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O. Kochukhov

Publications and source records attributed to O. Kochukhov.

At least 91 records · Page 5Linked to original sources

The complex magnetic field topology of the cool Ap star 49 Cam

49 Cam is a cool magnetic chemically peculiar star which has been noted for showing strong, complex Zeeman linear polarisation signatures. This paper describes magnetic and chemical surface maps obtained for 49 Cam using the INVERS10 magnetic Doppler imaging code and high-resolution spectropolarimetric data in all four Stokes parameters collected with the ESPaDOnS and Narval spectropolarimeters at the Canada-France-Hawaii Telescope and Pic du Midi Observatory. The reconstructed magnetic field maps of 49 Cam show a relatively complex structure. Describing the magnetic field topology in terms of spherical harmonics, we find significant contributions of modes up to l=3, including toroidal components. Observations cannot be reproduced using a simple low-order multipolar magnetic field structure. 49 Cam exhibits a level of field complexity that has not been seen in magnetic maps of other cool Ap stars. Hence we concluded that relatively complex magnetic fields are observed in Ap stars at both low and high effective temperatures. In addition to mapping the magnetic field, we also derive surface abundance distributions of nine chemical elements, including Ca, Sc, Ti, Cr, Fe, Ce, Pr, Nd, Eu. Comparing these abundance maps with the reconstructed magnetic field geometry, we find no clear relationship of the abundance distributions with the magnetic field for some elements. However, for other elements some distinct patterns are found. We discuss these results in the context of other recent magnetic mapping studies and theoretical predictions of radiative diffusion.

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Magnetic field topology and chemical abundance distributions of the young, rapidly rotating chemically peculiar star HR5624

The young, rapidly rotating Bp star HR5624 (HD133880) shows an unusually strong non-sinusoidal variability of its longitudinal magnetic field. This behaviour was previously interpreted as the signature of an exceptionally strong, quadrupole-dominated surface magnetic field geometry. We studied the magnetic field structure and chemical abundance distributions of HR5624 with the aim to verify the unusual quadrupolar nature of its magnetic field and to investigate correlations between the field topology and chemical spots. We analysed high resolution, time series Stokes parameter spectra of HR5624 with the help of a magnetic Doppler imaging inversion code based on detailed polarised radiative transfer modelling of the line profiles. Our magnetic Doppler inversions reveal that the field structure of HR5624 is considerably simpler and the field strength is much lower than proposed by previous studies. We find a maximum local field strength of 12 kG and a mean field strength of 4 kG. Our model implies that overall large-scale field topology of HR5624 is better described as a distorted, asymmetric dipole. The chemical abundance maps of Mg, Si, Ti, Cr, Fe, and Nd obtained in our study are characterised by large-scale, high-contrast abundance patterns. These structures correlate weakly with the magnetic field geometry and show no distinct element concentrations in the horizontal field regions predicted by theoretical atomic diffusion calculations. We conclude that the surface magnetic field topology of HR5624 is not as unusual as previously proposed. Considering these results together with other recent magnetic mapping analyses of early-type stars suggests that predominantly quadrupolar magnetic field topologies, invoked to be present in a significant number of stars, probably do not exist in real stars.

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The global and small-scale magnetic fields of fully convective, rapidly spinning M dwarf pair GJ65A and B

The nearby M dwarf binary GJ65AB, also known as BL Cet and UV Cet, is a unique benchmark for investigation of dynamo-driven activity of low-mass stars. Magnetic activity of GJ65 was repeatedly assessed by indirect means, such as studies of flares, photometric variability, X-ray and radio emission. Here we present a direct analysis of large-scale and local surface magnetic fields in both components. Interpreting high-resolution circular polarisation spectra (sensitive to a large-scale field geometry) we uncovered a remarkable difference of the global stellar field topologies. Despite nearly identical masses and rotation rates, the secondary exhibits an axisymmetric, dipolar-like global field with an average strength of 1.3 kG while the primary has a much weaker, more complex and non-axisymmetric 0.3 kG field. On the other hand, an analysis of the differential Zeeman intensification (sensitive to the total magnetic flux) shows the two stars having similar magnetic fluxes of 5.2 and 6.7 kG for GJ65A and B, respectively, although there is an evidence that the field strength distribution in GJ65B is shifted towards a higher field strength compared to GJ65A. Based on these complementary magnetic field diagnostic results we suggest that the dissimilar radio and X-ray variability of GJ65A and B is linked to their different global magnetic field topologies. However, this difference appears to be restricted to the upper atmospheric layers but does not encompass the bulk of the stars and has no influence on the fundamental stellar properties.

