The {rm HI} 21-cm intensity mapping signal experiences redshift space distortions due to the motion of the galaxies which contain the {rm HI} as well as the motions of the {rm HI} gas within the galaxies. A detailed modelling is essential if this signal is to be used for precision cosmology. Considering dark matter only simulations where the {rm HI} is assumed to reside in galaxies which are associated with haloes, in this work we introduce a technique to incorporate the {rm HI} motions within the galaxies. This is achieved through a line profile which accounts for both the rotational and random (thermal and turbulent) motions of the {rm HI} within galaxies. The functional form of the double horned line profiles used here is motivated by observations of $z=0$ spiral galaxies. Analyzing the simulated 21-cm power spectrum over the redshift range $1 le z le 6$ we find that the {rm HI} motions within galaxies makes a significant contribution that is manifested as an enhancement in the Finger of God (FoG) effect which can be modelled reasonably well through a Lorentzian damping profile with a single free parameter $sigma_p$. The value of $sigma_p$ is significantly enhanced if motions within the galaxies are included. This is particularly important at $z>3$ where $sigma_p$ is dominated by the internal motions and a measurement of the FoG effect here could provide a handle on the line profiles of high redshift galaxies.
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