arXiv subjects

Oleg Kochukhov

Publications and source records attributed to Oleg Kochukhov.

At least 37 records · Page 2Linked to original sources

arXiv2025

Performance of the Stellar Abundances and atmospheric Parameters Pipeline adapted for M dwarfs I. Atmospheric parameters from the spectroscopic module

M dwarfs are important targets in the search for Earth-like exoplanets due to their small masses and low luminosities. Several ongoing and upcoming space missions are targeting M dwarfs for this reason, and the ESA PLATO mission is one of these. In order to fully characterise a planetary system the properties of the host star must be known. For M dwarfs we can derive effective temperature, surface gravity, metallicity, and abundances of various elements from spectroscopic observations in combination with photometric data. The Stellar Abundances and atmospheric Parameters Pipeline (SAPP) has been developed as a prototype for one of the stellar science softwares within the PLATO consortium, it is aimed at FGK stars. We have modified it to be able to analyse the M dwarf among the PLATO targets. The current version of the pipeline for M dwarfs mostly relies on spectroscopic observations. The data processing is based on the machine learning algorithm The Payne and fits a grid of model spectra to an observed spectrum to derive effective temperature and metallicity. We use spectra in the H-band, as the near-infrared region is beneficial for M dwarfs. A method based on synthetic spectra was developed for the continuum normalisation of the spectra, taking into account the pseudo-continuum formed by numerous lines of the water molecule. Photometry is used to constrain the surface gravity. We tested the modified SAPP on spectra of M dwarfs from the APOGEE survey. Our validation sample of 26 stars includes stars with interferometric observations and binaries. We found a good agreement between our values and reference values from a range of studies. The overall uncertainties in the derived effective temperature, surface gravity, and metallicity is 100 K, 0.1 dex, and 0.15 dex, respectively. We find that the modified SAPP performs well on M dwarfs and identify possible areas of future development.

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arXiv2025

Multi-Observatory Study of Young Stellar Energetic Flares (MORYSEF): No Evidence For Abnormally Strong Stellar Magnetic Fields After Powerful X-ray Flares

We explore the empirical power-law relationship between X-ray luminosity (Lx) and total surface magnetic flux (Phi), established across solar magnetic elements, time- and disk-averaged emission from the Sun, older active stars, and pre-main-sequence (PMS) stars. Previous models of large PMS X-ray flares, lacking direct magnetic field measurements, showed discrepancies from this baseline law, which MHD simulations attribute to unusually strong magnetic fields during flares. To test this, we used nearly simultaneous Chandra X-ray and HET-HPF near-infrared observations of four young Orion stars, measuring surface magnetic fields during or just after powerful PMS X-ray flares. We also modeled these PMS X-ray flares, incorporating their measured magnetic field strengths. Our findings reveal magnetic field strengths at the stellar surface typical of non-flaring PMS stars, ruling out the need for abnormally strong fields during flares. Both PMS and solar flares deviate from the Lx-Phi law, with PMS flares exhibiting a more pronounced deviation, primarily due to their much larger active regions on the surface and larger flaring loop volumes above the surface compared to their solar counterparts. These deviations likely stem from the fact that powerful flares are driven by magnetic reconnection, while baseline X-ray emission may involve less efficient mechanisms like Alfven wave heating. Our results also indicate a preference for dipolar magnetic loops in PMS flares, consistent with Zeeman-Doppler imaging of fully convective stars. This requirement for giant dipolar loops aligns with MHD predictions of strong dipoles supported by polar magnetic surface active regions in fast-rotating, fully convective stars.

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arXiv2024

Multi-Observatory Research of Young Stellar Energetic Flares (MORYSEF): X-ray Flare Related Phenomena and Multi-epoch Behavior

