Least-squares Deconvolution Research Articles

Strong variable linear polarization in the cool active star II Peg

AbstractMagnetic fields of cool active stars are currently studied polarimetrically using only circular polarization observations. This provides limited information about the magnetic field geometry since circular polarization is only sensitive to the line-of-sight component of the magnetic field. Reconstructions of the magnetic field topology will therefore not be completely trustworthy when only circular polarization is used. On the other hand, linear polarization is sensitive to the transverse component of the magnetic field. By including linear polarization in the reconstruction the quality of the reconstructed magnetic map is dramatically improved. For that reason, we wanted to identify cool stars for which linear polarization could be detected at a level sufficient for magnetic imaging. Four active RS CVn binaries, II Peg, HR 1099, IM Peg, and σ Gem were observed with the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope. Mean polarization profiles in all four Stokes parameters were derived using the multi-line technique of least-squares deconvolution (LSD). Not only was linear polarization successfully detected in all four stars in at least one observation, but also, II Peg showed an extraordinarily strong linear polarization signature throughout all observations. This qualifies II Peg as the first promising target for magnetic Doppler imaging in all four Stokes parameters and, at the same time, suggests that other such targets can possibly be identified.

Discovery of the magnetic field in the pulsating B starβCephei

Although the star itself is not He enriched, the periodicity and the variability in the UV wind lines of the pulsating B1 IV star beta Cep are similar to what is observed in magnetic He-peculiar B stars, suggesting that beta Cep is magnetic. We searched for a magnetic field using spectropolarimetry. From UV spectroscopy, we analysed the wind variability and investigated the correlation with the magnetic data. Using 130 time-resolved circular polarisation spectra, obtained with the MuSiCoS spectropolarimeter at the 2m TBL from 1998 until 2005, we applied the least-squares deconvolution method on the Stokes V spectra and derived the longitudinal component of the integrated magnetic field over the visible hemisphere of the star. We performed a period analysis on the magnetic data and on EW measurements of UV wind lines obtained over 17 years. We also analysed the short- and long-term radial velocity variations, which are due to the pulsations and the 90-year binary motion. beta Cep hosts a sinusoidally varying magnetic field with an amplitude 97(4) G and an average value -6(3) G. From the UV wind line variability, we derive a period of 12.00075(11) days, which is the rotation period of the star, and is compatible with the observed magnetic modulation. Phases of maximum and minimum field match those of maximum emission in the UV wind lines, strongly supporting an oblique magnetic-rotator model. We discuss the magnetic behaviour as a function of pulsation behaviour and UV line variability. This paper presents the analysis of the first confirmed detection of a dipolar magnetic field in an upper main-sequence pulsating star. Maximum wind absorption originates in the magnetic equatorial plane. Maximum emission occurs when the magnetic north pole points to the Earth. Radial velocities agree with the ~90-y orbit around its Be-star binary companion.

Orbital parameters, chemical composition and magnetic field of the Ap binary HD 98088★

HD 98088 is a synchronised, double-lined spectroscopic binary system with a magnetic Ap primary component and an Am secondary component. We study this rare system using high-resolution MuSiCoS spectropolarimetric data, to gain insight into the effect of binarity on the origin of stellar magnetism and the formation of chemical peculiarities in A-type stars. Using a new collection of 29 high-resolution Stokes VQU spectra we re-derive the orbital and stellar physical parameters and conduct the first disentangling of spectroscopic observations of the system to conduct spectral analysis of the individual stellar components. From this analysis we determine the projected rotational velocities of the stars and conduct a detailed chemical abundance analysis of each component using both the SYNTH3 and ZEEMAN spectrum synthesis codes. The surface abundances of the primary component are typical of a cool Ap star, while those of the secondary component are typical of an Am star. We present the first magnetic analysis of both components using modern data. Using Least-Squares Deconvolution, we extract the longitudinal magnetic field strength of the primary component, which is observed to vary between +1170 and -920 G with a period consistent with the orbital period. There is no field detected in the secondary component. The magnetic field in the primary is predominantly dipolar, with the positive pole oriented approximately towards the secondary.

