Magnetic Field - Gas Density Relation and Observational Implications
  Revisited
  We revisit the relation between magnetic-field strength ($B$) and gas density
($\rho$) for contracting interstellar clouds and fragments (or, cores), which
is central in observationally determining the dynamical importance of magnetic
fields in cloud evolution and star formation. Recently, it has been claimed
that a relation $B \propto \rho^{2/3} $ is statistically preferred over $B
\propto \rho^{1/2}$ in molecular clouds, when magnetic field detections and
nondetections from Zeeman observations are combined. This finding has unique
observational implications on cloud and core geometry: The relation $B \propto
\rho^{2/3} $ can only be realized under spherical contraction. However, no
indication of spherical geometry can be found for the objects used in the
original statistical analysis of the $B-\rho$ relation. We trace the origin of
the inconsistency to simplifying assumptions in the statistical model used to
arrive at the $B\propto \rho^{2/3}$ conclusion and to an underestimate of
observational uncertainties in the determination of cloud and core densities.
We show that, when these restrictive assumptions are relaxed, $B \propto
\rho^{1/2}$ is the preferred relation for the (self-gravitating)
molecular-cloud data, as theoretically predicted four decades ago.
