We present a quantitative morphological analysis using HST NICMOS H160- and ACS I775- band imaging of 25 spectroscopically confirmed submillimetre galaxies (SMGs) which have redshifts between z=0.7-3.4. Our analysis also employs a comparison sample of more typical star-forming galaxies at similar redshifts (such as LBGs) which have lower far-infrared luminosities. This is the first large-scale study of the morphologies of SMGs in the near-infrared at ~0.1 resolution (<1kpc). We find that the half light radii of the SMGs (r_h=2.3+/-0.3 and 2.8+/-0.4kpc in the observed I- and H-bands respectively) and asymmetries are not statistically distinct from the comparison sample of star-forming galaxies. However, we demonstrate that the SMG morphologies differ more between the rest-frame UV and optical-bands than typical star-forming galaxies and interpret this as evidence for structured dust obscuration. We show that the composite observed H-band light profile of SMGs is better fit with a Sersic index with n~2, suggesting the stellar structure of SMGs is best described by a spheroid/elliptical galaxy light distribution. We also compare the sizes and stellar masses of SMGs to local and high-redshift populations, and find that the SMGs have stellar densities which are comparable to local early-type galaxies, as well as luminous, red and dense galaxies at z~1.5 which have been proposed as direct SMG descendants, although the SMG stellar masses and sizes are systematically larger. Overall, our results suggest that the physical processes occuring within the galaxies are too complex to be simply characterised by the rest-frame UV/optical morphologies which appear to be essentially decoupled from all other observables, such as bolometric luminosity, stellar or dynamical mass.
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