Detection of a magnetic field in three old and inactive solar-like planet-hosting stars

Our understanding of magnetic fields in late-type stars is strongly driven by what we know of the solar magnetic field. For this reason, it is crucial to understand how typical the solar dynamo is. To do this we need to compare the solar magnetic field with that of other stars as similar to the Sun as possible, both in stellar parameters and age, hence activity. We present here the detection of a magnetic field in three planet-hosting solar-like stars having a mass, age, and activity level comparable to that of the Sun. We used the HARPSpol spectropolarimeter to obtain high-resolution high-quality circularly polarised spectra of HD 70642, HD 117207, and HD 154088, using the Least-Squares Deconvolution technique to detect the magnetic field. From the Stokes I spectra, we calculated the logR activity index for each star. We compared the position of the stars in the Hertzsprung-Russell diagram to evolutionary tracks, to estimate their mass and age. We used the lithium abundance, derived from the Stokes I spectra, to further constrain the ages. We obtained a definite magnetic field detection for both HD 70642 and HD 154088, while for HD 117207 we obtained a marginal detection. Due to the lower signal-to-noise ratio of the observations, we were unable to detect the magnetic field in the second set of observations available for HD 117207 and HD 154088. On the basis of effective temperature, mass, age, and activity level the three stars can be considered solar analogs. HD 70642, HD 117207, and HD 154088 are ideal targets for a comparative study between the solar magnetic field and that of solar analogs.

Least-Squares Deconvolution based analysis of stellar spectra

In recent years, astronomical photometry has been revolutionised by space missions such as MOST, CoRoT and Kepler. However, despite this progress, high-quality spectroscopy is still required as well. Unfortunately, high-resolution spectra can only be obtained using ground-based telescopes, and since many interesting targets are rather faint, the spectra often have a relatively low S/N. Consequently, we have developed an algorithm based on the least-squares deconvolution profile, which allows to reconstruct an observed spectrum, but with a higher S/N. We have successfully tested the method using both synthetic and observed data, and in combination with several common spectroscopic applications, such as e.g. the determination of atmospheric parameter values, and frequency analysis and mode identification of stellar pulsations.

A high-resolution spectropolarimetric survey of Herbig Ae/Be stars – I. Observations and measurements★

This is the first in a series of papers in which we describe and report the analysis of a large survey of Herbig Ae/Be stars in circular spectropolarimetry. Using the ESPaDOnS and Narval high-resolution spectropolarimeters at the Canada-France-Hawaii and Bernard Lyot Telescopes, respectively, we have acquired 132 circularly-polarised spectra of 70 Herbig Ae/Be stars and Herbig candidates. The large majority of these spectra are characterised by a resolving power of about 65,000, and a spectral coverage from about 3700 ang to 1 micron. The peak SNR per CCD pixel ranges from below 100 (for the faintest targets) to over 1000 (for the brightest). The observations were acquired with the primary aim of searching for magnetic fields in these objects. However, our spectra are suitable for a variety of other important measurements, including rotational properties, variability, binarity, chemical abundances, circumstellar environment conditions and structure, etc. In this first paper, we describe the sample selection, the observations and their reduction, and the measurements that will comprise the basis of much of our following analysis. We describe the determination of fundamental parameters for each target. We detail the Least-Squares Deconvolution that we have applied to each of our spectra, including the selection, editing and tuning of the LSD line masks. We describe the fitting of the LSD Stokes I profiles using a multi-component model that yields the rotationally-broadened photospheric profile (providing the projected rotational velocity and radial velocity for each observation) as well as circumstellar emission and absorption components. Finally, we diagnose the longitudinal Zeeman effect via the measured circular polarisation, and report the longitudinal magnetic field and Stokes V Zeeman signature detection probability. As an appendix, we provide a detailed review of each star observed.

