Due to non-homogeneous mass distribution and non-uniform velocity rate inside the Sun, the solar outer shape is distorted in latitude. In this paper, we analyze the consequences of a temporal change in this figure on the luminosity. To do so, we use
the Total Solar Irradiance (TSI) as an indicator of luminosity. Considering that most of the authors have explained the largest part of the TSI modulation with magnetic network (spots and faculae) but not the whole, we could set constraints on radius and effective temperature variations (dR, dT). However computations show that the amplitude of solar irradiance modulation is very sensitive to photospheric temperature variations. In order to understand discrepancies between our best fit and recent observations of Livingston et al. (2005), showing no effective surface temperature variation during the solar cycle, we investigated small effective temperature variation in irradiance modeling. We emphasized a phase-shift (correlated or anticorrelated radius and irradiance variations) in the (dR, dT)-parameter plane. We further obtained an upper limit on the amplitude of cyclic solar radius variations, deduced from the gravitational energy variations. Our estimate is consistent with both observations of the helioseismic radius through the analysis of f-mode frequencies and observations of the basal photospheric temperature at Kitt Peak. Finally, we suggest a mechanism to explain faint changes in the solar shape due to variation of magnetic pressure which modifies the granules size. This mechanism is supported by our estimate of the asphericity-luminosity parameter, which implies an effectiveness of convective heat transfer only in very outer layers of the Sun.
