An evolving and mass dependent ${\rm \sigma_{\text{sSFR}}}$-${\rm
  M_{\star}}$ relation for galaxies
  The scatter (${\rm\sigma_{\text{sSFR}}}$) of the specific star formation
rates (sSFRs) of galaxies is a measure of the diversity in their star formation
histories (SFHs) at a given mass. In this paper we employ the EAGLE simulations
to study the dependence of the ${\rm \sigma_{\text{sSFR}}}$ of galaxies on
stellar mass (${\rm M_{\star}}$) through the ${\rm \sigma_{\text{sSFR}}}$-${\rm
M_{\star}}$ relation in $ {\rm z \sim 0-4}$. We find that the relation evolves
with time, with the dispersion depending on both stellar mass and redshift. The
models point to an evolving U-shape form for the ${\rm
\sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation with the scatter being
minimal at a characteristic mass $M^{\star}$ of ${\rm 10^{9.5}}$ ${\rm
M_{\odot}}$ and increasing both at lower and higher masses. This implication is
that the diversity of SFHs increases towards both at the low- and high-mass
ends. We find that active galactic nuclei feedback is important for increasing
the ${\rm \sigma_{\text{sSFR}}}$ for high mass objects. On the other hand, we
suggest that SNe feedback increases the ${\rm \sigma_{\text{sSFR}}}$ of
galaxies at the low-mass end. We also find that excluding galaxies that have
experienced recent mergers does not significantly affect the ${\rm
\sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation. Furthermore, we employ the
combination of the EAGLE simulations with the radiative transfer code SKIRT to
evaluate the effect of SFR/stellar mass diagnostics in the ${\rm
\sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation and find that the ${\rm
SFR/M_{\star}}$ methodologies (e.g. SED fitting, UV+IR, UV+IRX-$\beta$) widely
used in the literature to obtain intrinsic properties of galaxies have a large
effect on the derived shape and normalization of the ${\rm
\sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation.
