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

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

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 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 Giant planet formation

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 ) disc fragmentation  disc fragmentation (Stamatellos, Hubber & Whitworth 2007) 5000 AU 600 AU

The formation of low-mass objects by disc fragmentation

Edge-on discs

Face-on discs

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

Gammie (2001) Rice, Lodato, Armitage et al. (2003) Mejia et al. (2005) MAYBE Fragmentation when conditions are favourable [parametrised cooling] Boss ( ) Mayer, Quinn et al. (2004, 2006) YES Fragmentation (cooling by convection) Durisen, Mejia, Cai, Boley, Pickett et al. Gammie & Johnson (2003) Nelson et al. 2000, Nelson (2006) Stamatellos & Whitworth (2008) NO (close to the star) No Fragmentation (disc cannot cool fast) Rafikov (2005, 2006) Matzner & Levin (2005) Whitworth & Stamatellos (2006) NO (close to the star) No fragmentation close to the central star Can real discs fragment to form giant planets?

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

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

Gammie (2001) Rice, Lodato, Armitage et al. (2003) Mejia et al. (2005) MAYBE Fragmentation when conditions are favourable [parametrised cooling] Boss ( ) Mayer, Quinn et al. (2004, 2006) YES Fragmentation (cooling by convection) Durisen, Mejia, Cai, Boley, Pickett et al. Gammie & Johnson (2003) Nelson et al. 2000, Nelson (2006) Stamatellos & Whitworth (2008) NO (close to the star) No Fragmentation (disc cannot cool fast) Rafikov (2005, 2006) Matzner & Levin (2005) Whitworth & Stamatellos (2006) NO (close to the star) No fragmentation close to the central star Can real discs fragment to form giant planets?

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

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 Diffusion approximation  Viau et al  Oxley & Woolfson 2003 Monte Carlo approach

Smoothed Particle Hydrodynamics (with radiative transfer) 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. A new method to treat the energy equation in SPH simulations Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007 SPH particle Pseudo-cloud RiRi MiMi SPH particle potential SPH particle density Particle’s optical depth Particle’s column density

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 Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007 Particle’s optical depth Particle’s column density Pseudo-cloud SPH particle MiMi

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

SPH-RT: Equation of state & dust/gas opacities Dust & gas opacities  Ice mantle melting  Dust sublimation  Molecular opacity  H - absorption  B-F/F-F transitions Equation of state  Vibrational & rotational degrees of freedom of H 2  H 2 dissociation  H ionisation  Helium first and second ionisation Black & Bodenheimer 1975Bell & Lin 1994

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

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

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

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

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

Exploring the inner disc region (2-40 AU) Case 1 Ambient heating: T ext =10K Case 2 Stellar heating: T ext ~R -1 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) ]

Ambient heating: T ext =10K - Inner disc (2-40 AU)

Inner disc (2-40 AU) - Stellar heating: T ext ~R -1

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

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

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. Planet formation by gravitational instabilities in discs?

10m planetesimals50cm planetesimals Gas column density … BUT Gravitational instabilities may accelerate the core accretion scenario ! Rice et al. 2006

Exploring the outer disc region ( 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

Simulations of disc evolution - Outer disc ( AU)

Brown dwarf M=58 M J ρ=10 -2 g cm -3

Simulations of disc evolution - Outer disc ( AU)

Brown dwarf desert ? 100 AU 300 AU

SPH simulation (gas included)

N-BODY simulation (no gas)

Simulations of disc evolution - Outer disc ( AU)

Simulations of disc evolution - Outer disc ( AU) - with star irradiation

Statistical properties of objects produced by disc fragmentation: Radial distribution

Can real discs fragment? Whitworth & Stamatellos, A&A, 2006; Rafikov 2005; Matzner & Levin 2005 Discs cannot fragment to produce planets close (<100AU) to the star Whitworth & Stamatellos, A&A, 2006

time ~ 5000 yr (formation radius)time ~ yrtime ~ yr The brown dwarf desert Lack of BD companions to sun-like stars at r<5 AU (Marcy & Butler 2000)

Statistical properties of objects produced by disc fragmentation: Mass distribution Brown dwarfs Low-mass stars Planemos

Statistical properties of objects produced by disc fragmentation: Mass distribution Brown dwarfs Low-mass stars Planemos 10 objects 7 Brown dwarfs 3 low-mass stars planemo

Comparison with observations Credit: NASA / JPL-Caltech / K. Luhman, Penn State / B. Patten, Harvard-Smithsonian Using infrared photographs obtained with NASA's Spitzer Space Telescope, astronomers have discovered two very cold brown dwarfs orbiting the stars HD 3651 (left) and HN Peg (right). These brown dwarfs have masses of only 20 and 50 times the mass of Jupiter and have orbits that are more than 10 times larger than Pluto's orbit. HD 3651 and HN Peg are in the Sun's neighborhood of the Galaxy, with distances of only 36 and 60 light years from the Sun. Brown dwarfs form at wide orbits around young stars; some of them remain bound (30%); others are “liberated” (70%) in the field. HN Peg HD Μ J 50 Μ J >50 AU

Comparison with observations Close (2/3) and wide (1/3) brown dwarf - brown dwarf and brown dwarf -“planet” binaries are quite common (20%) outcome of disc fragmentation, and they may also liberated in the field. Chauvin et al M J 5-8M J Core accretion model M p <5M earth (Payne & Lodato 2007)

Planetary-mass objects are also formed with this mechanism and subsequently liberated in the field to become “free-floating planets”. Comparison with observations

Liberated brown-dwarfs frequently retain their own discs with sufficient mass (a few M J -- sometimes much larger), to sustain accretion and outflows. Ratio of brown dwarfs to stars should depend only weakly on environmental factors. As one disc can produce a large number (~4-7) of brown dwarfs, it may only be necessary for ~ 5-10% of discs around Sun-like stars to undergo fragmentation in order to supply all the observed brown dwarfs.

Formation of giant planets close to the star (R<50 AU) by disc fragmentation is unlikely, but… … discs can fragment at R>50 AU to form brown dwarfs (and/or low-mass hydrogen burning stars & planetary-mass objects)

Endnote: Defining brown dwarfs and planets Log(Mass/M  ) Deterium burning limit Hydrogen burning limit FORMATION BY DISC FRAGMENTATION FORMATION BY CORE ACCRETION … a need for a new definition ?