The growth history of local M33-mass bulgeless spiral galaxies

NGC\,7793, NGC\,300, M33 and NGC\,2403 are four nearby undisturbed and bulgeless low-mass spiral galaxies with similar morphology and stellar mass. They are ideal laboratories to study disc formation scenarios and stellar mass growth histories. We construct a simple chemical evolution model by assuming that discs grow gradually with continuous metal-free gas infall and metal-enriched gas outflow. By means of the classical $\chi^{2}$ methodology, applied to the model predictions, the best combination of free parameters capable of reproducing the corresponding present-day observations is determined, i.e. the radial dependence of the infall timescale $\tau=0.1r/{R_{\rm d}}+3.4\,{\rm Gyr}$ ($R_{\rm d}$ is the disc scale-length) and the gas outflow efficiency $b_{\rm out}=0.2$. The model results are in excellent agreement with the general predictions of the inside-out growth scenario for the evolution of spiral galaxies. About 80\% of the stellar mass of NGC\,7793 is assembled within the last 8\,Gyr and 40\% within the last 4\,Gyr. By comparing the best-fitting model results of the three other galaxies we obtain similar results, 72\% (NGC\,300), 66\% (NGC\,2403) and 79\% (M33) stellar mass were assembled within the past $\sim\rm 8\,Gyr$ (i.e. $z\,=\,1$). These four disc galaxies simultaneously increase their sizes and stellar masses as time goes by and they grow in size at $\sim\,0.30$ times the rate at which they grow in mass. The scale-lengths of these four discs are now 20\% -- 25\% larger than at $z\,=\,1$. Our best-fitting model predicted the stellar mass-metallicity relation and the metallicity gradients, constrained by the observed metallicities from HII-regions emission line analysis, agree well with the observations measured from individual massive red and blue supergiant stars and population synthesis of SDSS galaxies.