Surface Differential Rotation Research Articles

Coriolis darkening in late-type stars

Context. Modeling the surface brightness distribution of stars is of prime importance to interpret the large amount of available interferometric, spectropolarimetric, or photometric observations. Beyond stellar physics, this is also a prerequisite to characterize exoplanets or our Galaxy. Nevertheless, this remains quite challenging for cool stars as it requires one to model the magnetohydrodynamic turbulence that develops in their convective envelope. Aims. In Paper I (Raynaud, R., Rieutord, M., Petitdemange, L., Gastine, T., & Putigny, B. 2018, A&A, 609, A124), the effect of the Coriolis acceleration on the surface heat flux has been studied by means of hydrodynamic simulations. In this paper, we aim to investigate the additional effect of dynamo magnetic fields that can be generated in the thick convective envelopes of cool stars. We focus on an envelope thickness that is representative of either a ∼0.35 M⊙ M dwarf, a young red giant star or a pre-main sequence star. Methods. We performed a parametric study using numerical magnetohydrodynamic simulations of anelastic convection in thick rotating spherical shells. The stratification in density ranges from a few tens to a few hundreds. The setup assumes a constant entropy jump between the inner and outer layers to force convection, with stress-free boundary conditions for the velocity field. The magnetic Prandtl number was systematically varied in order to vary the magnetic field intensity. For each model, we computed the azimuthally and temporally averaged surface distribution of the heat flux, and examined the leading-order effect of the magnetic field on the obtained latitudinal luminosity profile. Results. We identify three different regimes. Close to the onset of convection, while the first unstable modes tend to convey heat more efficiently near the equator, magnetic fields are shown to generally enhance the mean heat flux close to the polar regions (and the tangent cylinder). By progressively increasing the Rayleigh number, the development of a prograde equatorial jet was previously shown to make the equator darker when no magnetic field is taken into account. For moderate Rayleigh numbers, magnetic fields can instead inverse the mean pole-equator brightness contrast (which means going from a darker to a brighter equator when a dynamo sets in) and finally induce a similar regime to that found close to the onset of convection. For more turbulent models with larger Rayleigh numbers, magnetic fields alternatively tend to smooth out the brightness contrast. This general behavior is shown to be related to the quenching of the surface differential rotation by magnetic fields and remains valid regardless of the magnetic morphology. Conclusions. Mean global trends regarding the impact of rotation and magnetic fields on the surface brightness distribution of cool stars are theoretically depicted and need to be tested by future observations. This work opens the door to more detailed theoretical studies including the effect of nonaxisymmetric and time-variable surface features associated with magnetic activity.

How well does surface magnetism represent deep Sun-like star dynamo action?

Context. For Sun-like stars, the generation of toroidal magnetic field from poloidal magnetic field is an essential piece of the dynamo mechanism powering their magnetism. Previous authors have estimated the net toroidal flux generated in each hemisphere of the Sun by exploiting its conservative nature. This only requires observations of the photospheric magnetic field and surface differential rotation. Aims. We explore this approach using a 3D magnetohydrodynamic dynamo simulation of a cool star, for which the magnetic field and its generation are precisely known throughout the entire star. Methods. Changes to the net toroidal flux in each hemisphere were evaluated using a closed line integral bounding the cross-sectional area of each hemisphere, following the application of Stokes theorem to the induction equation; the individual line segments correspond to the stellar surface, base, equator, and rotation axis. We evaluated the influence of the large-scale flows, the fluctuating flows, and magnetic diffusion on each of the line segments, along with their depth-dependence. Results. In the simulation, changes to the net toroidal flux via the surface line segment typically dominate the total line integral surrounding each hemisphere, with smaller contributions from the equator and rotation axis. The surface line integral is governed primarily by the large-scale flows, and the diffusive current; the latter acting like a flux emergence term due to the use of an impenetrable upper boundary in the simulation. The bulk of the toroidal flux is generated deep inside the convection zone, with the surface observables capturing this due to the conservative nature of the net flux. Conclusions. Surface magnetism and rotation can be used to produce an estimate of the net toroidal flux generated in each hemisphere, allowing us to constrain the reservoir of magnetic flux for the next magnetic cycle. However, this methodology cannot identify the physical origin or the location of the toroidal flux generation. In addition, not all dynamo mechanisms depend on the net toroidal field produced in each hemisphere, meaning this method may not be able to characterise every magnetic cycle.

