1. FORMATION OF LOW-MASS COMPANIONS BY DISC FRAGMENTATION
Anthony Whitworth,
Cardiff University, Wales, UK
Dimitris Stamatellos (Cardiff)
Simon Goodwin (Sheffield)
Thomas Bisbas (Cardiff)
PPARC
UKAFF
ECRTN
Multiplicity in Star Formation Toronto, 18 May 2007

2. Theory of prompt fragmentation of massive circumstellar discs
Toomre criterion: gravity overcomes internal pressure and rotation
Gammie criterion: fragment cools fast enough to condense out
Third criterion: fragment loses ang. mom. fast enough to condense out ?

3. ANALYTIC RESULTS:
Assuming Keplerian rotation and
prompt fragmentation is only possible at large radii,
and gives rise to low-mass companions:
i.e. brown dwarfs and planemos can form as distant companions to hydrogen-burning stars (Matzner & Levin 2005, Whitworth & Stamatellos 2006, also Rafikov 2005).

4. MISCELLANEOUS COMMENTS:
To form such massive extended discs only requires
Such discs will be hard to observe, because they fragment so quickly.
Such wide binary systems can be disrupted easily to produce brown dwarfs with a low velocity dispersion (Goodwin & Whitworth 2007)
Can close BD/BD binaries be produced by secondary fragmentation (due to H2 dissociation) or by 3-body capture?

5. (v) Cannot form massive planets by prompt fragmentation at
(vi) Convection won’t help, because
(vii) Impulsive perturbations won’t help; they promote Toomre instability, but they exacerbate the Gammie constraint (for any realistic opacity law, Whitworth et al. 2006).
(viii) To confirm these predictions, we need to do numerical simulations which treat the energy equation and the associated radiation transport. However, 3D multi-frequency radiation transport is prohibitively expensive computationally, so we need to use approximate methods, e.g. Whitehouse & Bate 2004,2006; Mayer et al. 2006; Rice et al
(ix) We have developed a new approximate method for treating the energy equation implicitly (Stamatellos, Whitworth, Bisbas & Goodwin 2007), which combines very efficiently with the DRAGON SPH code (Goodwin et al. 2004), up to
(x) The computational overhead is 3% (cf. 106%; Boss & Klein).

6. Energy equation accounts for:
compressional heating and expansive cooling;
artificial viscous dissipation;
external irradiation by central star (or nearby OB star and HII region);
radiative cooling, optically thin or thick.
Equation of state accounts for:
rotational and vibrational degrees of freedom of H2;
dissociation of H2;
ionization of Ho, Heo, He+;
(electron degeneracy pressure;)
(metallicity variations;)
(D-, H-burning.)
The opacity accounts for:
grains with icy mantles;
grain cores;
molecules;
H- ions;
bf & ff transitions;
electron scattering.

7. TESTS:
(i) Masunaga & Inutsuka, 1D spherical collapse with 3D multi-frequency radiation transport
(ii) Spiegel test, time-dependent analytic solution (optically thin and thick)
(iii) Hubeny test, equilibrium disc solution (optically thick)

8. Massive disk around low-mass hydrogen-burning star,
500,000 particles
(disc resolved)
No sink particles, condensations followed to density
600 AU

9. M=45 MJ Final frame of simulation: Brown dwarf Brown dwarf desert
600 AU

10. CONCLUSIONS:
Massive discs around low-mass H-burning stars only fragment promptly at
The resulting fragments tend to have low initial masses,
, and end up as a swarm of brown dwarfs.
Most of these brown dwarfs will be ejected at low velocities,
There is no evidence - yet - for secondary fragmentation due to H2 dissociation. BD/BD binaries could form by 3-body capture in the disc.
We need to simulate the formation of `discs’ from the collapse of turbulent cores.
It should be straightforward to explore the effects of different metallicities, strong ambient radiation field, etc.