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 Ssync gas is due to the cosmic ray electrons Ne sync gas embedded in a general magnetic field B, and where Sthermal 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 Swarm 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. Scold dust comes from cold dust pervading most of the spiral galaxy and has no dependence on SF nor B. Scold dust accounts for roughly half of the SFIR emission observed (Persson & Helou, 1987). There is thus a rough non-linear relation between Sradio and SFIR , both values being large at the same time, or small at the same time. At very high SF values, SFIR is large, thus Sradio becomes large, and B2 is likely to become large; at very low SF values, Swarm is small, thus Sradio 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).