Introduction

As a layer of the stellar upper atmosphere, the chromosphere lies above the photosphere and beneath the corona1. It serves as the locus of thermal inversion, where the temperature begins to rise after decreasing from the stellar core to the photosphere. This characteristic demarcates it as more than a transitional layer, transforming it into a site with various types of activity2,3,4,5, which significantly influences the space weather conditions surrounding orbiting planets6,7. The magnetic field predominantly governs such activity, storing and releasing energy, thereby significantly affecting the heating processes and efficiently driving large-scale eruptions in the chromosphere and corona8. Consequently, measuring the magnetic field of the upper atmosphere, including the chromosphere, is essential to understanding the physical mechanisms responsible for stellar coronal heating and eruptions9,10.

However, magnetic field measurements in the stellar upper atmosphere are very limited because of the weak signal, even for the Sun11,12,13,14,15,16. Although there have been attempts at magnetic field measurements in the chromospheres of accreting pre-main-sequence stars17,18, these signals are intertwined with the accretion process, which has a different energy-transfer mechanism compared to a solar-like chromosphere. In the absence of measurements, our knowledge about magnetic fields in the upper atmospheres of distant main-sequence stars other than the Sun relies on extrapolations19,20 of the measured photospheric magnetic fields21,22. However, comparisons between the measured and extrapolated magnetic fields in the solar upper atmosphere often reveal distinct discrepancies, suggesting that the assumptions of extrapolations are invalid at many locations on stars4,13,23. Furthermore, the majority of magnetic energy in stellar atmospheres is stored in small-scale fields24,25, which are crucial for understanding stellar activity mechanisms. Unlike the photosphere, where magnetic structures are more concentrated, chromospheric fields typically exhibit more diffuse patterns26. Solar observations demonstrate that this structural complexity can lead to varying measurement outcomes across the chromosphere27, with magnetic field vectors sometimes appearing in opposite directions between chromospheric and photospheric layers in the same region28.

M-dwarfs are low-mass stars with surface temperatures lower than those of the Sun and extended convective envelopes. They are the most common type of star in the solar neighborhood, making up over 60% of all stars, and they host the majority of known exoplanets29. With a mass less than 0.6M⊙, M-dwarfs have a lifetime longer than that of the Sun, and the habitable zones of their orbiting exoplanets are closer, often less than 0.3 astronomical unit (AU) away from the stars30. The probability of detecting habitable planets is higher around M-dwarfs compared to earlier-type stars. However, the habitability is more likely to be influenced by the magnetic activity originating primarily from the host stars20,31,32. Many M-dwarfs exhibit greatly elevated levels of magnetic activity compared to our Sun, exhibiting frequent superflares with total energies of 1033−38 erg33,34. While the surface magnetic fields of M-dwarfs have been measured over the past decades21,22,35, the energy driving this magnetic activity primarily originates from the magnetic fields in the upper atmospheres, which have not yet been measured36,37. In addition, many active M-dwarfs are fully convective stars, but it is still debated whether the lack of a tachocline will result in a dynamo different from the solar one. Understanding the key physical processes in these dynamos requires constraints from observations of small-scale magnetic field structures in stellar atmospheres, which are still lacking35.

Spectral lines originating at different atmospheric heights provide diagnostic windows into distinct stellar layers. While most absorption lines in stellar spectra form within the photosphere, the unique physical conditions in the chromosphere selectively enhance specific spectral features, particularly the Balmer lines and Calcium II lines. These enhanced emission features serve as valuable probes of chromospheric conditions and magnetic structures1. We analyzed a decade-long compilation of polarized spectra obtained with two high-resolution spectropolarimeters, ESPaDOnS and NARVAL (Methods). The data include the unpolarized normalized intensity (Stokes I, represented by normalization to the continuum I/Ic) and circular polarization (Stokes V, represented by V/Ic). This study focuses on three active mid to late M-dwarfs38: AD Leo, YZ CMi, and EV Lac, which have masses of 0.31–0.42 solar mass and rotation periods of 2.2–4.4 days (see Supplementary Information, SI hereafter, Table S1).

