The change of solar shape in time and depth. Some consequences for space climate S. Lefebvre a,b , J.P. Rozelot c,d, * , A.G. Kosovichev e a SAp/DAPNIA/DSN CEA Saclay, L’Orme des merisiers Ba ˆt. 709, 91191 Gif sur Yvette cedex, France b UMR 7158, CEA-CNRS-Uiversite ´ Paris VII, 91191 Gif sur Yvette cedex, France c OCA-GEMINI-FIZEAU, Av. Copernic, 06130 Grasse, France d Universite ´ de Nice-Sophia-Antipolis, Parc Valrose, F-06108 Nice, France e W.W. HEPL, Stanford University, Stanford, CA 94305-4085, USA Received 10 November 2006; received in revised form 30 December 2006; accepted 10 January 2007 Abstract During the last five years, studies of the Sun and Sun–Earth relationships have dramatically changed our view on solar terrestrial physics. We will here focus on new views on the solar interior. The internal non-homogeneous mass distribution and non-uniform angular velocity (function of the radial distance to the center and of the latitude) yield a complex outer shape. Beyond a ‘‘spherical’’ Sun is a new approach of solar-physics taking into account the gravitational energy which triggers the various layers. Such energy has been skipped in many ways up to now in theoretical models describing the solar output variability. In spite of many works on solar variations, there is not yet a consensus on the global experimental phenomenology. For instance, it is not yet known if this gravitational energy may explain faint observed irradiance variations, and the way the asphericity-luminosity parameter W acts on our stratosphere. Such issues must be solved to understand how the solar output variability may influence the Earth’s environment (helioclimatology). We will emphasize the key role of the subsurface layers (the leptocline, recently put in evidence by helioseismology) for a better prediction of the solar cycles. Regarding the solar core dynamics, the subject is of high priority for new investigations. We will conclude by giving some imprints on space-dedicated missions: GOLF-NG/DynaMICS in a joint effort with SDO (Solar Dynamics Observatory). Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Sun: characteristic and properties (96.60.j); Gravity field (91.10.Qm); Rotation (96.60.Bn); Interior (96.60.Jw); Transition regions (96.60.Xy) 1. Introduction The study of the rotation of stars is not trivial. In the- ory, the problem is exceedingly simple and can be formu- lated as follows. Let us consider a single star that rotates along a fixed direction in space, with an angular velocity X, and first assume that, for X = 0, the star is a gaseous body in gravitational equilibrium. The problem is to deter- mine the outer shape of the star when the initial sphere is set rotating at an angular velocity X. Such studies were conducted for the first time by Milne (1923), then fully achieved by Chandrasekhar (1933). The second point is to understand what happen if X is not constant, not only in latitude (differential rotation) but also throughout the body, from the surface to the core. We are faced today with such problems, not only in the solar case, but also for stars. With the advent of sophisti- cated techniques such as interferometry, one is now able to accurately determine the geometrical shape of the free boundary of stars, such as Altair or Achernar for which observations of the geometrical envelope have been made for the first time by Belle Van et al. (2001), and Domiciano 0273-1177/$30 Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.01.086 * Corresponding author. Tel.: +33 4 93 40 53 53; fax: +33 4 93 40 53 33. E-mail addresses: sandrine.lefebvre@cea.fr (S. Lefebvre), rozelot@ obs-azur.fr (J.P. Rozelot), sasha@quake.stanford.edu (A.G. Kosovichev). www.elsevier.com/locate/asr Advances in Space Research 40 (2007) 1000–1005