Rossiter-McLaughlin Effect Research Articles

A Well-aligned Orbit for the 45 Myr-old Transiting Neptune DS Tuc Ab

Abstract DS Tuc Ab is a Neptune-sized planet that orbits around a G star in the 45 Myr old Tucana-Horologium moving group. Here, we report the measurement of the sky-projected angle between the stellar spin axis and the planet’s orbital axis, based on the observation of the Rossiter–McLaughlin effect during three separate planetary transits. The orbit appears to be well aligned with the equator of the host star, with a projected obliquity of . In addition to the distortions in the stellar absorption lines due to the transiting planet, we observed variations that we attribute to large starspots, with angular sizes of tens of degrees. The technique that we have developed for simultaneous modeling of starspots and the planet-induced distortions may be useful in other observations of planets around active stars.

Detection of neutral atomic species in the ultra-hot Jupiter WASP-121b

ABSTRACT The class of ultra-hot Jupiters comprises giant exoplanets undergoing intense irradiation from their host stars. They have proved to be a particularly interesting population for their orbital and atmospheric properties. One such planet, WASP-121b, is in a highly misaligned orbit close to its Roche limit, and its atmosphere exhibits a thermal inversion. These properties make WASP-121b an interesting target for additional atmospheric characterization. In this paper, we present analyses of archival high-resolution optical spectra obtained during transits of WASP-121b. We model the Rossiter-McLaughlin effect and the Centre-to-Limb Variation and find that they do not significantly affect the transmission spectrum in this case. However, we discuss scenarios where these effects warrant more careful treatment by modelling the WASP-121 system and varying its properties. We report a new detection of atmospheric absorption from H α in the planet with a transit depth of $1.87\pm 0.11{{\ \rm per\ cent}}$. We further confirm a previous detection of the Na i doublet, and report a new detection of Fe i via cross-correlation with a model template. We attribute the H α absorption to an extended Hydrogen atmosphere, potentially undergoing escape, and the Fe i to equilibrium chemistry at the planetary photosphere. These detections help to constrain the composition and chemical processes in the atmosphere of WASP-121b.

Can we detect the stellar differential rotation of WASP-7 through the Rossiter–McLaughlin observations?

ABSTRACT The Rossiter–McLaughlin (RM) effect is the radial velocity signal generated when an object transits a rotating star. Stars rotate differentially and this affects the shape and amplitude of this signal, on a level that can no longer be ignored with precise spectrographs. Highly misaligned planets provide a unique opportunity to probe stellar differential rotation via the RM effect, as they cross several stellar latitudes. In this sense, WASP-7, and its hot Jupiter with a projected misalignment of ∼90°, is one of the most promising targets. The aim of this work is to understand if the stellar differential rotation is measurable through the RM signal for systems with a geometry similar to WASP-7. In this sense, we use a modified version of soap3.0 to explore the main hurdles that prevented the precise determination of the differential rotation of WASP-7. We also investigate whether the adoption of the next generation spectrographs, like ESPRESSO, would solve these issues. Additionally, we assess how instrumental and stellar noise influence this effect and the derived geometry of the system. We found that, for WASP-7, the white noise represents an important hurdle in the detection of the stellar differential rotation, and that a precision of at least 2 m s−1 or better is essential.

Is there Na I in the atmosphere of HD 209458b?

HD 209458b was the first transiting planet discovered, and the first for which an atmosphere, in particular Na I, was detected. With time, it has become one of the most frequently studied planets, with a large diversity of atmospheric studies using low- and high-resolution spectroscopy. Here, we present transit spectroscopy observations of HD 209458b using the HARPS-N and CARMENES spectrographs. We fit the Rossiter-McLaughlin effect by combining radial velocity data from both instruments (nine transits in total), measuring a projected spin-orbit angle of − 1.6 ± 0.3 deg. We also present the analysis of high-resolution transmission spectroscopy around the Na I region at 590 nm, using a total of five transit observations. In contrast to previous studies where atmospheric Na I absorption is detected, we find that for all of the nights, whether individually or combined, the transmission spectra can be explained by the combination of the centre-to-limb variation and the Rossiter-McLaughlin effect. This is also observed in the time-evolution maps and transmission light curves, but at lower signal-to-noise ratio. Other strong lines such as Hα, Ca II IRT, the Mg I triplet region, and K I D1 are analysed, and are also consistent with the modelled effects, without considering any contribution from the exoplanet atmosphere. Thus, the transmission spectrum reveals no detectable Na I absorption in HD 209458b. We discuss how previous pioneering studies of this benchmark object may have overlooked these effects. While for some star–planet systems these effects are small, for other planetary atmospheres the results reported in the literature may require revision.