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BD-19 5044L: discovery of a short-period SB2 system with a magnetic Bp primary in the open cluster IC 4725

Until recently almost nothing was known about the evolution of magnetic fields found in upper main sequence Ap/Bp stars during their long main sequence lifetime. We are thus studying magnetic Ap/Bp stars in open clusters in order to obtain observational evidence of how the properties of Ap/Bp magnetic stars, such as field strength and structure, evolve with age during the main sequence. One important aspect of this study is to search for the very rare examples of hot magnetic stars in short-period binary systems among magnetic cluster members. In this paper we characterize the object BD-19~5044L, which is both a member of the open cluster IC 4725 = M~25, and a short-period SB2 system containing a magnetic primary star. We have obtained a series of intensity and circular polarisation spectra distributed through the orbital and rotation cycles of BD-19 5044L with the ESPaDOnS spectropolarimeter at CFHT. We find that the orbit of BD-19 5044L AB is quite eccentric (e = 0.477), with a period of 17.63 d. The primary is a magnetic Bp star with a variable longitudinal magnetic field, a polar field strength of ~1400 G and a low obliquity, while the secondary is probably a hot Am star and does not appear to be magnetic. The rotation period of the primary (5.04 d) is not synchronised with the orbit, but the rotation angular velocity is close to being synchronised with the orbital angular velocity of the secondary at periastron, perhaps as a result of tidal interactions. The periastron separation is small enough (about 12 times the radius of the primary star) that BD-19 5044L may be one of the very rare known cases of a tidally interacting SB2 binary system containing a magnetic Ap/Bp star.

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Surface magnetism of cool stars

Magnetic fields are essential ingredients of many physical processes in the interiors and envelopes of cool stars. Yet their direct detection and characterisation is notoriously difficult, requiring high-quality observations and advanced analysis techniques. Significant progress has been recently achieved by several types of direct magnetic field studies on the surfaces of cool active stars. In particular, complementary techniques of the field topology mapping with polarisation data and total magnetic flux measurements from intensity spectra have been systematically applied to different classes of active stars leading to interesting and occasionally controversial results. In this paper we summarise the current status of direct magnetic field studies of cool stars, and investigations of surface inhomogeneities caused by the field, based on the material presented at the Cool Stars 19 splinter session.

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Doppler imaging of chemical spots on magnetic Ap/Bp stars. Numerical tests and assessment of systematic errors

Doppler imaging (DI) is a powerful spectroscopic inversion technique that enables conversion of a line profile time series into a two-dimensional map of the stellar surface inhomogeneities. In this paper we investigate the accuracy of chemical abundance DI of Ap/Bp stars and assess the impact of several different systematic errors on the reconstructed spot maps. We simulate spectroscopic observational data for different spot distributions in the presence of a moderately strong dipolar magnetic field. We then reconstruct chemical maps using different sets of spectral lines and making different assumptions about line formation in the inversion calculations. Our numerical experiments demonstrate that a modern DI code successfully recovers the input chemical spot distributions comprised of multiple circular spots at different latitudes or an element overabundance belt at the magnetic equator. For the optimal reconstruction the average reconstruction errors do not exceed ~0.10 dex. The errors increase to about 0.15 dex when abundance distributions are recovered from a few and/or blended spectral lines. Ignoring a 2.5 kG dipolar magnetic field in chemical abundance DI leads to an average relative error of 0.2 dex and maximum errors of 0.3 dex. Similar errors are encountered if a DI inversion is carried out neglecting a non-uniform continuum brightness distribution and variation of the local atmospheric structure. This series of numerical DI simulations proves that inversions with simplifying assumptions of the non-magnetic radiative transfer and a single model atmosphere are generally reliable. We assess magnetic field strengths of several dozen Ap/Bp stars previously studied with DI methods, concluding that the vast majority of the published chemical spot maps are unaffected by the systematic errors addressed in this paper. (Abridged)

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The MiMeS survey of magnetism in massive stars: Magnetic analysis of the O-type stars

