4.2.2. Expected weak relationship of B with SF

Mestel and Paris (1984) have followed the galactic magnetic field as it becomes distorted by the contraction of a part of a molecular cloud, under flux-freezing conditions. In so doing, the growing self-gravity generates a magnetic force density opposing gravity.

Under practical conditions, the radio emission from a spiral galaxy includes two main components:

where the S_{sync gas} is due to the cosmic ray electrons N_{e sync gas} embedded in a general magnetic field B, and where S_{thermal gas} comes from local HII regions and has no dependence on B. From synchrotron equations, we have:

Similarly, the far infrared emission from a spiral galaxy includes two main terms:

where S_{warm dust} comes from warm dust at local star formation (SF) sites so:

where A and p are constants, and SF could be either SFR or SFE. S_{cold dust} comes from cold dust pervading most of the spiral galaxy and has no dependence on SF nor B. S_{cold dust} accounts for roughly half of the S_FIR emission observed (Persson & Helou, 1987). There is thus a rough non-linear relation between S_radio and S_FIR , both values being large at the same time, or small at the same time. At very high SF values, S_FIR is large, thus S_radio becomes large, and B² is likely to become large; at very low SF values, S_warm is small, thus S_radio is small, and B² is likely to be small.

More refined predictions, using fully non-linear turbulent models, have been made elsewhere. Passot et al. (1995, their Fig. 8) thus predict that the SFR should first decrease with an increase of the galactic magnetic field B from 0 µGauss to 0.5 µGauss (due to disruptions preventing contraction), then SFR should increase with B increasing from 0.5 µGauss to 5 µGauss (due to gravitational collapse along B lines), and finally SFR should decrease with B increasing beyond 5 µGauss (due to filamentary formation).