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Context. Over the past 20 yr, the quietest areas of the solar surface have revealed a weak but extremely dynamic magnetism occurring at small scales (<500 km), which may provide an important contribution to the dynamics and energetics of the outer layers of the atmosphere. Understanding this magnetism requires the inference of physical quantities from high-sensitivity spectro-polarimetric data with high spatio-temporal resolution. Aims. We present high-precision spectro-polarimetric data with high spatial resolution (0.4") of the very quiet Sun at 1.56 mu m obtained with the GREGOR telescope to shed some light on this complex magnetism. Methods. We used inversion techniques in two main approaches. First, we assumed that the observed profiles can be reproduced with a constant magnetic field atmosphere embedded in a field-free medium. Second, we assumed that the resolution element has a substructure with either two constant magnetic atmospheres or a single magnetic atmosphere with gradients of the physical quantities along the optical depth, both coexisting with a global stray-light component. Results. Half of our observed quiet-Sun region is better explained by magnetic substructure within the resolution element. However, we cannot distinguish whether this substructure comes from gradients of the physical parameters along the line of sight or from horizontal gradients (across the surface). In these pixels, a model with two magnetic components is preferred, and we find two distinct magnetic field populations. The population with the larger filling factor has very weak (similar to 150 G) horizontal fields similar to those obtained in previous works. We demonstrate that the field vector of this population is not constrained by the observations, given the spatial resolution and polarimetric accuracy of our data. The topology of the other component with the smaller filling factor is constrained by the observations for field strengths above 250 G: we infer hG fields with inclinations and azimuth values compatible with an isotropic distribution. The filling factors are typically below 30%. We also find that the flux of the two polarities is not balanced. From the other half of the observed quiet-Sun area similar to 50% are two-lobed Stokes V profiles, meaning that 23% of the field of view can be adequately explained with a single constant magnetic field embedded in a non-magnetic atmosphere. The magnetic field vector and filling factor are reliable inferred in only 50% based on the regular profiles. Therefore, 12% of the field of view harbour hG fields with filling factors typically below 30%. At our present spatial resolution, 70% of the pixels apparently are non-magnetised.
Context. The High Energy Stereoscopic System Galactic plane survey (HGPS) is to date the most comprehensive census of Galactic gamma -ray sources at very high energies (VHE; 100 GeV <= E <= 100 TeV). As a consequence of the limited sensitivity of this survey, the 78 detected gamma -ray sources comprise only a small and biased subsample of the overall population. The larger part consists of currently unresolved sources, which contribute to large-scale diffuse emission to a still uncertain amount.Aims. We study the VHE gamma -ray source population in the Milky Way. For this purpose population-synthesis models are derived based on the distributions of source positions, extents, and luminosities.Methods. Several azimuth-symmetric and spiral-arm models are compared for spatial source distribution. The luminosity and radius function of the population are derived from the source properties of the HGPS data set and are corrected for the sensitivity bias of the HGPS. Based on these models, VHE source populations are simulated and the subsets of sources detectable according to the HGPS are compared with HGPS sources.Results. The power-law indices of luminosity and radius functions are determined to range between -1.6 and -1.9 for luminosity and -1.1 and -1.6 for radius. A two-arm spiral structure with central bar is discarded as spatial distribution of VHE sources, while azimuth-symmetric distributions and a distribution following a four-arm spiral structure without bar describe the HGPS data reasonably well. The total number of Galactic VHE sources is predicted to be in the range from 800 to 7000 with a total luminosity and flux of (1.6-6.3) x 10(36) ph s(-1) and (3-15) x 10(-10) ph cm(-2) s(-1), respectively.Conclusions. Depending on the model, the HGPS sample accounts for (68-87)% of the emission of the population in the scanned region. This suggests that unresolved sources represent a critical component of the diffuse emission measurable in the HGPS. With the foreseen jump in sensitivity of the Cherenkov Telescope Array, the number of detectable sources is predicted to increase by a factor between 5 and 9.