Large-scale Surface Magnetic Field Research Articles

Cyclic variations of the structure and energetics of solar magnetic fields

ABSTRACT The solar cycle is a complex phenomenon, a comprehensive understanding of which requires the study of various tracers. Here, we consider the solar cycle as manifested in the harmonics of the solar large-scale surface magnetic field, including zonal, sectorial, and tesseral harmonics, divided into odd and even relative to the solar equator. In addition to considering the amplitudes of the harmonics, we analyse their contribution to the magnetic energy. It turns out that the relative contribution of different types of harmonics to the magnetic energy is virtually independent of the cycle height. We identify different phases of the activity cycle using harmonics of different symmetries. A possible way to incorporate the obtained result into the solar dynamo theory is proposed.

Implications of Different Solar Photospheric Flux-transport Models for Global Coronal and Heliospheric Modeling

The concept of surface-flux transport (SFT) is commonly used in evolving models of the large-scale solar surface magnetic field. These photospheric models are used to determine the large-scale structure of the overlying coronal magnetic field, as well as to make predictions about the fields and flows that structure the solar wind. We compare predictions from two SFT models for the solar wind, open magnetic field footpoints, and the presence of coronal magnetic null points throughout various phases of a solar activity cycle, focusing on the months of April in even-numbered years between 2012 and 2020, inclusively. We find that there is a solar-cycle dependence to each of the metrics considered, but there is not a single phase of the cycle in which all the metrics indicate good agreement between the models. The metrics also reveal large, transient differences between the models when a new active region is rotating into the assimilation window. The evolution of the surface flux is governed by a combination of large-scale flows and comparatively small-scale motions associated with convection. Because the latter flows evolve rapidly, there are intervals during which their impact on the surface flux can only be characterized in a statistical sense, thus their impact is modeled by introducing a random evolution that reproduces the typical surface flux evolution. We find that the differences between the predicted properties are dominated by differences in the model assumptions and implementation, rather than the selection of a particular realization of the random evolution.

A decade-long magnetic monitoring of Vega

Aims. The very weak magnetic field detected at the surface of Vega hints at a widespread population of weakly magnetic stars of A and B spectral types. We contribute here to gather more clues about the origin of this magnetism by investigating the long-term stability of the field geometry of this prototypical star. Methods. We use spectropolarimetric data collected as part of a long-term campaign, with more than 2000 observations spread between 2008 and 2018. Using various sub-sets extracted from the whole time series, we reconstruct several maps of the large-scale surface magnetic field. Results. We confirm that the polarimetric signal is modulated according to a ~0.68 d period, which we interpret as the stellar rotation period. The surface magnetic field is organized in a complex geometry. We confirm the existence of a very localized, polar magnetic spot previously reported for Vega, with a radial field strength of about −5 G. We show that the surface of the star is also covered by a dipole, with a polar strength close to 9 G and a dipole obliquity close to 90°. Both magnetic structures are remarkably stable over one decade. The available data suggest that smaller-scale magnetic spots may not be limited to the polar region, although the poor reliability of their reconstruction does not allow us to firmly conclude about their temporal evolution.

TOI-1759 b: A transiting sub-Neptune around a low mass star characterized with SPIRou and TESS

We report the detection and characterization of the transiting sub-Neptune TOI-1759 b, using photometric time series from the Transiting Exoplanet Survey Satellite (TESS) and near-infrared spectropolarimetric data from the Spectro-Polarimètre Infra Rouge (SPIRou) on the Canada-France-Hawaii Telescope. TOI-1759 b orbits a moderately active M0V star with an orbital period of 18.849975 ± 0.000006 days, and we measured a planetary radius and mass of 3.06 ± 0.22 R⊕ and 6.8 ± 2.0 M⊕. Radial velocities were extracted from the SPIRou spectra using both the cross-correlation function and the line-by-line methods, optimizing the velocity measurements in the near-infrared domain. We analyzed the broadband spectral energy distribution of the star and the high-resolution SPIRou spectra to constrain the stellar parameters and thus improve the accuracy of the derived planet parameters. A least squares deconvolution analysis of the SPIRou Stokes V polarized spectra detects Zeeman signatures in TOI-1759. We modeled the rotational modulation of the magnetic stellar activity using a Gaussian process regression with a quasi-periodic covariance function and find a rotation period of 35.65−0.15+0.17 days. We reconstructed the large-scale surface magnetic field of the star using Zeeman-Doppler imaging, which gives a predominantly poloidal field with a mean strength of 18 ± 4 G. Finally, we performed a joint Bayesian Markov chain Monte Carlo analysis of the TESS photometry and SPIRou radial velocities to optimally constrain the system parameters. At 0.1176 ± 0.0013 au from the star, the planet receives 6.4 times the bolometric flux incident on Earth, and its equilibrium temperature is estimated at 433 ± 14 K. TOI-1759 b is a likely gas-dominated sub-Neptune with an expected high rate of photoevaporation. Therefore, it is an interesting target to search for neutral hydrogen escape, which may provide important constraints on the planetary formation mechanisms responsible for the observed sub-Neptune radius desert.

Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos of Sun-like Stars

Abstract We use the anelastic spherical harmonic code to model the convective dynamo of solar-type stars. Based on a series of 15 3D MHD simulations spanning four bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ( Δ Ω ∝ ( ∣ Ω ∣ / Ω ⊙ ) 0.46 ) in the MHD solutions than in their HD counterpart ∣ Ω ∣ / Ω ⊙ 0.66 ), yielding a better agreement with the observational trends based on power laws. We find that for a fluid Rossby number between 0.15 ≲ Ro f ≲ 0.65, the solutions possess long magnetic cycle, if Ro f ≲ 0.42 a short cycle and if Ro f ≳ 1 (antisolar-like differential rotation), a statistically steady state. We show that short-cycle dynamos follow the classical Parker–Yoshimura rule whereas the long-cycle period ones do not. We also find efficient energy transfer between reservoirs, leading to the conversion of several percent of the star's luminosity into magnetic energy that could provide enough free energy to sustain intense eruptive behavior at the star’s surface. We further demonstrate that the Rossby number dependency of the large-scale surface magnetic field in the simulation ( B L , surf ∼ Ro f − 1.26 ) agrees better with observations ( B V ∼ Ro s − 1.4 ± 0.1 ) and differs from dynamo scaling based on the global magnetic energy ( B bulk ∼ Ro f − 0.5 ).

Ultra-wideband, Multiepoch Radio Study of the First Discovered “Main-sequence Radio Pulse Emitter” CU Vir

Abstract The presence of a large-scale surface magnetic field in early-type stars leads to several unique electromagnetic phenomena producing radiation over X-ray to radio bands. Among them, the rarest type of emission is electron cyclotron maser emission (ECME) observed as periodic, circularly polarized radio pulses. The phenomenon was first discovered in the hot magnetic star CU Vir. Past observations of this star led to the consensus that the star produces only right circularly polarized ECME, suggesting that only one magnetic hemisphere takes part in the phenomenon. Here we present the first ultra-wideband (0.4–4 GHz) study of this star using the upgraded Giant Metrewave Radio telescope and the Karl G. Jansky Very Large Array, which led to the surprising discovery of ECME of both circular polarizations up to around 1.5 GHz. The GHz observations also allowed us to infer that the upper ECME cutoff frequency is at ≳5 GHz. The sub-GHz observation led to the unexpected observation of more than two pairs of ECME pulses per rotation cycle. In addition, we report the discovery of a “giant pulse” and transient enhancements, which are potentially the first observational evidence of “centrifugal breakout” of plasma from the innermost part of the stellar magnetosphere. The stark contrast between the star’s behavior at GHz and sub-GHz frequencies could either be due to propagation effects, a manifestation of varying magnetic field topology as a function of height, or a signature of an additional “ECME engine.”

Solar Cycle Evolution of Filaments over a Century: Investigations with the Meudon and McIntosh Hand-drawn Archives

Abstract Hand-drawn synoptic maps from the Meudon Observatory (1919 onwards) and the McIntosh archive (1967 onwards) are two important sources of long-term, manually recorded filament observations. In this study, we calibrate the Meudon maps and subsequently identify filaments through an automated method. We extract physical parameters from this filament database and perform a comparative study of their long-term evolution focusing on the cotemporal period of the McIntosh and Meudon observations. The spatiotemporal evolution of filaments manifests in the form of a filament butterfly diagram, further indicating that they are intimately related to the large-scale solar cycle. Physical descriptors such as the number and length of filaments, which are tracers of the solar surface magnetic field, have cycles which are phase locked with the ∼11 yr sunspot cycle. The tilt-angle distribution of filaments—both near to or distant from active region locations—indicates that their origin is due to either large-scale surface magnetic field or inter-active-region field evolution. This study paves the way for constructing a composite series of hand-drawn filament data with minimal gaps stretching over the time span of solar filament observations up to a century. On the one hand, this would serve as a useful constraint for models of magnetic field emergence and evolution on the Sun’s surface over multiple solar cycles, and on the other hand, this filament database may be used to guide the reconstruction of filament/prominence associated eruptive events before the space age.

