Zeeman line splitting measurements sampling dense gas in dark cloud and star-forming cores

We present measurements of Zeeman splitting in SO J(N) = 1(2)-1(1) line emi ssion/absorption arising from dense thermal gas (>10(6) cm(-3)) associated with ten compact H II and star-forming regions. No line-of-sight magnetic f ield, above an average 1 sigma limit of 0.57 mG, is detected toward any of these sources. The W3(OH) region, found in a previous study to have a line- of-sight field of 3 mG in its dense gas, is thus unique in this respect. Th e implication of this study is that the magnetic fields in dense clouds are supercritical in the sense that they are not capable of supporting their h ost clouds against gravitational collapse. The relatively low average field limit is consistent with those theories predicting the quick onset of and short timescales for ambipolar diffusion. Also presented are (1) Zeeman spl itting measurements of the CCS J(N) = 1(0)-0(1) line probing the 10(4-5) cm (-3) gas towards three positions in the Taurus star forming region, giving a 1 sigma average upper limit of 66 muG, and (2) measurements of Zeeman spl itting in the OH (2)Pi (3/2) J = 7=2 F = 3(+)-3(-) hyperfine line toward th e compact H II regions DR-21 and G10.62.