Limb-darkening Effect Research Articles

Video of scenery during a total eclipse: luminance and effects of solar limb darkening

A video of darkening scenery during the 15 min prior to totality of the 21 August 2017 total solar eclipse is presented and discussed. The luminances of the scenes at 1 min intervals are obtained by averaging pixel data of stills from the video. The experimental results are compared to the theoretical model of uniform radiance from the exposed area of the Sun during the eclipse. The measured values deviate from the model since light from the solar disk decreases towards the edges of the Sun.

A SEA BASS on the Exoplanet HD 209458b

Abstract We present here the first application of Stellar and Exoplanetary Atmospheres Bayesian Analysis Simultaneous Spectroscopy (SEA BASS) on real data sets. SEA BASS is a scheme that enables the simultaneous derivation of four-coefficient stellar limb-darkening profiles, transit depths, and orbital parameters from exoplanetary transits at multiple wavelengths. It relies on the wavelength independence of the system geometry and on the reduced limb-darkening effect in the infrared. This approach has been introduced by Morello et al. (without the SEA BASS acronym), who discuss several tests on synthetic data sets. Here, we (1) improve on the original algorithm using multiple Spitzer/InfraRed Array Camera passbands and a more effective set of geometric parameters, (2) demonstrate its ability with Hubble Space Telescope/Space Telescope Imaging Spectrograph data sets by (3) measuring the HD 209458 stellar limb-darkening profile over multiple passbands in the 290–570 nm range with sufficient precision to rule out some theoretical models that have been adopted previously in the literature, and (4) simultaneously extracting the transmission spectrum of the exoplanet atmosphere. The higher photometric precision of the next-generation instruments, such as those on board the James Webb Space Telescope, will enable modeling the star–planet systems with unprecedented detail, and increase the importance of SEA BASS for avoiding the potential biases introduced by inaccurate stellar limb-darkening models.

Sensitivity study of thermal performance characteristics based on optical parameters for direct steam generation in parabolic trough collectors

Solar parabolic trough collector is one of the most potential Concentrated Solar Power (CSP) technologies with high dispatchability. The performance of the Parabolic Trough Collector (PTC) is significantly influenced by the distribution of radiant flux around the line focus receiver. In this paper, an accurate estimation of radiant flux around the line focus receivers of different parabolic trough collectors of varying aperture widths from 5 to 7.5 m has been studied. Effects of total internal reflection in the glass tube, glass tube absorptivity, receiver reflectivity, limb-darkening effect, surface errors and anti-reflective coating have been considered. A direct steam generation model (recirculation mode) has been developed and the effect of geometric errors in the collector on its optical and thermal performance characteristics has been discussed. The thermal efficiency of the direct steam generation collector is influenced by the optical characteristics of the collector and hence the thermal efficiency at different optical errors has been evaluated for the fore-mentioned commercial collectors under the influence of declination. The thermal efficiency is more sensitive to optical errors at low insolation levels and vice versa. For a change in tracking from 0 to 10 mrad, for PTC7.3 configuration, thermal efficiency drops by 0.58% at 1000 W/m2, and 2.02% at 300 W/m2. The thermal efficiency is also more sensitive to optical errors at higher values of declination. The collector of low geometric concentration ratio has a low sensitivity and low thermal efficiency and vice versa. Hence, the overall efficiency of different collectors at different optical errors has to be studied so as to obtain the appropriate collector configuration for specified optical errors and location of installation. Based on the analysis, graphical results which could aid in the selection of best collectors based on the latitude location, DNI and optical errors has been developed. The evaluation of collectors has also been extended towards power plant characteristics. The nominal power has been set to 50 MW. The location of Jodhpur in India has been selected and the total power generated per unit area has been studied for different collectors, for different optical errors. Based on the graphical results developed, appropriate collectors may be chosen for those locations based on their associated optical errors.

