arXiv subjects

Sandra V. Jeffers

Publications and source records attributed to Sandra V. Jeffers.

At least 19 recordsLinked to original sources

arXiv2026

Multiwavelength Campaign Observations of a Young Solar-type Star, EK Draconis. III. Comparison between Starspot Mapping, Zeeman Doppler Imaging, and Multiwavelength Variability

Recent simultaneous multiwavelength observations of a nearby young solar-type star EK Dra in the optical, H$α$ spectrum, and X-ray, have provided evidence for stellar prominence eruptions associated with superflares. The large prominence eruption is suggested to have been caused by a large mid-latitude spot on the polarity inversion lines near the stellar limb from the concurrent Zeeman Doppler Imaging (ZDI) and optical photometry by the TESS. In this study, we perform starspot mapping for the TESS data of EK Dra to investigate the relation of starspots and magnetic fields from the photometry and ZDI. We also explore the multiwavelength rotational variability ascribed to starspots and active regions for the TESS, B-band, H$α$, and X-ray light curves. As a result, we find that (i) spot locations deduced from the TESS light curve are mostly consistent with the intensity map from the ZDI except for a polar spot, and (ii) the H$α$ light curve exhibits clear periodicity with respect to the TESS light curve because the H$α$ line is radiated around spots in the chromosphere. The X-ray light curve does not show such association probably because of multiple spots on high activity level and extended spatial structure of coronal active regions. The results provide clues to explore their association with stellar flares at different heights of active regions in chromospheric and coronal lines. Our study also enables us to quantify the stellar XUV radiation from the magnetic fields of active stars toward understanding atmospheric evolution of exoplanets.

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arXiv2025

An observationally based wind model contemporaneous with the radio detections in $τ$ Boötis

Recent low-frequency array (LOFAR) radio signal detections bearing from the $τ$ Boötis system have been cautiously attributed to auroral emissions from the hot Jupiter $τ$ Boötis Ab. The auroral emissions are believed to be excited by interaction between the exoplanet and the winds of its host star. Since stellar winds respond to stellar surface magnetism, three-dimensional stellar wind modelling, able to account for the star's contemporaneous magnetic field geometry, can aid the interpretation of radio detections. For the first time, we present spectropolarimetric observations of $τ$ Boötis A from the same epoch as the LOFAR detections. We derive a contemporaneous large-scale magnetic map of $τ$ Boötis A, which shows a poloidally dominated field with mean strength 1.6 G. From our magnetic map, we create a three-dimensional numerical wind model and characterise the wind properties around $τ$ Boötis Ab. To compute the wind power dissipated in $τ$ Boötis Ab's magnetosphere, we apply two approaches: A) the solar system-based empirical relation called Bode's law; and B) a resolved numerical model of the planetary magnetosphere. When consistently applying best-case assumptions, we redict radio flux densities around 50 mJy and 0.68 mJy respectively. Our values are much too small to be consistent with the reported observation of $890_{-500}^{+690}$ mJy; a stellar surface magnetic field scaling $\gtrsim 10$ is required to reproduce the observed signal strength. As $τ$ Boötis A has a rapid magnetic cycle, we speculate that wind variations cased by variation in stellar magnetism may explain the lack of detections from follow-up observations. Our work emphasises the importance of contemporaneous observations of stellar magnetism and observational signatures of star-planet interaction.

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arXiv2025

The magnetic and spin-down properties of slowly rotating fully convective M dwarfs

The evolution of the magnetism, winds and rotation of low-mass stars are all linked. One of the most common ways to probe the magnetic properties of low-mass stars is with the Zeeman-Doppler imaging (ZDI) technique. The magnetic properties of partially convective stars has been relatively well explored with the ZDI technique, but the same is not true of fully convective stars. In this work, we analyse a sample of stars that have been mapped with ZDI. Notably, this sample contains a number of slowly rotating fully convective M dwarfs whose magnetic fields were recently reconstructed with ZDI. We find that the dipolar, quadrupolar and octupolar field strengths of the slowly rotating fully convective stars do not follow the same Rossby number scaling in the unsaturated regime as partially convective stars. Based on these field strengths, we demonstrate that previous estimates of spin-down torques for slowly rotating fully convective stars could have been underestimated by an order of magnitude or more. Additionally, we also find that fully convective and partially convective stars fall into distinct sequences when comparing their poloidal and toroidal magnetic energies.

