titre : Clouds on stellar surfaces

Generally, magnetic ApBp stars are studied by spectropolarimety. Observations show that the atmospheres of these stars possess strong abundance anomalies (metal abundances that are several orders of magnitude larger than cosmic abundances are often found, underabundances can also occur). These abundance anomalies are inhomogeneously distributed over the surface. Mapping of magnetic structures and of abundances is obtained by Zeeman-Doppler imaging. Although the current precision of this imaging technic is insufficient for a detailed study, the existence of structures is recognized. Several works show also a dependence of these structures with depth.

How to explain these peculiarities ?

The only mechanism known to explain such anomalies is abundance stratification by atomic diffusion (Michaud, 1970). Among main sequence stars, ApBp stars are those having the most stable atmosphere (stability is a required condition for a significant effect due to atomic diffusion to take place). Although atomic diffusion is a physical process resulting from first principles and is well understood, its modelling is very complex for stellar atmospheres (more complex than for stellar interiors). The reasons are : Diffusion velocities are strongly dependent on the radiative accelerations, computation of which requires large quantities of atomic data. Those data are lacking for some elements (like rare earths). The computation of radiative accelerations requires to solve in detail the polarized radiation transfer equation, with hundreds of thousands of atomic transitions (observed or not), in the range 900-10000A, with resolution of 0.01A, estimating the Zeeman desaturation, and tacking into account the blending effect. The time-dependent stratification mechanism is a non-linear and non-local function of the considered element distribution through the atmosphere. This stratification process is very slow and then extremely sensitive to any perturbation in the medium.

Figure 1 : Stratification d’équilibre du fer dans une atmosphère de Bp magnétique (Teff=12000K, 20kG au pôle magnétique, cas dipolaire). En abscisse, le méridien magnétique (0 correspond au pôle, 90 à l’équateur magnétique) ; en ordonnée le numéro de la couche (la couche 75 correspond à peu près à la profondeur optique 1, la couche 30 à 10-5). L’abondance normale de Fe est ici 7.5 (en logarithme dans une échelle correspondant à 12 pour l’hydrogène). Les courbes de niveau et les niveaux de gris indiquent l’écart d’abondance de Fe par rapport à la normale.

The 2D equilibrium stratification model

A realistic calculation of the formation of such clouds is not conceivable presently. This type of calculation needs still some theoretical and numerical developments, and very important computer resources. However, an approximate modelling may be carried out at a reasonable price. One can, for instance, estimate the shape of those clouds, assuming that the process has reached an equilibrium stage (Alecian & Stift 2010, LeBlanc et al 2009). This kind of calculation (Figure 1) requires more than 6000H monoprocessor CPU on the SGI machine (Jade) at CINES. Figure 1 presents a 2D cut in the atmosphere of a magnetic Bp star. The iron abundance at equilibrium is shown along the magnetic meridian (bottom axis), for a simple dipolar geometry. One can notice a strong enhancement of the Fe abundance close to the magnetic equator and at an optical depth of 0.01. Because the geometry of the field is strictly dipolar, the cloud forms a belt around the star. Figure 2, gives a schematic view of such a star.

Figure 2 : Représentation schématique du rotateur oblique dipolaire correspondant au calcul de la Figure 1 (pôle magnétique cerclé en rouge). Les zones colorées représentent la distribution du fer. La ceinture de fer en altitude correspond à la surabondance visible à 90° dans la Figure 1. L’échelle de contraste et l’altitude de la ceinture de fer sont exagérées sur cette figure afin de rendre la représentation plus parlante. Cliquer sur l’image pour l’agrandir

First numerical simulations of the cloud build-up

Although detailed descriptions of the formation of these clouds are presently out of reach, a recent work (Alecian et al. 2011) allowed to progress in the understanding of this phenomenon, and to have a better idea of the clouds behaviour. For this purpose, the authors considered a fictitious element (the "cloudium") whose the atomic properties were inspired from those of mercury, and shaped to allow much faster computation. This numerical simulation of atomic diffusion in a stellar atmosphere (the first one ever done) allows establishing a realistic order of magnitude of the characteristic time of the clouds build-up, and shows two essential behaviours : In many cases the equilibrium state will never been reached. The hypothesis of a cyclic or chaotic build-up of these clouds is strengthened.

Figure 3 : Animation montrant la formation d’un nuage d’élément lourd dans une atmosphère magnétique (Teff=12000K, 7kG). La simulation numérique 1D montre la diffusion du cloudium, avec une abondance initiale égale à celle du mercure dans le Soleil. Au bout d’une trentaine d’années, un nuage (1000 fois plus abondant qu’au temps initial) se forme et s’élève dans l’atmosphère. Avec les paramètres de ce calcul, un état stationnaire (différent de l’équilibre) est atteint en quelques siècles. La fin du calcul montre le réajustement du nuage après une diminution forcée de l’abondance à la base de l’atmosphère. Cliquer sur l’image pour voir le film

References

Bi-dimensional element stratifications computed for magnetic Ap star atmospheres ALECIAN, G., STIFT, M.J., 2010, A&A, 516, A53. Time-dependent diffusion in stellar atmospheres, ALECIAN, G., STIFT, M .J., DORFI, E.A., 2011, MNRAS, 418, 986.

Contact

Georges Alecian
Observatoire de Paris-LUTH, CNRS, Université Paris-Diderot

Dernière modification le 21 décembre 2021