  The relation of the solar surface magnetic field with mesogranular cells is
studied using high spatial (~ 100 km) and temporal (~ 30 sec) resolution data
obtained with the IMaX instrument aboard SUNRISE. First, mesogranular cells are
identified using Lagrange tracers (corks) based on horizontal velocity fields
obtained through Local Correlation Tracking. After ~ 20 min of integration, the
tracers delineate a sharp mesogranular network with lanes of width below about
280 km. The preferential location of magnetic elements in mesogranular cells is
tested quantitatively. Roughly 85% of pixels with magnetic field higher than
100 G are located in the near neighborhood of mesogranular lanes. Magnetic flux
is therefore concentrated in mesogranular lanes rather than intergranular ones.
Secondly, magnetic field extrapolations are performed to obtain field lines
anchored in the observed flux elements. This analysis, therefore, is
independent of the horizontal flows determined in the first part. A probability
density function (PDF) is calculated for the distribution of distances between
the footpoints of individual magnetic field lines. The PDF has an exponential
shape at scales between 1 and 10 Mm, with a constant characteristic decay
distance, indicating the absence of preferred convection scales in the
mesogranular range. Our results support the view that mesogranulation is not an
intrinsic convective scale (in the sense that it is not a primary
energy-injection scale of solar convection), but also give quantitative
confirmation that, nevertheless, the magnetic elements are preferentially found
along mesogranular lanes.