Detection of Na, K, and Hαabsorption in the atmosphere of WASP-52b using ESPRESSO

WASP-52b is a low-density hot Jupiter orbiting a moderately active K2V star. Previous low-resolution studies have revealed a cloudy atmosphere and found atomic Na above the cloud deck. Here we report on the detection of excess absorption at the Na doublet, the Hαline, and the K D1line. We derived a high-resolution transmission spectrum based on three transits of WASP-52b, observed with the ultra-stable, high-resolution spectrograph ESPRESSO at the Very Large Telescope array. We measured a line contrast of 1.09 ± 0.16% for Na D1, 1.31 ± 0.13% for Na D2, 0.86 ± 0.13% for Hα, and 0.46 ± 0.13% for K D1, with a line FWHM range of 11–22 km s−1. We also found that the velocity shift of these detected lines during the transit is consistent with the planet’s orbital motion, thus confirming their planetary origin. We did not observe any significant net blueshift or redshift that could be attributed to planetary winds. We used activity indicator lines as control but found no excess absorption. However, we did notice signatures arising from the Center-to-Limb variation (CLV) and the Rossiter-McLaughlin (RM) effect at these control lines. This highlights the importance of the CLV + RM correction in correctly deriving the transmission spectrum, which, if not corrected, could resemble or cancel out planetary absorption in certain cases. WASP-52b is the second non-ultra-hot Jupiter to show excess Hαabsorption after HD 189733b. Future observations targeting non-ultra-hot Jupiters that show Hαcould help reveal the relation between stellar activity and the heating processes in the planetary upper atmosphere.

High-resolution spectroscopy and spectropolarimetry of the total lunar eclipse January 2019

Context. Observations of the Earthshine off the Moon allow for the unique opportunity to measure the large-scale Earth atmosphere. Another opportunity is realized during a total lunar eclipse which, if seen from the Moon, is like a transit of the Earth in front of the Sun. Aims. We thus aim at transmission spectroscopy of an Earth transit by tracing the solar spectrum during the total lunar eclipse of January 21, 2019. Methods. Time series spectra of the Tycho crater were taken with the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) at the Large Binocular Telescope in its polarimetric mode in Stokes IQUV at a spectral resolution of 130 000 (0.06 Å). In particular, the spectra cover the red parts of the optical spectrum between 7419–9067 Å. The spectrograph’s exposure meter was used to obtain a light curve of the lunar eclipse. Results. The brightness of the Moon dimmed by 10.m75 during umbral eclipse. We found both branches of the O2 A-band almost completely saturated as well as a strong increase of H2O absorption during totality. A pseudo O2 emission feature remained at a wavelength of 7618 Å, but it is actually only a residual from different P-branch and R-branch absorptions. It nevertheless traces the eclipse. The deep penumbral spectra show significant excess absorption from the Na I 5890-Å doublet, the Ca II infrared triplet around 8600 Å, and the K I line at 7699 Å in addition to several hyper-fine-structure lines of Mn I and even from Ba II. The detections of the latter two elements are likely due to an untypical solar center-to-limb effect rather than Earth’s atmosphere. The absorption in Ca II and K I remained visible throughout umbral eclipse. Our radial velocities trace a wavelength dependent Rossiter-McLaughlin effect of the Earth eclipsing the Sun as seen from the Tycho crater and thereby confirm earlier observations. A small continuum polarization of the O2 A-band of 0.12% during umbral eclipse was detected at 6.3σ. No line polarization of the O2 A-band, or any other spectral-line feature, is detected outside nor inside eclipse. It places an upper limit of ≈0.2% on the degree of line polarization during transmission through Earth’s atmosphere and magnetosphere.

