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Kochukhov, Oleg
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Publications (10 of 191) Show all publications
Rusomarov, N., Kochukhov, O. & Lundin, A. (2018). Magnetic field topology and chemical spot distributions of the Ap star HD 119419. Astronomy and Astrophysics, 609, Article ID A88.
Open this publication in new window or tab >>Magnetic field topology and chemical spot distributions of the Ap star HD 119419
2018 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 609, article id A88Article in journal (Refereed) Published
Abstract [en]

Context. Analysis of high-resolution spectropolarimetric time-series observations of early-type magnetic stars is currently the most advanced method of obtaining detailed information on their surface magnetic field topologies and horizontal spot distributions.

Aims. In this study we analyse a new set of high-quality full Stokes vector observations of the magnetic Ap star HD 119419 – a member of the 14 Myr old Lower Cen-Cru association – for the purpose of studying the surface field topology and mapping the chemical abundance spots.

Methods. We made use of the circular and linear polarisation data collected for HD 119419 with the HARPSpol instrument at the ESO 3.6-m telescope. These observations were analysed with a multi-line magnetic diagnostic technique and modelled in detail with a Magnetic Doppler imaging (MDI) code.

Results. We present a new set of high-precision mean longitudinal magnetic field measurements and derive a revised stellar rotational period by comparing our measurements with the literature data. We also redetermine the basic stellar atmospheric parameters. Our four Stokes parameter magnetic inversions reveal a moderately complex surface field topology with a mean field strength of 18 kG and a maximum local strength of 24 kG. A poloidal dipolar component dominates the magnetic energy spectrum of the surface field in HD 119419. However, significant contributions of the higher-order spherical harmonic components are also present. We show that the dipole plus quadrupole part of the reconstructed field geometry is incapable of reproducing the observed amplitudes and shapes of the Stokes Q and U profiles. The chemical abundance distributions of Fe, Cr, Ti, and Nd, derived self-consistently with the magnetic field geometry, are characterised by large abundance gradients and a lack of clear correlation with the magnetic field structure.

Conclusions. This full Stokes vector analysis of HD 119419 extends the modern hot-star magnetic mapping investigations to an open cluster Ap star with a well-determined age. Further, MDI studies of cluster members will allow us to study the field topologies and chemical abundance spots as a function of stellar age.

Keywords
stars: chemically peculiar, stars: atmospheres, stars: individual: HD 119419, stars: magnetic field
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-343856 (URN)10.1051/0004-6361/201731914 (DOI)000423434200006 ()
Funder
Knut and Alice Wallenberg FoundationSwedish Research CouncilSwedish National Space Board
Available from: 2018-03-02 Created: 2018-03-02 Last updated: 2018-03-02Bibliographically approved
Farihi, J., Fossati, L., Wheatley, P. J., Metzger, B. D., Mauerhan, J., Bachman, S., . . . Stone, N. (2018). Magnetism, X-rays and accretion rates in WD 1145+017 and other polluted white dwarf systems. Monthly notices of the Royal Astronomical Society, 474(1), 947-960
Open this publication in new window or tab >>Magnetism, X-rays and accretion rates in WD 1145+017 and other polluted white dwarf systems
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2018 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 474, no 1, p. 947-960Article in journal (Refereed) Published
Abstract [en]

This paper reports circular spectropolarimetry and X-ray observations of several polluted white dwarfs including WD 1145+017, with the aim to constrain the behaviour of disc material and instantaneous accretion rates in these evolved planetary systems. Two stars with previously observed Zeeman splitting, WD 0322-019 and WD 2105-820, are detected above 5 sigma and < B-z > > 1 kG, while WD 1145+017, WD 1929+011, and WD 2326+049 yield (null) detections below this minimum level of confidence. For these latter three stars, high-resolution spectra and atmospheric modelling are used to obtain limits on magnetic field strengths via the absence of Zeeman splitting, finding B-* < 20 kG based on data with resolving power R approximate to 40 000. An analytical framework is presented for bulk Earth composition material falling on to the magnetic polar regions of white dwarfs, where X-rays and cyclotron radiation may contribute to accretion luminosity. This analysis is applied to X-ray data for WD 1145+017, WD 1729+371, and WD 2326+049, and the upper bound count rates are modelled with spectra for a range of plasma kT = 1-10 keV in both the magnetic and non-magnetic accretion regimes. The results for all three stars are consistent with a typical dusty white dwarf in a steady state at 108-109 g s(-1). In particular, the non-magnetic limits for WD 1145+017 are found to be well below previous estimates of up to 10(12) g s(-1), and likely below 1010 g s(-1), thus suggesting the star-disc system may be average in its evolutionary state, and only special in viewing geometry.