Stellar activity and differential rotation of HD 111395

Aims. Stellar activity cycles and rotation periods are important parameters for characterising the stellar dynamo, which operates in late-type main-sequence stars. However, the number of stars with well-known cycle and rotation periods is rather low, so new detections are still important. Methods. To find activity cycles and rotation periods, we utilised the TIGRE telescope to monitor stars for periodic variations in chromospheric activity indicators. We employed the widely used CaII H&K lines and the CaII infrared triplet lines as stellar activity indicators. To verify a periodic variation and to determine the corresponding period, we performed a frequency analysis via the generalised Lomb-Scargle method of the taken time series. Results. We studied CaII data of the G5V star HD 111395 and derive an activity cycle period of 949 ± 5 d (≈2.6 yr). This cycle is coincident with coronal measurements from the X-ray telescope eROSITA on board SRG. Furthermore, the TIGRE CaII time series show a long-term trend that indicates an additional long-term cycle. Using the few available literature S-index data points, we estimate a probable cycle length of 12–15 yr for this potential long-term cycle. Finally, we determined rotation periods from each observation season. We computed a mean rotation period of 16.76 ± 0.36 d averaged over all observation seasons and chromospheric indicators. However, we also find a strong variation in the mean seasonal rotation periods, which follows the derived cycle period; therefore, we interpret this behaviour as a sign of surface differential rotation.

A star under multiple influences. Magnetic activity in V815 Her, a compact 2+2 hierarchical system

Close binaries with magnetically active components are astrophysical laboratories for studying the effects of binarity on activity. Of particular interest are binary and multiple star systems that contain a solar-type active component with an internal structure similar to the Sun, allowing us to study how the dynamo of a solar-type star would work under different conditions. We have conducted a comprehensive investigation of V815\,Her using photometric and spectroscopic data to understand the origin of the activity and what influences it in the short and long term. Using space photometry we performed light curve modeling in order to derive astrophysical and orbital parameters for the eclipsing binary subsystem V815\,Her B. Using archival photometric data covering a century we carried out a time frequency analysis. Spectral synthesis was applied to determine the basic astrophysical parameters of the rapidly rotating primary using high-resolution STELLA spectra recorded in 2018. Photometric analysis of archived data revealed multiple cycles on timescales between sim 6.5 and sim 26 years, some of which may be harmonic. From TESS photometry we obtained an orbital solution for the V815\,Her B subsystem. By placing the primary component on the Hertzsprung$-$Russell-diagram, we could deduce an age of approx 30\,Myr, in line with the high Li-6707 abundance. The STELLA spectra covering the 200 day-long observing season enabled us to create 19 time-series Doppler images, which revealed a constantly changing spotted surface on a timescale of a few weeks. From the consecutive image pairs we built up the average cross-correlation function map to measure the surface differential rotation of the spotted star, from which we derive a weak solar-type surface shear. We found evidence that the V815\,Her B component previously apostrophized as a "third body" is actually an eclipsing close binary subsystem of two M dwarfs with a period of 0.5\,d, that is, V815\,Her is a 2+2 hierarchical quadruple system. The system is apparently young, only a few times ten million years old, consistent with the spotted primary V815\,Her Aa being a zero-age main-sequence star. Spot activity on the primary was found to be vivid. Fast starspot decay suggests that convective-turbulent erosion plays a more significant role in such a rapidly rotating star. The weak surface shear of V815\,Her Aa due to differential rotation is presumably confined by tidal forces of the close companion V815\,Her Ab. The slowly increasing photometric cycle of about 6.5 years on average is interpreted as a spot cycle of V815\,Her Aa, which is probably modulated by the eccentric wide orbit.