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arXiv2024

Multiwavelength Campaign Observations of a Young Solar-type Star, EK Draconis. II. Understanding Prominence Eruption through Data-Driven Modeling and Observed Magnetic Environment

EK Draconis, a nearby young solar-type star (G1.5V, 50-120 Myr), is known as one of the best proxies for inferring the environmental conditions of the young Sun. The star frequently produces superflares and Paper I presented the first evidence of an associated gigantic prominence eruption observed as a blueshifted H$α$ Balmer line emission. In this paper, we present the results of dynamical modeling of the stellar eruption and examine its relationship to the surface starspots and large-scale magnetic fields observed concurrently with the event. By performing a one-dimensional free-fall dynamical model and a one dimensional hydrodynamic simulation of the flow along the expanding magnetic loop, we found that the prominence eruption likely occurred near the stellar limb (12$^{+5}_{-5}$-16$^{+7}_{-7}$ degrees from the limb) and was ejected at an angle of 15$^{+6}_{-5}$-24$^{+6}_{-6}$ degrees relative to the line of sight, and the magnetic structures can expand into a coronal mass ejection (CME). The observed prominence displayed a terminal velocity of $\sim$0 km s$^{-1}$ prior to disappearance, complicating the interpretation of its dynamics in Paper I. The models in this paper suggest that prominence's H$α$ intensity diminishes at around or before its expected maximum height, explaining the puzzling time evolution in observations. The TESS light curve modeling and (Zeeman) Doppler Imaging revealed large mid-latitude spots with polarity inversion lines and one polar spot with dominant single polarity, all near the stellar limb during the eruption. This suggests that mid-latitude spots could be the source of the pre-existing gigantic prominence we reported in Paper I. These results provide valuable insights into the dynamic processes that likely influenced the environments of early Earth, Mars, Venus, and young exoplanets.

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arXiv2024

CARMENES input catalog of M dwarfs: VII. New rotation periods for the survey stars and their correlations with stellar activity

Abridged: We measured photometric and spectroscopic $P_{\rm rot}$ for a large sample of nearby bright M dwarfs with spectral types from M0 to M9, as part of our continual effort to fully characterize the Guaranteed Time Observation programme stars of the CARMENES survey. We determine $P_{\rm rot}$ for 129 stars. Combined with the literature, we tabulate $P_{\rm rot}$ for 261 stars, or 75% of our sample. We evaluate the plausibility of all periods available for this sample by comparing them with activity signatures and checking for consistency between multiple measurements. We find that 166 of these stars have independent evidence that confirmed their $P_{\rm rot}$. There are inconsistencies in 27 periods, which we classify as debated. A further 68 periods are identified as provisional detections that could benefit from independent verification. We provide an empirical relation for the $P_{\rm rot}$ uncertainty as a function of the $P_{\rm rot}$ value, based on the dispersion of the measurements. We show that published formal errors seem to be often underestimated for periods $\gtrsim 10$ d. We highlight the importance of independent verification on $P_{\rm rot}$ measurements, especially for inactive M dwarfs. We examine rotation-activity relations with emission in X-rays, H$α$, Ca II H & K, and surface magnetic field strengths. We find overall agreement with previous works, as well as tentative differences in the partially versus fully convective subsamples. We show $P_{\rm rot}$ as a function of stellar mass, age, and galactic kinematics. With the notable exception of three transiting planet systems and TZ Ari, all known planet hosts in this sample have $P_{\rm rot} \gtrsim 15$ d. This indicates that important limitations need to be overcome before the radial velocity technique can be routinely used to detect and study planets around young and active stars.

