Star Formation Rate (SFR) inferences are based in the so-called constant SFR
approximation, where synthesis models are require to provide a calibration; we
aims to study the key points of such approximation to produce accurate SFR
inferences. We use the intrinsic algebra used in synthesis models, and we
explore how SFR can be inferred from the integrated light without any
assumption about the underling Star Formation history (SFH). We show that the
constant SFR approximation is actually a simplified expression of more deeper
characteristics of synthesis models: It is a characterization of the evolution
of single stellar populations (SSPs), acting the SSPs as sensitivity curve over
different measures of the SFH can be obtained. As results, we find that (1) the
best age to calibrate SFR indices is the age of the observed system (i.e. about
13Gyr for z=0 systems); (2) constant SFR and steady-state luminosities are not
requirements to calibrate the SFR; (3) it is not possible to define a SFR
single time scale over which the recent SFH is averaged, and we suggest to use
typical SFR indices (ionizing flux, UV fluxes) together with no typical ones
(optical/IR fluxes) to correct the SFR from the contribution of the old
component of the SFH, we show how to use galaxy colors to quote age ranges
where the recent component of the SFH is stronger/softer than the older
component.
Particular values of SFR calibrations are (almost) not affect by this work,
but the meaning of what is obtained by SFR inferences does. In our framework,
results as the correlation of SFR time scales with galaxy colors, or the
sensitivity of different SFR indices to sort and long scale variations in the
SFH, fit naturally. In addition, the present framework provides a theoretical
guide-line to optimize the available information from data/numerical
experiments to improve the accuracy of SFR inferences.