Low-mass H-burning stars, brown dwarfs, & planets
1 MJ= 0.01 M
13 MJ
80 MJ
Planets
Brown dwarfs
Mayor &
Queloz 1995
Rebolo et al. 1995
Stars
Low-mass H-burning stars, brown dwarfs, & planets
1 MJ= 0.01 M
13 MJ
80 MJ
Planets
Brown dwarfs
Mayor &
Queloz 1995
Rebolo et al. 1995
Stars
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
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 )
5000 AU
 disc fragmentation
(Stamatellos, Hubber & Whitworth 2007)
600 AU
The formation of low-mass objects by disc fragmentation
Edge-on discs
Face-on discs
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
Can real discs fragment to form giant planets?
Gammie (2001)
Rice, Lodato, Armitage et al. (2003)
MAYBE
Fragmentation when conditions are favourable
[parametrised cooling]
Mejia et al. (2005)
Boss (1997-2006)
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)
NO (close to the star)
No Fragmentation (disc cannot cool fast)
Stamatellos & Whitworth (2008)
Rafikov (2005, 2006)
Matzner & Levin (2005)
Whitworth & Stamatellos (2006)
NO (close to the star)
No fragmentation close to the central star
Isothermal discs: snapshots after 1000 yr of disc evolution
GASOLINE
(SPH)
GADGET2
(SPH)
40 AU
INDIANA U
(CYLIDRICAL-GRID)
Durisen et al. 2007
Wengen comparison test
FLASH
(AMR CARTESIAN-GRID)
GASOLINE
(SPH)
GADGET2
(SPH)
t=1.5 ORPS
there is still hope !
t=2.5 ORPS
Mayer et al. 2007
Can real discs fragment to form giant planets?
Gammie (2001)
Rice, Lodato, Armitage et al. (2003)
MAYBE
Fragmentation when conditions are favourable
[parametrised cooling]
Mejia et al. (2005)
Boss (1997-2006)
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)
NO (close to the star)
No Fragmentation (disc cannot cool fast)
Stamatellos & Whitworth (2008)
Rafikov (2005, 2006)
Matzner & Levin (2005)
Whitworth & Stamatellos (2006)
NO (close to the star)
No fragmentation close to the central star
Monte Carlo Radiative Transfer (Multi-frequency/3D)
Density
| x-z plane | Temperature
Density
| x-y 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
 Viau et al. 2005
Diffusion approximation
 Oxley & Woolfson 2003
Monte Carlo approach
ASmoothed
new method
Particle
to treat
Hydrodynamics
the energy equation
(with radiative
in SPH simulations
transfer)
Use the gravitational potential and the density of each SPH particle to define a pseudocloud around the particle, which determines how the particle cools/heats.
SPH particle potential
Pseudo-cloud
Ri
SPH particle
Mi
SPH particle density
Particle’s column
density
Particle’s optical
depth
Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007
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 pseudocloud around the particle, which determines how the particle cools/heats
SPH particle potential
SPH particle density
Pseudo-cloud
SPH particle
Particle’s column
density
Mi
Particle’s optical
depth
Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007
Energy equation in Smoothed Particle Hydrodynamics
Compressional
heating/coolin
g
Radiative cooling/heating rate
Thermalization
timescale
Time-stepping
Viscous
heating
SPH-RT: Equation of state & dust/gas opacities
Equation of state
Dust & gas opacities
 Vibrational & rotational
 Ice mantle melting
 Dust sublimation
 Molecular opacity
 H- absorption
 B-F/F-F transitions
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%)
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
The collapse of a 1-M molecular cloud
Stamatellos, Whitworth, Bisbas & Goodwin, A&A, 2007
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
Disc vertical temperature structure - Hubeny (1990)
Stamatellos & Whitworth, 2008, A&A in press
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
Case 2
Ambient heating: Text=10K
Stellar heating: Text~R-1
Ambient heating: Text=10K - Inner disc (2-40 AU)
Inner disc (2-40 AU) - Stellar heating: Text~R-1
Simulations of disc evolution - Inner disc (2-40 AU)
Ambient heating: Text=10K
The disc does not fragment because it
cannot cool fast enough (tcool>3Ω-1)
Stellar heating: Text~R-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
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.
… BUT
Gas column density
Gravitational instabilities may
accelerate the core accretion
scenario !
Rice et al. 2006
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
10m planetesimals
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
50cm planetesimals
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)
Simulations of disc evolution - Outer disc (40-400 AU)
Simulations of disc evolution - Outer disc (40-400 AU)
Simulations of disc evolution - Outer disc (40-400 AU)
ρ=10-2 g cm-3
Brown dwarf
M=58 MJ
Simulations of disc evolution - Outer disc (40-400 AU)
Simulations of disc evolution - Outer disc (40-400 AU)
300 AU
100 AU
Brown dwarf desert ?
SPH simulation (gas included)
N-BODY simulation (no gas)
Simulations of disc evolution - Outer disc (40-400 AU)
Simulations of disc evolution - Outer disc (40-400 AU) - with star irradiation
Simulations of disc evolution - Outer disc (40-400 AU) - with star irradiation
Simulations of disc evolution - Outer disc (40-400 AU) - with star irradiation
Statistical properties of objects produced by disc fragmentation: Radial distribution
Statistical properties of objects produced by disc fragmentation: Radial distribution
Can real discs fragment?
Whitworth & Stamatellos, A&A, 2006
Discs cannot fragment to produce planets close (<100AU) to the star
Whitworth & Stamatellos, A&A, 2006; Rafikov 2005; Matzner & Levin 2005
The brown dwarf desert
• Lack of BD companions to sun-like stars at r<5 AU (Marcy & Butler 2000)
time ~ 200000
5000 yryr(formation radius)
20000
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
Planemos
10 objects
• 7 Brown dwarfs
• 3 low-mass stars
• planemo
Low-mass stars
Comparison with observations
 Brown dwarfs form at wide orbits around young stars; some of them
remain bound (30%); others are “liberated” (70%) in the field.
HD 3651
HN Peg
20 ΜJ
>50 AU
>50 AU 50 ΜJ
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.
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
Core accretion model Mp<5Mearth
(Payne & Lodato 2007)
25 MJ
5-8MJ
Comparison with observations
 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 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)
Endnote: Defining brown dwarfs and planets
Deterium
burning limit
Hydrogen
burning limit
FORMATION
BY CORE
ACCRETION
FORMATION
BY DISC
FRAGMENTATION
Log(Mass/M)
… a need for a new definition ?