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arXiv2023

Multiwavelength Campaign Observations of a Young Solar-type Star, EK Draconis. I. Discovery of Prominence Eruptions Associated with Superflares

Young solar-type stars frequently produce superflares, serving as a unique window into the young Sun-Earth environments. Large solar flares are closely linked to coronal mass ejections (CMEs) associated with filament/prominence eruptions, but its observational evidence for stellar superflares remains scarce. Here, we present a 12-day multi-wavelength campaign observation of young solar-type star EK Draconis (G1.5V, 50-120 Myr age) utilizing TESS, NICER, and Seimei telescope. The star has previously exhibited blueshifted H$α$ absorptions as evidence for a filament eruption associated with a superflare. Our simultaneous optical and X-ray observations identified three superflares of $1.5\times10^{33}$ -- $1.2\times10^{34}$ erg. We report the first discovery of two prominence eruptions on a solar-type star, observed as blueshifted H$α$ emissions at speed of 690 and 430 km s$^{-1}$ and masses of $1.1\times10^{19}$ and $3.2\times10^{17}$ g, respectively. The faster, massive event shows a candidate of post-flare X-ray dimming with the amplitude of up to $\sim$10 \%. Several observational aspects consistently point to the occurrence of a fast CME associated with this event. The comparative analysis of the estimated length scales of flare loops, prominences, possible dimming region, and starspots provides the overall picture of the eruptive phenomena. Furthermore, the energy partition of the observed superflares in the optical and X-ray bands is consistent with flares from the Sun, M-dwarfs, and close binaries, yielding the unified empirical relations. These discoveries provide profound implications of impact of these eruptive events on the early Venus, Earth and Mars and young exoplanets.

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arXiv2023

Stellar Activity Cycles

The magnetic field of the Sun is generated by internal dynamo process with a cyclic period of 11 years or a 22 year magnetic cycle. The signatures of the Sun's magnetic cycle are observed in the different layers of its atmosphere and in its internal layers. In this review, we use the same diagnostics to understand the magnetic cycles of other stars with the same internal structure as the Sun. We review what is currently known about mapping the surface magnetic fields, chromospheric and coronal indicators, cycles in photometry and asteroseismology. We conclude our review with an outlook for the future.

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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

Modeling the Chromosphere and Transition Region of Planet-hosting Star GJ 436

Ahead of upcoming space missions intending to conduct observations of low-mass stars in the ultraviolet (UV) spectral region it becomes imperative to simultaneously conduct atmospheric modeling from the UV to the visible (VIS) and near-infrared (NIR). Investigations on extended spectral regions will help to improve the overall understanding of the diversity of spectral lines arising from very different atmospheric temperature regions. Here we investigate atmosphere models with a chromosphere and transition region for the M2.5V star GJ 436, which hosts a close-in Hot Neptune. The atmosphere models are guided by observed spectral features from the UV to the VIS/NIR originating in the chromosphere and transition region of GJ 436. High-resolution observations from the Hubble Space Telescope and Calar Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and optical Echelle Spectrographs (CARMENES) are used to obtain an appropriate model spectrum for the investigated M dwarf. We use a large set of atomic species considered in nonlocal thermodynamic equilibrium conditions within our PHOENIX model computations to approximate the physics within the low-density atmospheric regions. In order to obtain an overall match for the nonsimultaneous observations, it is necessary to apply a linear combination of two model spectra, where one of them better reproduces the UV lines while the other better represents the lines from the VIS/NIR range. This is needed to adequately handle different activity states across the observations.

