  The Hinode mission has revealed copious amounts of horizontal flux covering
the quiet Sun. Local dynamo action has been proposed to explain the presence of
this flux. We sought to test whether the quiet Sun flux detected by Hinode is
due to a local or the global dynamo by studying long-term variations in the
polarisation signals detectable at the disc centre of the quiet Sun between
November 2006 and May 2012, with particular emphasis on weak signals in the
internetwork. The investigation focusses on line-integrated circular
polarisation V_tot and linear polarisation LP_tot profiles obtained from the Fe
I 6302.5 \AA absorption line in Hinode SOT/SP. Both circular and linear
polarisation signals show no overall variation in the fraction of selected
pixels from 2006 until 2012. There is also no variation in the magnetic flux in
this interval of time. The probability density functions (PDF) of the
line-of-sight magnetic flux can be fitted with a power law from 1.17 x 10^17 Mx
to 8.53 x 10^18 Mx with index \alpha=-1.82 \pm 0.02 in 2007. The variation of
\alpha 's across all years does not exceed a significance of 1\sigma. Linearly
polarised features are also fitted with a power law, with index \alpha=-2.60
\pm 0.06 in 2007. Indices derived from linear polarisation PDFs of other years
also show no significant variation. Our results show that the ubiquitous
horizontal polarisation on the edges of bright granules seen by Hinode are
invariant during the minimum of cycle 23. This supports the notion that the
weak circular and linear polarisation is primarily caused by an independent
local dynamo.
