to have a robust continuum detection. For the remaining [56]{} galaxies we consider the continuum measurement as a limit and use it to calculate a lower limit to the [H$\alpha$]{} EW values. The redshift distribution of these galaxies is shown by Figure \[fig:specz\_distribution\].

Calculating optical colours {#sec:col_calculation}
---------------------------

Rest frame optical colours for the [ZFIRE-SP sample]{} are computed using an updated version of EAZY[^4] [@Brammer2008], which derives the best-fitting SEDs for galaxies using high quality ZFOURGE photometry to compute the colours. We investigate the robustness of the rest frame colour calculation of EAZY in Appendix \[sec:EAZY colour comparision\]. The main analysis of our sample is carried out using optical colours derived using two idealized, synthetic box car filters, which probes the bluer and redder regions of the rest frame SEDs. We select these filters to avoid regions of strong nebular emission lines as explained in Section \[sec:PEGASE\_models\] and Appendix \[sec:box car filters\].

In order to allow direct comparison between ZFIRE $z\sim2$ galaxies with $z=0.1$ SDSS galaxies from HG08, we further calculate optical colours for the [ZFIRE-SP sample]{} at $z=0.1$ using blue-shifted SDSS g and r filters. Blueshifting the filters simplifies the (g$-$r) colour calculation at $z=0.1$ ([$\mathrm{(g-r)_{0.1}}$]{}) by avoiding additional 