Recent SFR calibrations and the constant SFR approximation

¹ Instituto de Astrofísica de Canarias, c/ vía Láctea s/n, 38205 La Laguna, Tenerife, Spain
e-mail: mcs@iaa.es
² Departamento de Astrofísica, Universidad de La Laguna (ULL), 38205, La Laguna, Tenerife, Spain
³ Instituto de Astrofísica de Andalucía (IAA-CSIC), Placeta de la Astronomía s/n, 18008 Granada, Spain
⁴ Asociación ASPID, Apartado de Correos 412, 38200 La Laguna, Tenerife, Spain

Received: 29 December 2015
Accepted: 11 February 2016

Abstract

Aims. Star formation rate (SFR) inferences are based on the so-called constant SFR approximation, where synthesis models are required to provide a calibration. We study the key points of such an approximation with the aim to produce accurate SFR inferences.

Methods. We use the intrinsic algebra of synthesis models and explore how the SFR can be inferred from the integrated light without any assumption about the underlying star formation history (SFH).

Results. We show that the constant SFR approximation is a simplified expression of deeper characteristics of synthesis models: It characterizes the evolution of single stellar populations (SSPs), from which the SSPs as a 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 13 Gyr for z = 0 systems); (2) constant SFR and steady-state luminosities are not required to calibrate the SFR; (3) it is not possible to define a single SFR timescale over which the recent SFH is averaged, and we suggest to use typical SFR indices (ionizing flux, UV fluxes) together with untypical ones (optical or IR fluxes) to correct the SFR for 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 or softer than the older component.

Conclusions. Despite of SFR calibrations are unaffected by this work, the meaning of results obtained by SFR inferences does. In our framework, results such as the correlation of SFR timescales with galaxy colors, or the sensitivity of different SFR indices to variations in the SFH, fit naturally. This framework provides a theoretical guide-line to optimize the available information from data and numerical experiments to improve the accuracy of SFR inferences.