We simultaneously measured the mean longitudinal magnetic field (detailed in Method) of these stars in the photosphere 〈Bp〉 from mean photospheric lines, the lower chromosphere 〈BcL〉 from the Hα line, and the middle chromosphere 〈BcM〉 from the cores of the Calcium II infrared triplet (Ca IRT). Figure 1 shows examples of Stokes I and V profiles for each star. The anti-symmetric features in the Stokes V profiles are typical signatures of the Zeeman effect39. Figure 2 presents all measurements for the three targets, along with the corresponding rotational phases of the observations40,41. The mean longitudinal magnetic fields in the chromospheres of the three targets can reach several hundred Gauss, comparable to the photospheric fields.

Fig. 1: Examples of spectropolarimetric spectral lines of three stars.
Fig. 1: Examples of spectropolarimetric spectral lines of three stars.
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The profiles are sampled from the observations of 2007Jun25 (AD Leo), 2007Jan27(YZ CMi), 2005Sep18 (EV Lac), with above-average signal-to-noise. a The spectral profiles of LSD line profile (photosphere). b Hα (lower chromosphere). c Ca IRT (middle chromosphere). The gray lines show the unpolarized intensity profiles normalized to the unpolarized continuum intensity Ic. The color lines represent Stokes V profiles normalized to Ic, and the corresponding Null (N/Ic) profile with no expected signal from the targets. Both V/Ic and N/Ic are multiplied by 100 for the purpose of illustration. The error bars of V/Ic indicate the  ± 1σ uncertainties. The velocities have been corrected from the stellar system radial velocity to shift the line center of photospheric LSD to 0 km/s. The inferred magnetic field is printed in each panel.

Fig. 2: Phase-folded mean longitudinal magnetic field strengths in the photospheres and chromospheres.
Fig. 2: Phase-folded mean longitudinal magnetic field strengths in the photospheres and chromospheres.
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a AD Leo. b YZ CMi. c EV Lac. a–c The rotational phases were derived from the same ephemera. Red triangles are photospheric fields 〈Bp〉 inferred from LSD profiles; yellow squares are lower chromospheric fields 〈BcL〉 from Hα, blue pentagons are middle chromospheric fields 〈BcM〉 from Ca IRT. Filled markers are taken from a marked epoch with full phase coverage for each star. For these epochs, the linear Pearson correlation coefficients between the field strengths of two layers are also listed in the left block. For each marked epoch, we give a two-harmonic Fourier series to fit the pattern, showing the periodic signal of the magnetic field variation.

Results

Large-scale magnetic fields

The variation of the measured magnetic fields at different rotational phases can be used to characterize large-scale magnetic field structures40,42. We typically obtained one spectrum per observation night for each star, resulting in low sampling coverage within one rotation cycle. Given that the large-scale photospheric magnetic field structure can vary yearly but generally remains stable within an observing epoch (the few-month window each year during which the targets are visible)43,44, we grouped the data by epochs for further analysis. The time duration of one epoch was at least one month, which is much longer than the stellar rotational period. Therefore, our measurements of the magnetic fields were taken over multiple rotation cycles within each epoch. For each target, we focus on measurements from a marked epoch with full rotational phase coverage: AD Leo observed in 2008, YZ CMi observed in late December 2007 and early 2008, and EV Lac in 2007. We neglect the effect of differential rotation, since it is not detected for the photospheric field in the three targets40. In these epochs, we see that observations at different times form relatively stable patterns in a phase-folded diagram, as shown in Fig. 2 (SI 1B & Fig. S3), which can be fitted by a two-harmonic Fourier series. This stability suggests that the large-scale chromospheric fields co-rotating with the stars were nearly stable within an epoch, with a timescale of at least one month.

Layer-dependent magnetic fields

The different patterns of layers in the same epoch indicate that the large-scale magnetic fields vary with height. As shown in Fig. 2, while the sign of 〈BcL〉 is generally consistent with 〈Bp〉, frequent opposite signs in 〈BcM〉 highlight the different magnetic topologies with height. Among the three stars, AD Leo has the highest percentage of observations where 〈BcM〉 and 〈Bp〉 have opposite signs. Example spectra with the opposite sign between photosphere and middle chromosphere can be found in Fig. 1 for AD Leo and EV Lac, showing the same orientation of the anti-symmetric structure for V profile and opposite orientation of I profile. Disk-integrated spectral profiles average the magnetic field contributions over the entire visible surface of the star, potentially masking localized mixed-polarity magnetic features but providing a comprehensive view of the star’s overall magnetic structures. Considering that the chromospheric layer is close to the surface of a star (0.3% R⊙ for Sun), the variation in polarity and strength at different heights can be attributed to the variation of corresponding large-scale magnetic field structures with height, resulting in different contributions of positive- or negative-polarity fields to the observed signals. The sign change can be reproduced by extrapolation of the photospheric field (Fig. S4 & S5), but detailed variation between the patterns should be attributed to more complex effects close to the surface, like small-scale fields or more diffuse large-scale magnetic loops than predicted. This scenario is different from that on the Sun, where the polarity and topology of the magnetic field from the photosphere to the chromosphere are generally similar27,45.

