We combine far-infrared photometry from Herschel ( PEP/HERMES ) with deep mid-infrared spectroscopy from Spitzer to investigate the nature and the mass assembly history of a sample of 31 Luminous and Ultraluminous Infrared Galaxies at z \sim 1 and 2 selected in GOODS-S with 24 \mu m fluxes between 0.2 and 0.5 mJy .
We model the data with a self-consistent physical model ( GRASIL ) which includes a state-of-the-art treatment of dust extinction and reprocessing .
We find that all of our galaxies appear to require massive populations of old ( > 1 Gyr ) stars and , at the same time , to host a moderate ongoing activity of SF ( SFR \leq 100 M _ { \odot } /yr ) .
The bulk of the stars appear to have been formed a few Gyr before the observation in essentially all cases .
Only five galaxies of the sample require a recent starburst superimposed on a quiescent star formation history ( SFH ) .
We also find discrepancies between our results and those based on optical-only SED fitting for the same objects ; by fitting their observed Spectral Energy Distributions with our physical model we find higher extinctions ( by \Delta A _ { \mathrm { V } } \sim 0.81 and 1.14 ) and higher stellar masses ( by \Delta Log ( M _ { \star } ) \sim 0.16 and 0.36 dex ) for z \sim 1 and z \sim 2 ( U ) LIRGs , respectively .
The stellar mass difference is larger for the most dust obscured objects .
We also find lower SFRs than those computed from L _ { \mathrm { IR } } using the Kennicutt relation due to the significant contribution to the dust heating by intermediate-age stellar populations through ‘ cirrus ’ emission ( \sim 73 % and \sim 66 % of total L _ { \mathrm { IR } } for z \sim 1 and z \sim 2 ( U ) LIRGs , respectively ) .