We present a study of K _ { s } band luminosity evolution of the asymptotic giant branch ( AGB ) population in simple stellar systems using star clusters in the Large Magellanic Cloud ( LMC ) .
We determine physical parameters of LMC star clusters including center coordinates , radii , and foreground reddenings .
Ages of 83 star clusters are derived from isochrone fitting with the Padova models , and those of 19 star clusters are taken from the literature .
The AGB stars in 102 star clusters with log ( age ) = 7.3 – 9.5 are selected using near-infrared color magnitude diagrams based on 2MASS photometry .
Then we obtain the K _ { s } band luminosity fraction of AGB stars in these star clusters as a function of ages .
The K _ { s } band luminosity fraction of AGB stars increases , on average , as age increases from log ( age ) \sim 8.0 , reaching a maximum at log ( age ) \sim 8.5 , and it decreases thereafter .
There is a large scatter in the AGB luminosity fraction for given ages , which is mainly due to stochastic effects .
We discuss this result in comparison with five simple stellar population models .
The maximum K _ { s } band AGB luminosity fraction for bright clusters is reproduced by the models that expect the value of 0.7 – 0.8 at log ( age ) = 8.5 – 8.7 .
We discuss the implication of our results with regard to the study of size and mass evolution of galaxies .