Observed variations of the solar photospheric diameter

Here we derive a formulation connecting the observed variations of the solar diameter to the heliophysics of the photosphere, in particular in connection to the granulation pattern and morphology. The results from the measurements are next used to correlate the variations of the semi-diameter and of estimators of the solar activity along the solar cycle 23. The values obtained strongly support a broader physical description of the photosphere, intertwining the diameter variations with the irradiance, the sunspots, the 10.7 cm radio emission, and to a lesser degree with the integrated magnetic field and with the flares count.