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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

A transiting, temperate mini-Neptune orbiting the M dwarf TOI-1759 unveiled by TESS

We report the discovery and characterization of TOI-1759~b, a temperate (400 K) sub-Neptune-sized exoplanet orbiting the M~dwarf TOI-1759 (TIC 408636441). TOI-1759 b was observed by TESS to transit on sectors 16, 17 and 24, with only one transit observed per sector, creating an ambiguity on the orbital period of the planet candidate. Ground-based photometric observations, combined with radial-velocity measurements obtained with the CARMENES spectrograph, confirm an actual period of $18.85019 \pm 0.00014$ d. A joint analysis of all available photometry and radial velocities reveal a radius of $3.17 \pm 0.10\,R_\oplus$ and a mass of $10.8 \pm 1.5\,M_\oplus$. Combining this with the stellar properties derived for TOI-1759 ($R_\star = 0.597 \pm 0.015\,R_\odot$; $M_\star = 0.606 \pm 0.020\,M_\odot$; $T_{\textrm{eff}} = 4065 \pm 51$ K), we compute a transmission spectroscopic metric (TSM) value of over 80 for the planet, making it a good target for transmission spectroscopy studies. TOI-1759 b is among the top five temperate, small exoplanets ($T_\textrm{eq} < 500$ K, $R_p < 4 \,R_\oplus$) with the highest TSM discovered to date. Two additional signals with periods of 80 d and $>$ 200 d seem to be present in our radial velocities. While our data suggest both could arise from stellar activity, the later signal's source and periodicity are hard to pinpoint given the $\sim 200$ d baseline of our radial-velocity campaign with CARMENES. Longer baseline radial-velocity campaigns should be performed in order to unveil the true nature of this long period signal.

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arXiv2021

Topological changes in the magnetic field of LQ Hya during an activity minimum

Previous studies have related surface temperature maps, obtained with the Doppler imaging (DI) technique, of LQ Hya with long-term photometry. We compare surface magnetic field maps, obtained with the Zeeman Doppler imaging (ZDI) technique, with contemporaneous photometry, with the aim of quantifying the star's magnetic cycle characteristics. We inverted Stokes IV spectropolarimetry into magnetic field and surface brightness maps using a tomographic inversion code that models high signal-to-noise ratio mean line profiles produced by the least squares deconvolution (LSD) technique. The magnetic field and surface brightness maps reveal similar patterns to previous DI and ZDI studies: non-axisymmetric polar magnetic field structure, void of fields at mid-latitudes, and a complex structure in the equatorial regions. There is a weak but clear tendency of the polar structures to be linked with strong radial field and the equatorial ones with the azimuthal. We find a polarity reversal in the radial field between 2016 and 2017 coincident with an activity minimum seen in the long-term photometry. The inverted field strengths cannot easily be related with the observed spottedness, but we find that they are partially connected with the retrieved field complexity. Comparing to global magnetoconvection models for rapidly rotating young Suns, this field topology and dominance of the poloidal field component could be explained by a turbulent dynamo, where differential rotation does not play a major role (so called alpha^2 Omega or alpha^2 dynamos), and axi- and non-axisymmetric modes are excited simultaneously. The complex equatorial magnetic field structure could arise from the twisted (helical) wreaths often seen in these simulations, while the polar feature would be connected to the mostly poloidal non-axisymmetric component having a smooth spatial structure.

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arXiv2021

Coronal mass ejections and type II radio emission variability during a magnetic cycle on the solar-type star $ε$ Eridani

We simulate possible stellar coronal mass ejection (CME) scenarios over the magnetic cycle of $ε$ Eridani (18 Eridani; HD 22049). We use three separate epochs from 2008, 2011, and 2013, and estimate the radio emission frequencies associated with these events. These stellar eruptions have proven to be elusive, although a promising approach to detect and characterise these phenomena are low-frequency radio observations of potential type II bursts as CME induced shocks propagate through the stellar corona. Stellar type II radio bursts are expected to emit below 450 MHz, similarly to their solar counterparts. We show that the length of time these events remain above the ionospheric cutoff is not necessarily dependent on the stellar magnetic cycle, but more on the eruption location relative to the stellar magnetic field. We find that these type II bursts would remain within the frequency range of LOFAR for a maximum of 20-30 minutes post-eruption for the polar CMEs, (50 minutes for 2nd harmonics). We find evidence of slower equatorial CMEs, which result in slightly longer observable windows for the 2008 and 2013 simulations. Stellar magnetic geometry and strength has a significant effect on the detectability of these events. We place the CMEs in the context of the stellar mass-loss rate (27-48 $\times$ solar mass-loss rate), showing that they can amount to 3-50% of the stellar wind mass-loss rate for $ε$ Eridani. Continuous monitoring of likely stellar CME candidates with low-frequency radio telescopes will be required to detect these transient events.