Place, publisher, year, edition, pages
OXFORD UNIV PRESS, 2018
Keywords
circumstellar matter, stars: magnetic field, planetary systems, white dwarfs, X-rays: stars
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-348400 (URN)10.1093/mnras/stx2664 (DOI)000424339500070 ()
Available from: 2018-04-12 Created: 2018-04-12 Last updated: 2018-04-12Bibliographically approved
Oksala, M. E., Silvester, J., Kochukhov, O., Neiner, C. & Wade, G. A. (2018). Mixed poloidal-toroidal magnetic configuration and surface abundance distributions of the Bp star 36 Lyn. Monthly notices of the Royal Astronomical Society, 473(3), 3367-3376
Open this publication in new window or tab >>Mixed poloidal-toroidal magnetic configuration and surface abundance distributions of the Bp star 36 Lyn
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2018 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 473, no 3, p. 3367-3376Article in journal (Refereed) Published
Abstract [en]

Previous studies of the chemically peculiar Bp star 36 Lyn revealed a moderately strong magnetic field, circumstellar material and inhomogeneous surface abundance distributions of certain elements. We present in this paper an analysis of 33 high signal-to-noise ratio, high-resolution Stokes IV observations of 36 Lyn obtained with the Narval spectropolarimeter at the Bernard Lyot Telescope at Pic du Midi Observatory. From these data, we compute new measurements of the mean longitudinal magnetic field, B, using the multiline least-squares deconvolution (LSD) technique. A rotationally phased B curve reveals a strong magnetic field, with indications for deviation from a pure dipole field. We derive magnetic maps and chemical abundance distributions from the LSD profiles, produced using the Zeeman–Doppler imaging code InversLSD. Using a spherical harmonic expansion to characterize the magnetic field, we find that the harmonic energy is concentrated predominantly in the dipole mode (ℓ = 1), with significant contribution from both the poloidal and toroidal components. This toroidal field component is predicted theoretically, but not typically observed for Ap/Bp stars. Chemical abundance maps reveal a helium enhancement in a distinct region where the radial magnetic field is strong. Silicon enhancements are located in two regions, also where the radial field is stronger. Titanium and iron enhancements are slightly offset from the helium enhancements, and are located in areas where the radial field is weak, close to the magnetic equator.

Keywords
techniques: polarimetric, techniques: spectroscopic, stars: chemically peculiar, stars: individual: 36 Lyn
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-346360 (URN)10.1093/mnras/stx2487 (DOI)000423809400040 ()
Funder
Knut and Alice Wallenberg FoundationSwedish Research CouncilGöran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of Technology
Available from: 2018-03-23 Created: 2018-03-23 Last updated: 2018-03-23Bibliographically approved
Kochukhov, O. & Ryabchikova, T. A. (2018). Putting atomic diffusion theory of magnetic ApBp stars to the test: evaluation of the predictions of time-dependent diffusion models. Monthly notices of the Royal Astronomical Society, 474(2), 2787-2795
Open this publication in new window or tab >>Putting atomic diffusion theory of magnetic ApBp stars to the test: evaluation of the predictions of time-dependent diffusion models
2018 (English)In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 474, no 2, p. 2787-2795Article in journal (Refereed) Published
Abstract [en]