Discovery of a magnetic field in the rapidly rotating O-type secondary of the colliding-wind binary HD 47129 (Plaskett's star)

We report the detection of a strong, organized magnetic field in the secondary component of the massive O8III/I+O7.5V/III double-lined spectroscopic binary system HD 47129 (Plaskett's star), in the context of the Magnetism in Massive Stars (MiMeS) survey. Eight independent Stokes $V$ observations were acquired using the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope and the Narval spectropolarimeter at the T\'elescope Bernard Lyot. Using Least-Squares Deconvolution we obtain definite detections of signal in Stokes $V$ in 3 observations. No significant signal is detected in the diagnostic null ($N$) spectra. The Zeeman signatures are broad and track the radial velocity of the secondary component; we therefore conclude that the rapidly-rotating secondary component is the magnetized star. Correcting the polarized spectra for the line and continuum of the (sharp-lined) primary, we measured the longitudinal magnetic field from each observation. The longitudinal field of the secondary is variable and exhibits extreme values of $-810\pm 150$ G and $+680\pm 190$ G, implying a minimum surface dipole polar strength of $2850\pm 500$ G. In contrast, we derive an upper limit ($3\sigma$) to the primary's surface magnetic field of 230 G. The combination of a strong magnetic field and rapid rotation leads us to conclude that the secondary hosts a centrifugal magnetosphere fed through a magnetically confined wind. We revisit the properties of the optical line profiles and X-ray emission - previously interpreted as a consequence of colliding stellar winds - in this context. We conclude that HD 47129 represents a heretofore unique stellar system - a close, massive binary with a rapidly rotating, magnetized component - that will be a rich target for further study.

HD 96446: a puzzle for current models of magnetospheres?

Context. Oblique magnetic dipole fields have been detected in Bp stars for several decades, and more recently also in normal massive stars. In the past decade, it has been established that stellar magnetospheres form through the channelling and confinement of an outflowing stellar wind by the stellar magnetic field. This explains specific properties of magnetic massive stars, such as their rotationally modulated photometric light curve, Hα emission, UV spectra, and X-ray emission. Aims. In the framework of the MiMeS (Magnetism in Massive Stars) project, four HARPSpol observations of the magnetic Bp star HD 96446 have been obtained. HD 96446 is very similar to σ Ori E, the prototype of centrifugally supported rigidly rotating magnetospheres (CM) and is therefore a perfect target to study the validity of this model. Methods. We first updated the basic parameters of HD 96446 and studied its spectral variability. We then analysed the HARPSpol spectropolarimetric observations using the LSD (Least-Squares Deconvolution) technique to derive the longitudinal magnetic field and Zeeman signatures in various types of lines. With LTE spectrum modelling, we derived constraints on the field modulus, the rotational velocity, and the inclination angle, and measured non-solar abundances of several elements which we checked with NLTE modelling. Finally, we calculated the magnetic confinement and Alfven and Kepler radii from the stellar magnetic field and rotation properties, and we examined the various types of magnetospheres that may be present around HD 96446. Results. We find radial velocity variations with a period around 2.23 h, that we attribute to β Cep-type p-mode pulsations. We detect clear direct magnetic Stokes V signatures with slightly varying values of the longitudinal magnetic field, typical of an oblique dipole rotator, and show that these signatures are not much perturbed by the radial velocity variations. The magnetic confinement parameter and Alfven radius in the centrifugally supported, rigidly-rotating magnetosphere (CM) model points towards the presence of confined material in the magnetosphere. However, HD 96446 does not present signatures of the presence of such confined material, such as Hα emission. Conclusions. We conclude that, even though HD 96446 fulfills all criteria to host a CM with confined material, it does not. The rotation period must be significantly revised, or another model of magnetosphere with a leakage mechanism will need to be developed to explain the magnetic environment of this star.

