arXiv:1112.0029v2 [astro-ph.CO] 10 Jan 2012 Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 11 January 2012 (MN L A T E X style file v2.2) On the Evolution of the SFR Function of Massive Galaxies. Constraints at 0.4 <z< 1.8 from the GOODS-MUSIC Catalogue Fabio Fontanot 1,2 , Stefano Cristiani 1 , Paola Santini 3 , Adriano Fontana 3 , Andrea Grazian 3 and Rachel S. Somerville 4,5 1 INAF-Osservatorio Astronomico, Via Tiepolo 11, I-34131 Trieste, Italy 2 HITS-Heidelberger Institut f¨ ur Theoretische Studien, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany 3 INAF-Osservatorio Astronomico di Roma, via Frascati 33, I-00040, Monteporzio, Italy 4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 5 Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA email: fabio.fontanot@h-its.org Accepted ... Received ... ABSTRACT We study the evolution of the Star Formation Rate Function (SFRF) of massive (M ⋆ > 10 10 M ⊙ ) galaxies over the 0.4 <z< 1.8 redshift range and its implications for our understanding of the physical processes responsible for galaxy evolution. We use multiwavelength observations included in the GOODS-MUSIC catalogue, which provides a suitable coverage of the spectral region from 0.3 to 24 µm and either spectro- scopic or photometric redshifts for each object. Individual SFRs have been obtained by combining UV and 24 µm observations, when the latter were available. For all other sources an “SED fitting” SFR estimate has been considered. We then define a stellar mass limited sample, complete in the M ⋆ > 10 10 M ⊙ range and determine the SFRF using the 1/V max algorithm. We thus define simulated galaxy catalogues based on the predictions of three different state-of-the-art semi-analytical models of galaxy formation and evolution, and compare them with the observed SFRF. We show that the theoretical SFRFs are well described by a double power law functional form and its redshift evolution is approximated with high accuracy by a pure evolution of the typical SFR (SFR ⋆ ). We find good agreement between model predictions and the high-SFR end of the SFRF, when the observational errors on the SFR are taken into account. However, the observational SFRF is characterised by a double peaked struc- ture, which is absent in its theoretical counterparts. At z> 1.0 the observed SFRF shows a relevant density evolution, which is not reproduced by SAMs, due to the well known overprediction of intermediate mass galaxies at z ∼ 2. Semi-analytical models are thus able to reproduce the most intense SFR events observed in the GOODS- MUSIC sample and their redshift distribution. At the same time, the agreement at the low-SFR end is poor: all models overpredict the space density of SFR ∼ 1M ⊙ /yr and no model reproduces the double peaked shape of the observational SFRF. If con- firmed by deeper IR observations, this discrepancy will provide a key constraint on theoretical modelling of star formation and stellar feedback. Key words: galaxies: evolution - galaxies: fundamental parameters - cosmology: observations 1 INTRODUCTION The evolution of the star formation rate (SFR) over the cosmic time is a fundamental constraint for every theory of galaxy formation and evolution (see e.g. Hopkins 2004; Hopkins & Beacom 2006). Estimating SFRs for individual galaxies is a complex task, owing to the uncertainties in- volved in the reconstruction of this quantity from obser- vational data. It is widely accepted that dusty molecular clouds are the main sites for star formation: this implies that newly born stars are subject to significant dust atten- uation, until they are able to escape or disrupt their parent c  0000 RAS