Time variation of ellipticity of globular clusters in the Large Magellanic Cloud

Dynamical evolution of globular clusters in the Large Magellanic Cloud (LMC) is investigated by means of N-body simulations; particular attention is paid to time evolution in the ellipticitical figure of globular clusters. The simulations were started with a binary globular cluster. It merged into a single cluster with ellipticity of about 0.3. The simulations were continued until the cluster became rounder due to the effects of two body relaxation and of tidal field of LMC. It is found that the outward angular momentum transport due to the gravothermal contraction makes the inner region rounder; the ellipticity at about the initial half-mass radius (r _h) decreases with the e-folding time of 20 relaxation times. On the other hand, the outer region becomes rounder due to the stripping of stars by the tidal field; the ellipticity at about 3r _h decreases with the e-folding time of 80 crossing times therein, though the time scale depends on the direction of the tidal field relative to the spin of the cluster. These two effects are comparable at about the half-mass radius. Taking account of such theoretical results we reanalyzed observed data for the ellipticity at about the half-mass radius of LMC clusters. We estimated the relaxation time and crossing time for each of the observed clusters, from which we calculated the effective time of getting round of the cluster. We plotted the observed ellipticity of the clusters against their non-dimensional age — i.e., the age normalized by the effective time. We found that observed ellipticity distribution is consistent with our picture.