A&A 414, 613–632 (2004) Astronomy DOI: 10.1051/0004-6361:20031595 & c ESO 2004 Astrophysics Magnetic Doppler imaging of 53 Camelopardalis in all four Stokes parameters O. Kochukhov1,, S. Bagnulo2,G.A.Wade3, L. Sangalli3, N. Piskunov1,J.D.Landstreet4, P. Petit5, and T. A. A. Sigut4 1 Uppsala Astronomical Observatory, Box 515, 751 20 Uppsala, Sweden 2 European Southern Observatory, Casilla 19001, Santiago 19, Chile 3 Department of Physics, Royal Military College of Canada, Box 17000, Kingston, Ontario, K7K 4B4 Canada 4 Physics and Astronomy Department, University of Western Ontario, London, Ontario, N6A 3K7 Canada 5 Observatoire Midi-Pyr´en´ees, 14 avenue Edouard´ Belin, 31400 Toulouse, France Received 30 June 2003 / Accepted 10 October 2003 Abstract. We present the first investigation of the structure of the stellar surface magnetic field using line profiles in all four Stokes parameters. We extract the information about the magnetic field geometry and abundance distributions of the chemically peculiar star 53 Cam by modelling time-series of high-resolution spectropolarimetric observations with the help of a new magnetic Doppler imaging code. This combination of the unique four Stokes parameter data and state-of-the-art magnetic imaging technique makes it possible to infer the stellar magnetic field topology directly from the rotational variability of the Stokes spectra. In the magnetic imaging of 53 Cam we discard the traditional multipolar assumptions about the structure of magnetic fields in Ap stars and explore the stellar magnetic topology without introducing any global a priori constraints on the field structure. The complex magnetic model of 53 Cam derived with our magnetic Doppler imaging method achieves a good fit to the observed intensity, circular and linear polarization profiles of strong magnetically sensitive Fe spectral lines. Such an agreement between observations and model predictions was not possible with any earlier multipolar magnetic models, based on modelling Stokes I spectra and fitting surface averaged magnetic observables (e.g., longitudinal field, magnetic field modulus, etc.). Furthermore, we demonstrate that even the direct inversion of the four Stokes parameters of 53 Cam assuming a low- order multipolar magnetic geometry is incapable of achieving an adequate fit to our spectropolarimetric observations. Thus, as a main result of our investigation, we discover that the magnetic field topology of 53 Cam is considerably more complex than any low-order multipolar expansion, raising a general question about the validity of the multipolar assumption in the studies of magnetic field structures of Ap stars. In addition to the analysis of the magnetic field of 53 Cam, we reconstruct surface abundance distributions of Si, Ca, Ti, Fe and Nd. These abundance maps confirm results of the previous studies of 53 Cam, in particular dramatic antiphase variation of Ca and Ti abundances. Key words. stars: chemically peculiar – stars: magnetic fields – polarization – stars: individual: 53 Cam 1. Introduction evolve and disappear on a usually short time scale. However, except in the sun, a magnetic field structured on small scales is The magnetic field plays a fundamental role in the physics of difficult to detect through spectropolarimetric techniques, since the atmospheres of many different stars in the H-R diagram. in a stellar (hence disk-integrated) observation, the polarization Presumably in a large fraction of late-type stars, the magnetic signal coming from surface regions characterized by opposite field is responsible for phenomena that are well observed in the field polarity tends to cancel out. sun, such as, e.g., heating the corona, driving stellar winds, pro- ducing stellar flares. In late-type stars, the magnetic field is not The magnetic fields of early-type stars have quite different globally organized, but appears to be concentrated primarily in characteristics (and probably a different origin) than those of limited regions (spots) of opposite polarity that form, migrate, late-type stars. In early-type stars, the surface magnetic field is static on a timescale of at least many decades, and appears Send offprint requests to: O. Kochukhov, e-mail: [email protected] to be “frozen” into a rigidly rotating atmosphere. The mag- Based on observations obtained with the Bernard Lyot telescope netic field is organized on a large scale, permeating the en- of the Pic du Midi Observatory and Isaac Newton Telescope of the tire stellar surface, with a relatively high field strength (typ- La Palma Observatory. ically of a few hundreds up to a few tens of thousands of Present address: Institut f¨ur Astronomie, Universit¨at Wien, Gauss). The presence of a magnetic field occurs only in those T¨urkenschanzstraße 17, 1180 Wien, Austria. stars in which the photospheric abundances of several chemical Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20031595 614 O. Kochukhov et al.: Magnetic Doppler imaging of 53 Camelopardalis in all four Stokes parameters elements – mostly silicon, iron-peak and rare-earth elements – that in