The most powerful stellar flares driven by magnetic energy occur during the early pre-main sequence (PMS) phase. The Orion Nebula represents the nearest region populated by young stars, showing the greatest number of flares accessible to a single pointing of Chandra. This study is part of a multi-observatory project to explore stellar surface magnetic fields (with HET-HPF), particle ejections (VLBA), and disk ionization (ALMA) immediately following the detection of PMS super-flares with Chandra. In December 2023, we successfully conducted such a multi-telescope campaign. Additionally, by analyzing Chandra data from 2003, 2012, and 2016, we examine the multi-epoch behavior of PMS X-ray emission related to PMS magnetic cyclic activity and ubiquitous versus sample-confined mega-flaring. Our findings follow. 1) We report detailed stellar quiescent and flare X-ray properties for numerous HET/ALMA/VLBA targets, facilitating ongoing multi-wavelength analyses. 2) For numerous moderately energetic flares, we report correlations (or lack thereof) between flare energies and stellar mass/size (presence/absence of disks) for the first time. The former is attributed to the correlation between convection-driven dynamo and stellar volume, while the latter suggests the operation of solar-type flare mechanisms in PMS stars. 3) We find that most PMS stars exhibit minor long-term baseline variations, indicating the absence of intrinsic magnetic dynamo cycles or observational mitigation of cycles by saturated PMS X-rays. 4) We conclude that X-ray mega-flares are ubiquitous phenomena in PMS stars, which suggests that all protoplanetary disks and nascent planets are subject to violent high-energy emission and particle irradiation events.

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arXiv2024

Magnetic Fields in a sample of planet-hosting M dwarf stars from Kepler, K2, and TESS observed by APOGEE

Stellar magnetic fields have a major impact on space weather around exoplanets orbiting low-mass stars. From an analysis of Zeeman-broadened Fe I lines measured in near-infrared SDSS/APOGEE spectra, mean magnetic fields are determined for a sample of 29 M dwarf stars that host closely orbiting small exoplanets. The calculations employed the radiative transfer code Synmast and MARCS stellar model atmospheres. The sample M dwarfs are found to have measurable mean magnetic fields ranging between $\sim$0.2 to $\sim$1.5 kG, falling in the unsaturated regime on the $<$B$>$ vs P$_{\rm rot}$ plane. The sample systems contain 43 exoplanets, which include 23 from Kepler, nine from K2, and nine from TESS. We evaluated their equilibrium temperatures, insolation, and stellar habitable zones and found that only Kepler-186f and TOI-700d are inside the habitable zones of their stars. Using the derived values of $<$B$>$ for the stars Kepler-186 and TOI-700 we evaluated the minimum planetary magnetic field that would be necessary to shield the exoplanets Kepler-186f and TOI-700d from their host star's winds, considering reference magnetospheres with sizes equal to those of the present-day and young Earth, respectively. Assuming a ratio of 5$\%$ between large-to-small scale B-fields, and a young-Earth magnetosphere, Kepler-186f and TOI-700d would need minimum planetary magnetic fields of, respectively, 0.05 and 0.24 G. These values are considerably smaller than Earth's magnetic field of 0.25 G$\lesssim$B$\lesssim$0.65 G, which suggests that these two exoplanets might have magnetic fields sufficiently strong to protect their atmospheres and surfaces from stellar magnetic fields.

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arXiv2024

Imprint of the magnetic activity cycle on solar asteroseismic characterisation based on 26 years of GOLF and BiSON data

Building on the success of previous missions, asteroseismic modelling will play a key role in future space-based missions, such as PLATO, CubeSpec, and Roman. Despite remarkable achievements, asteroseismology has revealed significant discrepancies in the physics of theoretical stellar models, which have the potential to bias stellar characterisation at the precision level demanded by PLATO. The current modelling strategies largely overlook magnetic activity, assuming that its effects are masked by filtering the so-called surface effects. Given the presence of activity cycles in multiple solar-like oscillators, and activity variations in a significant fraction of Kepler observations of main-sequence stars (Santos et al. 2019b, 2021, 2023), we measured the impact of magnetic activity on the asteroseismic characterisation of the Sun based on 26.5 years of GOLF and BiSON observations. While magnetic activity is partially absorbed in the treatment of surface effects, we found a discernible imprint of the activity cycle in the determination of the solar age. Notably, this imprint persists across both BiSON and GOLF datasets, with significant variations of up to 6.5% observed between solar minima and maxima. Considering that the Sun exhibits low levels of activity, our study underscores the looming challenge posed by magnetic activity for future photometry missions, and prompts a potential reevaluation of the asteroseismic characterisation of Kepler's most active targets.