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 ⊕ 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 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, 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 estimate the wind braking torque. We conclude that the remaining uncertainty on the 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 a similar Rossby number. Future asteroseismic observations may help to improve the precision of the stellar age.

Lithium in Kepler Red Giants: Defining Normal and Anomalous

The orders-of-magnitude variations in the lithium abundances of evolved stars have long been a puzzle. Diluted signals, ambiguous evolutionary states, and unknown masses have made it challenging to both map the expected lithium signals and explain the anomalously lithium-rich stars. Using a set of asteroseismically characterized evolved stars, we show here that the base lithium abundance in red giant stars is mass-dependent, with higher-mass stars having higher “normal” lithium abundances, while highly lithium-enhanced stars may cluster around 0.8 or 1.8 M ☉. We confirm previous studies that have shown that lithium enhancement and rapid rotation are often coincident but find that the actual correlation between lithium abundance and rotation rate, whether surface, internal, or radial differential rotation, is weak. Our data support previous assertions that most lithium-rich giants are in the core-helium-burning phase. We also note a tentative correlation between the highest lithium abundances and unusual carbon-to-nitrogen ratios, which is suggestive of binary interactions, though we find no simple correlation between lithium richness and indicators of binarity.

Exploring the stellar surface phenomena of WASP-52 and HAT-P-30 with ESPRESSO

We analyse spectroscopic and photometric transits of the hot Jupiters WASP-52 b and HAT-P30 b obtained with ESPRESSO, Eulercam and NGTS for both targets, and additional TESS data for HAT-P-30. Our goal is to update the system parameters and refine our knowledge of the host star surfaces. For WASP-52, the companion planet has occulted starspots in the past, and as such our aim was to use the reloaded Rossiter-McLaughlin technique to directly probe its starspot properties. Unfortunately, we find no evidence for starspot occultations in the datasets herein. Additionally, we searched for stellar surface differential rotation (DR) and any centre-to-limb variation (CLV) due to convection, but return a null detection of both. This is unsurprising for WASP-52, given its relatively cool temperature, high magnetic activity (which leads to lower CLV), and projected obliquity near 0° (meaning the transit chord is less likely to cross several stellar latitudes). For HAT-P-30, this result was more surprising given its hotter effective temperature, lower magnetic field, and high projected obliquity (near 70°). To explore the reasons behind the null DR and CLV detection for HAT-P-30, we simulated a variety of scenarios. We find that either the CLV present on HAT-P-30 is below the solar level or the presence of DR prevents a CLV detection given the precision of the data herein. A careful treatment of both DR and CLV is required, especially for systems with high impact factors, due to potential degeneracies between the two. Future observations and/or a sophisticated treatment of the red noise present in the data (likely due to granulation) is required to refine the DR and CLV for these particular systems; such observations would also present another opportunity to try to examine starspots on WASP-52.

EI Eridani: A star under the influence

Context. Homogeneous photometric time series spanning decades provide a unique opportunity to study the long-term cyclic behavior of active spotted stars such as our target EI Eridani. In addition, with ultraprecise space photometry data, it is possible to investigate the accompanying flare activity in detail. However, the rotation period of ≈2 days for EI Eri makes it impossible to achieve time-resolved surface images from a single ground-based observing site. Therefore, for this purpose, spectroscopic data from a multi-site observing campaign are needed. Aims. We use our photometric time series of more than 40 yr to analyze the long-term behavior of EI Eri. We investigate flare activity using photometric data obtained with the Transiting Exoplanet Survey Satellite (TESS). The MUlti-SIte Continuous Spectroscopy (MUSICOS) campaign in 1998 was designed to achieve high-resolution, multi-wavelength spectroscopic observations from many sites around the globe, which meant that uninterrupted phase coverage of EI Eri became available. We use these data to reconstruct successive surface-temperature maps of the star in order to study the changes of starspots on a very short timescale. Methods. We used long-term seasonal period analysis of our photometric time series to study changes in the rotational period. We also applied short-term Fourier-transform to look for activity cycle-like changes. We also studied the phase and frequency distribution of hand-selected flares. We applied our multi-line Doppler imaging code to reconstruct four consecutive Doppler images. These images were also used to measure surface differential rotation with our cross-correlation technique. In addition, we carried out tests to demonstrate how Doppler imaging is affected by the fact that the data came from several different instruments with different spectral resolutions. Results. Seasonal period analysis of the light curve reveals a smooth, significant change in period, possibly indicating the evolution of active latitudes. Temperature curves from B − V and V − I show slight differences, indicating the activity of EI Eri is spot dominated. Short-term Fourier transform reveals smoothly changing cycles of between 4.5 and 5.5 yr and of between 8.9 and 11.6 yr. The time-resolved spotted surface of EI Eri from Doppler imaging enabled us to follow the evolution of the different surface features. Cross-correlating the consecutive Doppler maps reveals surface shear of α = 0.036 ± 0.007. Our tests validate our approach and show that the surface-temperature distribution is adequately reconstructed by our method. The tests also indicate how accurately the cross-correlation method can reproduce the surface shear as a function of the spectral resolution.