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arXiv2021

The CARMENES search for exoplanets around M dwarfs. Stellar atmospheric parameters of target stars with SteParSyn

We determined effective temperatures, surface gravities, and metallicities for a sample of 343 M dwarfs observed with CARMENES, the double-channel, high-resolution spectrograph installed at the 3.5 m telescope at Calar Alto Observatory. We employed SteParSyn, a Bayesian spectral synthesis implementation particularly designed to infer the stellar atmospheric parameters of late-type stars following a Markov chain Monte Carlo approach. We made use of the BT-Settl model atmospheres and the radiative transfer code turbospectrum to compute a grid of synthetic spectra around 75 magnetically insensitive Fe I and Ti I lines plus the TiO $γ$ and $ε$ bands. To avoid any potential degeneracy in the parameter space, we imposed Bayesian priors on Teff and log g based on the comprehensive, multi-band photometric data available for the sample. We find that this methodology is suitable down to M7.0 V, where refractory metals such as Ti are expected to condense in the stellar photospheres. The derived $T_{\rm eff}$, $\log{g}$, and [Fe/H] range from 3000 to 4200 K, 4.5 to 5.3 dex, and -0.7 to 0.2 dex, respectively. Although our $T_{\rm eff}$ scale is in good agreement with the literature, we report large discrepancies in the [Fe/H] scales, which might arise from the different methodologies and sets of lines considered. However, our [Fe/H] is in agreement with the metallicity distribution of FGK-type stars in the solar neighbourhood and correlates well with the kinematic membership of the targets in the Galactic populations. Lastly, excellent agreement in $T_{\rm eff}$ is found for M dwarfs with interferometric angular diameter measurements, as well as in the [Fe/H] between the components in the wide physical FGK+M and M+M systems included in our sample.

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arXiv2021

A young spectroscopic binary in a quintuple system part of the Local Association

Double-lined spectroscopic binaries (SB2) allow us to determine a lower limit of the masses of their components directly to test stellar models. In this work, our aim is to derive the orbital and physical parameters of GJ1284, a young SB2. We also revise the membership of this system and its two wide co-moving companions, GJ898 and GJ897AB, to a young moving group to assess, along with other youth indicators, their age. Afterwards, we compare the results from these analyses and the photometry of these systems with several pre-main-sequence evolutionary models. We determine the orbit of the GJ1284 system alongside its systemic velocity from high resolution spectra. Additionally, we use TESS photometry to derive the rotational period of the GJ1284 and its two wide companions. GJ1284 is a binary system located at approximately 16 pc with an eccentric orbit ($ e = 0.505 $) of 11.83 d period made up of an M2-M2.5 + M3-M3.5. The revised systemic velocity of $ γ= 0.84 \pm 0.14\,\mathrm{km\,s}^{-1} $ suggests that it is a member of the Local Association. The kinematics together with other activity and youth indicators imply an age of 110-800 Myr for this system and its two companions. The isochronal ages derived from the comparison of the photometry with several evolutionary models are younger than the age estimated from the activity indicators for the three co-moving systems. The masses for the components of GJ1284, derived from their luminosity and age using the different models, are not consistent with the masses derived from the photometry, except for the PARSEC models, but are compatible with dynamical masses of double-lined eclipsing binaries with similar ages and spectral types. The effect of magnetic activity in the form of spots can reconcile to some extent the photometric and dynamical masses, but is not considered in most of the evolutionary models.

