  Plasma beta is an important and fundamental physical quantity in order to
understand plasma dynamics, particularly in the context of magnetically active
stars, because it tells about the domination of magnetic versus thermodynamic
processes on the plasma motion. We estimate the value ranges of plasma beta in
different regions within the solar atmosphere and we describe a possible
mechanism that helps forming a penumbra. For that we evaluate data from a 3D
magnetohydrodynamic model of the solar corona above a magnetically active
region. We compare our results with previously established data that is based
on magnetic field extrapolations and that was matched for some observations.
Our model data suggest that plasma beta in the photosphere should be considered
to be larger than unity outside of sunspots. However, in the corona we also
find that the beta value range reaches lower than previously thought, which
coincides with a recent observation. We present an idea based on a
gravity-driven process in a high-beta regime that might be responsible for the
formation of the penumbra around sunspot umbra, where the vertical field
strength reaches a given threshold. This process would also explain
counter-Evershed flows. Regarding the thermal and magnetic pressure within the
mixed-polarity solar atmosphere, including non-vertical magnetic field and
quiet regions, plasma beta may reach unity at practically any height from the
photosphere to the outer corona.