Accounting for differential rotation in calculations of the Sun’s angular momentum-loss rate

Context. Sun-like stars shed angular momentum due to the presence of magnetised stellar winds. Magnetohydrodynamic models have been successful in exploring the dependence of this ‘wind-braking torque’ on various stellar properties; however the influence of surface differential rotation is largely unexplored. As the wind-braking torque depends on the rotation rate of the escaping wind, the inclusion of differential rotation should effectively modulate the angular momentum-loss rate based on the latitudinal variation of wind source regions. Aims. Here we aim to quantify the influence of surface differential rotation on the angular momentum-loss rate of the Sun, in comparison to the typical assumption of solid-body rotation. Methods. To do this, we exploited the dependence of the wind-braking torque on the effective rotation rate of the coronal magnetic field, which is known to be vitally important in magnetohydrodynamic models. This quantity has been evaluated by tracing field lines through a potential field source surface (PFSS) model, driven by ADAPT-GONG magnetograms. The surface rotation rates of the open magnetic field lines were then used to construct an open-flux weighted rotation rate, from which the influence on the wind-braking torque could be estimated. Results. During solar minima, the rotation rate of the corona decreases with respect to the typical solid-body rate (the Carrington rotation period is 25.4 days), as the sources of the solar wind are confined towards the slowly rotating poles. With increasing activity, more solar wind emerges from the Sun’s active latitudes which enforces a Carrington-like rotation. Coronal rotation often displays a north-south asymmetry driven by differences in active region emergence rates (and consequently latitudinal connectivity) in each hemisphere. Conclusions. The effect of differential rotation on the Sun’s current wind-braking torque is limited. The solar wind-braking torque is ∼10 − 15% lower during solar minimum, (compared with the typical solid body rate), and a few percent larger during solar maximum (as some field lines connect to more rapidly rotating equatorial latitudes). For more rapidly rotating Sun-like stars, differential rotation may play a more significant role, depending on the configuration of the large-scale magnetic field.

The magnetic field and multiple planets of the young dwarf AU Mic

ABSTRACT In this paper, we present an analysis of near-infrared spectropolarimetric and velocimetric data of the young M dwarf AU Mic, collected with SPIRou at the Canada–France–Hawaii telescope from 2019 to 2022, mostly within the SPIRou Legacy Survey. With these data, we study the large- and small-scale magnetic field of AU Mic, detected through the unpolarized and circularly polarized Zeeman signatures of spectral lines. We find that both are modulated with the stellar rotation period (4.86 d), and evolve on a time-scale of months under differential rotation and intrinsic variability. The small-scale field, estimated from the broadening of spectral lines, reaches 2.61 ± 0.05 kG. The large-scale field, inferred with Zeeman–Doppler imaging from Least-Squares Deconvolved profiles of circularly polarized and unpolarized spectral lines, is mostly poloidal and axisymmetric, with an average intensity of 550 ± 30 G. We also find that surface differential rotation, as derived from the large-scale field, is ≃30 per cent weaker than that of the Sun. We detect the radial velocity (RV) signatures of transiting planets b and c, although dwarfed by activity, and put an upper limit on that of candidate planet d, putatively causing the transit-timing variations of b and c. We also report the detection of the RV signature of a new candidate planet (e) orbiting further out with a period of 33.39 ± 0.10 d, i.e. near the 4:1 resonance with b. The RV signature of e is detected at 6.5σ while those of b and c show up at ≃4σ, yielding masses of $10.2^{+3.9}_{-2.7}$ and $14.2^{+4.8}_{-3.5}$ M⊕ for b and c, and a minimum mass of $35.2^{+6.7}_{-5.4}$ M⊕ for e.

