  The formation of sunspots requires the concentration of magnetic flux near
the surface. The negative magnetic pressure instability (NEMPI) might be a
possible mechanism for accomplishing this, but it has mainly been studied in
simple systems using an isothermal equation of state without a natural free
surface. We study NEMPI in a stratified Cartesian mean-field model where
turbulence effects are parameterized. We use an ideal equation of state and
include radiation transport, which establishes selfconsistently a free surface.
We use a Kramers-type opacity with adjustable exponents chosen such that the
deeper layers are approximately isentropic. No convection is therefore possible
in this model, allowing us to study NEMPI with radiation in isolation. We
restrict ourselves to two-dimensional models. We use artificially enhanced
mean-field coefficients to allow NEMPI to develop, making it therefore possible
to study the reason why it is much harder to excite in the presence of
radiation. NEMPI yields moderately strong magnetic flux concentrations a
certain distance beneath the surface where optical depth is unity. The
instability is oscillatory and in the form of upward travelling waves. This
seems to be a new effect that has not been found in earlier models without
radiative transport. The horizontal wavelength is about ten times smaller than
what has been found previously in more idealized isothermal models. In our
models, NEMPI saturates at field strengths too low to explain sunspots.
Furthermore, the structures appear too narrow and too far beneath the surface
to cause significant brightness variations at the radiative surface. We
speculate that the failure to reproduce effects resembling sunspots may be
related to the neglect of convection.
