Larson (1981) compiled the observations for molecular cloud complexes,
molecular cloud and molecular clumps published in 1974-1979.
He obtained an empirical relation
that the size of a structure is well correlated
to the random velocity in the structure which is measured by the
width of the emission line (see Appendix E).
Figure 1.34(left) shows this correlation and this is well expressed
as

(1.20) |

In the next chapter (2.9), we will see
the virial relation, that is, for an isolated system to achieve
a mechanical equlibrium the gravitaional to thermal energy ratio has
to be equal to 2:1 for gas.
The ratio of the gravitational energy
to the thermal energy is also fitted as

(1.22) |

Since there is a mutual relation between mass, size, and the velocity dispersion to achive a mechanical equlibrium (the Virial relation), there is only one independent correlation in the above two correlations (eqs.[1.19] and [1.21]). Although several reasons to explain the correlation are proposed, we have no consensus yet.

Kohji Tomisaka 2009-12-10