Discovery of a magnetic field in the early B-type starσLupi

Magnetic early B-type stars are rare. To identify them, we use the strongest indirect indicator of a magnetic field in B stars, which is periodic variability of UV stellar wind lines occurring symmetric about the approximate rest wavelength. Probable magnetic candidates are targets for follow-up spectropolarimetry to search for a magnetic field. From the UV wind line variability the B1/B2V star sigma Lupi emerged as a new magnetic candidate star. AAT spectropolarimetric measurements with SEMPOL were obtained. The longitudinal component of the magnetic field integrated over the visible surface of the star was determined with the Least-Squares Deconvolution method. The UV line variations of sigma Lupi are similar to what is known in magnetic B stars, but no periodicity could be determined. We detected a varying longitudinal magnetic field with amplitude of about 100 G with error bars of typically 20 G, which supports an oblique magnetic-rotator configuration. The EW variations of the UV lines, the magnetic and the optical-line variations are consistent with the photometric period of 3.02 d, which we identify with the rotation period of the star. Additional observations with ESPaDOnS attached to the CFHT confirmed this discovery, and allowed the determination of a precise magnetic period. Analysis revealed that sigma Lupi is a He-strong star, with an enhanced N abundance and an underabundance of C, and has a chemically spotted surface. Like in other magnetic B stars the UV wind emission appears to originate close to the magnetic equatorial plane, with maximum emission when a magnetic pole points towards the Earth. The 3.01972(43) d magnetic rotation period is consistent with the photometric period, with maximum light corresponding to maximum magnetic field.

A critical evaluation of the principal component analysis detection of polarized signatures using real stellar data

The general context of this study concerns the post-processing of multiline spectropolarimetric observations of stars, and in particular these numerical analysis techniques aiming at the detection and the characterization of polarized signatures. Hereafter, using real observational data, we compare and clarify a number of points concerning various methods of analysis. Indeed, simple line addition, least-squares deconvolution and denoising by principal component analysis have been applied, and compared to each other, to polarized stellar spectra available from the TBLegacy database of the Narval spectropolarimeter. Such a comparison between various approaches of distinct sophistication levels allows us to make a safe choice for the next implementation of on-line post-processing of our unique database for the stellar physics community.

New measurements of rotation and differential rotation in A-F stars: are there two populations of differentially rotating stars?

We present projected rotational velocities and new measurements of the rotational profile of some 180 nearby stars with spectral types A-F. The overall broadening profile is derived analysing spectral line shape from hundreds of spectral lines by the method of least-squares deconvolution. Rigid and differential rotation can be distinguished in 56 cases. Ten stars with significant differential rotation rates are identified. As of now, 33 differential rotators detected by line profile analysis have been confirmed. The frequency of differential rotators decreases towards high effective temperature and rapid rotation. There is evidence for two populations of differential rotators with a gap in between at spectral type early-F. The gap can only partly be explained by an upper bound found for the horizontal shear of F stars. Apparently, the physical conditions of differential rotation change at early-F spectral types.

Magnetic field structure in single late-type giants: the effectively single giant V390 Aurigae

We have studied the active giant V390 Aur using spectropolarimetry to obtain direct and simultaneous measurements of the magnetic field and the activity indicators in order to get a precise insight of its activity. We used the spectropolarimeter NARVAL at the Bernard Lyot Telescope (Observatoire du Pic du Midi, France) to obtain a series of Stokes I and Stokes V profiles. The Least Square deconvolution (LSD) technique was applied to detect the Zeeman signature of the magnetic field in each of our 13 observations and to measure its longitudinal component. We could also monitor the CaII K & H and IR triplet, as well as the H_alpha lines which are activity indicators. In order to reconstruct the magnetic field geometry of V390 Aur, we applied the Zeeman Doppler Imaging (ZDI) inversion method and present a map for the magnetic field. Based on the obtained spectra, we also refined the fundamental parameters of the star and the Li abundance. The ZDI revealed a structure in the radial magnetic field consisting of a polar magnetic spot of positive polarity and several negative spots at lower latitude. A high latitude belt is present on the azimuthal field map, indicative of a toroidal field close to the surface. It was found that the photometric period cannot fit the behaviour of the activity indicators formed in the chromosphere. Their behaviour suggests slower rotation compared to the photosphere, but our dataset is too short to be able to estimate the exact periods for them.Accepted for publication in A&A All these results can be explained in terms of an \alpha-\omega dynamo operation, taking into account the stellar structure and rotation properties of V390 Aur that we study using up to-date stellar models computed at solar metallicity. The calculated Rossby number also points to a very efficient dynamo