Absolute calibration of brightness temperature of the Venus disk observed by the Longwave Infrared Camera onboard Akatsuki

The Venus Climate Orbiter Akatsuki arrived at Venus in December 2015, and the Longwave Infrared Camera (LIR) onboard the spacecraft started making observations. LIR has acquired more than 8000 images during the first two Venusian years since orbit insertion without any serious faults. However, brightness temperature derived from LIR images contained an unexpected bias that related not to natural phenomena but to a thermal condition of the instrument. The bias could be partially eliminated by keeping the power supply unit for LIR always active, while the residual bias was simply correlated with the baffle temperature. Therefore, deep-space images were acquired at different baffle temperatures on orbit, and a reference table for eliminating the bias from images was prepared. In the corrected images, the brightness temperature was ~ 230 K at the center of the Venus disk, where the effect of limb darkening is negligible. The result is independent of the baffle temperature and consistent with the results of previous studies. Later, a laboratory experiment with the proto model of LIR showed that when the germanium (Ge) lens was heated, its actual temperature was slightly higher than the temperature measured by a thermal sensor attached to the lens holder. The experiment confirmed that transitory baffle heating accounted for the background bias found in the brightness temperature observed by LIR.

Photometric observations and light curve solutions of the W UMa stars NSVS 2244206, NSVS 908513, CSS J004004.7+385531 and VSX J062624.4+570907

Photometric observations in Sloan g′ and i′ bands of four W UMa stars, NSVS 2244206, NSVS 908513, CSS J004004.7+385531 and VSX J062624.4+570907, are presented. The light curve solutions reveal that all targets have overcontact configurations with fillout factors within 0.15–0.26. Their components are G-K spectral types and are almost in thermal contact. They are also relatively close in size and luminosity: the radius ratios r2/r1 are within 0.75–0.90; the luminosity ratios l2/l1 are within 0.53–0.63. The results of the light curve solution of CSS J004004.7+385531 imply the weak limb-darkening effect of its primary component and possible presence of additional absorbing features in the system.

Photosphere, thermalization surface and spectra of black hole accretion flows under electron scattering

Abstract We examine the expected spectra of black hole accretion flows, which are assumed to be steady and spherically symmetric, considering the separation of the apparent photosphere and thermalization surface under electron scattering. Although the flow itself is spherical, the apparent shape of the photosphere is not spherical, since the density distribution gradually decreases with radius. Furthermore, due to electron scattering, the thermalization surface decouples with the photosphere, and is located deep inside the photosphere for scattering-dominated flows. Since the shape of the thermalization surface is also aspherical, the temperature there is not uniform, which causes a strong limb-darkening effect, and we may observe a non-blackbody spectrum with multi-color-type.

Populations of rotating stars

(abridged) We present a new tool for building synthetic colour-magnitude diagrams of coeval stellar populations. We study, from a theoretical point of view, the impact of axial rotation of stars on various observed properties of single-aged stellar populations: magnitude at the turnoff, photometric properties of evolved stars, surface velocities, surface abundances, and the impact of rotation on the age determination of clusters by an isochrone fitting. Stellar models for different initial masses, metallicities, and zero-age main sequence (ZAMS) rotational velocities are used for building interpolated stellar tracks, isochrones, and synthetic clusters for various ages and metallicities. The synthetic populations account for the effects of the initial distribution of the rotational velocities on the ZAMS, the impact of the inclination angle and the effects of gravity and limb darkening, unresolved binaries and photometric errors. Interpolated tracks, isochrones, and synthetic clusters can be computed through a public web interface. For clusters with a metallicity in the range [0.002, 0.014] and an age between 30 Myr and 1 Gyr, the fraction of fast rotators on the main sequence (MS) band is the largest just below the turnoff. This is a natural consequence of the increase in the MS lifetime due to rotation. The fraction of fast rotators one magnitude below the turnoff also increases with the age of the cluster between 30 Myr and 1 Gyr. There is an increase in the fraction of enriched stars when the metallicity decreases. We show that the use of isochrones computed from rotating stellar models with an initial rotation that is representative of the average initial rotation of the stars in clusters provides a reasonable estimate of the age, even though stars in a real cluster did not start their evolution with an identical initial rotation.

Asteroseismology of DAV white dwarf stars and G29–38

Asteroseismology is a powerful tool used for detecting the inner structure of stars, which is also widely used to study white dwarfs. We discuss the asteroseismology of DAV stars. The period-to-period fitting method is discussed in detail, including its reliability in detecting the inner structure of DAV stars. If we assume that all observed modes of some DAV stars are the l = 1 cases, the errors associated with model fitting will be always large. If we assume that the observed modes are composed of l = 1 and 2 modes, the errors associated with model fitting in this case will be small. However, there will be modes identified as l = 2 that do not have observed quintuplets. G29–38 has been observed spectroscopically and photometrically for many years. Thompson et al. made l modes identifications in the star through the limb darkening effect. With 11 known l modes, we also study the asteroseismology of G29–38, which reduces the blind l fittings and is a fair choice. Unfortunately, our two best-fitting models are not in line with the previous atmospheric results. Based on factors like only a few observed modes, stability and identification of eigenmodes, identification of spherical degrees, construction of physical and realistic models and so on, detecting the inner structure of DAV stars by asteroseismology needs further development.

