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The Offset and Host Light Distributions of Long Gamma-Ray Bursts: A New View from HST Observations of Swift Bursts

[Abridged] We present the results of an extensive Hubble Space Telescope (HST) imaging study of ~100 Swift long-duration gamma-ray bursts (LGRBs) spanning 0.03 < z < 9.4 using relative astrometry from afterglow observations to locate the bursts within their host galaxies. We measure the distribution of LGRB offsets from their host centers, as well as their relation to the underlying host light distribution. We find that the host-normalized offsets (R/R_h) of LGRBs are more centrally concentrated than expected for an exponential disk profile, with a median of 0.67, and in particular they are more concentrated than the underlying surface brightness profiles of their host galaxies. The distribution of offsets is inconsistent with the distribution for Type II supernovae (SNe) but consistent with the distribution for Type Ib/c SNe. The fractional flux distribution, with a median of 0.75, indicates that LGRBs prefer some of the brightest locations in their host galaxies but are not as strongly correlated as previous studies indicated. More importantly, we find a clear correlation between the offset and fractional flux, where bursts at R/R_h < 0.5 exclusively occur at fractional fluxes > 0.6 while bursts at R/R_h > 0.5 uniformly trace the light of their hosts. This indicates that the spatial correlation of LGRB locations with bright star forming regions seen in the full sample is dominated by the contribution from bursts at small offset and that LGRBs in the outer parts of galaxies show no preference for unusually bright star forming regions. We conclude that LGRBs strongly prefer the bright, inner regions of their hosts indicating that the star formation taking place there is more favorable for LGRB progenitor production. This indicates that another environmental factor beyond metallicity, such as binary interactions or IMF differences, may be operating in the central regions of LGRB hosts.