A novel method for fast and robust estimation of fluorescence decay dynamics using constrained least-squares deconvolution with Laguerre expansion

We report a novel method for estimating fluorescence impulse response function (fIRF) from noise-corrupted time-domain fluorescence measurements of biological tissue. This method is based on the use of high-order Laguerre basis functions and a constrained least-squares approach that addresses the problem of overfitting due to increased model complexity. The new method was extensively evaluated on fluorescence data from simulation, fluorescent standard dyes, ex vivo tissue samples of atherosclerotic plaques and in vivo oral carcinoma. Current results demonstrate that this method allows for rapid and accurate deconvolution of multiple channel fluorescence decays without adaptively adjusting the Laguerre scale parameter. The appropriate choice of the scale parameter is essential for accurate estimation of the fIRF. The method described here is anticipated to play an important role in the development of computational techniques for real-time analysis of time-resolved fluorescence data from biological tissues and to support the advancement of fluorescence lifetime instrumentation for biomedical diagnostics by providing a means for on-line robust analysis of fluorescence decay.

Detecting and modelling the magnetic field of theβ Cephei star V 2052 Ophiuchi

Aims. Following the indirect detection of a magnetic field in the β Cephei star V 2052 Oph by Neiner and collaborators in 2003 with the Musicos spectropolarimeter, we remeasured the magnetic field of this star to attempt to directly confirm the detection of a magnetic field and study its configuration in greater detail. Methods. We used the Narval spectropolarimeter installed at TBL (Pic du Midi, France), which is about 20 times more efficient than the Musicos spectropolarimeter. We applied the least-squares deconvolution (LSD) technique to various groups of lines to measure the circular polarisation of the light coming from V 2052 Oph. We synthesized the measured Stokes V profiles with a centred and off-centred dipole model. Results. For the first time, we clearly detect the Zeeman signature in the Stokes V profiles of V 2052 Oph and thus directly prove the presence of a magnetic field in this star. The modulation with the rotation period is also confirmed and reflects an oblique dipole field. Thanks to the small error bars on the measurements, we are able to study the behaviour of different groups of lines and the centring of the dipole in the star. We find that the dipole is most likely off-centred along the magnetic axis and that He spots are present at the surface next to the magnetic axis. Conclusions. We conclude that V 2052 Oph is a magnetic He-strong β Cep star, with a dipole field, probably off-centred, with Bpol ∼ 400 G and He patches close to the magnetic poles.

Revisiting the Rigidly Rotating Magnetosphere model for Ori E - I. Observations and data analysis★

We have obtained 18 new high-resolution spectropolarimetric observations of the B2Vp star sigma Ori E with both the Narval and ESPaDOnS spectropolarimeters. The aim of these observations is to test, with modern data, the assumptions of the Rigidly Rotating Magnetosphere (RRM) model of Townsend & Owocki (2005), applied to the specific case of sigma Ori E by Townsend et al. (2005). This model includes a substantially offset dipole magnetic field configuration, and approximately reproduces previous observational variations in longitudinal field strength, photometric brightness, and Halpha emission. We analyze new spectroscopy, including H I, He I, C II, Si III and Fe III lines, confirming the diversity of variability in photospheric lines, as well as the double S-wave variation of circumstellar hydrogen. Using the multiline analysis method of Least-Squares Deconvolution (LSD), new, more precise longitudinal magnetic field measurements reveal a substantial variance between the shapes of the observed and RRM model time-varying field. The phase resolved Stokes V profiles of He I 5876 A and 6678 A lines are fit poorly by synthetic profiles computed from the magnetic topology assumed by Townsend et al. (2005). These results challenge the offset dipole field configuration assumed in the application of the RRM model to sigma Ori E, and indicate that future models of its magnetic field should also include complex, higher-order components.