We present the analysis performed on spectropolarimetric data of 97 O-type targets included in the framework of the MiMeS (Magnetism in Massive Stars) Survey. Mean Least-Squares Deconvolved Stokes I and V line profiles were extracted for each observation, from which we measured the radial velocity, rotational and non-rotational broadening velocities, and longitudinal magnetic field. The investigation of the Stokes I profiles led to the discovery of 2 new multi-line spectroscopic systems (HD46106, HD204827) and confirmed the presence of a suspected companion in HD37041. We present a modified strategy of the Least-Squares Deconvolution technique aimed at optimising the detection of magnetic signatures while minimising the detection of spurious signatures in Stokes V. Using this analysis, we confirm the detection of a magnetic field in 6 targets previously reported as magnetic by the MiMeS collaboration (HD108, HD47129A2, HD57682, HD148937, CPD-28 2561, and NGC 1624-2), as well as report the presence of signal in Stokes V in 3 new magnetic candidates (HD36486, HD162978, HD199579). Overall, we find a magnetic incidence rate of 7+/-3%, for 108 individual O stars (including all O-type components part of multi-line systems), with a median uncertainty of the longitudinal field measurements of about 50\,G. An inspection of the data reveals no obvious biases affecting the incidence rate or the preference for detecting magnetic signatures in the magnetic stars. Similar to A- and B-type stars, we find no link between the stars' physical properties (e.g. Teff, mass, age) and the presence of a magnetic field. However, the Of?p stars represent a distinct class of magnetic O-type stars.

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Magnetic fields of young solar twins

The goal of this work is to study the magnetic fields of six young solar-analogue stars both individually, and collectively, to search for possible magnetic field trends with age. If such trends are found, they can be used to understand magnetism in the context of stellar evolution of solar-like stars and, the past of the Sun and the solar system. This is also important for the atmospheric evolution of the inner planets, Earth in particular. We used Stokes IV data from two different spectropolarimeters, NARVAL and HARPSpol. The least-squares deconvolution multi-line technique was used to increase the signal-to-noise ratio of the data. We then applied a modern Zeeman-Doppler imaging code in order to reconstruct the magnetic topology of all stars and the brightness distribution of one of our studied stars. Our results show a significant decrease in the magnetic field strength and energy as the stellar age increases from 100Myr to 250Myr while there is no significant age dependence of the mean magnetic field strength for stars with ages 250-650Myr. The spread in the mean field strength between different stars is comparable to the scatter between different observations of individual stars. The meridional field component has the weakest strength compared to the radial and azimuthal field components in 15 out of the 16 magnetic maps. It turns out that 89-97% of the magnetic field energy is contained in l=1-3. There is also no clear trend with age and distribution of field energy into poloidal/toroidal and axisymmetric/non-axisymmetric components within the sample. The two oldest stars in this study do show a twice as strong octupole component compared to the quadrupole component. This is only seen in one out of 13 maps of the younger stars. One star, chi1 Ori displays two field polarity switches during almost 5 years of observations suggesting a magnetic cycle length of either 2, 6 or 8 years.

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Magnetic Doppler imaging of the chemically peculiar star HD 125248

Intermediate-mass, chemically peculiar stars with strong magnetic fields give us an excellent opportunity to study the topology of their surface magnetic fields and the interplay between magnetic geometries and abundance inhomogeneities in their atmospheres. We reconstruct detailed maps of the surface magnetic field and abundance distributions for the magnetic Ap star HD 125248. We performed the analysis based on phase-resolved, four Stokes parameter spectropolarimetric observations obtained with the HARPSpol instrument. These data were interpreted with the magnetic Doppler imaging technique. We improved the atmospheric parameters of the star, T_eff = 9850K +/- 250K and logg = 4.05 +/- 0.10. We performed detailed abundance analysis and discovered vertical stratification effects for the FeII and CrII ions. We computed LSD Stokes profiles and studied their behavior with rotational phase. We improved the rotational period of the star P_rot = 9.29558(6)d. Magnetic Doppler imaging of HD 125248 showed that its magnetic field is mostly poloidal and quasi-dipolar with two large spots of different polarity and field strength. The chemical maps of Fe, Cr, Ce, Nd, Gd, and Ti show abundance contrasts of 0.9-3.5 dex. Among these elements, the Fe abundance map does not show high-contrast features. Cr is overabundant around the negative magnetic pole and has 3.5 dex abundance range. The rare earth elements and Ti are overabundant near the positive magnetic pole. The magnetic field of HD 125248 has strong deviations from the classical axisymmetric dipole field geometry. The comparison to results derived for other stars using four Stokes magnetic Doppler imaging suggests evidence that the field topology becomes simpler with increasing age. The abundance maps show weak correlation with the magnetic field geometry, but they do not agree with the atomic diffusion calculations.

