  Evidence for the emergence of twisted flux tubes into the solar atmosphere
has, so far, come from indirect signatures. In this work, we investigate the
topological input of twisted flux tube emergence directly by studying helicity
and winding fluxes. In magnetohydrodynamic simulations with domains spanning
from the top of the convection zone to the lower corona, we simulate the
emergence of twisted flux tubes with a range of different initial field
strengths. One important feature of this work is the inclusion of a
convectively-unstable layer beneath the photosphere. We find approximately
self-similar behaviour in the helicity input for the different field strengths
considered. As the tubes rise and reach the photosphere, there is a strong
input of negative helicity since we consider left-handed twisted tubes. This
phase is then followed by a reduction of the negative input and, for low
initial field strengths, a net positive helicity input. This phase corresponds
to the growing influence of convection on the field and the development of
serpentine field structures during emergence. The winding flux can be used to
detect when the twisted cores of the tubes reach the photosphere, giving clear
information about the input of topologically complex magnetic field into the
solar atmosphere. In short, the helicity and winding fluxes can provide much
information about how a magnetic field emerges that is not directly available
from other sources, such as magnetograms. In evaulating the helicity content of
these simualtions we test numerous means for creating synthetic magnetograms,
including methods which acount for both the evolving geometry and the finite
extent of the photosphere. Whilst the general qualitative behaviours are same
in each case, the different forms of averaging do affect the helicity and
winding inputs quantitatively.