A series of recent theoretical atomic diffusion studies has address the challenging problem of predicting inhomogeneous vertical and horizontal chemical element distributions in the atmospheres of magnetic ApBp stars. Here we critically assess the most sophisticated of such diffusion models - based on a time-dependent treatment of the atomic diffusion in a magnetized stellar atmosphere - by direct comparison with observations as well by testing the widely used surface mapping tools with the spectral line profiles predicted by this theory. We show that the mean abundances of Fe and Cr are grossly underestimated by the time-dependent theoretical diffusion model, with discrepancies reaching a factor of 1000 for Cr. We also demonstrate that Doppler imaging inversion codes, based either on modelling of individual metal lines or line-averaged profiles simulated according to theoretical three-dimensional abundance distribution, are able to reconstruct correct horizontal chemical spot maps despite ignoring the vertical abundance variation. These numerical experiments justify a direct comparison of the empirical two-dimensional Doppler maps with theoretical diffusion calculations. This comparison is generally unfavourable for the current diffusion theory, as very few chemical elements are observed to form overabundance rings in the horizontal field regions as predicted by the theory and there are numerous examples of element accumulations in the vicinity of radial field zones, which cannot be explained by diffusion calculations.

Place, publisher, year, edition, pages
OXFORD UNIV PRESS, 2018
Keywords
diffusion, line: profiles, stars: abundances, stars: chemically peculiar
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-348401 (URN)10.1093/mnras/stx2961 (DOI)000424343600096 ()
Funder
Knut and Alice Wallenberg FoundationSwedish Research CouncilSwedish National Space Board
Available from: 2018-04-12 Created: 2018-04-12 Last updated: 2018-04-12Bibliographically approved
Landstreet, J. D., Kochukhov, O., Alecian, E., Bailey, J. D., Mathis, S., Neiner, C. & Wade, G. A. (2017). BD-19 5044L: discovery of a short-period SB2 system with a magnetic Bp primary in the open cluster IC 4725. Astronomy and Astrophysics, 601, Article ID A129.
Open this publication in new window or tab >>BD-19 5044L: discovery of a short-period SB2 system with a magnetic Bp primary in the open cluster IC 4725
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2017 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 601, article id A129Article in journal (Refereed) Published
Abstract [en]

Context. 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. Aims. In this paper we characterise 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. Methods. 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. From these data we determine the orbital and stellar properties of each component. Results. 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 similar to 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. Because this system is a member of IC 4725, the two stars have a common age of log t = 8.02 +/- 0.05 dex. Conclusions. 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.

Place, publisher, year, edition, pages
EDP Sciences, 2017
Keywords
binaries: spectroscopic, stars: chemically peculiar, stars: evolution, stars: magnetic field, stars: individual: BD-19 5044L
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-327046 (URN)10.1051/0004-6361/201630233 (DOI)000402313500129 ()
Available from: 2017-08-03 Created: 2017-08-03 Last updated: 2017-08-03Bibliographically approved
van Leeuwen, F., Korn, A., Edvardsson, B., Heiter, U., Kochukhov, O., Nordlander, T. & Zschocke, S. (2017). Gaia Data Release 1: Open cluster astrometry: performance, limitations, and future prospects. Astronomy and Astrophysics, 601, Article ID A19.
Open this publication in new window or tab >>Gaia Data Release 1: Open cluster astrometry: performance, limitations, and future prospects
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2017 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 601, article id A19Article in journal (Refereed) Published
Abstract [en]

Context. The first Gaia Data Release contains the Tycho-Gaia Astrometric Solution (TGAS). This is a subset of about 2 million stars for which, besides the position and photometry, the proper motion and parallax are calculated using Hipparcos and Tycho-2 positions in 1991.25 as prior information. Aims. We investigate the scientific potential and limitations of the TGAS component by means of the astrometric data for open clusters. Methods. Mean cluster parallax and proper motion values are derived taking into account the error correlations within the astrometric solutions for individual stars, an estimate of the internal velocity dispersion in the cluster, and, where relevant, the effects of the depth of the cluster along the line of sight. Internal consistency of the TGAS data is assessed. Results. Values given for standard uncertainties are still inaccurate and may lead to unrealistic unit-weight standard deviations of least squares solutions for cluster parameters. Reconstructed mean cluster parallax and proper motion values are generally in very good agreement with earlier Hipparcos-based determination, although the Gaia mean parallax for the Pleiades is a significant exception. We have no current explanation for that discrepancy. Most clusters are observed to extend to nearly 15 pc from the cluster centre, and it will be up to future Gaia releases to establish whether those potential cluster-member stars are still dynamically bound to the clusters. Conclusions. The Gaia DR1 provides the means to examine open clusters far beyond their more easily visible cores, and can provide membership assessments based on proper motions and parallaxes. A combined HR diagram shows the same features as observed before using the Hipparcos data, with clearly increased luminosities for older A and F dwarfs.

