Constraining the population of 6 < z < 10 star-forming galaxies with deep near-IR images of lensing clusters

(abridged) We present the first results of our deep survey of lensing clusters aimed at constraining the abundance of star-forming galaxies at z~6-10. Deep near-IR photometry of two lensing clusters (A1835 and AC114) was obtained with ISAAC/VLT. These images, combined with existing data in the optical bands, including HST images, were used to select very high redshift candidates at z>~6 among the optical-dropouts. We have identified 18(8) first and second-category optical dropouts in A1835 (AC114), detected in more than one filter up to H(Vega)~23.8 (AB~25.2,uncorrected for lensing). Among them, 8(5) exhibit homogeneous SEDs compatible with star-forming galaxies at z>~6, and 5(1) are more likely intermediate-redshift EROs based on luminosity considerations. We have also identified a number of fainter sources in these fields fulfilling our photometric selection and located around the critical lines. We use all these data to make a first attempt at constraining the density of star-forming galaxies present at 6<z<10 using lensing clusters. Taken at face value, it appears that the number of candidates found seems to be higher than the one achieved in blank fields with similar photometric depth in the near-IR. The luminosity function derived for z>6 candidates appears compatible with that of LBGs at z~3. The turnover observed by Bouwens et al. (2005) towards the bright end relative to the z~3 LF is not observed in this sample. Also the upper limit for the UV SFR density at z~6-10 is compatible with the usual values derived at z~5-6, but higher than the estimates obtained in the NICMOS Ultra Deep Field (UDF). Increasing the number of blank and lensing fields with ultra-deep near-IR photometry is essential to get more accurate constraints on the abundance of z>6 galaxies.