The surface magnetic activity of the weak-line T Tauri stars TWA 7 and TWA 25

ABSTRACT We present an analysis of spectropolarimetric observations of the low-mass weak-line T Tauri stars TWA 25 and TWA 7. The large-scale surface magnetic fields have been reconstructed for both stars using the technique of Zeeman Doppler imaging. Our surface maps reveal predominantly toroidal and non-axisymmetric fields for both stars. These maps reinforce the wide range of surface magnetic fields that have been recovered, particularly in pre-main sequence stars that have stopped accreting from the (now depleted) central regions of their discs. We reconstruct the large scale surface brightness distributions for both stars, and use these reconstructions to filter out the activity-induced radial velocity jitter, reducing the RMS of the radial velocity variations from 495 to 32 m s −1 for TWA 25, and from 127 to 36 m s −1 for TWA 7, ruling out the presence of close-in giant planets for both stars. The TWA 7 radial velocities provide an example of a case where the activity-induced radial velocity variations mimic a Keplerian signal that is uncorrelated with the spectral activity indices. This shows the usefulness of longitudinal magnetic field measurements in identifying activity-induced radial velocity variations.

Spatial–temporal evolution of photospheric weak-field shifts in solar cycles 21–24

Context. Weak magnetic field elements make a dominant contribution to the total magnetic field on the solar surface. Even so, little is known of their long-term occurrence. Aims. We study the long-term spatial–temporal evolution of the weak-field shift and skewness of the distribution of photospheric magnetic field values during solar cycles 21−24 in order to clarify the role and relation of the weak field values to the overall magnetic field evolution. Methods. We used Wilcox Solar Observatory (WSO) and the Synoptic Optical Long-term Investigations of the Sun Vector SpectroMagnetograph synoptic maps to calculate weak-field shifts for each latitude bin of each synoptic map, and thereby constructed a time–latitude butterfly diagram for shifts. We also calculated butterfly diagrams for skewness for all field values and for weak field values only. Results. The weak-field shifts and (full-field) skewness depict a similar spatial–temporal solar cycle evolution to that of the large-scale surface magnetic field. The field distribution has a systematic non-zero weak-field shift and a large skewness already at (and after) the emergence of the active region, even at the highest resolution. We find evidence for coalescence of opposite-polarity fields during the surge evolution. This is clearly more effective at the supergranulation scale. However, a similar dependence of magnetic field coalescence on spatial resolution was not found in the unipolar regions around the poles. Conclusions. Our results give evidence for the preference of even the weakest field elements toward the prevailing magnetic polarity since the emergence of an active region, and for a systematic coalescence of stronger magnetic fields of opposite polarities to produce weak fields during surge evolution and at the poles. We also find that the supergranulation process is reduced or turned off in the unipolar regions around the poles. These observations improve the understanding not only of the development of the weakest magnetic field elements, but also of the dynamics of magnetic fields at large, and even of processes below the solar surface.

Magnetic field and chromospheric activity evolution of HD 75332: a rapid magnetic cycle in an F star without a hot Jupiter

ABSTRACT Studying cool star magnetic activity gives an important insight into the stellar dynamo and its relationship with stellar properties, as well as allowing us to place the Sun’s magnetism in the context of other stars. Only 61 Cyg A (K5V) and τ Boo (F8V) are currently known to have magnetic cycles like the Sun’s, where the large-scale magnetic field polarity reverses in phase with the star’s chromospheric activity cycles. τ Boo has a rapid ∼240 d magnetic cycle, and it is not yet clear whether this is related to the star’s thin convection zone or if the dynamo is accelerated by interactions between τ Boo and its hot Jupiter. To shed light on this, we studied the magnetic activity of HD 75332 (F7V) which has similar physical properties to τ Boo and does not appear to host a hot Jupiter. We characterized its long-term chromospheric activity variability over 53 yr and used Zeeman Doppler Imaging to reconstruct the large-scale surface magnetic field for 12 epochs between 2007 and 2019. Although we observe only one reversal of the large-scale magnetic dipole, our results suggest that HD 75332 has a rapid ∼1.06 yr solar-like magnetic cycle where the magnetic field evolves in phase with its chromospheric activity. If a solar-like cycle is present, reversals of the large-scale radial field polarity are expected to occur at around activity cycle maxima. This would be similar to the rapid magnetic cycle observed for τ Boo, suggesting that rapid magnetic cycles may be intrinsic to late-F stars and related to their shallow convection zones.

