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Description
Context. Over the last decade a large number of dusty star-forming galaxies has been discovered up to redshift z=2-3 and recent studies have attempted to push the highly confused Herschel SPIRE surveys beyond that distance. To search for z>=4 galaxies they often consider the sources with fluxes rising from 250{mu}m to 500{mu}m (so-called "500{mu}m-risers"). Herschel surveys offer a unique opportunity to efficiently select a large number of these rare objects, and thus gain insight into the prodigious star-forming activity that takes place in the very distant Universe. Aims. We aim to implement a novel method to obtain a statistical sample of 500{mu}m-risers and fully evaluate our selection inspecting different models of galaxy evolution. Methods. We consider one of the largest and deepest Herschel surveys, the Herschel Virgo Cluster Survey. We develop a novel selection algorithm which links the source extraction and spectral energy distribution fitting. To fully quantify selection biases we make end-to-end simulations including clustering and lensing. Results. We select 133 500{mu}m-risers over 55deg^2^, imposing the criteria: S_500_>S_350_>S_250_, S_250_>13.2mJy and S_500_>30mJy. Differential number counts are in fairly good agreement with models, displaying a better match than other existing samples. The estimated fraction of strongly lensed sources is 24_+6_^-5^% based on models.Conclusions. We present the faintest sample of 500{mu}m-risers down to S_250_=13.2mJy. We show that noise and strong lensing have an important impact on measured counts and redshift distribution of selected sources. We estimate the flux-corrected star formation rate density at 4<z<5 with the 500{mu}m-risers and find it to be close to the total value measured in far-infrared. This indicates that colour selection is not a limiting effect to search for the most massive, dusty z>4 sources.
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