# Modeling of the HERMES J105751.1+573027 submillimeter source lensed by a dark matter dominated foreground group of galaxies

### Abstract

We present the results of a gravitational lensing analysis of the bright $zs=2.957$ sub-millimeter galaxy (SMG), HERMES J105751.1+573027 found in {it Herschel}/SPIRE Science Demonstration Phase data from the Herschel Multi-tiered Extragalactic Survey (HerMES) project. The high resolution imaging available in optical and Near-IR channels, along with CO emission obtained with the Plateau de Bure Interferometer, allow us to precisely estimate the intrinsic source extension and hence estimate the total lensing magnification to be $mu=10.9pm 0.7$. We measure the half-light radius $R{rm eff}$ of the source in the rest-frame Near-UV and $V$ bands that characterize the unobscured light coming from stars and find $R{rm eff,*}= [2.0 pm 0.1]$ kpc, in good agreement with recent studies on the Submillimeter Galaxy population. This lens model is also used to estimate the size of the gas distribution ($R{rm eff,gas}= [1.1pm0.5]$) kpc by mapping back in the source plane the CO (J=5-4) transition line emission. The lens modeling yields a relatively large Einstein radius $R{rm Ein}= 4farcs10 pm 0farcs02$, corresponding to a deflector velocity dispersion of [$483pm 16] ,kms$. This shows that HERMES J105751.1+573027 is lensed by a {it galaxy group-size} dark matter halo at redshift $zlsim 0.6$. The projected dark matter contribution largely dominates the mass budget within the Einstein radius with $f{rm dm}(<R{rm Ein})sim 80%$. This fraction reduces to $f{rm dm}(<R{rm eff,G1}simeq 4.5kpc)sim 47%$ within the effective radius of the main deflecting galaxy of stellar mass $M_{rm *,G1}=[8.5pm 1.6] times 10^{11}msun$. At this smaller scale the dark matter fraction is consistent with results already found for massive lensing ellipticals at $zsim0.2$ from the SLACS survey.

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