Evidence for Spin–Orbit Alignment in the TRAPPIST-1 System

Abstract In an effort to measure the Rossiter–McLaughlin effect for the TRAPPIST-1 system, we performed high-resolution spectroscopy during transits of planets e, f, and b. The spectra were obtained with the InfraRed Doppler spectrograph on the Subaru 8.2 m telescope, and were supplemented with simultaneous photometry obtained with a 1 m telescope of the Las Cumbres Observatory Global Telescope. By analyzing the anomalous radial velocities, we found the projected stellar obliquity to be λ = 1 ± 28° under the assumption that the three planets have coplanar orbits, although we caution that the radial-velocity data show correlated noise of unknown origin. We also sought evidence for the expected deformations of the stellar absorption lines, and thereby detected the “Doppler shadow” of planet b with a false-alarm probability of 1.7%. The joint analysis of the observed residual cross-correlation map including the three transits gave °. These results indicate that the the TRAPPIST-1 star is not strongly misaligned with the common orbital plane of the planets, although further observations are encouraged to verify this conclusion.

The Transit and Light Curve Modeller

ABSTRACT Transit and Light Curve Modeller (TLCM), a computer code with the purpose of analysing photometric time series of transits simultaneously with the out-of-transit light variations and radial velocity curves of transiting/eclipsing binary systems, is presented here. Joint light-curve and radial velocity fits are possible with it. The code is based on the combination of a genetic algorithm and simulated annealing. Binning, beaming, reflection, and ellipsoidal effects are included. Both objects may have their own luminosities and therefore one can use TLCM to analyse the eclipses of both exoplanet and well-detached binary systems. A simplified Rossiter–McLaughlin effect is included in the radial velocity fit, and drifts and offsets of different instruments can also be fitted. The impact of poorly known limb darkening on the Rossiter–McLaughlin effect is shortly studied. TLCM is able to manage red-noise effects via wavelet analysis. It is also possible to add parabolic or user-defined baselines and features to the code. I also predict that light variations due to beaming in some systems exhibiting radial velocity drift should be observed by, e.g. PLATO. The fit of the beaming effect is improved by invoking a physical description of the ellipsoidal effects, which has an impact on the modelling of the relativistic beaming; I also point out the difficulties that are stemming from the fact that beaming and first-order reflection effects have the same form of time dependence. Recipe is given, which describes how to analyse grazing transit events. The code is freely available.

Planet and star synergy at high-spectral resolution. A rationale for the characterization of exoplanet atmospheres

Context. Spectroscopy of exoplanet atmospheres at high-resolving powers is rapidly gaining popularity for measuring the presence of atomic and molecular species. While this technique is particularly robust against contaminant absorption in the Earth’s atmosphere, the non-stationary stellar spectrum, in the form of either Doppler shift or distortion of the line profile during planetary transits, creates a non-negligible source of noise that can alter or even prevent detection. Aims. Our aim was to use state-of-the art three-dimensional stellar simulations to directly remove the signature of the star from observations prior to cross correlation with templates for the planet’s atmosphere, which are commonly used to extract the faint exoplanet signal from noisy data. Methods. We computed synthetic spectra from 3D simulations of stellar convection resolved both spatially and temporally, and we coupled them with an analytical model reproducing the correct geometry of a transiting exoplanet. We applied the method to the early K-dwarf, HD 189733, and re-analyzed transmission and emission spectroscopy of its hosted exoplanet. In addition, we also analyzed emission spectroscopy of the non transiting exoplanet 51 Pegasi b, orbiting a solar-type star. Results. We find a significant improvement in planet detectability when removing the stellar spectrum with our method. In all cases, we show that the method is superior to a simple parametrisation of the stellar line profile or to the use of 1D stellar models. We show that this is due to the intrinsic treatment of convection in 3D simulations, which allows us to correctly reproduce asymmetric and blue-shifted spectral lines, and intrinsically model center-to-limb variation and Rossiter-McLaughlin effect potentially altering the interpretation of exoplanet transmission spectra. In the case of 51 Pegasi b, we succeed in confirming a previous tentative detection of the planet’s K-band spectrum due to the improved suppression of stellar residuals. Conclusions. Future high-resolution observations will benefit from the synergy with stellar spectroscopy and can be used to test the correct modeling of physical processes in stellar atmospheres. We highlight key improvements in modeling techniques and knowledge of opacity sources to extend this work to shorter wavelengths and later-type stars.

