500{mu}m-risers sources

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.