Long-term evolution of a magnetic massive merger product

ABSTRACT About 10 per cent of stars more massive than ${\approx}1.5\, {\mathrm{M}}_{\odot }$ have strong, large-scale surface magnetic fields and are being discussed as progenitors of highly magnetic white dwarfs and magnetars. The origin of these fields remains uncertain. Recent three-dimensional (3D) magnetohydrodynamical simulations have shown that strong magnetic fields can be generated in the merger of two massive stars. Here, we follow the long-term evolution of such a 3D merger product in a 1D stellar evolution code. During a thermal relaxation phase after the coalescence, the merger product reaches critical surface rotation, sheds mass and then spins down primarily because of internal mass readjustments. The spin of the merger product after thermal relaxation is mainly set by the co-evolution of the star–torus structure left after coalescence. This evolution is still uncertain, so we also consider magnetic braking and other angular momentum-gain and -loss mechanisms that may influence the final spin of the merged star. Because of core compression and mixing of carbon and nitrogen in the merger, enhanced nuclear burning drives a transient convective core that greatly contributes to the rejuvenation of the star. Once the merger product relaxed back to the main sequence, it continues its evolution similar to that of a genuine single star of comparable mass. It is a slow rotator that matches the magnetic blue straggler τ Sco. Our results show that merging is a promising mechanism to explain some magnetic massive stars and it may also be key to understand the origin of the strong magnetic fields of highly magnetic white dwarfs and magnetars.

Stellar mergers as the origin of magnetic massive stars.

About ten per cent of 'massive' stars (those of more than 1.5 solar masses) have strong, large-scale surface magnetic fields1-3. It has been suggested that merging of main-sequence and pre-main-sequence stars could produce such strong fields4,5, and the predicted fraction of merged massive stars is also about ten per cent6,7. The merger hypothesis is further supported by a lack of magnetic stars in close binaries8,9, which is as expected if mergers produce magnetic stars. Here we report three-dimensional magnetohydrodynamical simulations of the coalescence of two massive stars and follow the evolution of the merged product. Strong magnetic fields are produced in the simulations, and the merged star rejuvenates such that it appears younger and bluer than other coeval stars. This can explain the properties of the magnetic 'blue straggler' star τ Sco in the Upper Scorpius association that has an observationally inferred, apparent age of less than five million years, which is less than half the age of its birth association10. Such massive blue straggler stars seem likely to be progenitors of magnetars, perhaps giving rise to some of the enigmatic fast radio bursts observed11, and their supernovae may be affected by their strong magnetic fields12.

The evolution of surface magnetic fields in young solar-type stars II: the early main sequence (250–650 Myr)★

There is a large change in surface rotation rates of sun-like stars on the pre-main sequence and early main sequence. Since these stars have dynamo-driven magnetic fields, this implies a strong evolution of their magnetic properties over this time period. The spin-down of these stars is controlled by interactions between stellar and magnetic fields, thus magnetic evolution in turn plays an important role in rotational evolution. We present here the second part of a study investigating the evolution of large-scale surface magnetic fields in this critical time period. We observed stars in open clusters and stellar associations with known ages between 120 and 650 Myr, and used spectropolarimetry and Zeeman Doppler Imaging to characterize their large-scale magnetic field strength and geometry. We report 15 stars with magnetic detections here. These stars have masses from 0.8 to 0.95 M⊙, rotation periods from 0.326 to 10.6 d, and we find large-scale magnetic field strengths from 8.5 to 195 G with a wide range of geometries. We find a clear trend towards decreasing magnetic field strength with age, and a power law decrease in magnetic field strength with Rossby number. There is some tentative evidence for saturation of the large-scale magnetic field strength at Rossby numbers below 0.1, although the saturation point is not yet well defined. Comparing to younger classical T Tauri stars, we support the hypothesis that differences in internal structure produce large differences in observed magnetic fields, however for weak-lined T Tauri stars this is less clear.

