  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.
