Line broadening and anomalous velocities

The intrinsic broadening of the line emitted by a cloud, due to thermal motion and internal turbulence, gives a limit of this deprojecting technique. In fact, a cloud of temperature T generate a line emission with a width which corresponds to a $\Delta v$ :

$$\Delta v = \sqrt{\frac{2kT}{m_H}}$$ (2.5)

where $k$ is the Boltzmann constant and $m_H$ is the proton mass. For example, for a HI cloud of temperature 100 K at galactic longitude $30^{\circ}$, this corresponds to a $\Delta v$ of about 1 km/s, which in turn means a distance uncertainty of 100 pc along the line of sight. Therefore the resolution of matter radial distribution can not be smaller than this value. Internal turbulence of clouds also contributes to broaden the line profile, with $\Delta v$ spanning a wide range of values. For molecular clouds $\Delta v$ can reach values of 10-20 km/s.
Line broadening is also responsible for the emission observed at velocities outside the dynamical range predicted by the rotational curve. In the deprojection process it is then necessary to take into account the line broadening to include also the matter with anomalous velocities.