Complexity of magnetic structure

The correlation between the large-scale magnetic fields, as shown in Table 1 (more details in Table S2), can characterize the complexity of magnetic structure in the upper layers of the star during the marked epoch, or even considering the decade-long observations (see SI 1B and Figs. S6–S9). The difference between the large-scale fields is larger, as indicated by correlation coefficients approaching zero. YZ CMi displays distinct sinusoidal rotational modulation and exhibits the strongest correlation between photospheric and chromospheric fields among our observations, suggesting a more organized and stable magnetic field topology. The modulation patterns and correlations among different layers in the other two stars, EV Lac and AD Leo, exhibit more complex characteristics. In EV Lac, 〈BcL〉 also shows a substantial correlation with 〈Bp〉, similar to YZ CMi. However, there is a notable negative correlation between 〈BcM〉 and the fields in the lower layers. AD Leo exhibits weaker correlations between the layers; magnetic fields in both chromospheric layers appear to be anti-correlated with the photospheric field during the marked epoch, while 〈BcL〉 and 〈BcM〉 are highly correlated. These observations suggest that YZ CMi has a more organized large-scale magnetic field structure than the other two stars (SI 1C). Previous theoretical investigations showed that more complex magnetic fields can support less prominence mass on M-dwarfs, resulting in weaker stellar winds19,46. AD Leo and YZ CMi are both believed to be fully convective stars with a strong dipole magnetic field43,47. Although the topologies are similar, YZ CMi has  >30 times stronger stellar wind than AD Leo48. The difference in stellar winds from these M-dwarfs appears to be consistent with our evaluation of magnetic field complexity.

Table 1 Correlation coefficients (ρ) of magnetic fields between layers (P for photosphere, cL and cM for lower and middle chromosphere)
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Relationship to flare occurrence and energetics

The occurrence frequency of solar flares has been found to be related to the complexity of magnetic field structures in active regions49. From observations of the Transiting Exoplanet Survey Satellite (TESS), we found that the flare frequency distributions on these stars likely relate to the complexity of the magnetic field (SI 1D and Fig. S10). The correlation analysis described above suggests that AD Leo has the most complex large-scale magnetic field among the three stars. We notice that, compared to the other two stars, AD Leo has fewer low-energy flares and more high-energy flares (especially superflares). The difference in stellar winds from these M-dwarfs appears to be consistent with our evaluation of magnetic field complexity. This suggests that the occurrence frequency of superflares might be related to the complexity of large-scale magnetic fields on M-dwarfs. The potential explanation is that a richer small-scale field on the surface may produce a more complex field, which can lead to increased magnetic energy dissipation (thus more large flares and fewer small flares) and prune the flare frequency distribution.

Discussion

Our observations reveal stable large-scale magnetic fields in the lower and middle chromospheres of active M-dwarfs at a month-long timescale. The longitudinal magnetic fields at different atmospheric layers are generally correlated, which aligns well with those in solar observations27,45,50. Given the cancellation effect of opposite-polarity fields during disk integration, the average chromospheric fields could be as strong as the photospheric fields. The high magnetic field strengths we measured in the chromosphere, comparable to photospheric values, coupled with the complex structural variations identified across atmospheric layers, suggest that diffuse or even more complex magnetic field structures dominate the chromospheric topology of these active M-dwarfs. This finding aligns with observational evidence that these stars harbor abundant small-scale magnetic structures throughout their atmospheres25,35. This scenario also indicates that a substantial amount of magnetic energy is stored in the upper atmospheres of these stars, which may be released through flares, coronal mass ejections, and intense UV and X-ray radiation1,51. Such frequent eruptions and enhanced radiation likely have a large impact on the start and sustainability of life on nearby orbiting exoplanets32,52.