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The MiMeS Survey of Magnetism in Massive Stars: Introduction and overview

The MiMeS project is a large-scale, high resolution, sensitive spectropolarimetric investigation of the magnetic properties of O and early B type stars. Initiated in 2008 and completed in 2013, the project was supported by 3 Large Program allocations, as well as various programs initiated by independent PIs and archival resources. Ultimately, over 4800 circularly polarized spectra of 560 O and B stars were collected with the instruments ESPaDOnS at the Canada-France-Hawaii Telescope, Narval at the Télescope Bernard Lyot, and HARPSpol at the European Southern Observatory La Silla 3.6m telescope, making MiMeS by far the largest systematic investigation of massive star magnetism ever undertaken. In this paper, the first in a series reporting the general results of the survey, we introduce the scientific motivation and goals, describe the sample of targets, review the instrumentation and observational techniques used, explain the exposure time calculation designed to provide sensitivity to surface dipole fields above approximately 100 G, discuss the polarimetric performance, stability and uncertainty of the instrumentation, and summarize the previous and forthcoming publications.

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Magnetic field topology of tau Sco. The uniqueness problem of Stokes V ZDI inversions

The early B-type star tau Sco exhibits an unusually complex, relatively weak surface magnetic field. Its topology was previously studied with the Zeeman Doppler imaging (ZDI) modelling of high-resolution circular polarisation (Stokes V) observations. Here we assess the robustness of the Stokes V ZDI reconstruction of the magnetic field geometry of tau Sco and explore the consequences of using different parameterisations of the surface magnetic maps. We succeeded in reproducing previously published magnetic field maps of tau Sco using both general harmonic expansion and a direct, pixel-based representation of the magnetic field. These maps suggest that the field topology of tau Sco is comprised of comparable contributions of the poloidal and toroidal magnetic components. At the same time, we also found that available Stokes V observations can be successfully fitted employing restricted harmonic expansions, by either neglecting the toroidal field altogether or linking the radial and horizontal components of the poloidal field as required by the widely used potential field extrapolation technique. These alternative modelling approaches lead to a stronger and topologically more complex surface field structure. The field distributions recovered with different ZDI options differ significantly, yielding indistinguishable Stokes V profiles but different linear polarisation (Stokes Q and U) signatures. Our investigation underscores the well-known problem of non-uniqueness of the Stokes V ZDI inversions. For the magnetic stars with properties similar to tau Sco (relatively complex field, slow rotation) the outcome of magnetic reconstruction depends sensitively on the adopted field parameterisation. Stokes Q and U spectropolarimetric observations represent the only way of breaking the degeneracy of surface magnetic field models.

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The magnetic field topology and chemical abundance distributions of the Ap star HD 32633

Previous observations of the Ap star HD 32633 indicated that its magnetic field was unusually complex in nature and could not be characterised by a simple dipolar structure. Here we derive magnetic field maps and chemical abundance distributions for this star using full Stokes vector (Stokes $IQUV$) high-resolution observations obtained with the ESPaDOnS and Narval spectropolarimeters. Our maps, produced using the Invers10 magnetic Doppler imaging (MDI) code, show that HD 32633 has a strong magnetic field which features two large regions of opposite polarity but deviates significantly from a pure dipole field. We use a spherical harmonic expansion to characterise the magnetic field and find that the harmonic energy is predominately in the $\ell=1$ and $\ell=2$ poloidal modes with a small toroidal component. At the same time, we demonstrate that the observed Stokes parameter profiles of HD 32633 cannot be fully described by either a dipolar or dipolar plus quadrupolar field geometry. We compare the magnetic field topology of HD 32633 with other early-type stars for which MDI analyses have been performed, supporting a trend of increasing field complexity with stellar mass. We then compare the magnetic field topology of HD 32633 with derived chemical abundance maps for the elements Mg, Si, Ti, Cr, Fe, Ni and Nd. We find that the iron-peak elements show similar distributions, but we are unable to find a clear correlation between the location of local chemical enhancements or depletions and the magnetic field structure.

