Deep Extragalactic VIsible Legacy Survey (DEVILS): Evolution of the
  $\sigma_{\mathrm{SFR}}$-M$_{\star}$ relation and implications for
  self-regulated star formation
  We present the evolution of the star-formation dispersion - stellar mass
relation ($\sigma_{SFR}$-M$_{\star}$) in the DEVILS D10 region using new
measurements derived using the ProSpect spectral energy distribution fitting
code. We find that $\sigma_{SFR}$-M$_{\star}$ shows the characteristic
'U-shape' at intermediate stellar masses from 0.1<z<0.7 for a number of
metrics, including using the deconvolved intrinsic dispersion. A physical
interpretation of this relation is the combination of stochastic star-formation
and stellar feedback causing large scatter at low stellar masses and AGN
feedback causing asymmetric scatter at high stellar masses. As such, the shape
of this distribution and its evolution encodes detailed information about the
astrophysical processes affecting star-formation, feedback and the lifecycle of
galaxies. We find that the stellar mass that the minimum ${\sigma}_{SFR}$
occurs evolves linearly with redshift, moving to higher stellar masses with
increasing lookback time and traces the turnover in the star-forming sequence.
This minimum ${\sigma}_{SFR}$ point is also found to occur at a fixed specific
star-formation rate (sSFR) at all epochs (sSFR~10$^{-9.6}$yr$^{-1}$). The
physical interpretation of this is that there exists a maximum sSFR at which
galaxies can internally self-regulate on the tight sequence of star-formation.
At higher sSFRs, stochastic stellar processes begin to cause galaxies to be
pushed both above and below the star-forming sequence leading to increased SFR
dispersion. As the Universe evolves, a higher fraction of galaxies will drop
below this sSFR threshold, causing the dispersion of the low-stellar mass end
of the star-forming sequence to decrease with time.