Place, publisher, year, edition, pages
EDP Sciences, 2017
Keywords
astrometry, open clusters and associations: general
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-327214 (URN)10.1051/0004-6361/201730552 (DOI)000402313500019 ()
Available from: 2017-08-07 Created: 2017-08-07 Last updated: 2017-08-07Bibliographically approved
Kochukhov, O., Silvester, J., Bailey, J. D., Landstreet, J. D. & Wade, G. A. (2017). Magnetic field topology and chemical abundance distributions of the young, rapidly rotating, chemically peculiar star HR5624. Astronomy and Astrophysics, 605, Article ID A13.
Open this publication in new window or tab >>Magnetic field topology and chemical abundance distributions of the young, rapidly rotating, chemically peculiar star HR5624
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2017 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 605, article id A13Article in journal (Refereed) Published
Abstract [en]

Context. The young, rapidly rotating Bp star HR5624 (HD 133880) 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.

Aims. 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. Methods. 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.

Results. We refined the stellar parameters, revised the rotational period, and obtained new longitudinal magnetic field measurements. 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, which is about a factor of three weaker than predicted by quadrupolar field models. Our model implies that overall large-scale field topology of HR5624 is better described as a distorted, asymmetric dipole rather than an axisymmetric quadrupole. 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, in particular, show no distinct element concentrations in the horizontal field regions predicted by theoretical atomic diffusion calculations.

Conclusions. 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. This finding agrees with an outcome of the MHD simulations of fossil field evolution in stably stratified stellar interiors.

Place, publisher, year, edition, pages
EDP SCIENCES S A, 2017
Keywords
stars: atmospheres, stars: chemically peculiar, stars: magnetic field, starspots, stars: individual: HR 5624
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-337757 (URN)10.1051/0004-6361/201730919 (DOI)000412231200073 ()
Funder
Knut and Alice Wallenberg FoundationSwedish Research CouncilSwedish National Space Board
Available from: 2018-01-12 Created: 2018-01-12 Last updated: 2018-01-12Bibliographically approved
Lavail, A., Kochukhov, O., Hussain, G. A., Alecian, E., Herczeg, G. J. & Johns-Krull, C. (2017). Magnetic fields of intermediate mass T Tauri stars. Astronomy and Astrophysics, 608, Article ID A77.
Open this publication in new window or tab >>Magnetic fields of intermediate mass T Tauri stars
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2017 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 608, article id A77Article in journal (Refereed) Published
Abstract [en]

Aims: In this paper, we aim to measure the strength of the surface magnetic fields for a sample of five intermediate mass T Tauri stars and one low mass T Tauri star from late-F to mid-K spectral types. While magnetic fields of T Tauri stars at the low mass range have been extensively characterized, our work complements previous studies towards the intermediate mass range; this complementary study is key to evaluate how magnetic fields evolve during the transition from a convective to a radiative core.

Methods: We studied the Zeeman broadening of magnetically sensitive spectral lines in the H-band spectra obtained with the CRIRES high-resolution near-infrared spectrometer. These data are modelled using magnetic spectral synthesis and model atmospheres. Additional constraints on non-magnetic line broadening mechanisms are obtained from modelling molecular lines in the K band or atomic lines in the optical wavelength region.

Results: We detect and measure mean surface magnetic fields for five of the six stars in our sample: CHXR 28, COUP 107, V2062 Oph, V1149 Sco, and Par 2441. Magnetic field strengths inferred from the most magnetically sensitive diagnostic line range from 0.8 to 1.8 kG. We also estimate a magnetic field strength of 1.9 kG for COUP 107 from an alternative diagnostic. The magnetic field on YLW 19 is the weakest in our sample and is marginally detected, with a strength of 0.8 kG.

