The well-known solar cycle controls almost the entire appearance of the solar photosphere. We therefore presume that the continuous emission of visible light from the solar surface follows the solar cyclic variation. In this study, we examine the solar cyclic variation of photospheric brightness in the visible range using solar images taken by the Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI). The photospheric brightness in the visible range is quantified via the relative intensity acquired from in the raw solar images. In contrast to total solar irradiance, the relative intensity is out of phase with the solar cycle. During the solar minimum of solar cycles 23--24, the relative intensity shows enhanced heliolatitudinal asymmetry due to a positive asymmetry of the sunspot number. This result can be explained by the strength of the solar magnetic field that controls the strength of convection, implying that the emission in the visible range is controlled by the strength of convection. This agrees with the photospheric brightness increasing during a period of long spotless days.

The sun is not equally bright over the whole sphere, but rather is darkened toward the limb. This effect is well-known as limb darkening. The limb darkening coefficient is defined by the ratio of the center intensity to limb intensity. In this study, we calculate the limb darkening coefficient using the photospheric intensity estimated from solar images taken by solar and helispheric observatory (SOHO) and solar dynamics observatory (SDO). The photospheric intensity data cover almost two solar cycles from May 1996 to December 2016. The limb darkening coefficient for a size of 0.9 diameter is about 0.69 and this value is consistent with solar limb darkening. The limb darkening coefficient estimated from SOHO shows a temporal increase at solar maximum and a gradual increase since the solar minimum of 2008. The limb darkening coefficient estimated from SDO shows a constant value of about 0.65 and a decreasing trend since 2014. The increase in the coefficient reflects the effect of weakened solar activity. However, the decrease since 2014 is caused by the aging effect.