The impact of thermodynamics on gravitational collapse: filament
  formation and magnetic field amplification
  Stars form by the gravitational collapse of interstellar gas. The
thermodynamic response of the gas can be characterized by an effective equation
of state. It determines how gas heats up or cools as it gets compressed, and
hence plays a key role in regulating the process of stellar birth on virtually
all scales, ranging from individual star clusters up to the galaxy as a whole.
We present a systematic study of the impact of thermodynamics on gravitational
collapse in the context of high-redshift star formation, but argue that our
findings are also relevant for present-day star formation in molecular clouds.
  We consider a polytropic equation of state, P = k rho^Gamma, with both
sub-isothermal exponents Gamma < 1 and super-isothermal exponents Gamma > 1. We
find significant differences between these two cases. For Gamma > 1, pressure
gradients slow down the contraction and lead to the formation of a virialized,
turbulent core. Weak magnetic fields are strongly tangled and efficiently
amplified via the small-scale turbulent dynamo on timescales corresponding to
the eddy-turnover time at the viscous scale. For Gamma < 1, on the other hand,
pressure support is not sufficient for the formation of such a core.
Gravitational contraction proceeds much more rapidly and the flow develops very
strong shocks, creating a network of intersecting sheets and extended
filaments. The resulting magnetic field lines are very coherent and exhibit a
considerable degree of order. Nevertheless, even under these conditions we
still find exponential growth of the magnetic energy density in the kinematic
regime.
