We present a study of 21 dark gamma-ray burst (GRB) host galaxies, predominantly using X-ray afterglows obtained with the Chandra X-Ray Observatory (CXO) to precisely locate the burst in deep Hubble Space Telescope (HST) imaging of the burst region. The host galaxies are well-detected in F160W in all but one case and in F606W imaging in approx 60 per cent of cases. We measure magnitudes and perform a morphological analysis of each galaxy. The asymmetry, concentration and ellipticity of the dark burst hosts are compared against the host galaxies of optically bright GRBs. In agreement with other studies, we find that dark GRB hosts are redder and more luminous than the bulk of the GRB host population. The distribution of projected spatial offsets for dark GRBs from their host galaxy centroids is comparable to that of optically-bright bursts. The dark GRB hosts are physically larger, more massive and redder, but are morphologically similar to the hosts of bright GRBs in terms of concentration and asymmetry. Our analysis constrains the fraction of high redshift (z greater than 5) GRBs in the sample to approx 14 per cent, implying an upper limit for the whole long-GRB population of less than 4.4 per cent. If dust is the primary cause of afterglow darkening amongst dark GRBs, the measured extinction may require a clumpy dust component in order to explain the observed offset and ellipticity distributions.
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