A dominant magnetic dipole for the evolved Ap star candidate EK Eridani

EK Eri is one of the most slowly rotating active giants known, and has been proposed to be the descendant of a strongly magnetic Ap star. We have performed a spectropolarimetric study of EK Eri over 4 photometric periods with the aim of inferring the topology of its magnetic field. We used the NARVAL spectropolarimeter at the Bernard Lyot telescope at the Pic du Midi Observatory, along with the least-squares deconvolution method, to extract high signal-to-noise ratio Stokes V profiles from a timeseries of 28 polarisation spectra. We have derived the surface-averaged longitudinal magnetic field Bl. We fit the Stokes V profiles with a model of the large-scale magnetic field and obtained Zeeman Doppler images of the surface magnetic strength and geometry. Bl variations of up to about 80 G are observed without any reversal of its sign, and which are in phase with photometric ephemeris. The activity indicators are shown to vary smoothly on a timescale compatible with the rotational period inferred from photometry (308.8 d.), however large deviations can occur from one rotation to another. The surface magnetic field variations of EK Eri appear to be dominated by a strong magnetic spot (of negative polarity) which is phased with the dark (cool) photometric spot. Our modeling shows that the large-scale magnetic field of EK Eri is strongly poloidal. For a rotational axis inclination of i = 60{\deg}, we obtain a model that is almost purely dipolar. In the dipolar model, the strong magnetic/photometric spot corresponds to the negative pole of the dipole, which could be the remnant of that of an Ap star progenitor of EK Eri. Our observations and modeling conceptually support this hypothesis, suggesting an explanation of the outstanding magnetic properties of EK Eri as the result of interaction between deep convection and the remnant of an Ap star magnetic dipole.

No magnetic field in the spotted HgMn starμ Leporis

Chemically peculiar stars of the mercury-manganese (HgMn) type represent a new class of spotted late-B stars, in which evolving surface chemical inhomogeneities are apparently unrelated to the presence of strong magnetic fields but are produced by some hitherto unknown astrophysical mechanism. The goal of this study is to perform a detailed line profile variability analysis and carry out a sensitive magnetic field search for one of the brightest HgMn stars - mu Lep. We acquired a set of very high-quality intensity and polarization spectra of mu Lep with the HARPSpol polarimeter. These data were analyzed with the multiline technique of least-squares deconvolution in order to extract information on the magnetic field and line profile variability. Our spectra show very weak but definite variability in the lines of Sc, all Fe-peak elements represented in the spectrum of mu Lep, as well as Y, Sr, and Hg. Variability might also be present in the lines of Si and Mg. Anomalous profile shapes of Ti II and Y II lines suggest a dominant axisymmetric distribution of these elements. At the same time, we found no evidence of the magnetic field in mu Lep, with the 3 sigma upper limit of only 3 G for the mean longitudinal magnetic field. This is the most stringent upper limit on the possible magnetic field derived for a spotted HgMn star. The very weak variability detected for many elements in the spectrum mu Lep suggests that low-contrast chemical inhomogeneities may be common in HgMn stars and that they have not been recognized until now due to the limited precision of previous spectroscopic observations and a lack of time-series data. The null result of the magnetic field search reinforces the conclusion that formation of chemical spots in HgMn stars is not magnetically driven.

