Bright small-scale magnetic elements found mainly in intergranular lanes at
the solar surface are named bright points (BPs). They show high contrasts in
Fraunhofer G-band observations and are described by nearly vertical slender
flux tubes or sheets. A recent comparison between BP observations in the
ultraviolet (UV) and visible spectral range recorded with the balloon-borne
observatory SUNRISE and state-of-the-art magnetohydrodynamical (MHD)
simulations revealed a kiloGauss magnetic field for 98% of the synthetic BPs.
Here we address the opposite question, namely which fraction of pixels hosting
kiloGauss fields coincides with an enhanced G-band brightness. We carried out
3D radiation MHD simulations for three magnetic activity levels (corresponding
to the quiet Sun, weak and strong plage) and performed a full spectral line
synthesis in the G-band. Only 7% of the kiloGauss pixels in our quiet-Sun
simulation coincide with a brightness lower than the mean quiet-Sun intensity,
while 23% of the pixels in the weak-plage simulation and even 49% in the
strong-plage simulation are associated with a local darkening. Dark
strong-field regions are preferentially found in the cores of larger flux
patches that are rare in the quiet Sun, but more common in plage regions, often
in the vertices of granulation cells. The significant brightness shortfall in
the core of larger flux patches coincide with a slight magnetic field
weakening. KiloGauss elements in the quiet Sun are on average brighter than
similar features in plage regions. Almost all strong-field pixels display a
more or less vertical magnetic field orientation. Hence in the quiet Sun,
G-band BPs correspond almost one-to-one with kiloGauss elements. In weak plage
the correspondence is still very good, but not perfect.Comment: Accepted for publication in Astronomy & Astrophysic