These findings provide critical constraints for understanding the energy budget responsible for heating and eruptions in the stellar upper atmospheres, thus enabling evaluation of the impact of various types of stellar magnetic activity on the habitability of surrounding exoplanets. Considering that chromospheric magnetic fields of stars other than the Sun have never been measured before, our study contributes observations that can inform investigations of magnetic fields in stellar upper atmospheres.

Methods

Spectropolarimetric observations

The Echelle SpectroPolarimetric Device for the Observation of Stars (ESPaDOnS) is an instrument that includes an achromatic polarimeter. This device has been stationed at the Cassegrain focus of the 3.6 m Canada-France-Hawaii Telescope at the top of Mauna Kea in Hawaii, USA, since early 200553. Meanwhile, NARVAL (not an acronym) is a stellar spectropolarimeter that was designed based on ESPaDOnS and was adapted to the specifics of the 2m Télescope Bernard Lyot (TBL), situated atop Pic du Midi in southwest France since 200654. Under polarimetric mode, ESPaDOnS and NARVAL provide complete coverage of the 370 to 1050 nm wavelength range and reach a resolution of R = 65,000 in a single exposure. During this run, polarimetric exposures are divided into four consecutive subexposures. Each subexposure collects data at different angles of the two half-wave rotatable Fresnel rhombs in the polarimetric module. This sequence is designed to eliminate spurious polarization signatures at first-order55. In the standard procedures to extract the spectropolarimetric data, “Null” spectra are obtained by pair-processing sub-exposures corresponding to identical azimuths of the retarding plate or Cassegrain bonnette42, in parallel with polarized spectra. These “Null” spectra are not expected to contain any signal and should be pure noise if there is no spurious polarized signature in the V profile. We checked our V profile if any significant signal can be seen in the “Null” profile and whether it is similar to the V profile in order to exclude spurious signatures. The total efficiency of the instrument, including the spectrograph and CCD detector, is around 12%. The software package Libre-ESpRIT42,56 is used for extracting the normalized, reduced data for unpolarized and polarized spectra corresponding to each observing sequence. All reduced spectra used in this work can be extracted from the PolarBase database57.

We only used the data from 2005-2019 observed with polarimetric mode, with the peak S/N of the Stokes V signal over 60. The basic stellar parameters of the selected M-dwarfs used in this work are taken from the study dedicated to their large-scale surface magnetic topologies40. The observation time is phased with the ephemeris: HJD = HJD0 + ProtE, where the zero point of heliocentric Julian dates is chosen equal to HJD0 = 2,453,950.0 and the rotational periods have been estimated from Zeeman-Doppler Imaging (ZDI) inversion40. Due to the Earth’s orbit, ground-based observations for our targets have only a few-month window per year, known as an epoch. A detailed observation log, including the information, can be found in Source Data.

Magnetic fields measurement from the photosphere to the middle chromosphere

Using the Least Squares Deconvolution (LSD, detailed below) method42, we extracted average photospheric information from thousands of photospheric spectral lines and produced mean Stokes I and V profiles for all the unpolarized and polarized spectra, respectively. The longitudinal (line-of-sight projected) component of the stellar-disk integrated photospheric magnetic field 〈Bp〉 was estimated from the first-order moment of the Stokes V profile based on the center-of-gravity (COG) method42,58 decribed below. The cores of the Calcium II infrared triplet (Ca IRT) at wavelengths 849.8 nm, 854.2 nm, and 866.2 nm, typically formed in the middle chromosphere1,59, were analyzed. We applied the LSD method to these lines and subtracted the photospheric components to obtain the pure chromospheric Stokes I and V profiles (Fig. S1). The mean longitudinal magnetic field in the middle chromosphere 〈BcM〉 was estimated from these profiles using the COG method. Simultaneously, we measured the lower chromospheric longitudinal magnetic field 〈BcL〉 from the pure emitting hydrogen Hα line at 656.3 nm (Details in SI 1A & Fig. S2)45,60.

