The evolution of turbulent galactic discs: gravitational instability,
  feedback and accretion
  We study the driving of turbulence in star-froming disc galaxies of different
masses at different epochs, using an analytic "bathtub" model. The disc of gas
and stars is assumed to be in marginal Toomre instability. Turbulence is
assumed to be sustained via an energy balance between its dissipation and three
simultaneous energy sources. These are stellar feedback, inward transport due
to disc instability and clumpy accretion via streams. The transport rate is
computed with two different formalisms, with similar results. To achieve the
energy balance, the disc self-regulates either the mass fraction in clumps or
the turbulent viscous torque parameter. In this version of the model, the
efficiency by which the stream kinetic energy is converted into turbulence is a
free parameter, $\xi_a$. We find that the contributions of the three energy
sources are in the same ball park, within a factor of $\sim\!2$ in all discs at
all times. In haloes that evolve to a mass $\leq 10^{12}\,\Msun$ by $z=0$
($\leq 10^{11.5}\,\Msun$ at $z\!\sim\!2$), feedback is the main driver
throughout their lifetimes. Above this mass, the main driver is either
transport or accretion for very low or very high values of $\xi_a$,
respectively. For an assumed $\xi_a(t)$ that declines in time, galaxies in
halos with present-day mass $>\!10^{12}$ M$_\odot$ make a transition from
accretion to transport dominance at intermediate redshifts, $z\! \sim\!3$, when
their mass was $\geq\!10^{11.5}\,\Msun$. The predicted relation between
star-formation rate and gas velocity dispersion is consistent with
observations.