Surface structure of 45 Hercules: an otherwise unremarkable Ap star with a surprisingly weak magnetic field

ABSTRACTThe origin of magnetic fields and their role in chemical spot formation on magnetic Ap stars is currently not understood. Here, we contribute to solving this problem with a detailed observational characterization of the surface structure of 45 Her, a weak-field Ap star. We find this object to be a long-period, single-lined spectroscopic binary and determine the binary orbit as well as fundamental and atmospheric parameters of the primary. We study magnetic field topology and chemical spot distribution of 45 Her with the help of the Zeeman Doppler imaging technique. Magnetic mapping reveals the stellar surface field to have a distorted dipolar topology with a surface-averaged field strength of 77 G and a dipolar component strength of 119 G – confirming it as one of the weakest well-characterized Ap-star fields known. Despite its feeble magnetic field, 45 Her shows surface chemical inhomogeneities with abundance contrasts of up to 6 dex. Of the four chemical elements studied, O concentrates at the magnetic equator, whereas Ti, Cr, and Fe avoid this region. Apart from this trend, the positions of Fe-peak element spots show no apparent correlation with the magnetic field geometry. No signs of surface differential rotation or temporal evolution of chemical spots on the time-scale of several years were detected. Our findings demonstrate that chemical spot formation does not require strong magnetic fields to proceed and that both the stellar structure and the global field itself remain stable for sub-100 G field strengths contrary to theoretical predictions.

Measuring the Obliquities of the TRAPPIST-1 Planets with MAROON-X

A star’s obliquity with respect to its planetary system can provide us with insight into the system’s formation and evolution, as well as hinting at the presence of additional objects in the system. However, M dwarfs, which are the most promising targets for atmospheric follow-up, are underrepresented in terms of obliquity characterization surveys due to the challenges associated with making precise measurements. In this paper, we use the extreme-precision radial velocity (RV) spectrograph MAROON-X to measure the obliquity of the late M dwarf TRAPPIST-1. With the Rossiter–McLaughlin effect, we measure a system obliquity of and a stellar rotational velocity of 2.1 ± 0.3 km s−1. We were unable to detect stellar surface differential rotation, and we found that a model in which all planets share the same obliquity was favored by our data. We were also unable to make a detection of the signatures of the planets using Doppler tomography, which is likely a result of the both the slow rotation of the star and the low signal-to-noise ratio of the data. Overall, TRAPPIST-1 appears to have a low obliquity, which could imply that the system has a low primordial obliquity. It also appears to be a slow rotator, which is consistent with past characterizations of the system and estimates of the star’s rotation period. The MAROON-X data allow for a precise measurement of the stellar obliquity through the Rossiter–McLaughlin effect, highlighting the capabilities of MAROON-X and its ability to make high-precision RV measurements around late, dim stars.

