2021ApJ...917...35M

Magnetic and energetic properties are presented for 17 dense cores within a few hundred parsecs of the Sun. Their plane-of-sky field strengths B_pos are estimated from the dispersion of polarization directions, following Davis, Chandrasekhar, and Fermi (DCF). Their ratio of mass to magnetic critical mass is 0.5≲M/M_B≲3, indicating nearly critical field strengths. The field strength B_pos is correlated with column density N as B_pos∝N^p, where p=1.05±0.08, and with density n as B_pos∝ n^q, where q=0.66±0.05. These magnetic properties are consistent with those derived from Zeeman studies, with less scatter. Relations between virial mass M_V, magnetic critical mass M_B, and Alfven amplitude σ_B/B match the observed range of M/M_B for cores observed to be nearly virial, 0.5≲M/M_V≲2, with moderate Alfven amplitudes, 0.1≲σ_B/B≲0.4. The B - N and B - n correlations in the DCF and Zeeman samples can be explained when such bound, Alfvenic, and nearly critical cores have central concentration and spheroidal shape. For these properties, B∝N because M/M_B is nearly constant compared to the range of N, and B∝n^2/3 because M^1/3 is nearly constant compared to the range of n^2/3. The observed core fields that follow B∝n^2/3 need not be much weaker than gravity, in contrast to core fields that follow B∝n^2/3 owing to spherical contraction at constant mass. Instead, the nearly critical values of M/M_B suggest that the observed core fields are nearly as strong as possible, among values that allow gravitational contraction.