Normalized surface brightness of thermal emission from HD 131835 inferred from ALMA continuum (solid, dashed, and dotted red lines for the best-fit frank, rave, and parametric radial profiles, respectively) and of scattered light from VLT/SPHERE (blue line), and radial profile of intensity of molecular line emission of ¹²CO and ¹³CO observed with ALMA (solid and dashed orange lines; ¹³CO intensity is normalized in such a way that the ¹³CO/¹²CO intensity ratio is preserved). The vertical dash-dot lines indicate the locations of the inner and the outer ring based on local maxima at 65.4 au and 96.5 au in the frank radial profile. The third, innermost component is partially within a region of high uncertainty for the scattered light observation (grey region) and appears to be asymmetric, and we do not include it in our theoretical models. For further details, see Section 2.