Magnetic topologies of two weak-line T Tauri stars TAP 4 and TAP 40

ABSTRACT We present a Zeeman–Doppler imaging study of two weak-line T Tauri stars TAP 4 and TAP 40, based on the high-resolution spectropolarimetric observations with ESPaDOnS at the Canada–France–Hawaii Telescope in November 2013, in the framework of the Magnetic Topologies of Young Stars and Survival of close-in giant Exoplanets large programme. We apply two Zeeman–Doppler imaging codes to the Stokes I and V profiles to reconstruct their brightness and large-scale magnetic field images. The results given by the two imaging codes are in good agreement with each other. TAP 4 shows a large polar cool spot and several intermediate-latitude warm spots on its surface, whereas TAP 40 exhibits very weak variations in its Stokes I profiles, suggesting a mostly unspotted photosphere. We detect Zeeman signatures in the Stokes V profiles of both stars. The reconstructed magnetic maps reveal dominantly toroidal fields, which enclose about 60 per cent of the total magnetic energy for both TAP 4 and TAP 40. Both stars show prominent circular ring features of the azimuthal magnetic field. We derive a solar-like surface differential rotation on TAP 4 from the tomographic modelling. The brightness image of TAP 4 is used to predict the radial velocity (RV) jitters induced by its activity. After filtering out the activity jitter, the rms of its RVs is reduced from 1.7 to 0.2 km s−1, but we do not detect any periodic signals in the filtered RVs of TAP 4, implying that it is unlikely to host a close-in exoplanet more massive than ∼3.5MJup at 0.1 au.

The active weak-line T Tauri star LkCa 4 observed with SPIRou and TESS

ABSTRACTWe report results of a spectropolarimetric and photometric monitoring of the weak-line T Tauri star LkCa 4 within the SPIRou Legacy Survey large programme, based on data collected with SPIRou at the Canada–France–Hawaii Telescope and the TESS space probe between October 2021 and January 2022. We applied Zeeman–Doppler Imaging to our spectropolarimetric and photometric data to recover a surface brightness distribution compatible with TESS photometry, as well as the large-scale magnetic topology of the star. As expected from the difference in wavelength between near-infrared and optical data, the recovered surface brightness distribution is less contrasted than the previously published one based on ESPaDOnS data, but still features mid-latitude dark and bright spots. The large-scale magnetic field is consistent in shape and strength with the one derived previously, with a poloidal component resembling a 2.2 kG dipole and a toroidal component reaching 1.4 kG and encircling the star at the equator. Our new data confirm that the surface differential rotation of LkCa 4 is about 10 times weaker than that of the Sun, and significantly different from zero. Using our brightness reconstruction and Gaussian Process Regression, we were able to filter the radial velocity activity jitter down to a precision of 0.45 and 0.38 $\text{km}\, \text{s}^{-1}$ (from an amplitude of 6.10 $\text{km}\, \text{s}^{-1}$), respectively, yielding again no evidence for a close-in massive planet orbiting the star.

A study of the rapid rotator ζ Aql: differential surface rotation?

ABSTRACT We report new, extremely precise photopolarimetry of the rapidly-rotating A0 main-sequence star ζ Aql, covering the wavelength range ∼400–900 nm, which reveals a rotationally-induced signal. We model the polarimetry, together with the flux distribution and line profiles, in the framework of Roche geometry with ω-model gravity darkening, to establish the stellar parameters. An additional constraint is provided by TESS photometry, which shows variability with a period, Pphot, of 11.1 h. Modelling based on solid-body surface rotation gives rotation periods, Prot, that are in only marginal agreement with this value. We compute new ester stellar-structure models to predict horizontal surface-velocity fields, which depart from solid-body rotation at only the ∼2 per cent level (consistent with a reasonably strong empirical upper limit on differential rotation derived from the line-profile analysis). These models bring the equatorial rotation period, Prot(e), into agreement with Pphot, without requiring any ‘fine tuning’ (for the Gaia parallax). We confirm that surface abundances are significantly subsolar ([M/H] ≃ −0.5). The star’s basic parameters are established with reasonably good precision: $M = 2.53\pm 0.16\, \mbox{M}_{\odot }$, log (L/L⊙) = 1.72± 0.02, $R_{\rm p}= 2.21\pm 0.02\, \mbox{R}_{\odot }$, Teff = 9693 ± 50 K, $i = 85{^{+5}_{-7}}^\circ$, and ωe/ωc = 0.95 ± 0.02. Comparison with single-star solar-abundance stellar-evolution models incorporating rotational effects shows excellent agreement (but somewhat poorer agreement for models at [M/H] ≃ −0.4).