Long Term Variations in Chromospheric Features from Ca-K Images at Kodaikanal

There is a collection of about 100 years of Ca-K line spectroheliograms at the Kodaikanal Observatory (KKL) obtained on daily basis with a single instrument that can be used to study long term variations of various chromospheric features. All the Ca-K images have been digitized using specially developed digitizers with uniform and highly stable light source, high quality lens and 4k×4k format CCD camera. The digitization has been carried out in a room with controlled temperature and humidity. The digitized data are in 16-bit format with pixel resolution of 0.86 arcsec. The digitized images have been calibrated by a process that includes flat-fielding, density to intensity conversion, centering the image, and rotation of the image to make the solar north pole in the fixed direction. Then we applied correction for the limb darkening effect and also made the background in the image uniform. The image background was normalized to unity that enabled us to use the intensity contrast to identify different features, such as plages, enhanced (EN), active (AN), and quite network on images and classified them by using different image contrast and area threshold values. After several experiments with different threshold values for different features and careful analysis of a large number of images, we could fix the threshold values of intensity contrast larger than 1.35 and area larger than 1 arcmin2 for plages, larger than 1.35 but area less than 1 arcmin2 for EN, and between 1.25 – 1.35 for AN. We compared the quarterly averaged and half yearly averaged plage areas obtained from KKL with the Mount Wilson (MWO) data and sunspot number. We find that the plage area extracted from the KKL is highly correlated with the MWO plage area, though there is a slight difference between the two data set in cycle 19. The plage area of KKL is also highly correlated with the sunspot number. The areas of EN and AN are also found to have smaller quasi-periodic variations apart from the solar cycle variations.

Photosphere and Spectrum of Black-Hole Accretion Flow Near to the Eddington Rate

Abstract We examine the observational appearance of optically thick, spherically symmetric accretion onto a black hole at around the critical accretion rate. We find that the apparent photosphere deviates markedly from a sphere, but becomes a parabolic-like shape. In addition, the observed temperature over the apparent photosphere is not uniform, but varies significantly from the center to the limb, which shows a strong limb-darkening effect. As a result, the expected spectrum is not a simple blackbody, but becomes a multi-color-type blackbody.

Variation of Spectral Radiance of the Zenith Sky During the Annular Eclipse on May 21, 2012

The absolute brightness of the zenith sky was measured using a simple calibrated spectrometer during the annular solar eclipse event on May 21, 2012 in Fujioka City, Japan (36.2924°N, 139.0823°E). The sensitivity of the spectrometer was calibrated as a function of wavelength between 400 and 700 nm with an integral sphere. The brightness of the sky decreased to 6 % of its usual condition at the maximum magnitude of the annular eclipse of 0.95 for all wavelengths. The curve describing the variation of sky brightness accords well with the total luminosity of the solar disk estimated by a simple model that accounts for the limb darkening effect. This study provides zenith sky radiance as a function of wavelength and solar elevation angle, which is useful for the investigation of new optical instruments for atmospheric studies.

ILLUMINANCE DURING A SOLAR ECLIPSE WITH LIMB DARKENING: A MATHEMATICAL MODEL

We present a mathematical model that predicts the variation of illuminance during a solar eclipse, considering continuous effects of limb darkening. We assume that (1) the Sun and the Moon constitute perfect spheres, (2) the Moon crosses the Sun with a constant apparent velocity, and (3) sunspots, prominences, and coronae can be neglected. We compare predictions of this model with actual measurements made by M<TEX>$\ddot{o}$</TEX>llmann & Vollmer (2006) during a total solar eclipse in Turkey, and with predictions of existing models. The new model is shown to describe the actual phenomenon more accurately than existing models.

