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tokens: kpc which is almost the same as the scale length of the molecular disc which is ∼4.05 kpc. However, for our sample galaxies, the scale length of the molecular scale height is found to be approximately a factor of 2 greater than the scale length of the exponential surface density profile (see Fig. 6 ). This result strongly indicates that the coupling with the other disc components and with the dark matter halo significantly influence the molecular scale height. Figure 7. The behaviour of the molecular scale height in the absence of any external influence in NGC 3198. The solid red and the black dashed lines represent the molecular gas surface density profile (), and it’s fit to an exponential profile, respectively (marked by the left axis). The solid magenta and the dashed-dotted blue lines represent the estimated molecular scale height (HWHM) and its fit to a rising exponential function, respectively (marked by the right axis). The scale lengths of the exponential fits to the ( l CO ) and the HWHM profile ( l scl ) are found to be ∼4.05 and ∼4.06 kpc (as quoted in the top left), are almost the same. Next, we use the solutions of the hydrostatic equilibrium equation and the observed rotation curves to build a dynamical model of the molecular discs for our sample galaxies. We then incline these dynamical models to the observed inclinations and project it to the sky-plane to produce a column density map. These maps then convolved with the telescope beam (13 arcsec × 13 arcsec) to produce simulated maps that are equivalent to the observed ones. In Figs 8 and 9 we compare these simulated maps with the observed maps. In the left-hand columns of the figures, we plot the modelled column density maps in contour on top of the observed maps in colour scale. As we do not solve the hydrostatic equation for the central regions of our sample galaxies, the central region should be excluded for any comparison. Further, the convolution with the telescope beam at the edge of the central region would corrupt an area equivalent to the beam size. We hence exclude a region that we do not solve from the centre plus the beam size. The vertical dashed lines in each panel of the left-hand column represent this excluded region. As can be seen from the figure, the contours (modelled) match to the observed map reasonably well. However, for two galaxies NGC 925 and NGC 2976, the model seems to deviate from the observation. This is due to azimuthal asymmetry in their column density distribution that is one of our implicit assumptions. We would like to emphasize here that, the molecular surface density profiles of our sample galaxies are calculated through spectral stacking method (Schruba et al. 2011 ). This produces surface density profiles that are much more sensitive than what will be observed in the moment zero maps. Because of this, the surface density profiles of our sample galaxies extend to a much larger radius as given in Schruba et al. ( 2011 ) than what can be