Properties and evolutions of starspots on three detached eclipsing binaries in the LAMOST–Kepler survey

ABSTRACT Spotted detached eclipsing binaries (DEBs) offer insights into starspots on binaries. In this work, we study three spotted DEBs, KIC 8097825, KIC 6859813 and KIC 5527172, which have been observed using Kepler photometry and Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) spectroscopy. The physical parameters of binaries are determined by binary modelling. The size, lifetime and single/-double-dip ratio (SDR) of starspots are derived by starspot analysis. KIC 8097825 has large starspots. KIC 6859813 has a spot rotation period shorter than its orbital period but the system should be synchronized by inference from time-scale estimation. The difference may be the result of the surface differential rotation. KIC 5527172 has a long spot lifetime and an M-dwarf component with an inflation radius. The primaries of these binaries and the secondary of KIC 8097825 have spots. Adding spotted DEBs from the literature, we compare the starspots on binaries with those on the single stars. The spot sizes of starspots on 65 per cent of binaries are smaller than the median of those on single stars. The lifetimes of starspots on binaries are consistent with those on single stars when the rotation periods are larger than 3 d. SDRs for half of the binaries are consistent with those of single-star systems, while the other half are smaller. The relative lifetime positively correlates with the rms and SDR but negatively correlates with the rotation period. These relations are similar to those of spots on single-star systems. Binaries with luminosity ratios close to the unit tend to have more double dips.

Effect of Differential Rotation on the Magnetic Braking of Low-mass and Solar-like Stars: A Proof-of-concept Study

Abstract On the main sequence, low-mass and solar-like stars are observed to spin down over time, and magnetized stellar winds are thought to be predominantly responsible for this significant angular momentum loss. Previous studies have demonstrated that the wind torque can be predicted via formulations dependent on stellar properties, such as magnetic field strength and geometry, stellar radius and mass, wind mass-loss rate, and stellar rotation rate. Although these stars are observed to experience surface differential rotation, torque formulations so far have assumed solid-body rotation. Surface differential rotation is expected to affect the rotation of the wind and thus the angular momentum loss. To investigate how differential rotation affects the torque, we use the PLUTO code to perform 2.5D magnetohydrodynamic, axisymmetric simulations of stellar winds, using a colatitude-dependent surface differential rotation profile that is solar-like (i.e., rotation is slower at the poles than the equator). We demonstrate that the torque is determined by the average rotation rate in the wind so that the net torque is less than that predicted by assuming solid-body rotation at the equatorial rate. The magnitude of the effect is essentially proportional to the magnitude of the surface differential rotation, for example, resulting in a torque for the Sun that is ∼20% smaller than predicted by the solid-body assumption. We derive and fit a semianalytic formulation that predicts the torque as a function of the equatorial spin rate, magnitude of differential rotation, and wind magnetization (depending on the dipolar magnetic field strength and mass-loss rate, combined).

The T Tauri star V410 Tau in the eyes of SPIRou and TESS

ABSTRACT We report results of a spectropolarimetric and photometric monitoring of the weak-line T Tauri star V410 Tau based on data collected mostly with SPIRou, the near-infrared (NIR) spectropolarimeter recently installed at the Canada-France-Hawaii Telescope, as part of the SPIRou Legacy Survey large programme, and with TESS between October and December 2019. Using Zeeman–Doppler Imaging (ZDI), we obtained the first maps of photospheric brightness and large-scale magnetic field at the surface of this young star derived from NIR spectropolarimetric data. For the first time, ZDI is also simultaneously applied to high-resolution spectropolarimetric data and very-high-precision photometry. V410 Tau hosts both dark and bright surface features and magnetic regions similar to those previously imaged with ZDI from optical data, except for the absence of a prominent dark polar spot. The brightness distribution is significantly less contrasted than its optical equivalent, as expected from the difference in wavelength. The large-scale magnetic field (${\sim}410$ G), found to be mainly poloidal, features a dipole of ${\sim}390$ G, again compatible with previous studies at optical wavelengths. NIR data yield a surface differential rotation slightly weaker than that estimated in the optical at previous epochs. Finally, we measured the radial velocity of the star and filtered out the stellar activity jitter using both ZDI and Gaussian Process Regression down to a precision of ${\sim}0.15$ and 0.08 $\mathrm{km}\, \mathrm{s}^{-1}$ RMS, respectively, confirming the previously published upper limit on the mass of a potential close-in massive planet around V410 Tau.

