The instantaneous radial growth rate of stellar discs

We present a new and simple method to measure the instantaneous mass and radial growth rates of the stellar discs of spiral galaxies, based on their star formation rate surface density (SFRD) profiles. Under the hypothesis that discs are exponential with time-varying scalelengths, we derive a universal theoretical profile for the SFRD, with a linear dependence on two parameters: the specific mass growth rate $\nu_\textrm{M} \equiv \dot{M_\star}/M_\star$ and the specific radial growth rate $\nu_\textrm{R} \equiv \dot{R}_\star/R_\star$ of the disc. We test our theory on a sample of 35 nearby spiral galaxies, for which we derive a measurement of $\nu_\textrm{M}$ and $\nu_\textrm{R}$. 32/35 galaxies show the signature of ongoing inside-out growth ($\nu_\textrm{R} > 0$). The typical derived e-folding timescales for mass and radial growth in our sample are ~ 10 Gyr and ~ 30 Gyr, respectively, with some systematic uncertainties. More massive discs have a larger scatter in $\nu_\textrm{M}$ and $\nu_\textrm{R}$, biased towards a slower growth, both in mass and size. We find a linear relation between the two growth rates, indicating that our galaxy discs grow in size at ~ 0.35 times the rate at which they grow in mass; this ratio is largely unaffected by systematics. Our results are in very good agreement with theoretical expectations if known scaling relations of disc galaxies are not evolving with time.