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We study the statistical properties of interstellar dust polarization at highGalactic latitude, using the Stokes parameter Planck maps at 353 GHz. Our aimis to advance the understanding of the magnetized interstellar medium (ISM),and to provide a model of the polarized dust foreground for cosmic microwavebackground component-separation procedures. Focusing on the southern Galacticcap, we examine the statistical distributions of the polarization fraction($p$) and angle ($\psi$) to characterize the ordered and turbulent componentsof the Galactic magnetic field (GMF) in the solar neighbourhood. We relatepatterns at large angular scales in polarization to the orientation of the mean(ordered) GMF towards Galactic coordinates $(l_0,b_0)=(70^\circ \pm5^\circ,24^\circ \pm 5^\circ)$. The histogram of $p$ shows a wide dispersion upto 25 %. The histogram of $\psi$ has a standard deviation of $12^\circ$ aboutthe regular pattern expected from the ordered GMF. We use these histograms tobuild a phenomenological model of the turbulent component of the GMF, assuminga uniform effective polarization fraction ($p_0$) of dust emission. To modelthe Stokes parameters, we approximate the integration along the line of sight(LOS) as a sum over a set of $N$ independent polarization layers, in each ofwhich the turbulent component of the GMF is obtained from Gaussian realizationsof a power-law power spectrum. We are able to reproduce the observed $p$ and$\psi$ distributions using: a $p_0$ value of (26 $\pm$ 3)%; a ratio of 0.9$\pm$ 0.1 between the strengths of the turbulent and mean components of theGMF; and a small value of $N$. We relate the polarization layers to the densitystructure and to the correlation length of the GMF along the LOS.

Planck intermediate results. XLIV. The structure of the Galactic magnetic field from dust polarization maps of the southern Galactic cap