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.
