Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime
where the complex form of a free electromagnetic field given by F=E+iB is null
(F.F=0), and they can indeed be interpreted as the collective history swept out
by moving vortex lines of the field. Formally, the nullity condition is similar
to the definition of "C-lines" associated with a monochromatic electric or
magnetic field, which are curves in space where the polarization ellipses
degenerate to circles. However, it was noted that RS vortices of monochromatic
fields generally oscillate at optical frequencies and are therefore
unobservable while electric and magnetic C-lines are steady. Here I show that
under the additional assumption of having definite helicity, RS vortices are
not only steady but they coincide with both sets of C-lines, electric and
magnetic. The two concepts therefore become one for waves of definite frequency
and helicity. Since the definition of RS vortices is relativistically invariant
while that of C-lines is not, it may be useful to regard the vortices as a
wideband generalization of C-lines for waves of definite helicity.