Chemical spots in the absence of magnetic field in the binary HgMn star 66 Eridani

According to our current understanding, a subclass of the upper main sequence chemically peculiar stars, called mercury-manganese (HgMn), is non-magnetic. Nevertheless, chemical inhomogeneities were recently discovered on their surfaces. At the same time, no global magnetic fields stronger than 1-100 G are detected by modern studies. The goals of our study are to search for magnetic field in the HgMn binary system 66 Eri and to investigate chemical spots on the stellar surfaces of both components. Our analysis is based on high quality spectropolarimetric time-series observations obtained during 10 consecutive nights with the HARPSpol instrument at the ESO 3.6-m telescope. To increase the sensitivity of the magnetic field search we employed a least-squares deconvolution (LSD). We used spectral disentangling to measure radial velocities and study line profile variability. Chemical spot geometry was reconstructed using multi-line Doppler imaging. We report a non-detection of magnetic field in 66 Eri, with error bars 10-24 G for the longitudinal field. Circular polarization profiles also do not indicate any signatures of complex surface magnetic fields. For a simple dipolar field configuration we estimated an upper limit of the polar field strength to be 60-70 G. For the HgMn component we found variability in spectral lines of Ti, Ba, Y, and Sr with the rotational period equal to the orbital one. The surface maps of these elements reconstructed with the Doppler imaging technique, show relative underabundance on the hemisphere facing the secondary component. The contrast of chemical inhomogeneities ranges from 0.4 for Ti to 0.8 for Ba.

Magnetic fields and differential rotation on the pre-main sequence - I. The early-G star HD 141943 - brightness and magnetic topologies

Spectroscopic and spectropolarimetric observations of the pre-main sequence early-G star HD 141943 were obtained at four observing epochs (in 2006, 2007, 2009 and 2010). The observations were undertaken at the 3.9-m Anglo-Australian Telescope using the UCLES echelle spectrograph and the SEMPOL spectropolarimeter visitor instrument. Brightness and surface magnetic field topologies were reconstructed for the star using the technique of least-squares deconvolution to increase the signal-to-noise of the data. The reconstructed brightness maps show that HD 141943 had a weak polar spot and a significant amount of low latitude features, with little change in the latitude distribution of the spots over the 4 years of observations. The surface magnetic field was reconstructed at three of the epochs from a high order (l <= 30) spherical harmonic expansion of the spectropolarimetric observations. The reconstructed magnetic topologies show that in 2007 and 2010 the surface magnetic field was reasonably balanced between poloidal and toroidal components. However we find tentative evidence of a change in the poloidal/toroidal ratio in 2009 with the poloidal component becoming more dominant. At all epochs the radial magnetic field is predominantly non-axisymmetric while the azimuthal field is predominantly axisymmetric with a ring of positive azimuthal field around the pole similar to that seen on other active stars.

Least-squares deconvolution of the stellar intensity and polarization spectra

Least squares deconvolution (LSD) is a powerful method of extracting high-precision average line profiles from the stellar intensity and polarization spectra. Despite its common usage, the LSD method is poorly documented and has never been tested using realistic synthetic spectra. In this study we revisit the key assumptions of the LSD technique, clarify its numerical implementation, discuss possible improvements and give recommendations how to make LSD results understandable and reproducible. We also address the problem of interpretation of the moments and shapes of the LSD profiles in terms of physical parameters. We have developed an improved, multiprofile version of LSD and have extended the deconvolution procedure to linear polarization analysis taking into account anomalous Zeeman splitting of spectral lines. This code is applied to the theoretical Stokes parameter spectra. We test various methods of interpreting the mean profiles, investigating how coarse approximations of the multiline technique translate into errors of the derived parameters. We find that, generally, the Stokes parameter LSD profiles do not behave as a real spectral line with respect to the variation of magnetic field and elemental abundance. This problem is especially prominent for the Stokes I variation with abundance and Stokes Q variation with magnetic field. At the same time, the Stokes V LSD spectra closely resemble profile of a properly chosen synthetic line for the magnetic field strength up to 1 kG. We conclude that the usual method of interpreting the LSD profiles by assuming that they are equivalent to a real spectral line gives satisfactory results only in a limited parameter range and thus should be applied with caution. A more trustworthy approach is to abandon the single-line approximation of the average profiles and apply LSD consistently to observations and synthetic spectra.