Emmy Noether Application

2400 AU
150 AU
Figure 4: Shows the structure (iso-densities) of the filamentary core which harbours a protostellar
disc. The initial conditions for this simulation were taken from calculations of Tilley &
Pudritz (2005) in which cores formed from supersonic turbulence. Here, an initially elongated
core collapses to a filament at which a thin sheet is attached. This off-centre sheet supports
the central disc with high angular momentum gas (see also Figure 5 for density slices through
the filament). Figure taken from Banerjee et al. (2006)
like in the case of a singular isothermal sphere Shu (1977). These results are also confirmed
by many other calculations (e.g., Foster & Chevalier, 1993; Hennebelle et al., 2003).
Already in our earliest investigation where we studied high-mass (M ∼ 170M⊙) and lowmass
(M ∼ 2.1M⊙, resembling the parameters of Barnard 68) collapsing cloud cores we
showed again that mass accretion rates are much higher than expected from the collapse
of a singular isothermal sphere (Banerjee et al., 2004). We re-visited this particular point
in Banerjee & Pudritz (2007) where focused on the early stage of massive star formation.
Here, we find mass accretion rates as high as 10 −3 M⊙ yr −1 . These might exceed the limits
calculated by Wolfire & Cassinelli (1987) necessary to overcome the radiation pressure. The
high accretion rates results have a simple explanation: The infall velocities are supersonic
which means that the estimate for the mass accretion ˙ M ∼ c 3 /G cannot be valid in this
regime and has to be replaced by ˙ M ∼ v 3 r /G, where vr is the proper gas infall speed.
Therefore, even moderate infall speeds of Mach 3 will result in a almost 30 times higher
accretion rate than given by c 3 /G. This does not yet account for the fact that the gas heats
during contraction which implies even higher infall speeds in the warm core. We find that the
infall speed is always of the order of 2 − 3 times the local sound speed. Together with this
effect the mass accretion rates can easily exceed 100 × c 3 /G as shown in Figure 3. Recent
observations of collapsing cloud cores clearly indicate supersonic infall speeds (Beltrán et al.,
2006; Furuya et al., 2006).
Similar theoretical results were obtained by McKee & Tan (2002) in a different approach.
These authors show that high accretion rates can be obtained if the surrounding pressure
stays high. This will be naturally achieved in the turbulent environment in which stars form.
If our results will persist even in a more realistic setup (i.e. including radiation feedback) this
would support an unified picture of star formation where low-mass and high-mass stars form
though accretion of the gas from their respective parental cloud core.
Turbulent Cloud Cores
To move towards a more realistic description of massive star formation we studied the collapse
of massive cloud cores which were assembled in a turbulent environment (Banerjee
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37 AU