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arXiv2021

The CARMENES search for exoplanets around M dwarfs: Not-so-fine hyperfine-split vanadium lines in cool star spectra

(Abridged) We characterize a series of neutral vanadium atomic absorption lines in the 800--910nm wavelength region of high signal-to-noise, high-resolution, telluric-corrected M-dwarf spectra from the CARMENES survey. Many of these lines are prominent and exhibit a distinctive broad and flat-bottom shape, which is a result of hyperfine structure (HFS). We investigate the potential and implications of these HFS split lines for abundance analysis of cool stars. With standard spectral synthesis routines, as provided by the spectroscopy software iSpec and the latest atomic data (including HFS) available from the VALD3 database, we modeled these striking line profiles. We used them to measure V abundances of cool dwarfs. We determined V abundances for 135 early M dwarfs (M0.0V to M3.5V) in the CARMENES guaranteed time observations sample. They exhibit a [V/Fe]-[Fe/H] trend consistent with that derived from nearby FG dwarfs. The tight ($\pm$ 0.1 dex) correlation between [V/H] and [Fe/H] suggests the potential application of V as an alternative metallicity indicator in M dwarfs. We also show hints that neglecting to model HFS could partially explain the temperature correlation in V abundance measurements observed in previous studies of samples involving dwarf stars with $T_{\rm eff} \lesssim 5300$K. Our work suggests that HFS can impact certain absorption lines in cool photospheres more severely than in Sun-like ones. Therefore, we advocate that HFS should be carefully treated in abundance studies in stars cooler than $\sim 5000$K. On the other hand, strong HFS split lines in high-resolution spectra present an opportunity for precision chemical analyses of large samples of cool stars. The V-to-Fe trends exhibited by the local M dwarfs continue to challenge theoretical models of V production in the Galaxy.

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arXiv2020

The impact of unresolved magnetic spots on high precision radial velocity measurements

The Doppler method of exoplanet detection has been extremely successful, but suffers from contaminating noise from stellar activity. In this work a model of a rotating star with a magnetic field based on the geometry of the K2 star Epsilon Eridani is presented and used to estimate its effect on simulated radial velocity measurements. A number of different distributions of unresolved magnetic spots were simulated on top of the observed large-scale magnetic maps obtained from eight years of spectropolarimetric observations. The radial velocity signals due to the magnetic spots have amplitudes of up to 10 m s$^{-1}$, high enough to prevent the detection of planets under 20 Earth masses in temperate zones of solar type stars. We show that the radial velocity depends heavily on spot distribution. Our results emphasize that understanding stellar magnetic activity and spot distribution is crucial for detection of Earth analogues.

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arXiv2019

Do non-dipolar magnetic fields contribute to spin-down torques?

Main sequence low-mass stars are known to spin-down as a consequence of their magnetised stellar winds. However, estimating the precise rate of this spin-down is an open problem. The mass-loss rate, angular momentum-loss rate and the magnetic field properties of low-mass stars are fundamentally linked making this a challenging task. Of particular interest is the stellar magnetic field geometry. In this work, we consider whether non-dipolar field modes contribute significantly to the spin-down of low-mass stars. We do this using a sample of stars that have all been previously mapped with Zeeman-Doppler imaging. For a given star, as long as its mass-loss rate is below some critical mass-loss rate, only the dipolar fields contribute to its spin-down torque. However, if it has a larger mass-loss rate, higher order modes need to be considered. For each star, we calculate this critical mass-loss rate, which is a simple function of the field geometry. Additionally, we use two methods of estimating mass-loss rates for our sample of stars. In the majority of cases, we find that the estimated mass-loss rates do not exceed the critical mass-loss rate and hence, the dipolar magnetic field alone is sufficient to determine the spin-down torque. However, we find some evidence that, at large Rossby numbers, non-dipolar modes may start to contribute.

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