The Importance of the Magnetic Field from an SMA-CSO-Combined Sample of Star-Forming Regions

Submillimeter dust polarization measurements of a sample of 50 star-forming regions, observed with the SMA and the CSO covering pc-scale clouds to mpc-scale cores, are analyzed in order to quantify the magnetic field importance. The magnetic field misalignment $\delta$ – the local angle between magnetic field and dust emission gradient – is found to be a prime observable, revealing distinct distributions for sources where the magnetic field is preferentially aligned with or perpendicular to the source minor axis. Source-averaged misalignment angles $⟨\mathrm{\mid }\delta \mathrm{\mid }⟩$ fall into systematically different ranges, reflecting the different source-magnetic field configurations. Possible bimodal $⟨\mathrm{\mid }\delta \mathrm{\mid }⟩$-distributions are found for the separate SMA and CSO samples. Combining both samples broadens the distribution with a wide maximum peak at small $⟨\mathrm{\mid }\delta \mathrm{\mid }⟩$-values. Assuming the 50 sources to be representative, the prevailing source-magnetic field configuration is one that statistically prefers small magnetic field misalignments $\mathrm{\mid }\delta \mathrm{\mid }$. When interpreting $\mathrm{\mid }\delta \mathrm{\mid }$ together with an MHD force equation, as developed in the framework of the polarization-intensity gradient method, a sample-based scaling fits the magnetic field tension-to-gravity force ratio $⟨{\mathrm{\Sigma }}_B⟩$ versus $⟨\mathrm{\mid }\delta \mathrm{\mid }⟩$ with $\langle\Sigma_B\rangle = 0.116 \cdot \exp(0.047\cdot \langle|\delta|\rangle)\pm 0.20$ (mean error), providing a way to estimate the relative importance of the magnetic field, only based on measurable field misalignments $\mathrm{\mid }\delta \mathrm{\mid }$. The force ratio ${\mathrm{\Sigma }}_B$ discriminates systems that are collapsible on average ($\langle \Sigma_B\rangle <1$) from other molecular clouds where the magnetic field still provides enough resistance against gravitational collapse ($⟨{\mathrm{\Sigma }}_B⟩>1$) (abridged).