A study of solar photospheric temperature gradient variation using limb   darkening measurements
  The variation in area of quiet magnetic network measured over the sunspot cycle should modulate the spatially averaged photospheric temperature gradient, since temperature declines with optical depth more gradually in magnetic flux tube atmospheres. Yet, limb darkening measurements show no dependence upon activity level, even at an rms precision of 0.04%. We study the sensitivity of limb darkening to changes in area filling factor using a 3D MHD model of the magnetized photosphere. The limb darkening change expected from the measured 11 yr area variation lies below the level of measured limb darkening variations, for a reasonable range of magnetic flux in quiet network and internetwork regions. So the remarkably constant limb darkening observed over the solar activity cycle is not inconsistent with the measured 11 year change in area of quiet magnetic network. Our findings offer an independent constraint on photospheric temperature gradient changes reported from measurements of the solar spectral irradiance from the Spectral Irradiance Monitor (SIM), and recently, from wavelength differential spectrophotometry using the Solar Optical Telescope (SOT) aboard the HINODE spacecraft. 
Serena Criscuoli, Peter Foukal
astro-ph.SR