many cases cannot be described in terms of pure dipo- are largely different than in the solar case. These are the mag- lar topologies or axisymmetric superpositions of dipole and netic chemically peculiar stars of the upper main sequence, or quadrupole components. Furthermore, recently Bagnulo et al. Ap stars, that exhibit a wealth of characteristics that are not (2001) have suggested that even general non-axisymmetric observed in other “normal” stars or non-magnetic metallic-line low-order multipolar models may not provide an adequate ap- and mercury-manganese peculiar stars located in the same re- proximation of the actual magnetic topologies in some Ap stars gion of the H-R diagram (see, e.g., Landstreet 1992). Due to and that the magnetic field may be structured on much smaller its global nature, the magnetic field of Ap stars can be much scales than was previously thought. more easily detected and studied than that of late-type stars. New advances in the quality and quantity of the available Therefore, Ap stars represent a primary target for spectropo- observational data have been recently obtained thanks to an ex- larimetric observations, and for the development and testing of tensive observational campaign with the MuSiCoS spectropo- the instruments and modelling techniques for studies of stellar larimeter at the 2-m Telescope Bernard Lyot of the Pic du magnetic fields. Midi Observatory (Wade et al. 2000a). Complete time series of The reason why certain (some 10–15%) upper main se- Stokes IQUV profiles for a number of bright magnetic chem- quence stars are magnetic and chemically peculiar, and why ically peculiar stars have been collected in the last few years, the remaining ones are “normal” stars, is a mystery. One of opening the possibility to study magnetic stars with unprece- the key and basic problems to be solved is, in fact, the origin dented observational constraint. At the same time, Piskunov & of the magnetic field itself – see Moss (2001) for a recent re- Kochukhov (2002) and Kochukhov & Piskunov (2002) have view on this theme. Another interesting yet not well understood completed the development of a computer code for Doppler phenomenon is the interplay between magnetic field and geo- imaging of magnetic stars that, based on no a priori model graphic distribution of the chemical elements over the stellar parameterization, performs the inversion of Stokes IQUV pro- surface. The study of this kind of phenomenon is the scope of files, and recovers the star’s vector magnetic field morphology the diffusion theory. Introduced by Michaud (1970), diffusion and element distribution. The availability of these new data theory explains the presence of chemically peculiarities in up- and modelling tools now makes it possible to do a much more per main sequence stars as the result of a competition between meaningful analysis of the magnetic morphology and element radiative pressure and gravitational settling. If present, a mag- distribution than in the past. As a final goal, the reconstruc- netic field influences the distribution of chemical elements – tion of the magnetic field and the surface abundance distri- see Alecian & Stift (2002) for a study of how the radiative ac- butions of the chemical elements for a significant number of celerations experienced by chemical elements in a stellar at- chemically peculiar stars will allow us to set constraints to the mosphere depend on field strength and orientation. Thus, we diffusion theory, and to better correlate the characteristics of expect that magnetic field topology and geographic distribu- the magnetic field with other fundamental stellar parameters. tion of chemical elements are correlated. For instance, certain Altogether, a clearer picture of the magnetic morphologies of elements may concentrate more in regions characterized by a chemically peculiar stars may give a crucial contribution to un- radial field rather than in regions where the vector field is par- derstanding the problem of the origin of the magnetic field in allel to the stellar surface. A priori, the distribution of chemical early-type stars. elements may also depend on the local magnetic field modu- Along the lines of the strategy discussed above, here we lus. As a matter of fact, we are not yet capable of doing precise present an exhaustive study of a famous and well-observed predictions: assuming a certain model atmosphere, and a given magnetic star, 53 Camelopardalis. Our investigation is utterly magnetic morphology, only few schematic suggestions can be unique, by the virtue of the fact that we use the first high- made on how (some) elements diffuse in the stellar atmosphere resolution four Stokes parameter stellar spectroscopic observa- (e.g., Michaud et al. 1981). These simple models generally fail tions, and that these data are interpreted using a sophisticated to account for the observed abundance distributions and cannot magnetic Doppler imaging code incorporating detailed spec- fully explain the enormous star-to-star variations of the geom- trum synthesis calculations of the Stokes IQUV profiles.