Super star clusters ( SSCs ) are typically found in interacting galaxies and trace an extreme form of star-formation .
We present a K -band study of SSC candidates in a sample of local luminous infrared galaxies ( LIRGs ) using two adaptive optics instruments ( VLT/NACO and Gemini/ALTAIR/NIRI ) .
In addition to facilitating SSC detections in obscured environments , this work introduces SSC studies in hosts with higher star-formation rates ( SFRs ) than most previous studies .
We find that the luminosity functions ( LFs ) of the clusters are reasonably well-fitted by a single power-law with the values of the index \alpha ranging between 1.5 to 2.4 with an average value of \alpha \approx 1.9 .
This value appears to be less steep than the average \alpha \approx 2.2 in normal spiral galaxies .
Due to the host galaxy distances involved ( median D _ { L } \sim 70 Mpc ) blending effects have to be taken into account , and are investigated using Monte Carlo simulations of blending effects for LFs and a photometric SSC analysis of the well-studied Antennae system which is artificially redshifted to distances of our sample .
While blending tends to flatten LFs our analyses show that \Delta \alpha is less than \sim 0.1 in our sample .
The simulations also show that in the luminosity range , M _ { K } < -13 , considered in this work the extracted SSC luminosities are generally dominated by a single dominant star cluster rather than several knots of SF .
We present resolution- and distance-dependent SSC surface density confusion limits and show how blending rates and aperture sizes affect the LFs .
The smallest possible apertures should be used in crowded regions .