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arXiv2024

Magnetic Fields of M Dwarfs from the Pleiades Open Cluster

Average magnetic field measurements are presented for 62 M-dwarf members of the Pleiades open cluster, derived from Zeeman-enhanced Fe I lines in the H-band. An MCMC methodology was employed to model magnetic filling factors using SDSS-IV APOGEE high-resolution spectra, along with the radiative transfer code SYNMAST, MARCS stellar atmosphere models, and the APOGEE DR17 spectral line list. There is a positive correlation between mean magnetic fields and stellar rotation, with slow-rotator stars (Rossby number, Ro$>$0.13) exhibiting a steeper slope than rapid-rotators (Ro$<$0.13). However, the latter sample still shows a positive trend between Ro and magnetic fields, which is given by $<$B$>$ = 1604 $\times$ Ro$^{-0.20}$. The derived stellar radii, when compared with physical isochrones, show that on average, our sample shows radius inflation, with median enhanced radii ranging from +3.0$\%$ to +7.0$\%$, depending on the model. There is a positive correlation between magnetic field strength and radius inflation, as well as with stellar spot coverage, correlations that together indicate that stellar spot-filling factors generated by strong magnetic fields might be the mechanism that drives radius inflation in these stars. We also compare our derived magnetic fields with chromospheric emission lines (H$α$, H$β$ and Ca II K), as well as with X-ray and H$α$ to bolometric luminosity ratios, and find that stars with higher chromospheric and coronal activity tend to be more magnetic.

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arXiv2024

Using ZDI maps to determine magnetic forces and torques at the photospheres of Early-type stars

We use the magnetic field components measured by Zeeman Doppler imaging (ZDI) to calculate the stellar surface force and torque due to magnetic stresses for the fast rotators $σ$ Ori E, 36 Lyn and CU Vir, and the slow rotator $τ$ Sco. If we assume the stars have spherical photospheres, the estimated torques give spin down time scales no larger than $7 \times 10^5$ yr. For $σ$ Ori E, the predicted spin down time scale, $\simeq 6000$ yr, is much less than the observationally measured time scale of $\simeq 10^6$ yr. However, for CU Vir, we find that the spin down time scale from its ZDI map is $7 \times 10^5$ yr in good agreement with its average rate of spin down from 1960 to 2010. With the exception of $τ$ Sco, the net force due to magnetic stresses at the stellar surface are large compared to the surface-integrated pressure. We discuss possible reasons for the large values of the forces (and torques), and suggest that the likely explanation is that rotation and the magnetic stresses create significant departures from spherical symmetry.

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arXiv2024

Accretion and magnetism on young eccentric binaries: DQ Tau and AK Sco

The accretion and ejection of mass in pre-main sequence (PMS) stars are key processes in stellar evolution as they shape the stellar angular momentum transport necessary for the stars' stability. Magnetospheric accretion onto classical T Tauri stars and low-mass PMS stars has been widely studied in the single-star case. This process can not be directly transferred to PMS binary systems, as tidal and gravitation effects, and/or accretion from a circumbinary disc (with variable separation of the components in the case of eccentric orbits) are in place. This work examines the accretion process of two PMS eccentric binaries, DQ Tau and AK Sco, using high-resolution spectropolarimetric time series. We investigate how magnetospheric accretion can be applied to these systems by studying the accretion-related emission lines and the magnetic field of each system. We discover that both systems are showing signs of magnetospheric accretion, despite their slightly different configurations, and the weak magnetic field of AK Sco. Furthermore, the magnetic topology of DQ Tau A shows a change relative to the previous orbital cycle studied: previously dominated by the poloidal component, it is now dominated by the toroidal component. We also report an increase of the component's accretion and the absence of an accretion burst at the apastron, suggesting that the component's magnetic variation might be the cause of the inter-cycle variations of the system's accretion. We conclude on the presence of magnetospheric accretion for both systems, together with gravitational effects, especially for AK Sco, composed of more massive components.

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arXiv2024

From convective stellar dynamo simulations to Zeeman-Doppler images

Zeeman-Doppler imaging (ZDI) is used to reconstruct the surface magnetic field of late-type stars from high resolution spectropolarimetric observations. The results are usually described in terms of characteristics of the field topology, i.e. poloidality vs. toroidality and axi-symmetry vs. non-axisymmetry in addition to the field strength. We want to test how well these characteristics are preserved when applying the ZDI method on simulated data, i.e. how accurately the field topology is preserved and to what extent stellar parameters influence the reconstruction. We use published magnetic field data from direct numerical MHD simulations. These have variable rotation rates, and hence represent different levels of activity, of an otherwise Sun-like setup. Our ZDI reconstruction is based on spherical harmonics expansion. By comparing the original values to those of the reconstructed images, we study the ability to reconstruct the surface magnetic field in terms of various characteristics of the field. The main large-scale features are reasonably well recovered, but the strength of the recovered magnetic field is just a fraction of the original input. The quality of the reconstruction shows clear correlations with the data quality. Furthermore, there are some spurious dependencies between stellar parameters and the characteristics of the field. Our study uncovers some limits of ZDI. Firstly, the recovered field strength will generally be lower than the "real" value as smaller structures with opposite polarities will be blurred in the inversion. Secondly, the axisymmetry is overestimated. The poloidality vs. toroidality is better recovered. The reconstruction works better for a stronger field and faster rotation velocity. Still, the ZDI method works surprisingly well even for a weaker field and slow rotation, provided the data has a high signal-to-noise and good rotation phase coverage.

