD A – about 23 AU separation Binary star systems: HD – about 150 AU separation HD – about 130 AU separation HD – about 100 AU separation Gamma Cephei – about 20 AU separation Gl 86 – about 20 AU separation [ At least ~ 29 multiple stars have planets to date (M. Mugrauer, 2004)]

marginally gravitationally unstable disk Q=1 highly unstable Q=2 as in Nelson (2000) Q = c s  /(  G 

no binary 245 years 20 AU radius disk

20 AU radius disk after one binary rotation period: 239 years to binary – at apastron M s = 1 M sun M d = 0.09 M sun a = 50 AU e = 0.5 ^

Differences between Nelson (2000) and Boss (2006) Nelson (2000) used (2D) 60,000 SPH particles Thin disk so adiabatic gradient assumed in vertical direction, as if cooled by convection Surface T > 100 K means higher midplane T Artificial viscosity converts KE into heat in shock fronts and elsewhere (  = to 0.005) Cooling time ~ 10 P Boss (2006) used over 1,000,000 grid points (3D) Fully 3D so vertical convection cools disk midplane in optically thick regions, radiation cools in optically thin regions Surface T = 50 K means lower midplane T No artificial viscosity so no irreversible heating in shock fronts and  0 assumed Cooling time ~ 1-2 P

GQ Lup b – 1 Myr-old gas giant planet at 100 AU? (Neuhauser et al. 2005)

200 AU radius disk with 0.16 M sun orbiting a 1M sun protostar after yrs (Boss 2006) => SIM!

Extrasolar Planet Census: Low-mass Host Stars * Most planet-host stars are G dwarf stars like the Sun, while most nearby stars are M dwarfs, less massive than the Sun. * M4 dwarf star Gl876 (0.32 M Sun ) has two known gas giant planets and one sub-Neptune-mass planet. * Microlensing surveys appear to have found two Jupiter-mass planets orbiting M dwarfs. * Two M dwarfs with known planets (Gl 876, Gl 436) both have solar metallicity – neither is metal-rich. * Another M dwarf with a known planet (Gl 581) is metal-poor ([Fe/H] = -0.25) compared to the Sun. * While the frequency of giant planets around M dwarfs is uncertain, it is clearly not zero.

Initial disk surface density: Q min = 1.5 Surface density needed for Q = 1 disk instability 0.5 M Sun protostar M Sun disk

20 AU radius disk

20 AU radius disk

0.5 M Sun protostar M Sun disk Disk surface density at 208 yr

0.5 M Sun protostar M Sun disk 0.93 M Jupiter clump gas density at 208 yr

Clump formation by disk instability after 445 yrs in a 0.02 M Sun disk orbiting a 0.1 M Sun star (Boss 2006). Jupiter-mass clump at 7 AU

0.065 M Sun disk with Q min = 1.5 orbiting a 0.5 M Sun protostar after 215 yrs

Discovery space with latest discoveries added Discovery space with planets around M dwarf stars highlighted Gl 876 Gl 436 OGLE-2005-BLG-390 Gl 581 OGLE-2003-BLG-235 OGLE-2005-BLG-071 Gl 876 OGLE-2005-BLG-169

Heretical Explanation for Microlensing Planets Most stars form in regions of high-mass star formation (e.g., Orion, Carina) where their protoplanetary disks can be photoevaporated away by nearby O stars. Photoevaporation converts gas giant protoplanets into ice giants if the protoplanet orbits outside a critical radius, which depends on the mass of the host star. For solar-mass stars, the critical radius is > 5 AU, while for a 0.3 M Sun M dwarf star, the critical radius is > 1.5 AU. If M dwarfs have disks massive enough to undergo disk instability, then their gas giant protoplanets orbiting outside ~1.5 AU will be photoevaporated down to super-Earth mass, for M dwarfs in regions of high-mass star formation. In low-mass star formation regions (e.g., Taurus), their gas giant protoplanets will survive to become gas giant planets.