Hubble Space Telescope allows us to study the central surface brightness profiles for globular clusters at unprecedented detail. We have mined the HST archives to obtain 38 WFPC2 images of galactic globular clusters with adequate exposure times and filters, which we use to measure their central structure. We outline a reliable method to obtain surface brightness profiles from integrated light that we test on an extensive set of simulated images. Most clusters have central surface brightness about 0.5 mag brighter than previous measurements made from ground-based data, with the largest differences around 2 magnitudes. Including the uncertainties in the slope estimates, the surface brightness slope distribution is consistent with half of the sample having flat cores and the remaining half showing a gradual decline from 0 to -0.8 (dlog(Sigma)/dlogr). We deproject the surface brightness profiles in a non-parametric way to obtain luminosity density profiles. The distribution of luminosity density logarithmic slopes show similar features with half of the sample between -0.4 and -1.8. These results are in contrast to our theoretical bias that the central regions of globular clusters are either isothermal (i.e. flat central profiles) or very steep (i.e. luminosity density slope ~-1.6) for core-collapse clusters. With only 50% of our sample having central profiles consistent with isothermal cores, King models appear to poorly represent most globular clusters in their cores.
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