Up: Interstellar turbulent velocity fields: chemistry

Appendix B: Centroid velocity increments

The centroid velocity (C) is the mean radial velocity: if we call T(u) the intensity as a function of the radial velocity, then by definition $C=\left( \int uT(u){\rm d}u\right) /\left( \int T(u){\rm d}u\right)$ . In the case of an optically thin medium, $T(u)\propto N(u)$ , where N(u) is the column density as a function of the radial velocity ( $N(u)=\int ^{s_{0}}_{0}n(u){\rm d}s$ ). It is then easy to show that $C=\left( \int u(s)n(s){\rm d}s\right) /\overline{N}$ . This quantity is very commonly used because of the lack of information about the velocity spatial repartition along the line of sight. The centroid velocity increment at scale a is then: $\delta C_{a}=C(r+a)-C(r)$ , where r is a position on the plane of the sky. The probability density function (PDF) of this quantity in a turbulent velocity field is essentially indistinguishable from a Gaussian for the integral scale and develops more and more non-Gaussian wings as the lag decrease (see Lis et al. 1996; Pety 1999; Miesch et al. 1999).

Up: Interstellar turbulent velocity fields: chemistry