MASCARA-3b

We report the discovery of MASCARA-3b, a hot Jupiter orbiting its bright (V = 8.33) late F-type host every 5.55149 ± 0.00001 days in an almost circular orbit (e = 0.050−0.017+0.020). This is the fourth exoplanet discovered with the Multi-site All-Sky CAmeRA (MASCARA), and the first of these that orbits a late-type star. Follow-up spectroscopic measurements were obtained in and out of transit with the Hertzsprung SONG telescope. Combining the MASCARA photometry and SONG radial velocities reveals a radius and mass of 1.36 ± 0.05 RJup and 4.2 ± 0.2 MJup. In addition, SONG spectroscopic transit observations were obtained on two separate nights. From analyzing the mean out-of-transit broadening function, we obtain v sin i⋆ = 20.4 ± 0.4 km s−1. In addition, investigating the Rossiter-McLaughlin effect, as observed in the distortion of the stellar lines directly and through velocity anomalies, we find the projected obliquity to be λ = 1.2−7.4+8.2 deg, which is consistent with alignment.

The GAPS Programme with HARPS-N at TNG

Aims. In the framework of the GAPS project, we observed the planet-hosting star KELT-9 (A-type star, v sin i ~ 110 km s−1) with the HARPS-N spectrograph at the Telescopio Nazionale Galileo. In this work we analyse the spectra and the extracted radial velocities to constrain the physical parameters of the system and to detect the planetary atmosphere of KELT-9b. Methods. We extracted the mean stellar line profiles from the high-resolution optical spectra via an analysis based on the least-squares deconvolution technique. Then we computed the stellar radial velocities with a method optimised for fast rotators by fitting the mean stellar line profile with a purely rotational profile instead of using a Gaussian function. Results. The new spectra and analysis led us to update the orbital and physical parameters of the system, improving in particular the value of the planetary mass to Mp = 2.88 ± 0.35 MJup. We discovered an anomalous in-transit radial velocity deviation from the theoretical Rossiter-McLaughlin effect solution, calculated from the projected spin-orbit angle λ = −85.78 ± 0.46 degrees measured with Doppler tomography. We prove that this deviation is caused by the planetary atmosphere of KELT-9b, thus we call this effect Atmospheric Rossiter-McLaughlin effect. By analysing the magnitude of the radial velocity anomaly, we obtained information on the extension of the planetary atmosphere as weighted by the model used to retrieve the stellar mean line profiles, which is up to 1.22 ± 0.02 Rp. Conclusions. The Atmospheric Rossiter-McLaughlin effect will be observable for other exoplanets whose atmosphere has non-negligible correlation with the stellar mask used to retrieve the radial velocities, in particular ultra-hot Jupiters with iron in their atmospheres. The duration and amplitude of the effect will depend not only on the extension of the atmosphere, but also on the in-transit planetary radial velocities and on the projected rotational velocity of the parent star.

WOBBLE: A Data-driven Analysis Technique for Time-series Stellar Spectra

In recent years, dedicated extreme-precision radial velocity (EPRV) spectrographs have produced vast quantities of high-resolution, high-signal-to-noise time-series spectra for bright stars. These data contain valuable information for the dual purposes of planet detection via the measured RVs and stellar characterization via the co-added spectra. However, considerable data analysis challenges exist in extracting these data products from the observed spectra at the highest possible precision, including the issue of poorly-characterized telluric absorption features and the common use of an assumed stellar spectral template. In both of these examples, precision-limiting reliance on external information can be sidestepped using the data directly. Here we propose a data-driven method to simultaneously extract precise RVs and infer the underlying stellar and telluric spectra using a linear model (in the log of flux). The model employs a convex objective and convex regularization to keep the optimization of the spectral components fast. We implement this method in wobble, an open-source python package which uses TensorFlow in one of its first non-neural-network applications to astronomical data. In this work, we demonstrate the performance of wobble on archival HARPS spectra. We recover the canonical exoplanet 51 Pegasi b, detect the secular RV evolution of the M dwarf Barnard's Star, and retrieve the Rossiter-McLaughlin effect for the Hot Jupiter HD 189733b. The method additionally produces extremely high-S/N composite stellar spectra and detailed time-variable telluric spectra, which we also present here.

