The magnetic field strength in molecular clouds is a fundamental quantity for theories of star formation .
It is estimated by Zeeman splitting measurements in a few dense molecular cores , but its volume–averaged value within large molecular clouds ( over several parsecs ) is still uncertain .
In this work we provide a new method to constrain the average magnetic field strength in molecular clouds .
We compare the power spectrum of gas density of molecular clouds with that of two 350 ^ { 3 } numerical simulations of supersonic MHD turbulence .
The numerical simulation with approximate equipartition of kinetic and magnetic energies ( model A ) yields the column density power spectrum P ( k ) \propto k ^ { -2.25 \pm 0.01 } , the super–Alfvénic simulation ( model B ) P ( k ) \propto k ^ { -2.71 \pm 0.01 } .
The column density power spectrum of the Perseus , Taurus and Rosetta molecular cloud complexes is found to be well approximated by a power law , P _ { o } ( k ) \propto k ^ { - a } , with a = 2.74 \pm 0.07 , 2.74 \pm 0.08 and 2.76 \pm 0.08 respectively .
We conclude that the observations are consistent with the presence of super–Alfvénic turbulence in molecular clouds ( model B ) while model A is inconsistent ( more than 99 % confidence ) with the observations .