Context: The magnetic topology of the solar photosphere in its quietest regions is hidden by the difficulties to disentangle magnetic flux through the resolution element from the field strength of unresolved structures. The observation of spectral lines with strong coupling with hyperfine structure, like the observed Mn i line at 553.7 nm, allows such differentiation.
Aims: To analyse the distribution of field strengths in the network and intranetwork of the solar photosphere through inversion of the Mn i line at 553.7 nm.
Methods: An inversion code for the magnetic field using the principal component analysis (PCA) has been developed. Statistical tests are run on the code to validate it. The code has to draw information from the small-amplitude spectral feature appearing in the core of the Stokes V profile of the observed line for field strengths below a certain threshold, coinciding with lower limit of the Paschen-Back effect in the fine structure of the involved atomic levels.
Results: The inversion of the observed profiles, using the circular polarisation (V) and the intensity (I), shows the presence of magnetic fields strengths in a range from 0 to 2 kG, with predominant weak strength values. Mixed regions with mean strength field values of 1130 and 435 Gauss are found associated with the network and intranetwork, respectively.
Conclusions: The Mn i line at 553 nm probes the field strength distribution in the quiet sun and shows the predominance of weak, hectoGauss fields in the intranetwork, and strong, kiloGauss fields in the network. It also shows that both network and intranetwork are to be understood at our present spatial resolutions as field distributions, of which we hint at the mean properties.