Conclusions: We populate an uncharted area of the pre-main-sequence HR diagram with mean magnetic field measurements from high-resolution near-infrared spectra. Our sample of intermediate mass T Tauri stars in general exhibits weaker magnetic fields than their lower mass counterparts. Our measurements will be used in combination with other spectropolarimetric studies of intermediate mass and lower mass T Tauri stars to provide input into pre-main-sequence stellar evolutionary models.

Keywords
stars: pre-main sequence, stars: magnetic field, line: profiles
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-345062 (URN)10.1051/0004-6361/201731889 (DOI)000417620400004 ()
Funder
Knut and Alice Wallenberg FoundationSwedish Research CouncilSwedish National Space Board
Available from: 2018-03-08 Created: 2018-03-08 Last updated: 2018-03-08Bibliographically approved
Shulyak, D., Reiners, A., Engein, A., Malo, L., Yadav, R., Morin, J. & Kochukhov, O. (2017). Strong dipole magnetic fields in fast rotating fully convective stars. NATURE ASTRONOMY, 1(8)
Open this publication in new window or tab >>Strong dipole magnetic fields in fast rotating fully convective stars
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2017 (English)In: NATURE ASTRONOMY, ISSN 2397-3366, Vol. 1, no 8Article in journal (Refereed) Published
Abstract [en]

M dwarfs are the most numerous stars in our Galaxy, with masses between approximately 0.5 and 0.1 solar masses. Many of them show surface activity qualitatively similar to our Sun and generate flares, high X-ray fluxes and largescale magnetic fields(1-4). Such activity is driven by a dynamo powered by the convective motions in their interiors(2),(5-8). Understanding properties of stellar magnetic fields in these stars finds a broad application in astrophysics, including theory of stellar dynamos and environment conditions around planets that may be orbiting these stars. Most stars with convective envelopes follow a rotation-activity relationship where various activity indicators saturate in stars with rotation periods shorter than a few days(2,6,8). The activity gradually declines with rotation rate in stars rotating more slowly. It is thought that, due to a tight empirical correlation between X-ray radiance and magnetic flux(9), the stellar magnetic fields will also saturate, to values around 4kG (ref. (10)). Here we report the detection of magnetic fields above the presumed saturation limit in four fully convective M dwarfs. By combining results from spectroscopic and polarimetric studies, we explain our findings in terms of bistable dynamo models(11,12):stars with the strongest magnetic fields are those in a dipole dynamo state, whereas stars in a multipole state cannot generate fields stronger than about 4kG. Our study provides observational evidence that the dynamo in fully convective M dwarfs generates magnetic fields that can differ not only in the geometry of their large-scale component, but also in the total magnetic energy.

National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-342612 (URN)10.1038/s41550-017-0184 (DOI)000415185700008 ()
Funder
Swedish Research CouncilSwedish National Space Board
Available from: 2018-02-23 Created: 2018-02-23 Last updated: 2018-02-23Bibliographically approved
Kochukhov, O., Petit, P., Strassmeier, K. G., Carroll, T. A., Fares, R., Folsom, C. P., . . . Shulyak, D. (2017). Surface magnetism of cool stars. Astronomical Notes - Astronomische Nachrichten, 338(4), 428-441
Open this publication in new window or tab >>Surface magnetism of cool stars
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2017 (English)In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 338, no 4, p. 428-441Article in journal (Refereed) Published
Abstract [en]

Magnetic fields are essential ingredients of many physical processes in the interiors and envelopes of cool stars. Yet their direct detection and characterization 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 field topology mapping with polarization 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 summarize 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.

Place, publisher, year, edition, pages
WILEY-V C H VERLAG GMBH, 2017
Keywords
stars: activity, stars: late-type, stars: low-mass, stars: magnetic field, starspots
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-324614 (URN)10.1002/asna.201713310 (DOI)000400944700007 ()
Funder
Swedish Research CouncilSwedish National Space Board
Available from: 2017-06-16 Created: 2017-06-16 Last updated: 2017-06-16Bibliographically approved
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