Understanding Solar Activity: Advances and Challenges M. Faurobert, C. Fang and T. Corbard (eds) EAS Publications Series, 55 (2012) 83–86 www.eas.org INVERSION OF ZEEMAN LINE PROFILES USING CENTRAL MOMENTS P. Mein 1 , H. Uitenbroek 2 , N. Mein 1 , V. Bommier 1 and M. Faurobert 3 Abstract. A new inversion method derived from central moments of Zeeman line profiles (ICM), is used to determine magnetic field vectors (Mein et al. 2011). Two quantities A1 and A2 combining moments of profiles I ± S (S = Q, U, V ) are nearly linear functions of the longi- tudinal and transverse components and lead to the field components through very fast iterations. Optimized exponents reduce noise effects. The ICM inversion does not require Milne Eddington approximation and can be used in a wide range of solar models. 1 ICM inversion method We propose a new inversion method using functions derived from central moments of Zeeman line profiles. We restrictthis paper to the 630.2 FeI line with the FALC solar model near disk center. All synthetic profiles are obtained with the RH radiative transfer code (Uitenbroek 2001, 2003). 1.1 Definitions For any polarized line profile P (λ)= I (λ) ± S(λ) with S = Q, U, V we define line depths R(λ)=1 - P (λ)/I c and two kinds of moments M 1 (P, β 1 )=  +∞ -∞ R β1 (λ)λ dλ k  +∞ -∞ R β1 (λ)dλ (β 1 = 1) 1 LESIA, Observatoire de Paris, CNRS, UPMC Paris 06, Universit´ e Paris Diderot, 5 place Jules Janssen, 92195 Meudon, France 2 National Solar Observatory, operated by the Association of Universities for Research in Astronomy, Inc. (AURA), for the National Science Foundation, Sacramento Peak, PO Box 62, Sunspot, NM 88349, USA 3 UMR 6525 H. Fizeau, Universit´ ede Nice Sophia Antipolis, CNRS, Observatoire de la Cˆote d’Azur, Campus Valrose, 06108 Nice, France c  EAS, EDP Sciences 2012 DOI: 10.1051/eas/1255011 Article published by EDP Sciences