  The net effect of the small scale magnetic field on the Sun's (bolometric)
brightness is studied with realistic 3D MHD simulations. The direct effect of
brightening within the magnetic field itself is consistent with measurements in
high-resolution observations. The high 'photometric accuracy' of the
simulations, however, reveal compensating brightness effects that are hard to
detect observationally. The influence of magnetic concentrations on the
surrounding nonmagnetic convective flows (a 'proximity effect') reduces the
brightness by an amount exceeding the brightening by the magnetic
concentrations themselves. The net photospheric effect of the small scale field
(~ -0.34% at a mean flux density of 50 G) is thus negative. We conclude that
the main contribution to the observed positive correlation between the magnetic
field and total solar irradiance must be magnetic dissipation in layers around
the temperature minimum and above (not included in the simulations). This
agrees with existing inferences from observations.