The Global and Small-scale Magnetic Fields of Fully Convective, Rapidly Spinning M Dwarf Pair GJ65 A and B

Abstract The nearby M dwarf binary GJ65 AB, also known as BL Cet and UV Cet, is a unique benchmark for investigation of dynamo-driven activity of low-mass stars. Magnetic activity of GJ65 was repeatedly assessed by indirect means, such as studies of flares, photometric variability, X-ray, and radio emission. Here, we present a direct analysis of large-scale and local surface magnetic fields in both components. Interpreting high-resolution circular polarization spectra (sensitive to a large-scale field geometry) we uncovered a remarkable difference of the global stellar field topologies. Despite nearly identical masses and rotation rates, the secondary exhibits an axisymmetric, dipolar-like global field with an average strength of 1.3 kG while the primary has a much weaker, more complex, and non-axisymmetric 0.3 kG field. On the other hand, an analysis of the differential Zeeman intensification (sensitive to the total magnetic flux) shows the two stars having similar magnetic fluxes of 5.2 and 6.7 kG for GJ65 A and B, respectively, although there is evidence that the field strength distribution in GJ65 B is shifted toward a higher field strength compared to GJ65 A. Based on these complementary magnetic field diagnostic results, we suggest that the dissimilar radio and X-ray variability of GJ65 A and B is linked to their different global magnetic field topologies. However, this difference appears to be restricted to the upper atmospheric layers but does not encompass the bulk of the stars and has no influence on the fundamental stellar properties.

The solar proxy κ1 Cet and the planetary habitability around the young Sun

AbstractAmong the solar proxies, κ1 Cet, stands out as potentially having a mass very close to solar and a young age. We report magnetic field measurements and planetary habitability consequences around this star, a proxy of the young Sun when life arose on Earth. Magnetic strength was determined from spectropolarimetric observations and we reconstruct the large-scale surface magnetic field to derive the magnetic environment, stellar winds, and particle flux permeating the interplanetary medium around κ1 Cet. Our results show a closer magnetosphere and mass-loss rate 50 times larger than the current solar wind mass-loss rate when Life arose on Earth, resulting in a larger interaction via space weather disturbances between the stellar wind and a hypothetical young-Earth analogue, potentially affecting the habitability. Interaction of the wind from the young Sun with the planetary ancient magnetic field may have affected the young Earth and its life conditions.

MAGNETIC FIELD AND WIND OF KAPPA CETI: TOWARD THE PLANETARY HABITABILITY OF THE YOUNG SUN WHEN LIFE AROSE ON EARTH

ABSTRACT We report magnetic field measurements for κ 1 Cet, a proxy of the young Sun when life arose on Earth. We carry out an analysis of the magnetic properties determined from spectropolarimetric observations and reconstruct the large-scale surface magnetic field to derive the magnetic environment, stellar winds, and particle flux permeating the interplanetary medium around κ 1 ?> Cet. Our results show a closer magnetosphere and mass-loss rate of M ˙ = 9.7 × 10 − 13 M ⊙ yr − 1 ?> , i.e., a factor of 50 times larger than the current solar wind mass-loss rate, resulting in a larger interaction via space weather disturbances between the stellar wind and a hypothetical young-Earth analogue, potentially affecting the planet’s habitability. Interaction of the wind from the young Sun with the planetary ancient magnetic field may have affected the young Earth and its life conditions.

Magnetic fields on young, moderately rotating Sun-like stars – I. HD 35296 and HD 29615

Observations of the magnetic fields of young solar-type stars provide a way to investigate the signatures of their magnetic activity and dynamos. Spectropolarimetry enables the study of these stellar magnetic fields and was thus employed at the T\'{e}lescope Bernard Lyot and the Anglo-Australian Telescope to investigate two moderately rotating young Sun-like stars, namely HD 35296 (V119 Tau, HIP 25278) and HD 29615 (HIP 21632). The results indicate that both stars display rotational variation in chromospheric indices consistent with their spot activity, with variations indicating a probable long-term cyclic period for HD 35296. Additionally, both stars have complex, and evolving, large-scale surface magnetic fields with a significant toroidal component. High levels of surface differential rotation were measured for both stars. For the F8V star HD 35296 a rotational shear of $\Delta\Omega$ = 0.22$^{+0.04}_{-0.02}$ rad/d was derived from the observed magnetic profiles. For the G3V star HD 29615 the magnetic features indicate a rotational shear of $\Delta\Omega$ = 0.48$_{-0.12}^{+0.11}$ rad/d, while the spot features, with a distinctive polar spot, provide a much lower value of $\Delta\Omega$ of 0.07$_{-0.03}^{+0.10}$ rad/d. Such a significant discrepancy in shear values between spot and magnetic features for HD 29615 is an extreme example of the variation observed for other lower-mass stars. From the extensive and persistent azimuthal field observed for both targets it is concluded that a distributed dynamo operates in these moderately rotating Sun-like stars, in marked contrast to the Sun's interface-layer dynamo.

