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Our galaxy and other spirals are known to have magnetic fields $ \sim 10^{-6} $ Gauss that play an important role in the interstellar medium; the question arises as to the origin of these fields. The primordial origin theory builds the present fields by amplifying a flux-frozen field $ \stackrel {>}{\sim} 10^{-12} $ Gauss, postulated to pre-exist in the gas from which galaxies form, through the collapse of the protogalaxy and subsequent shearing due to the galaxy's differential rotation. The field's increase due to shearing is limited by ambipolar diffusion which slowly pushes field out of the disk once there is an appreciable magnetic pressure. This effect yields a decrease in field strength which at later times $ \sim t^{-1/2} $ with a proportionality constant determined by measurable properties of the interstellar medium and giving a magnitude consistent with measured values (Kulsrud, R.M., `` The Present State of a Primordial Galactic Field '' , IAU Symposium 140, Galactic and Extragalactic Magnetic Fields, Heidelberg,1989).
We present the magnetic field expected from the primordial theory using mathematical models. A simple analytic calculation of a field initially uniform in the disk and assuming a fixed profile with height yielded a field that rapidly reverses with radius. A complementary numerical simulation of the field as a function of height and time only at a given corotating point showed that the height profile in fact remained constant in shape to a first approximation as the field increased and diminished in accord with the analytic time profile. We will discuss a more realistic simulation including both horizontal and vertical variation, a mixing term to approximate cloud motions, and also nonuniform initial configuration .
We acknowledge the support of an NSF Minority Graduate Fellowship, an AT\&T Cooperative Research Fellowship, and NSF grant AST-9121847 .
