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

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

The formation of low-mass objects by disc fragmentation

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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)

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)

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


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 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



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: 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) ]

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 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)


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)


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?

QuickTime™ and aTIFF (Uncompressed) decompressor

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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


Brown dwarf desert ?

100 AU100 AU

300 AU

SPH simulation (gas included)

N-BODY simulation (no gas)

Simulations of disc evolution - Outer disc (40-400 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 ~ 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


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”.



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

Log(Mass/M)

Deterium burning limit

Hydrogen burning limit

FORMATIONBY DISC

FRAGMENTATION

FORMATION BY CORE

ACCRETION

… a need for a new definition ?

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

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