Limb Darkening study using Venus nightside infrared spectra from VIRTIS-Venus Express data

The Limb Darkening (LD) effect consists in an attenuation of the measured radiance at increasing emergence angles, due to the larger portion of the atmosphere traversed by the radiation observed at higher emergence angles. The behaviour of radiance emerging with atmosphere as function of the emergence angle (i.e., the Limb Darkening Function) is related to several atmosphere and cloud properties, e.g., atmospheric opacity, temperature lapse rate, aerosol single scattering albedo, optical depth, cloud particles size, cloud scale height. In addition, the retrieval of the Limb Darkening Function allows the computation of radiances as they would be acquired in Nadir observations, which is an important process of data reduction.In this work Limb Darkening is studied on infrared images of the Venus nightside. The images are provided by the VIRTIS instrument (Visible and InfraRed Thermal Imaging Spectrometer) onboard the Venus Express mission. Analysis is performed at wavelengths characterised by emission coming from below the clouds (i.e., 1.03μm, 1.31μm, 1.74μm, 2.30μm) and from upper clouds (i.e., 3.72μm, 4.00μm), respectively.In the first case, the Limb Darkening Function is retrieved at different latitude ranges (−40° to 0°, −50° to −40°, −60° to −50°, −70° to −60°) and different optical depths. To this end, a novel approach is developed, based on a statistical analysis of observed data. This statistical analysis is possible thanks to the very extended dataset provided by the VIRTIS instrument. These empirical Limb Darkening Functions are then compared and interpreted with the aid of radiative transfer models.An agreement between our results and results of synthetic models is found between −60° and 0°, allowing us to consider our approach well validated. Furthermore, by means of a detailed analysis of the LDFs obtained at different latitudes, it is possible to infer a slight increase of the mode3/mode2 density ratio between −60° and −50°, that becomes larger between −70° and −60°: the mode3/mode2 ratio inferred at these latitudes is about two times its equatorial value.The study of Limb Darkening from upper clouds region allows to obtain the upper cloud scale height, its variation with the atmospheric height, and the brightness temperature at different latitudes (the latitude intervals used are the same of the low atmosphere study).All the latitudes are characterised by a thin layer at the upper clouds base having a short scale height (i.e., <1km). Above that layer, scale height is calculated for every latitude interval.Between −50° and 0°, the retrieved scale height is about 4km (i.e., 3.7±0.3km between −40° and 0° and 4.5±0.8km between −50° and −40°) and is constant with the height.Between −60° and −50°, a scale height of 4−5km is found at low temperatures (226–231K), whereas at higher temperature, we are able to give a lower (2–3km) and an upper (7–9km) limit.Between −70° and −60° no Limb Darkening is observed, suggesting a low scale height (i.e., <1km), as well as a low lapse rate.

The effects of a solar eclipse on photo-oxidants in different areas of China

Abstract. This study investigates the effects of the total solar eclipse of 22 July 2009 on surface ozone and other photo-oxidants over China. A box model was used to study the sensitivity of ozone to the limb darkening effect during an eclipse event, and to show that the impact on ozone is small (less than 0.5 %). In addition, the regional model WRF-Chem was applied to study the effects of the eclipse on meteorological and chemical parameters, focusing on different regions in China. Chemical and meteorological observations were used to validate the model and to show that it can capture the effects of the total solar eclipse well. Model calculations show distinct differences in the spatial distributions of meteorological and chemical parameters with and without the eclipse. The maximum impacts of the eclipse occur over the area of totality, where there is a decrease in surface temperature of 1.5 °C and decrease in wind speed of 1 m s−1. The maximum impacts on atmospheric pollutants occur over parts of north and east China where emissions are greater, with an increase of 5 ppbv in NO2 and 25 ppbv in CO and a decrease of 10 ppbv in O3 and 4 ppbv in NO. This study also demonstrates the effects of the solar eclipse on surface photo-oxidants in different parts of China. Although the sun was obscured to a smaller extent in polluted areas than in clean areas, the impacts of the eclipse in polluted areas are greater and last longer than they do in clean areas. In contrast, the change in radical concentrations (OH, HO2 and NO3) in clean areas is much larger than in polluted areas mainly because of the limited source of radicals in these areas. The change in radical concentrations during the eclipse reveals that nighttime chemistry dominates in both clean and polluted areas. As solar eclipses provide a natural opportunity to test more thoroughly our understanding of atmospheric chemistry, especially that governed by photolysis, a comprehensive experimental campaign during a future solar eclipse is highly desirable.

