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

Context. Morphology is the most accessible tracer of galaxies physical structure, but its interpretation in the framework of galaxy evolution still remains problematic. Its quantification at high redshift requires deep high-angular resolution imaging, which is why space data (HST) are usually employed. At z > 1, the HST visible cameras however probe the UV flux, which is dominated by the emission of young stars, which could bias the estimated morphologies towards late-type systems. Aims. In this paper we quantify the effects of this morphological k-correction at 1 < z < 2 by comparing morphologies measured in the K and I-bands in the COSMOS area. The Ks-band data indeed have the advantage of probing old stellar populations in the rest frame for z < 2, enabling determination of galaxy morphological types unaffected by recent star formation. Methods. In Paper I we presented a new non-parametric method of quantifying morphologies of galaxies on seeing-limited images based on support vector machines. Here we use this method to classify similar to 50 000 Ks selected galaxies in the COSMOS area observed with WIRCam at CFHT. We use a 10-dimensional volume, including 5 morphological parameters, and other characteristics of galaxies such as luminosity and redshift. The obtained classification is used to investigate the redshift distributions and number counts per morphological type up to z similar to 2 and to compare them to the results obtained with HST/ACS in the I-band on the same objects. 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. We use this value to assess the accuracy of our classification as a function of physical parameters of the galaxy and to correct for classification errors. Results. The classification is found to be reliable up to z similar to 2. The mean probability is p similar to 0.8. It decreases with redshift and with size, especially for the early-type population, but remains above p similar to 0.7. The classification globally agrees with the one obtained using HST/ACS for z < 1. Above z similar to 1, the I-band classification tends to find less early-type galaxies than the Ks-band one by a factor similar to 1.5, which might be a consequence of morphological k-correction effects. Conclusions. We argue therefore that studies based on I-band HST/ACS classifications at z > 1 could be underestimating the elliptical population. Using our method in a K-s <= 21.5 magnitude-limited sample, we observe that the fraction of the early-type population is (21.9% +/- 8%) at z similar to 1.5-2 and (32.0% +/- 5%) at the present time. We will discuss the evolution of the fraction of galaxies in types from volume-limited samples in a forthcoming paper.