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The variation in area of quiet magnetic network measured over the sunspotcycle should modulate the spatially averaged photospheric temperature gradient,since temperature declines with optical depth more gradually in magnetic fluxtube atmospheres. Yet, limb darkening measurements show no dependence uponactivity level, even at an rms precision of 0.04%. We study the sensitivity oflimb darkening to changes in area filling factor using a 3D MHD model of themagnetized photosphere. The limb darkening change expected from the measured 11yr area variation lies below the level of measured limb darkening variations,for a reasonable range of magnetic flux in quiet network and internetworkregions. So the remarkably constant limb darkening observed over the solaractivity cycle is not inconsistent with the measured 11 year change in area ofquiet magnetic network. Our findings offer an independent constraint onphotospheric temperature gradient changes reported from measurements of thesolar spectral irradiance from the Spectral Irradiance Monitor (SIM), andrecently, from wavelength differential spectrophotometry using the SolarOptical Telescope (SOT) aboard the HINODE spacecraft.

A study of solar photospheric temperature gradient variation using limb darkening measurements