Context. The understanding of fossil fields' origin, topology, and stability is one of the corner stones of the stellar magnetism theory. On one hand, since they survive on secular time scales, they may modify the structure and the evolution of their host stars. On the other hand, they must have a complex stable structure since it has been demonstrated that the simplest purely poloidal or toroidal fields are unstable on dynamical time scales. In this context, the only stable configuration found today is the one resulting from a numerical simulation by Braithwaite and collaborators who studied the evolution of an initial stochastic magnetic field, which is found to relax on a mixed stable configuration (poloidal and toroidal) that seems to be in equilibrium and then diffuses. Aims. We investigate an equilibrium field in a semi-analytical way. In this first article, we study the barotropic magnetohydrostatic equilibrium states. Methods. The problem reduces to a Grad-Shafranov-like equation with arbitrary functions. These functions are constrained by deriving the lowest-energy equilibrium states for given invariants of the considered axisymmetric problem, in particular for a given helicity known to be one of the causes of such problems. These theoretical results were applied to realistic stellar cases, the solar radiative core and the envelope of an Ap star, and discussed. In both cases we assumed that the field is initially confined in the stellar radiation zone.Results. The generalization of the force-free Taylor's relaxation states studied in laboratory experiments (in spheromaks) that become non force-free in the self-gravitating stellar case are obtained. The case of general baroclinic equilibrium states will be studied in Paper II.

The existence of stable magnetic configurations in white dwarfs, neutron stars and various nonconvective stellar regions is now well recognized. It has recently been shown numerically that various families of equilibria, including axisymmetric mixed poloidal-toroidal configurations, are stable.Here we test the stability of an analytically-derived non force-free magnetic equilibrium, using threedimensional magnetohydrodynamic simulations: the mixed configuration is compared with the dynamical evolution of its purely poloidal and purely toroidal components, both known to be unstable. The mixed equilibrium shows no sign of instability under white noise perturbations. This configuration therefore provides a good description of magnetic equilibrium topology inside non-convective stellar objects and will be useful to initialize magneto-rotational transport in stellar evolution codes.

We study the impact of a fossil magnetic field on the physical quantities which describe the structure of a young Sun of 500 Myr. We consider for the first time a non force-free field composed of a mixture of poloidal and toroidal magnetic fields and we propose a specific configuration to illustrate our purpose. In the present paper, we estimate the relative role of the different terms which appear in the modified stellar structure equations. We note that the Lorentz tension plays a non negligible role in addition to the magnetic pressure. This is interesting because most of the previous stellar evolution codes ignored that term and the geometry of the field. The solar structure perturbations are, as already known, small and consequently we have been able to estimate each term semi-analytically. We develop a general treatment to calculate the global modification of the structure and of the energetic balance. We estimate also the gravitational multipolar moments associated with the presence of a fossil large-scale magnetic field in radiative zone. The values given for the young Sun help the future implementation in stellar evolution codes. This work can be repeated for any other field configuration and prepares the achievement of a solar MHD model where we will follow the transport of such field on secular timescales and the associated transport of momentum and chemicals. The described method will be applied at the present Sun and the results will be compared with the coming balloon or space measurements.Comment: 11 pages, accepted for publication in MNRA

Context. On its asteroseismic side, the initial run of CoRoT was partly devoted to the solar like star HD 49933. The eigenmodes of this F dwarf have been observed with unprecedented accuracy. Aims. We investigate quantitatively the impact of changes in the modeling parameters like mass and composition. More importantly we investigate how a sophisticated physics affects the seismological picture of HD 49933. We consider the effects of diffusion, rotation and the changes in convection efficiency. Methods. We use the CESAM stellar evolution code coupled to the ADIPLS adiabatic pulsation package to build secular models and their associated oscillation frequencies. We also exploited the hydrodynamical code STAGGER to perform surface convection calculations. The seismic variables used in this work are: the large frequency separation, the derivative of the surface phase shift, and the eigenfrequencies ν =0,n=14 and ν =0,n=27 . Results. Mass and uncertainties on the composition have much larger impacts on the seismic variables we consider than the rotation. The derivative of the surface phase shift is a promising variable for the determination of the helium content. The seismological variables of HD 49933 are sensitive to the assumed solar composition and also to the presence of diffusion in the models.

I detail the results of simulations of magnetic relaxation, as is assumed to happen in stellar radiation zones: starting from an initially stochastically organized magnetic field, this one self-organizes towards a large-scale, mainly dipolar configuration with both poloidal and toroidal components. While previous studies focused on the description of static equilibria, I include here the rotation in the numerical setup which substantially modifies the outcome of the simulations. In particular, magnetic equilibria are found, whose configuration remain stable over diffusive timescales (in general of the order of the main-sequence lifetime) rather than dynamic ones, as would be the case in presence of MHD instability. Their privileged axis are inclined with respect to the rotation axis, as observed in early-type, magnetic main sequence stars. The stationary internal flows and the dependence of the final equilibrium state on the rotation rate are described. Implications on stellar evolution are discussed.

Abstract.We study the impact on the stellar structure of a large-scale magnetic field in stellar radiation zones. The field is in magneto-hydrostatic (MHS) equilibrium and has a non force-free character, which allows us to study its influence both on the mechanical and and on the energetic balances. This approach is illustrated in the case of an A p star where the magnetic field matches at the surface with an external potential one. Perturbations of the stellar structure are semianalytically computed. The relative importance of the magnetic physical quantities is discussed and a hierarchy, aiming at distinguishing various refinement degrees in the implementation of a large-scale magnetic field in a stellar evolution code, is established. This treatment also allows us to deduce the gravitational multipolar moments and the change in effective temperature associated with the presence of a magnetic field.

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Abstract. The Magnetism in Massive Stars (MiMeS) Project is a consensus collaboration among many of the foremost international researchers of the physics of hot, massive stars, with the basic aim of understanding the origin, evolution and impact of magnetic fields in these objects. At the time of writing, MiMeS Large Programs have acquired over 950 high-resolution polarised spectra of about 150 individual stars with spectral types from B5-O4, discovering new magnetic fields in a dozen hot, massive stars. The quality of this spectral and magnetic matériel is very high, and the Collaboration is keen to connect with colleagues capable of exploiting the data in new or unforeseen ways. In this paper we review the structure of the MiMeS observing programs and report the status of observations, data modeling and development of related theory.