A robust morphological classification of high-redshift galaxies using   support vector machines on seeing limited images. II. Quantifying   morphological k-correction in the COSMOS field at 1<z<2: Ks band vs. I band
  We quantify the effects of \emph{morphological k-correction} at $1<z<2$ by comparing morphologies measured in the K and I-bands in the COSMOS area. Ks-band data have indeed the advantage of probing old stellar populations for $z<2$, enabling a determination of galaxy morphological types unaffected by recent star formation. In paper I we presented a new non-parametric method to quantify morphologies of galaxies on seeing limited images based on support vector machines. Here we use this method to classify $\sim$$50 000$ $Ks$ selected galaxies in the COSMOS area observed with WIRCam at CFHT. The obtained classification is used to investigate the redshift distributions and number counts per morphological type up to $z\sim2$ and to compare to the results obtained with HST/ACS in the I-band on the same objects from other works. We associate to every galaxy with $Ks<21.5$ and $z<2$ a probability between 0 and 1 of being late-type or early-type. The classification is found to be reliable up to $z\sim2$. The mean probability is $p\sim0.8$. It decreases with redshift and with size, especially for the early-type population but remains above $p\sim0.7$. The classification is globally in good agreement with the one obtained using HST/ACS for $z<1$. Above $z\sim1$, the I-band classification tends to find less early-type galaxies than the Ks-band one by a factor $\sim$1.5 which might be a consequence of morphological k-correction effects. We argue therefore that studies based on I-band HST/ACS classifications at $z>1$ could be underestimating the elliptical population. [abridged] 
M. Huertas-Company, L. Tasca, D. Rouan, D. Pelat, J.P. Kneib, O. Le   Fevre, P. Capak, J. Kartaltepe, A. Koekemoer, H.J. McC...