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We investigate X-ray isophote twists created by triaxiality differences between the luminous stellar distributions and the dark halos in elliptical galaxies. For a typically oblate luminous galaxy embedded in a more prolate halo formed by dissipationless collapse, the triaxiality difference of ΔT simeq 0.7 leads to typical isophote twists of langΔψXrang simeq 16° ± 19° at 3 effective stellar radii. In a model that includes baryonic dissipation, the effect is smaller, with ΔT simeq 0.3 and langΔψXrang simeq 5° ± 8°. Thus, accurate measurements of X-ray isophote twists may be able to set constraints on the interactions between baryons and dissipationless dark matter during galaxy formation. The 30° X-ray isophote twist in the E4 galaxy NGC 720 cannot be reproduced by our model, suggesting an intrinsic misalignment between the halo and the stars rather than a projection effect.


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