  Star-formation rates (SFRs) of galaxies are commonly calculated by converting
the measured Halpha luminosities (L_Halpha) into current SFRs. This conversion
is based on a constant initial mass function (IMF) independent of the total
SFR. As recently recognised the maximum stellar mass in a star cluster is
limited by the embedded total cluster mass and, in addition, the maximum
embedded star cluster mass is constrained by the current SFR. The combination
of these two relations leads to an integrated galaxial initial stellar mass
function (IGIMF, the IMF for the whole galaxy) which is steeper in the high
mass regime than the constant canonical IMF, and is dependent on the SFR of the
galaxy. Consequently, the L_Halpha-SFR relation becomes non-linear and flattens
for low SFRs. Especially for dwarf galaxies the SFRs can be underestimated by
up to three orders of magnitude. We revise the existing linear L_Halpha-SFR
relations using our IGIMF notion. These are likely to lead to a revision of the
cosmological star formation histories. We also demonstrate that in the case of
the Sculptor dwarf irregular galaxies the IGIMF-formalism implies a linear
dependence of the total SFR on the total galaxy gas mass. A constant gas
depletion time scale of a few Gyrs results independently of the galaxy gas mass
with a reduced scatter compared to the conventional results. Our findings are
qualitatively independent of the explicit choice of the IGIMF details and
challenges current star formation theory in dwarf galaxies.