Accurate stellar rotational velocities using the Fourier transform of the cross correlation maximum

We propose a method for measuring the projected rotational velocity $v sin i$ with high-precision even in spectra with blended lines. Though not automatic, our method is designed to be applied systematically to large numbers of objects without excessive computational requirement. We calculate the cross correlation function (CCF) of the object spectrum against a zero-rotation template and use the Fourier transform (FT) of the CCF central maximum to measure the parameter $v sin i$ taking the limb darkening effect and its wavelength dependence into account. The procedure also improves the definition of the CCF base line resulting in errors related to the continuum position under 1 % even for $vsin i$ = 280 km/s. Tests with high-resolution spectra of F-type stars indicate that an accuracy well below 1 % can be attained even for spectra where most lines are blended. We have applied the method to measure $v sin i$ in 251 A-type stars. For stars with $vsin i$ over 30 km/s (2-3 times our spectra resolution) our measurement errors are below 2.5 % with a typical value of 1%. We compare our results with Royer et al. (2002a) using 155 stars in common, finding systematic differences of about 5 % for rapidly rotating stars.

Observational Appearance and Spectrum of Black-Hole Winds

We examine the observational appearance of an optically thick, spherically symmetric, relativistic wind (a black-hole wind), focusing our attention on the emerging spectrum. In a relativistic flow, the apparent optical depth becomes small (large) in the downstream (upstream) direction due to the Lorentz-Fitzgerald contraction. As a result, the location of the apparent photosphere of the wind is remarkably modified, and there appears a relativistic limb-darkening (center-brightening) effect, where the comoving temperature distribution of the apparent photosphere is enhanced (reduced) at the center (in the limb). In addition, due to the usual Doppler boost, the observed temperature distribution is greatly changed. These relativistic effects modify the expected spectrum. When the wind speed is subrelativistic, the observed temperature distribution is almost uniform, and the spectra of the black-hole wind are blackbody-like. When the wind speed becomes relativistic, on the other hand, the observed temperature distribution, $T_{\rm obs}$, exhibits a power-law nature of $T_{\rm obs}$$\propto$$r^{-1}$, where $r$ is the distance from the disk center, and the observed spectra $S_{\nu}$ become a modified blackbody, which has a power-law part of $S_{\nu}$$\propto$$\nu$, where $\nu$ is the frequency. We briefly examine the effects of the spatial variation of the wind speed and the mass-loss rate.

Water in the atmosphere of HD 209458b from 3.6-8 μm IRAC photometric observations in primary transit

The hot Jupiter HD 209458b was observed during primary transit at 3.6, 4.5, 5.8 and 8.0 μm using the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. We describe the procedures we adopted to correct for the systematic effects present in the IRAC data and the subsequent analysis. The light curves were fitted including limb-darkening effects and fitted using Markov Chain Monte Carlo and prayer-bead Monte Carlo techniques, obtaining almost identical results. The final depth measurements obtained by a combined Markov Chain Monte Carlo fit are at 3.6 μm, 1.469 ± 0.013 and 1.448 ± 0.013 per cent; at 4.5 μm, 1.478 ± 0.017 per cent; at 5.8 μm, 1.549 ± 0.015 per cent; and at 8.0 μm, 1.535 ± 0.011 per cent. Our results clearly indicate the presence of water in the planetary atmosphere. Our broad-band photometric measurements with IRAC prevent us from determining the additional presence of other molecules such as CO, CO2 and methane for which spectroscopy is needed. While water vapour with a mixing ratio of combined with thermal profiles retrieved from the day side may provide a very good fit to our observations, this data set alone is unable to resolve completely the degeneracy between water abundance and atmospheric thermal profile.

Observational Appearance and Spectrum of Black-Hole Winds with Supercritical Accretion Disks

Abstract We examine the observational appearance and expected spectra of an optically thick, spherically symmetric, relativistic wind (a black-hole wind), blowing off from the central region of a geometrically thick supercritical accretion disk. Due to the relativistic limb-darkening (center-brightening) effect as well as the usual Doppler boost, the black-hole wind becomes luminous as the wind speed increases. We found that the spectra of the black-hole wind is somewhat similar to a blackbody one, while the spectra of a naked supercritical accretion disk is known to have a flat spectral energy distribution (SED) when viewing from the pole-on direction. In the case of a black-hole wind with a supercritical accretion disk, the spectra generally becomes a hybrid type, but we found that in almost all cases the characteristic flat SED of a supercritical disk disappears. That is, when the speed of the wind gas is low, the apparent photosphere of the black-hole wind becomes larger than the supercritical region. In this case the spectra of a black-hole wind dominates. As the wind speed increases, the apparent photosphere shrinks and the spectra of the disk emergent. However, when the wind speed becomes sufficiently high, the inner part of the naked supercritical disk is not seen, even if the inclination angle is small.