Mean line profiles derived by the Least-Squares Deconvolution method

Least-squares deconvolution (LSD) is a cross-correlation method, enabling the acquisition of average unpolarized and polarized line profiles with an improved signal-to-noise ratio. This enhancement uses spectral features formed in approximately the same disc region and height42. Line lists for photospheric analysis are generated from spectrum synthesis via model atmospheres extracted from the Vienna Atomic Line Database (VALD)61. We predominantly employed stronger lines corresponding to the photospheric absorption of an early-to-mid M spectral type star, aligning with the characteristics of our targets. Lines that deviate from the average behavior of the photosphere, particularly chromospheric emissions and telluric lines, are excluded from the list. Approximately 5000 intermediate to strong atomic absorption spectral lines are simultaneously utilized to extract the average polarization information in line profiles. This approach yields typical noise levels of about 0.06% (relative to the unpolarized continuum level) per 1.8 km/s velocity bin, resulting in a multiplex gain in Stokes V S/N of  ~10 for the photospheric mask. We applied the same approach to the three lines of Ca IRT and obtained an S/N gain of  ~1.6. LSD is not applied to the Hα line. We analyze Hα individually since its broad Balmer wings break the LSD narrow-line approximation.

Mean longitudinal magnetic field

In observations of these low-mass stars, we obtain only disk-integrated Stokes profiles. Consequently, the quantity we derive with the center-of-gravity (COG) technique is the longitudinal field, 〈Bℓ〉, i.e., the first moment of the circular polarization (Stokes V) profile that represents the line-of-sight (LOS) integral over the visible stellar hemisphere. Because it is an LOS projection, 〈Bℓ〉 can take positive or negative values depending on whether the net signed flux points toward or away from the observer; its magnitude should not be interpreted as the absolute field strength at a specific atmospheric height. COG method is applicable for both the spatially resolved and unresolved profiles, and 〈Bℓ〉 can be obtained from the first moment of the normalized Stokes V 39,42,58:

$$\langle {B}_{\ell }\rangle=-\!\!2.14\times 1{0}^{-11}\frac{\int\upsilon V(\upsilon )d\upsilon }{{\lambda }_{0}{g}_{{{{\rm{eff}}}}}c\int[{I}_{c}-I(\upsilon )]d\upsilon },$$
(1)

where ν is the velocity to the line center, λ0 is the wavelength of the spectral line, c is the speed of light, and geff is the effective Landé factor. Note that this formula works for a magnetic field (kilo-Gauss) that is even stronger than that in the case of the weak field approximation (WFA), which assumes that the Zeeman splitting is significantly smaller than the line’s Doppler width. Under WFA, circular polarization signatures are proportional to 〈Bℓ〉 in the first order and can have the same estimation of 〈Bℓ〉 as the COG method for weak fields with a similar expression58. In a strong field, WFA breaks. However, the COG method is still valid. The corresponding uncertainty mainly results from the photon noise of Stokes I and V profiles. This formula is used to estimate the mean photospheric longitudinal field from the mean photospheric line profiles obtained using the LSD method, with typical geff = 1.24 and λ0 = 650 nm. In the chromosphere, the COG method is still valid and can be applied to chromospheric spectral lines62. In our work, we take geff = 1 and λ0 = 656.28 nm for the Hα line. For the LSD profiles of Ca IRT formed in the middle chromosphere, we have typical values of geff = 0.968 and λ0 = 858.56 nm, taking from the LSD process, and the geff of each line is taken from the VALD.

Subtract the photospheric components from CaIRT line profiles

Information about the middle chromosphere is extracted from the Ca IRT. Both the Stokes I and V signals of these three lines can be contaminated by photospheric signals from the stellar disk17. Considering the weak signal and similar profile shapes of the triplet, we applied the LSD method to the Ca IRT and obtained the mean Ca IRT Stokes I and V profiles. Assuming the wing of the broad absorption band (slightly outside the emission core) anchors to the photosphere in unpolarized Stokes I profiles, we use a Lorentzian model to fit the photospheric component17. This component has a broad enough Doppler profile, where the Zeeman splitting is negligible, and WFA is applicable (see Methods: Mean longitudinal magnetic field). Under the first-order, the corresponding photospheric model in circular polarized Stokes V profile is a derivation of the Lorentzian model multiplied by a fixed coefficient of  −4.67 × 10−12geff〈Bp〉λ0c, where 〈Bp〉 is the mean longitudinal photospheric field estimated from the LSD. Figure S1 shows an example for modeling the photospheric components in Stokes I&V. The residual profiles for both Stokes I&V are used to estimate the mean longitudinal middle chromospheric field 〈BcM〉. The emission core of Ca IRT should be purely from the chromosphere, and we measured its magnetic fields with the COG method.