Azimuthally-averaged Toomre parameter (a) and the cooling time in units of the local orbital period (b) for runs 1–3 (red, green and blue, respectively). The time at which these quantities are shown are just prior to fragmentation (runs 1 and 2), and just prior to a period of disc expansion (run 3). The dashed blue line shows run 3 after the expansion. Each disc is gravitationally unstable such that spiral arms form, but only in runs 1 and 2 does the Toomre parameter fall below unity so that bound fragments form. In all cases, the cooling time is sufficiently short for a condensed fragment to collapse. The expansion of the disc in run 3 (and characteristic of most runs with an increased metallicity) acts to stabilise it.