MULTIPLE SCATTERING POLARIZATION OF SUBSTELLAR-MASS OBJECTS: T DWARFS

While there have been multiple observational programs aimed at detecting linear polarization of optical radiation emitted by ultracool dwarfs, there has been comparatively less rigorous theoretical analysis of the problem. The general expectation has been that the atmospheres of those substellar-mass objects with condensate clouds would give rise to linear polarization due to scattering. Because of rotation-induced non-sphericity, there is expected to be incomplete cancellation of disk-integrated net polarization and thus a finite polarization. For cloudless objects, however, only molecular Rayleigh scattering will contribute to any net polarization and this limit has not been well studied. Hence in this paper we present a detailed multiple scattering analysis of the polarization expected from those T-dwarfs whose spectra show absence of condensates. For this, we develop and solve the full radiative transfer equations for linearly polarized radiation. Only atomic and molecular Rayleigh scattering are considered to be the source of polarization. We compute the local polarization at different angular directions in a plane-parallel atmospheres calculated for the range of effective temperatures of T dwarfs and then average over the whole surface of the object. The effects of gravity and limb darkening as well as rotation induced non-sphericity are included. It is found that the amount of polarization decreases with the increase in effective temperature. It is also found that significant polarization at any local point in the atmosphere arises only in the optical (B-band). However, the disk integrated polarization--even in the B-band--is negligible. Hence we conclude that, unlike the case for cloudy L dwarfs, polarization of cloudless T-dwarfs by atomic and molecular scattering may not be detectable.

3D simulations of M star atmosphere velocities and their influence on molecular FeH lines

<i>Context. <i/>The measurement of line broadening in cool stars is in general a difficult task. In order to detect slow rotation or weak magnetic fields, an accuracy of 1 km s<sup>-1<sup/> is needed. In this regime the broadening from convective motion becomes important. We present an investigation of the velocity fields in early to late M-type star hydrodynamic models, and we simulate their influence on molecular line shapes. The M star model parameters range between of and effective temperatures from 2500 K to 4000 K.<i>Aims. <i/>Our aim is to characterize the - and -dependence of the velocity fields and express them in terms of micro- and macro-turbulent velocities in the one dimensional sense. We present a direct comparison between 3D hydrodynamical velocity fields and 1D turbulent velocities. The velocity fields strongly affect the line shapes of , and it is our goal to give a rough estimate of the and parameter range in which 3D spectral synthesis is necessary and where 1D synthesis suffices. We want to distinguish between the velocity-broadening from convective motion and the rotational- or Zeeman-broadening in M-type stars we are planning to measure. For the latter, lines are an important indicator.<i>Methods. <i/>In order to calculate M-star structure models, we employ the 3D radiative-hydrodynamics (RHD) code CO<sup>5<sup/>BOLD. The spectral synthesis in these models is performed with the line synthesis code LINFOR3D. We describe the 3D velocity fields in terms of a Gaussian standard deviations and project them onto the line of sight to include geometrical and limb-darkening effects. The micro- and macro-turbulent velocities are determined with the “curve of growth” method and convolution with a Gaussian velocity profile, respectively. To characterize the and dependence of lines, the equivalent width, line width, and line depth are examined.<i>Results. <i/>The velocity fields in M-stars strongly depend on and . They become stronger with decreasing and increasing . The projected velocities from the 3D models agree within ~100 m s<sup>-1<sup/> with the 1D micro- and macro-turbulent velocities. The line quantities systematically depend on and .<i>Conclusions. <i/>The influence of hydrodynamic velocity fields on line shapes of M-type stars can well be reproduced with 1D broadening methods. lines turn out to provide a means to measure and in M-type stars. Since different lines all behave in a similar manner, they provide an ideal measure for rotational and magnetic broadening.