On the nature of the extragalactic number counts in the K-band

We investigate the causes of the different shape of the $K$-band number counts when compared to other bands, analyzing in detail the presence of a change in the slope around $Ksim17.5$. We present a near-infrared imaging survey, conducted at the 3.5m telescope of the Calar Alto Spanish-German Astronomical Center (CAHA), covering two separated fields centered on the HFDN and the Groth field, with a total combined area of $sim0.27$deg$^{2}$ to a depth of $Ksim19$ ($3sigma$,Vega). We derive luminosity functions from the observed $K$-band in the redshift range [0.25-1.25], that are combined with data from the references in multiple bands and redshifts, to build up the $K$-band number count distribution. We find that the overall shape of the number counts can be grouped into three regimes: the classic Euclidean slope regime ($dlog N/dmsim0.6$) at bright magnitudes; a transition regime at intermediate magnitudes, dominated by $M^{ast}$ galaxies at the redshift that maximizes the product $phi^{ast}frac{dV_{c}}{dOmega}$; and an $alpha$ dominated regime at faint magnitudes, where the slope asymptotically approaches -0.4($alpha$+1) controlled by post-$M^{ast}$ galaxies. The slope of the $K$-band number counts presents an averaged decrement of $sim50%$ in the range $15.5<K<18.5$ ($dlog N/dmsim0.6-0.30$). The rate of change in the slope is highly sensitive to cosmic variance effects. The decreasing trend is the consequence of a prominent decrease of the characteristic density $phi^{ast}_{K,obs}$ ($sim60%$ from $z=0.5$ to $z=1.5$) and an almost flat evolution of $M^{ast}_{K,obs}$ (1$sigma$ compatible with $M^{ast}_{K,obs}=-22.89pm0.25$ in the same redshift range).