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arXiv2024

Weakened Magnetic Braking in the Exoplanet Host Star 51 Peg

The consistently low activity level of the old solar analog 51 Peg not only facilitated the discovery of the first hot Jupiter, but also led to the suggestion that the star could be experiencing a magnetic grand minimum. However, the 50 year time series showing minimal chromospheric variability could also be associated with the onset of weakened magnetic braking (WMB), where sufficiently slow rotation disrupts cycling activity and the production of large-scale magnetic fields by the stellar dynamo, thereby shrinking the Alfven radius and inhibiting the efficient loss of angular momentum to magnetized stellar winds. In this Letter, we evaluate the magnetic evolutionary state of 51 Peg by estimating its wind braking torque. We use new spectropolarimetric measurements from the Large Binocular Telescope to reconstruct the large-scale magnetic morphology, we reanalyze archival X-ray measurements to estimate the mass-loss rate, and we detect solar-like oscillations in photometry from the Transiting Exoplanet Survey Satellite, yielding precise stellar properties from asteroseismology. Our estimate of the wind braking torque for 51 Peg clearly places it in the WMB regime, driven by changes in the mass-loss rate and the magnetic field strength and morphology that substantially exceed theoretical expectations. Although our revised stellar properties have minimal consequences for the characterization of the exoplanet, they have interesting implications for the current space weather environment of the system.

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arXiv2023

Optimising spectroscopic observations of transiting exoplanets

When observing the atmospheres of transiting exoplanets using high-resolution spectroscopy, one aims to detect well-resolved spectral features with high signal-to-noise ratios (SNR) as is possible today with modern spectrographs. However, obtaining such high-quality observations comes with a trade-off: a lower cadence of fewer, longer exposures across the transit collects more photons thanks to reduced overheads, enhancing the SNR of each observation, while a higher cadence of several, shorter exposures minimises spectral feature smearing due to the continuously changing radial velocity of the planet. Considering that maximising SNR and minimising smearing are both beneficial to analysis, there is a need to establish where the optimal compromise lies. In this work, we model real transit events based on targets as they would be observed with VLT/CRIRES+ at Paranal Observatory. Creating four hypothetical scenarios, we simulate each observation across 100 realisations of the same transit event in order to vary the time resolution only. We remove telluric and stellar lines using the SYSREM algorithm and analyse them through cross-correlation with model templates, measuring how successfully each time resolution and case detects the planetary signal. We demonstrate that there is a continuous change in the detection significance based on time resolutions, and that the function of this significance has clear maxima. The strength and location of this maxima varies on e.g. planet system parameters, instrumentation, and no. of removal iterations. We discuss why observers should therefore take several factors into account, using a strategy akin to the 'exposure triangle' from traditional photography where a balance must be struck by considering the full context of the observation. Our method is robust and may be employed by observers to estimate best observational strategies for other targets.

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arXiv2023

First Chromospheric Activity and Doppler Imaging Study of PW And Using a New Doppler Imaging Code: SpotDIPy

Measuring coverage of dark spots on cool stars is important in understanding how stellar magnetic activity scales with the rotation rate and convection zone depth. In this respect, it is crucial to infer surface magnetic patterns on G and K stars, to reveal solar-like stellar dynamos in action. Molecular bands serve as invaluable indicators of cool spots on the surfaces of stars, as they play a crucial role in enabling accurate assessments of the extent of spot coverage across the stellar surface. Therefore, more reliable surface images can be obtained considering the inversion of atomic lines with molecular bands. In this context, we simultaneously carry out Doppler imaging (DI) using atomic lines as well as Titanium Oxide (TiO) band profiles of PW And (K2 V) and also investigate chromospheric activity indicators for the first time in the literature, using the high-resolution spectra. The surface spot distribution obtained from the inversion process represents both atomic line and TiO-band profiles quite accurately. The chromospheric emission is also correlated with photospheric spot coverage, except during a possible flare event during the observations. We detect frequent flare activity, using TESS photometry. We also introduce a new open-source, Python-based DI code SpotDIPy that allows performing surface reconstructions of single stars using the maximum entropy method. We test the code by comparing surface reconstruction simulations with the extensively used DoTS code. We show that the surface brightness distribution maps reconstructed via both codes using the same simulated data are consistent with each other.