Short-term variations of surface magnetism and prominences of the young Sun-like star V530 Per

Aims. We investigate magnetic tracers in the photosphere and the chromosphere of the ultra-rapid rotator (P ~ 0.32 d) V530 Per, a cool member of the open cluster α Persei, to characterize the short-term variability of the magnetic activity and large-scale magnetic field of this prototypical young, rapidly rotating solar-like star. Methods. With time-resolved spectropolarimetric observations spread over four close-by nights, we reconstructed the brightness distribution and large-scale magnetic field geometry of V530 Per through Zeeman-Doppler imaging. Simultaneously, we estimated the short-term variability of the surface through latitudinal differential rotation. Using the same data set, we also mapped the spatial distribution of prominences through tomography of Hα emission. Results. As in our previous study, a large dark spot occupies the polar region of V530 Per with smaller, dark, and bright spots at lower latitudes. The large-scale magnetic field is dominated by a toroidal, mostly axisymmetric component. The maximal radial field strength is equal to ~1 kG. The surface differential rotation is consistent with a smooth Sun-like shear dΩ = 0.053 ± 0.004 rad d−1, close to the solar shear level. The prominence pattern displays a stable component that is confined close to the corotation radius. We also observe rapidly evolving Hα emitting structures, over timescales ranging from minutes to days. The fast Hα evolution was not linked to any detected photospheric changes in the spot or magnetic coverage.

A confined dynamo: Magnetic activity of the K-dwarf component in the pre-cataclysmic binary system V471 Tauri

Context.Late-type stars in close binary systems can exhibit strong magnetic activity owing to rapid rotation supported by tidal locking. On the other hand, tidal coupling may suppress the differential rotation which is a key ingredient of the magnetic dynamo.Aims.We studied the red dwarf component in the eclipsing binary system V471 Tau in order to unravel the relations between the different activity layers, from the stellar surface through the chromosphere up to the corona. Our aim is to study how the magnetic dynamo in the late-type component is affected by the close white dwarf companion.Methods.We used space photometry, high-resolution spectroscopy, and X-ray observations from different space instruments to explore the main characteristics of magnetic activity. We applied a light curve synthesis program to extract the eclipsing binary model and to analyze the residual light variations. Photometric periods were obtained using a Fourier-based period search code. We searched for flares by applying an automated flare detection code. Spectral synthesis was used to derive or specify some of the astrophysical parameters. Doppler imaging was used to reconstruct surface temperature maps, which were cross-correlated to derive surface differential rotation. We applied different conversion techniques to make it possible to compare the X-ray emissions obtained from different space instruments.Results.From the K2 photometry we found that 5–10 per cent of the apparent surface of the red dwarf is covered by cool starspots. From seasonal photometric period changes we estimated a weak differential rotation. From the flare activity we derived a cumulative flare frequency diagram which suggests that frequent flaring could have a significant role in heating the corona. Using high-resolution spectroscopy we reconstructed four Doppler images for different epochs which reveal an active longitude, that is, a permanent dominant spot facing the white dwarf. From short term changes in the consecutive Doppler images we derived a weak solar-type surface differential rotation withαDR = 0.0026 shear coefficient, similar to that provided by photometry. The long-term evolution of X-ray luminosity reveals a possible activity cycle length of ≈12.7 yr, traces of which were also discovered in the Hαspectra.Conclusions.We conclude that the magnetic activity of the red dwarf component in V471 Tau is strongly influenced by the close white dwarf companion. We confirm the presence of a permanent dominant spot (active longitude) on the red dwarf facing the white dwarf. The weak differential rotation of the red dwarf is very likely the result of tidal confinement by the companion. We find that the periodic appearance of the inter-binary Hαemission from the vicinity of the inner Lagrangian point is correlated with the activity cycle.