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Due to non-homogeneous mass distribution and non-uniform velocity rate insidethe Sun, the solar outer shape is distorted in latitude. In this paper, weanalyze 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 ofluminosity. Considering that most of the authors have explained the largestpart of the TSI modulation with magnetic network (spots and faculae) but notthe whole, we could set constraints on radius and effective temperaturevariations (dR, dT). However computations show that the amplitude of solarirradiance modulation is very sensitive to photospheric temperature variations.In order to understand discrepancies between our best fit and recentobservations of Livingston et al. (2005), showing no effective surfacetemperature variation during the solar cycle, we investigated small effectivetemperature 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 ofcyclic solar radius variations, deduced from the gravitational energyvariations. Our estimate is consistent with both observations of thehelioseismic radius through the analysis of f-mode frequencies and observationsof the basal photospheric temperature at Kitt Peak. Finally, we suggest amechanism to explain faint changes in the solar shape due to variation ofmagnetic pressure which modifies the granules size. This mechanism is supportedby our estimate of the asphericity-luminosity parameter, which implies aneffectiveness of convective heat transfer only in very outer layers of the Sun.

Solar gravitational energy and luminosity variations