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Activity and Magnetic Field Structure of the Sun-Like Planet Hosting Star HD 1237

We analyse the magnetic activity characteristics of the planet hosting Sun-like star, HD 1237, using HARPS spectro-polarimetric time-series data. We find evidence of rotational modulation of the magnetic longitudinal field measurements consistent with our ZDI analysis, with a period of 7 days. We investigate the effect of customising the LSD mask to the line depths of the observed spectrum and find that it has a minimal effect on shape of the extracted Stokes V profile but does result in a small increase in the S/N ($\sim$ 7%). We find that using a Milne-Eddington solution to describe the local line profile provides a better fit to the LSD profiles in this slowly rotating star, which also impacts the recovered ZDI field distribution. We also introduce a fit-stopping criterion based on the information content (entropy) of the ZDI maps solution set. The recovered magnetic field maps show a strong (+90 G) ring-like azimuthal field distribution and a complex radial field dominating at mid latitudes ($\sim$45 degrees). Similar magnetic field maps are recovered from data acquired five months apart. Future work will investigate how this surface magnetic field distribution impacts the coronal magnetic field and extended environment around this planet-hosting star.

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Diagnostic of stellar magnetic fields with cumulative circular polarisation profiles

Information about stellar magnetic field topologies is obtained primarily from high-resolution circular polarisation (Stokes $V$) observations. Due to their generally complex morphologies, the stellar Stokes $V$ profiles are usually interpreted with elaborate inversion techniques such as Zeeman Doppler imaging (ZDI). Here we further develop a new method of interpretation of circular polarisation signatures in spectral lines using cumulative Stokes $V$ profiles (anti-derivative of Stokes $V$). This method is complimentary to ZDI and can be applied for validation of the inversion results or when the available observational data are insufficient for an inversion. Based on the rigorous treatment of polarised line formation in the weak-field regime, we show that, for rapidly rotating stars, the cumulative Stokes $V$ profiles contain information about the spatially resolved longitudinal magnetic field density. Rotational modulation of these profiles can be employed for a simple, qualitative characterisation of the stellar magnetic field topologies. We apply this diagnostic method to the archival observations of the weak-line T Tauri star V410 Tau and Bp He-strong star HD 37776. We show that the magnetic field in V410 Tau is dominated by an azimuthal component, in agreement with the ZDI map that we recover from the same data set. For HD 37776 the cumulative Stokes $V$ profile variation indicates the presence of multiple regions of positive and negative field polarity. This behaviour agrees with the ZDI results but contradicts the popular hypothesis that the magnetic field of this star is dominated by an axisymmetric quadrupolar component.

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Revisiting the Rigidly Rotating Magnetosphere model for $σ$ Ori E - II. Magnetic Doppler imaging, arbitrary field RRM, and light variability

The initial success of the Rigidly Rotating Magnetosphere (RRM) model application to the B2Vp star sigma OriE by Townsend, Owocki & Groote (2005) triggered a renewed era of observational monitoring of this archetypal object. We utilize high-resolution spectropolarimetry and the magnetic Doppler imaging (MDI) technique to simultaneously determine the magnetic configuration, which is predominately dipolar, with a polar strength Bd = 7.3-7.8 kG and a smaller non-axisymmetric quadrupolar contribution, as well as the surface distribution of abundance of He, Fe, C, and Si. We describe a revised RRM model that now accepts an arbitrary surface magnetic field configuration, with the field topology from the MDI models used as input. The resulting synthetic Ha emission and broadband photometric observations generally agree with observations, however, several features are poorly fit. To explore the possibility of a photospheric contribution to the observed photometric variability, the MDI abundance maps were used to compute a synthetic photospheric light curve to determine the effect of the surface inhomogeneities. Including the computed photospheric brightness modulation fails to improve the agreement between the observed and computed photometry. We conclude that the discrepancies cannot be explained as an effect of inhomogeneous surface abundance. Analysis of the UV light variability shows good agreement between observed variability and computed light curves, supporting the accuracy of the photospheric light variation calculation. We thus conclude that significant additional physics is necessary for the RRM model to acceptably reproduce observations of not only sigma Ori E, but also other similar stars with significant stellar wind-magnetic field interactions.

