tokens: heating term varies with radius, the equilibrium is different at different radii in the disc. This variation changes the minimum density required to maintain a two-phase structure in the ISM. 2.2 Star formation and feedback The star formation recipe used here is as described in Stinson et al. ( 2006 ) with some modifications. In the recipe, stars form following a Schmidt law: where ρ * is the density of new stars formed, ρ g is the density of eligible gas, is the dynamical time and c * is the chosen efficiency (see Section 3 ). Gas is considered eligible for star formation if it lies above a set density threshold, below a maximum temperature and belongs to a converging flow. The original recipe required that gas particles be below a set temperature threshold to form stars. We now compare the effective temperature associated with the total energy (including thermal and non-cooling, as discussed below) to the threshold value. This ensures that feedback will always locally limit star formation. In this work, the temperature threshold value is taken at 100 K. The key star formation model parameters that apply here are the minimum density threshold for gas to form stars ( n th ), the star formation efficiency per dynamical time ( c * ) and the feedback efficiency (ε fb ) relative to the standard amount from SNe, as described below. We employ the SN feedback method of Agertz et al. ( 2013 ). This model differs from the older blastwave model of Stinson et al. ( 2006 ) and the newer superbubble model of Keller et al. ( 2014 ) in that it is a simpler way to deposit the energy from SNe that still produces similar results and robust feedback regulation. Specifically, rather than being a complex function of local properties, the conversion time for injected energy is a set parameter. This gives us direct knowledge of how long feedback energy remains available as effective pressure and removes the associated uncertainty in interpreting our results. In more detailed models, feedback energy might take the form of pockets of hot gas, cosmic rays, radiation pressure, winds and small-scale turbulence, all injected on initially very small scales (∼pc; see e.g. Hopkins et al. 2012 ). Many of these processes are difficult to model, convert energy rapidly from one form to another and suffer from numerical effects including excess dissipation. The associated effective pressures become important for driving dynamics when they act on scales comparable to the scaleheight. A simple model ensures a well-characterized coupling of feedback energy to the dynamics on these scales. It also allows us to sidestep the unresolved issue of the relative importance of different types of feedback energy and how efficiently it converts into different forms. We normalize our energy input relative to that of SNe. A single SN deposits 10 51 erg of energy into the surrounding ISM. Based on the stellar initial mass function of Chabrier ( 2003 ), approximately one in 100 stars
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