  Small scale magnetic fields can be observed on the Sun in G-band filtergrams
as MBPs (magnetic bright points) or identified in spectro-polarimetric
measurements due to enhanced signals of Stokes profiles. These magnetic fields
and their dynamics play a crucial role in understanding the coronal heating
problem and also in surface dynamo models. MBPs can theoretically be described
to evolve out of a patch of a solar photospheric magnetic field with values
below the equipartition field strength by the so-called convective collapse
model. After the collapse, the magnetic field of MBPs reaches a higher stable
magnetic field level. The magnetic field strength distribution of small scale
magnetic fields as seen by MBPs is inferred. Furthermore, we want to test the
model of convective collapse and the theoretically predicted stable value of
about 1300 G. We used four different data sets of high-resolution Hinode/SOT
observations that were recorded simultaneously with the broadband filter device
(G-band, Ca II-H) and the spectro-polarimeter. To derive the magnetic field
strength distribution of these small scale features, the spectropolarimeter
(SP) data sets were treated by the Merlin inversion code. The four data sets
comprise different solar surface types: active regions (a sunspot group and a
region with pores), as well as quiet Sun. In all four cases the obtained
magnetic field strength distribution of MBPs is similar and shows peaks around
1300 G. This agrees well with the theoretical prediction of the convective
collapse model. The resulting magnetic field strength distribution can be
fitted in each case by a model consisting of log-normal components. The
important parameters, such as geometrical mean value and multiplicative
standard deviation, are similar in all data sets, only the relative weighting
of the components is different.
