On the effect of cosmological inflow on turbulence and instability in
  galactic discs
  We analyse the evolution of turbulence and gravitational instability of a
galactic disc in a quasi-steady state governed by cosmological inflow. We focus
on the possibility that the coupling between the in-streaming gas and the disc
is maximal, e.g., via dense clumps, and ask whether the streams could be the
driver of turbulence in an unstable disc with a Toomre parameter Q~1. Our
fiducial model assumes an efficiency of ~0.5 per dynamical time for the decay
of turbulence energy, and ~0.02 for each of the processes that deplete the disc
gas, i.e., star formation, outflow, and inflow within the disc into a central
bulge. In this case, the in-streaming drives a ratio of turbulent to rotation
velocity sigma/V~0.2-0.3, which at z~2 induces an instability with Q~1, both as
observed. However, in conflict with observations, this model predicts that
sigma/V remains constant with time, independent of the cosmological accretion
rate, because mass and turbulence have the same external source. Such strongly
coupled cosmological inflow tends to stabilize the disc at low z, with Q ~ a
few, which may be consistent with observations. The instability could instead
be maintained for longer, with a properly declining sigma/V, if it is
self-regulated to oscillations about Q~1 by a duty cycle for disc depletion.
However, the 'off' phases of this duty cycle become long at low z, which may be
hard to reconcile with observations. Alternatively, the coupling between the
in-streaming gas and the disc may weaken in time, reflecting an evolving nature
of the accretion. If, instead, that coupling is weak at all times, the likely
energy source for self-regulated stirring up of the turbulence is the inflow
within the disc down the potential gradient (studied in a companion paper).