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arXiv2023

Asteroseismology and Spectropolarimetry of the Exoplanet Host Star $λ$ Serpentis

The bright star $λ$ Ser hosts a hot Neptune with a minimum mass of 13.6 $M_\oplus$ and a 15.5 day orbit. It also appears to be a solar analog, with a mean rotation period of 25.8 days and surface differential rotation very similar to the Sun. We aim to characterize the fundamental properties of this system, and to constrain the evolutionary pathway that led to its present configuration. We detect solar-like oscillations in time series photometry from the Transiting Exoplanet Survey Satellite (TESS), and we derive precise asteroseismic properties from detailed modeling. We obtain new spectropolarimetric data, and we use them to reconstruct the large-scale magnetic field morphology. We reanalyze the complete time series of chromospheric activity measurements from the Mount Wilson Observatory, and we present new X-ray and ultraviolet observations from the Chandra and Hubble space telescopes. Finally, we use the updated observational constraints to assess the rotational history of the star and to estimate the wind braking torque. We conclude that the remaining uncertainty on stellar age currently prevents an unambiguous interpretation of the properties of $λ$ Ser, and that the rate of angular momentum loss appears to be higher than for other stars with similar Rossby number. Future asteroseismic observations may help to improve the precision of the stellar age.

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arXiv2023

Company for the ultra-high density, ultra-short period sub-Earth GJ 367 b: discovery of two additional low-mass planets at 11.5 and 34 days

GJ 367 is a bright (V $\approx$ 10.2) M1 V star that has been recently found to host a transiting ultra-short period sub-Earth on a 7.7 hr orbit. With the aim of improving the planetary mass and radius and unveiling the inner architecture of the system, we performed an intensive radial velocity follow-up campaign with the HARPS spectrograph -- collecting 371 high-precision measurements over a baseline of nearly 3 years -- and combined our Doppler measurements with new TESS observations from sectors 35 and 36. We found that GJ 367 b has a mass of $M_\mathrm{b}$ = 0.633 $\pm$ 0.050 M$_{\oplus}$ and a radius of $R_\mathrm{b}$ = 0.699 $\pm$ 0.024 R$_{\oplus}$, corresponding to precisions of 8% and 3.4%, respectively. This implies a planetary bulk density of $ρ_\mathrm{b}$ = 10.2 $\pm$ 1.3 g cm$^{-3}$, i.e., 85% higher than Earth's density. We revealed the presence of two additional non transiting low-mass companions with orbital periods of $\sim$11.5 and 34 days and minimum masses of $M_\mathrm{c}\sin{i_\mathrm{c}}$ = 4.13 $\pm$ 0.36 M$_{\oplus}$ and $M_\mathrm{d}\sin{i_\mathrm{d}}$ = 6.03 $\pm$ 0.49 M$_{\oplus}$, respectively, which lie close to the 3:1 mean motion commensurability. GJ 367 b joins the small class of high-density planets, namely the class of super-Mercuries, being the densest ultra-short period small planet known to date. Thanks to our precise mass and radius estimates, we explored the potential internal composition and structure of GJ 367 b, and found that it is expected to have an iron core with a mass fraction of 0.91$^{+0.07}_{-0.23}$. How this iron core is formed and how such a high density is reached is still not clear, and we discuss the possible pathways of formation of such a small ultra-dense planet.

