low-mass h-burning stars, brown dwarfs, & planets 13 m j 80 m j planets mayor & queloz 1995...
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Low-mass H-burning stars, brown dwarfs, & planets
13 MJ 80 MJ
Planets
Mayor & Queloz 1995
Brown dwarfs
Rebolo et al. 1995
Stars
1 MJ= 0.01 M
Low-mass H-burning stars, brown dwarfs, & planets
13 MJ 80 MJ
Planets
Mayor & Queloz 1995
Brown dwarfs
Rebolo et al. 1995
Stars
1 MJ= 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. 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
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. 2003 )
disc fragmentationdisc fragmentation (Stamatellos, Hubber & Whitworth 2007)
5000 AU
600 AU
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)
MAYBEFragmentation when conditions are favourable
[parametrised cooling]
Boss (1997-2006)
Mayer, Quinn et al. (2004, 2006)
YESFragmentation (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. 2007Wengen comparison test
GADGET2(SPH)
40 AU
FLASH(AMR CARTESIAN-GRID)
Gammie (2001)
Rice, Lodato, Armitage et al. (2003)
Mejia et al. (2005)
MAYBEFragmentation when conditions are favourable
[parametrised cooling]
Boss (1997-2006)
Mayer, Quinn et al. (2004, 2006)
YESFragmentation (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 | Temperature Density | 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. 2006 Diffusion approximation Viau et al. 2005
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 particlePseudo-cloud
RiMi
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-cloudSPH particle
Mi
Energy equation in Smoothed Particle Hydrodynamics
Compressional heating/cooling
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 H2
H2 dissociation
H ionisation
Helium first and second ionisation
Black & Bodenheimer 1975 Bell & 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. 2007Stamatellos et al. 2007
Masunaga & Inutsuka 2000 (1D)
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
Exploring the inner disc region (2-40 AU)
Case 1
Ambient heating: Text=10K
Case 2
Stellar heating: Text~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) ]
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 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
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
Radiative-SPH simulations of circumstellar discs withRadiative-SPH simulations of circumstellar discs withrealistic opacities, cooling+heating, and EOSrealistic 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?
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10m planetesimals 50cm planetesimals
Gas column density… BUT
Gravitational instabilities may accelerate the core accretion scenario !
Rice et al. 2006
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
Simulations of disc evolution - Outer disc (40-400 AU)
Brown dwarf
M=58 MJ
ρ=10ρ=10-2-2 g cm g cm-3-3
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 ~ 20000 yrtime ~ 200000 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
Browndwarfs
Low-mass stars
Planemos
Statistical properties of objects produced by disc fragmentation: Mass distribution
Browndwarfs
Low-mass starsPlanemos
10 objects• 7 Brown dwarfs• 3 low-mass stars• planemo
Comparison with observations
Credit: NASA / JPL-Caltech / K. Luhman, Penn State / B. Patten, Harvard-SmithsonianUsing 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 PegHD 3651
20 ΜJ
50 ΜJ
>50 AU
>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. 2005
25 MJ
5-8MJ
Core accretion model Mp<5Mearth
(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
Comparison with observations
Liberated brown-dwarfs frequently retain their own discs with sufficient mass (a few MJ -- 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)