Constraining the population of $6 \la {z} \la 10$star-forming galaxies with deep near-IR images of lensing clusters

We present the first results of our deep survey of lensing clusters aimed at constraining the abundance of star-forming galaxies at $z\sim6{-}10$, using lensing magnification to improve the search efficiency and subsequent spectroscopic studies. 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 $z\ga 6$among the optical-dropouts. Photometric selection criteria have been defined based on the well-proven dropout technique, specifically tuned to target star-forming galaxies in this redshift domain. 
We have identified 18(8) first and second-category optical dropouts in A1835 (AC114), detected in more than one filter up to H(Vega) $\sim 23.8$(AB~ 25.2, uncorrected for lensing). Among them, 8(5) exhibit homogeneous SEDs compatible with star-forming galaxies at $z\ga 6$, 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 $6\la z \la10$using lensing clusters. Magnification effects and sample incompleteness are addressed through a careful modeling of the lensing clusters. A correction was also introduced to account for the expected fraction of false-positive detections among this photometric sample. 
It appears that the number of candidates found in these lensing fields, corrected for magnification, incompleteness and false-positive detections, is higher than the one achieved in blank fields with similar photometric depth in the near-IR. The luminosity function derived for $z\ga 6$candidates appears compatible with that of LBGs at $z\simeq 3$, without any renormalization. The turnover observed by Bouwens et al. (2005) towards the bright end relative to the $z\sim 3$LF is not observed in this sample. Also the upper limit for the UV SFR density at $z\sim6{-}10$, integrated down to $L_{1500}=0.3~L^{*}_{z=3}$, of $\rho_\star=7.4$$\times$$10^{-2}~M_{\odot}$yr-1Mpc-3is compatible with the usual values derived at $z \simeq 5{-}6$, but higher than the estimates obtained in the NICMOS Ultra Deep Field (UDF). The same holds for the upper limit of the SFR density in the $z \simeq 8{-}10$interval ($\rho_\star=1.1$$\times$10-1). This systematic trend towards the bright end of the LF with respect to blank fields could be due to field-to-field variance, a positive magnification bias from intermediate-redshift EROs, and/or residual contamination. Given the low S/Nratio of the high-zcandidates, and the large correction factors applied to this sample, increasing the number of blank and lensing fields with ultra-deep near-IR photometry is essential to obtain more accurate constraints on the abundance of $z \ga 6$galaxies.