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arXiv2023

A close-in giant planet escapes engulfment by its star

When main-sequence stars expand into red giants, they are expected to engulf close-in planets. Until now, the absence of planets with short orbital periods around post-expansion, core-helium-burning red giants has been interpreted as evidence that short-period planets around Sun-like stars do not survive the giant expansion phase of their host stars. Here we present the discovery that the giant planet 8 Ursae Minoris b orbits a core-helium-burning red giant. At a distance of only 0.5 au from its host star, the planet would have been engulfed by its host star, which is predicted by standard single-star evolution to have previously expanded to a radius of 0.7 au. Given the brief lifetime of helium-burning giants, the nearly circular orbit of the planet is challenging to reconcile with scenarios in which the planet survives by having a distant orbit initially. Instead, the planet may have avoided engulfment through a stellar merger that either altered the evolution of the host star or produced 8 Ursae Minoris b as a second-generation planet. This system shows that core-helium-burning red giants can harbour close planets and provides evidence for the role of non-canonical stellar evolution in the extended survival of late-stage exoplanetary systems.

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arXiv2023

Constraints on Magnetic Braking from the G8 Dwarf Stars 61 UMa and $τ$ Cet

During the first half of their main-sequence lifetimes, stars rapidly lose angular momentum to their magnetized winds, a process known as magnetic braking. Recent observations suggest a substantial decrease in the magnetic braking efficiency when stars reach a critical value of the Rossby number, the stellar rotation period normalized by the convective overturn timescale. Cooler stars have deeper convection zones with longer overturn times, reaching this critical Rossby number at slower rotation rates. The nature and timing of the transition to weakened magnetic braking has previously been constrained by several solar analogs and two slightly hotter stars. In this Letter, we derive the first direct constraints from stars cooler than the Sun. We present new spectropolarimetry of the old G8 dwarf $τ$ Cet from the Large Binocular Telescope, and we reanalyze a published Zeeman Doppler image of the younger G8 star 61 UMa, yielding the large-scale magnetic field strengths and morphologies. We estimate mass-loss rates using archival X-ray observations and inferences from Ly$α$ measurements, and we adopt other stellar properties from asteroseismology and spectral energy distribution fitting. The resulting calculations of the wind braking torque demonstrate that the rate of angular momentum loss drops by a factor of 300 between the ages of these two stars (1.4-9 Gyr), well above theoretical expectations. We summarize the available data to help constrain the value of the critical Rossby number, and we identify a new signature of the long-period detection edge in recent measurements from the Kepler mission.

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arXiv2022

Accretion process, magnetic fields, and apsidal motion in the pre-main sequence binary DQ Tau

Classical T Tauri stars (CTTSs) are young stellar objects that accrete materials from their accretion disc influenced by their strong magnetic field. The magnetic pressure truncates the disc at a few stellar radii and forces the material to leave the disc plane and fall onto the stellar surface by following the magnetic field lines. However, this global scheme may be disturbed by the presence of a companion interacting gravitationally with the accreting component. This work is aiming to study the accretion and the magnetic field of the tight eccentric binary DQ Tau, composed of two equal-mass ($\sim$ 0.6 \msun ) CTTSs interacting at different orbital phases. We investigated the variability of the system using a high-resolution spectroscopic and spectropolarimetric monitoring performed with ESPaDOnS at the CFHT. We provide the first ever magnetic field analysis of this system, the Zeeman-Doppler imaging revealed a stronger magnetic field for the secondary than the primary (1.2 kG and 0.5 kG, respectively), but the small-scale fields analysed through Zeeman intensification yielded similar strengths (about 2.5 kG). The magnetic field topology and strengths are compatible with the accretion processes on CTTSs. Both components of this system are accreting, with a change of the main accretor during the orbital motion. In addition, the system displays a strong enhancement of the mass accretion rate at periastron and apastron. We also discovered, for the first time in this system, the apsidal motion of the orbital ellipse.

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arXiv2022

First results of a magnetic survey of classical Cepheids

We report recent ESPaDOnS and HARPSpol spectropolarimetric observations from our ongoing magnetic survey of the brightest twenty-five classical Cepheids. Stokes $V$ magnetic signatures are detected in eight of fifteen targets observed to date. The Stokes $V$ profiles show a diversity of morphologies with weak associated longitudinal field measurements of order 1 G. Many of the Stokes $V$ profiles are difficult to interpret in the context of the normal Zeeman effect. They consist of approximately unipolar single or double lobe(s) of positive or negative circular polarization. We hypothesize that these unusual signatures are due to the Zeeman effect modified by atmospheric velocity or magnetic field gradients. In contrast, the Stokes $V$ profiles of Polaris and MY Pup appear qualitatively similar to the complex magnetic signatures of non-pulsating cool supergiants, possibly due to the low pulsation amplitudes of these two stars.

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