Variable magnetic field geometry of the young sun HN Pegasi (HD 206860)

The large-scale magnetic field of solar-type stars reconstructed from their spectropolarimetric observations provide important insight into their underlying dynamo processes.We aim to investigate the temporal variability of the large-scale surface magnetic field and chromospheric activity of a young solar analogue, the G0 dwarf HN Peg.The large-scale surface magnetic field topology is reconstructed using Zeeman Doppler Imaging at six observational epochs covering seven years.We also investigated the chromospheric activity variations by measuring the flux in the line cores of the three chromospheric activity indicators: Ca II H&K, H alpha, and the Ca II IRT lines.The magnetic topology of HN Peg shows a complex and variable geometry. While the radial field exhibits a stable positive polarity magnetic region at the poles at each observational epoch, the azimuthal field is strongly variable in strength, where a strong band of positive polarity magnetic field is present at equatorial latitudes. This field disappears during the middle of our time span, reappearing again during the last two epochs of observations. The mean magnetic field derived from the magnetic maps also follow a similar trend to the toroidal field, with the field strength at a minimum in epoch 2009.54. Summing the line of sight magnetic field over the visible surface at each observation, HN Peg exhibits a weak longitudinal magnetic field ranging from -14 G to 13 G, with no significant long-term trend, although there is significant rotational variability within each epoch. Those chromospheric activity indicators exhibit more long-term variations over the time span of observations, where the minimal is observed in Epoch 2008.71.

Stellar magnetism: empirical trends with age and rotation

We investigate how the observed large-scale surface magnetic fields of low-mass stars (~0.1 -- 2 Msun), reconstructed through Zeeman-Doppler imaging (ZDI), vary with age t, rotation and X-ray emission. Our sample consists of 104 magnetic maps of 73 stars, from accreting pre-main sequence to main-sequence objects (1 Myr < t < 10 Gyr). For non-accreting dwarfs we empirically find that the unsigned average large-scale surface field <|Bv|> is related to age as $t^{-0.655 \pm 0.045}$. This relation has a similar dependence to that identified by Skumanich (1972), used as the basis for gyrochronology. Likewise, our relation could be used as an age-dating method ("magnetochronology"). The trends with rotation we find for the large-scale stellar magnetism are consistent with the trends found from Zeeman broadening measurements (sensitive to large- and small-scale fields). These similarities indicate that the fields recovered from both techniques are coupled to each other, suggesting that small- and large-scale fields could share the same dynamo field generation processes. For the accreting objects, fewer statistically significant relations are found, with one being a correlation between the unsigned magnetic flux and rotation period. We attribute this to a signature of star-disc interaction, rather than being driven by the dynamo.

Modelling the hidden magnetic field of low-mass stars

Zeeman-Doppler imaging is a spectropolarimetric technique that is used to map the large-scale surface magnetic fields of stars. These maps in turn are used to study the structure of the stars' coronae and winds. This method, however, misses any small-scale magnetic flux whose polarisation signatures cancel out. Measurements of Zeeman broadening show that a large percentage of the surface magnetic flux may be neglected in this way. In this paper we assess the impact of this 'missing flux' on the predicted coronal structure and the possible rates of spin down due to the stellar wind. To do this we create a model for the small-scale field and add this to the Zeeman-Doppler maps of the magnetic fields of a sample of 12 M dwarfs. We extrapolate this combined field and determine the structure of a hydrostatic, isothermal corona. The addition of small-scale surface field produces a carpet of low-lying magnetic loops that covers most of the surface, including the stellar equivalent of solar 'coronal holes' where the large-scale field is opened up by the stellar wind and hence would be X-ray dark. We show that the trend of the X-ray emission measure with rotation rate (the so-called 'activity-rotation relation') is unaffected by the addition of small-scale field, when scaled with respect to the large-scale field of each star. The addition of small-scale field increases the surface flux; however, the large-scale open flux that governs the loss of mass and angular momentum in the wind remains unaffected. We conclude that spin-down times and mass loss rates calculated from surface magnetograms are unlikely to be significantly influenced by the neglect of small-scale field.