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Doppler Imaging of LQ Hya for 1998-2002

We study the spot distribution on the surface of LQ~Hya during the observing seasons October 1998 -- November 2002. We look for persistent active longitudes, trends in the level of spot activity and compare to photometric data, specifically to the derived time epochs of the lightcurve minima. We apply the Doppler Imaging technique on photospheric spectral lines using an inversion code to retrieve images of the surface temperature. We present new temperature maps using multiple spectral lines for a total of 7 seasons. We calculate spot coverage fractions from each map, and as a result we find a general trend that is interpreted to be an indication of a spot cycle. There is a minimum during the observing season of March 1999. After this the activity increases until November 2000, followed by a general decrease in activity again. We find no evidence for active longitudes persisting over multiple observing seasons. The spot activity appears to be concentrated to two latitude regions. The high latitude spots are particularly strong when the spot coverage is at a maximum. Using the currently accepted rotation period, we find spot structures to show a trend in the phase-time plot, indicative of a need for a longer period. We conclude that the long-term activity of LQ~Hya is more chaotic than that of some magnetically active binary stars analyzed with similar methods, but still with clear indications of an activity cycle.

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A comprehensive and critical re-analysis of FORS spectropolarimetric observations: the case of HD92207

Stellar spectropolarimetry has become extremely popular during the last decade, and has led to major advances in our understanding of stellar magnetic fields and of their impact on stellar structure and evolution. Many important discoveries have been obtained thanks to observations performed with the FORS low-resolution spectropolarimeters of the ESO Very Large Telescope. We first review and summarise the major results of a homogeneous re-reduction and analysis of all single-slit FORS1 spectropolarimetric observations. This work revealed a non-negligible dependence of the results upon the adopted reduction and analysis procedure, as well as the presence of instabilities, revealing that photon noise is not the only source of uncertainty. As a consequence of our new analysis and assessment of the uncertainties, we are not able to confirm a large number of magnetic field detections presented in the past for a variety of stars. We further summarise the results of FORS2 spectropolarimetric observations of the A0 supergiant HD92207 which allowed us to explore further the nature of the instabilities, roughly constraining their maximum impact on the derived Stokes profiles and magnetic field values. We finally present new results obtained with a further independent pipeline on the FORS2 data of HD92207, confirming our previous analysis, and discuss simple quality-check controls which can be performed on the data in order to distinguish between genuine and spurious signals. All together, our results reveal that the FORS spectropolarimeters are indeed reliable instruments, when their capabilities are not pushed beyond the limits of a Cassegrain mounted low-resolution spectrograph.

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Magnetic field topology and chemical spot distributions in the extreme Ap star HD 75049

Intermediate-mass, magnetic chemically peculiar (Ap) stars provide a unique opportunity to study the topology of stellar magnetic fields in detail and to investigate magnetically driven processes of spot formation. Here we aim to derive the surface magnetic field geometry and chemical abundance distributions for the extraordinary Ap star HD 75049. This object hosts a surface field of ~30 kG, one of the strongest known for any non-degenerate star. We used time-series of high-resolution HARPS intensity and circular polarisation observations. These data were interpreted with the help of magnetic Doppler imaging and model atmospheres incorporating effects of a non-solar chemical composition and a strong magnetic field. We refined the rotational period of HD 75049 to Prot=4.048267+/-0.000036 d. We also derived basic stellar parameters, Teff=10250+/-250 K and logg=4.3+/-0.1. Magnetic Doppler imaging revealed that the field topology of HD 75049 is poloidal and dominated by a dipolar contribution with a peak surface field strength of 39 kG. At the same time, deviations from the classical axisymmetric oblique dipolar configuration are significant. Chemical surface maps of Si, Cr, Fe, and Nd show abundance contrasts of 0.5-1.4 dex, which is low compared with many other Ap stars. Nd is found to be enhanced close to the magnetic pole, whereas Si and Cr are concentrated predominantly at the magnetic equator. The iron distribution shows low-contrast features both at the magnetic equator and the pole. The morphology of the magnetic field and the properties of chemical spots in HD 75049 are qualitatively similar to those of Ap stars with weaker fields. Consequently, whatever mechanism forms and sustains global magnetic fields in intermediate-mass main-sequence stars, it operates in the same way over the entire observed range of magnetic field strengths.

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