Single Colour Diagnostics of the Mass-to-light Ratio: Predictions from
  Galaxy Formation Models
  Accurate galaxy stellar masses are crucial to better understand the physical
mechanisms driving the galaxy formation process. We use synthetic star
formation and metal enrichment histories predicted by the {\sc galform} galaxy
formation model to investigate the precision with which various colours
$(m_{a}-m_{b})$ can alone be used as diagnostics of the stellar mass-to-light
ratio. As an example, we find that, at $z=0$, the {\em intrinsic}
(B$_{f435w}-$V$_{f606w}$) colour can be used to determine the intrinsic
rest-frame $V$-band stellar mass-to-light ratio
($\log_{10}\Gamma_{V}=\log_{10}[(M/M_{\odot})/(L_{V}/L_{V\odot})]$) with a
precision of $\sigma_{lg\Gamma}\simeq 0.06$ when the initial mass function and
redshift are known beforehand. While the presence of dust, assuming a universal
attenuation curve, can have a systematic effect on the inferred mass-to-light
ratio using a single-colour relation, this is typically small as it is often
possible to choose a colour for which the dust reddening vector is
approximately aligned with the $(m_{a}-m_{b})-\log_{10}\Gamma_{V}$ relation.
The precision with which the stellar mass-to-light ratio can be recovered using
a single colour diagnostic rivals implementations of SED fitting using more
information but in which simple parameterisations of the star formation and
metal enrichment histories are assumed. To facilitate the wide use of these
relations, we provide the optimal observer frame colour to estimate the stellar
mass-to-light ratio, along with the associated parameters, as a function of
redshift ($0<z<1.5$) for two sets of commonly used filters.
