  Small-scale internetwork (IN) features are thought to be the major source of
fresh magnetic flux in the quiet Sun. During its first science flight in 2009,
the balloon-borne observatory Sunrise captured images of the magnetic fields in
the quiet Sun at a high spatial resolution. Using these data we measure the
rate at which the IN features bring magnetic flux to the solar surface. In a
previous paper it was found that the lowest magnetic flux in small-scale
features detected using the Sunrise observations is 9 x 10^14 Mx. This is
nearly an order of magnitude smaller than the smallest fluxes of features
detected in observations from the Hinode satellite. In this paper, we compute
the flux emergence rate (FER) by accounting for such small fluxes, which was
not possible before Sunrise. By tracking the features with fluxes in the range
10^15-10^18 Mx, we measure an FER of 1100 Mx cm^-2 day^-1. The smaller features
with fluxes less than or equal to 10^16 Mx are found to be the dominant
contributors to the solar magnetic flux. The FER found here is an order of
magnitude higher than the rate from Hinode, obtained with a similar feature
tracking technique. A wider comparison with the literature shows, however, that
the exact technique of determining the rate of the appearance of new flux can
lead to results that differ by up to two orders of magnitude, even when applied
to similar data. The causes of this discrepancy are discussed and first
qualitative explanations proposed.

Solar and Stellar Astrophysics