  The Main Sequence (MS) of star-forming galaxies plays a fundamental role in
driving galaxy evolution and in our efforts to understand it. However,
different studies find significant differences in the normalization, slope and
shape of the MS. These discrepancies arise mainly from the different selection
criteria adopted to isolate star-forming galaxies, that may include or exclude
galaxies with specific star formation rate (SFR) substantially below the MS
value. To obviate this limitation of all current criteria, we propose an
objective definition of the MS that does not rely at all on a pre-selection of
star-forming galaxies. Constructing the 3D SFR-Mass-Number plot, the MS is then
defined as the ridge line of the star-forming peak, as illustrated with various
figures. The advantages of such definition are manifold. If generally adopted
it will facilitate the inter-comparison of results from different groups using
the same star formation rate (SFR) and stellar mass diagnostics, or to
highlight the relative systematics of different diagnostics. All this could
help understanding MS galaxies as systems in a quasi-steady state equilibrium
and would also provide a more objective criterion for identifying quenching
galaxies.

Astrophysics of Galaxies