Using one-dimensional models, we show that a helical magnetic field with an
appropriate sign of helicity can compensate the Faraday depolarization
resulting from the superposition of Faraday-rotated polarization planes from a
spatially extended source. For radio emission from a helical magnetic field,
the polarization as a function of the square of the wavelength becomes
asymmetric with respect to zero. Mathematically speaking, the resulting
emission occurs then either at observable or at unobservable (imaginary)
wavelengths. We demonstrate that rotation measure (RM) synthesis allows for the
reconstruction of the underlying Faraday dispersion function in the former
case, but not in the latter. The presence of positive magnetic helicity can
thus be detected by observing positive RM in highly polarized regions in the
sky and negative RM in weakly polarized regions. Conversely, negative magnetic
helicity can be detected by observing negative RM in highly polarized regions
and positive RM in weakly polarized regions. The simultaneous presence of two
magnetic constituents with opposite signs of helicity is shown to possess
signatures that can be quantified through polarization peaks at specific
wavelengths and the gradient of the phase of the Faraday dispersion function.
Similar polarization peaks can tentatively also be identified for the
bi-helical magnetic fields that are generated self-consistently by a dynamo
from helically forced turbulence, even though the magnetic energy spectrum is
then continuous. Finally, we discuss the possibility of detecting magnetic
fields with helical and non-helical properties in external galaxies using the
Square Kilometre Array.Comment: 12 pages, 12 figures, ApJ, in press (with 3-D turbulence results now
included