Minerva-Australis. I. Design, Commissioning, and First Photometric Results

The Minerva-Australis telescope array is a facility dedicated to the follow-up, confirmation, characterization, and mass measurement of planets orbiting bright stars discovered by the Transiting Exoplanet Survey Satellite (TESS)—a category in which it is almost unique in the Southern Hemisphere. It is located at the University of Southern Queensland’s Mount Kent Observatory near Toowoomba, Australia. Its flexible design enables multiple 0.7 m robotic telescopes to be used both in combination, and independently, for high-resolution spectroscopy and precision photometry of TESS transit planet candidates. Minerva-Australis also enables complementary studies of exoplanet spin–orbit alignments via Doppler observations of the Rossiter–McLaughlin effect, radial velocity searches for nontransiting planets, planet searches using transit timing variations, and ephemeris refinement for TESS planets. In this first paper, we describe the design, photometric instrumentation, software, and science goals of Minerva-Australis, and note key differences from its Northern Hemisphere counterpart, the Minerva array. We use recent transit observations of four planets, WASP-2b, WASP-44b, WASP-45b, and HD 189733b, to demonstrate the photometric capabilities of Minerva-Australis.

TESS Spots a Compact System of Super-Earths around the Naked-eye Star HR 858

Abstract Transiting Exoplanet Survey Satellite (TESS) observations have revealed a compact multiplanet system around the sixth-magnitude star HR 858 (TIC 178155732, TOI 396), located 32 pc away. Three planets, each about twice the size of Earth, transit this slightly evolved, late F-type star, which is also a member of a visual binary. Two of the planets may be in mean motion resonance. We analyze the TESS observations, using novel methods to model and remove instrumental systematic errors, and combine these data with follow-up observations taken from a suite of ground-based telescopes to characterize the planetary system. The HR 858 planets are enticing targets for precise radial velocity observations, secondary eclipse spectroscopy, and measurements of the Rossiter–McLaughlin effect.

HD 2685 b: a hot Jupiter orbiting an early F-type star detected by TESS

We report on the confirmation of a transiting giant planet around the relatively hot (Teff = 6801 ± 76 K) star HD 2685, whose transit signal was detected in Sector 1 data of NASA’s TESS mission. We confirmed the planetary nature of the transit signal using Doppler velocimetric measurements with CHIRON, CORALIE, and FEROS, as well as using photometric data obtained with the Chilean-Hungarian Automated Telescope and the Las Cumbres Observatory. From the joint analysis of photometry and radial velocities, we derived the following parameters for HD 2685 b: P = 4.12688−0.00004+0.00005 days, e = 0.091−0.047+0.039, MP = 1.17 ± 0.12 MJ, and RP =1.44 ± 0.05 RJ. This system is a typical example of an inflated transiting hot Jupiter in a low-eccentricity orbit. Based on the apparent visual magnitude (V = 9.6 mag) of the host star, this is one of the brightest known stars hosting a transiting hot Jupiter, and it is a good example of the upcoming systems that will be detected by TESS during the two-year primary mission. This is also an excellent target for future ground- and space-based atmospheric characterization as well as a good candidate for measuring the projected spin-orbit misalignment angle through the Rossiter–McLaughlin effect.

High-resolution spectroscopy of Boyajian’s star during optical dimming events

Boyajian's star is an apparently normal main sequence F-type star with a very unusual light curve. The dipping activity of the star, discovered during the Kepler mission, presents deep, asymmetric, and aperiodic events. Here we present high resolution spectroscopic follow-up during some dimming events recorded post-Kepler observations, from ground-based telescopes. We analise data from the HERMES, HARPS-N and FIES spectrographs to characterise the stellar atmosphere and to put some constraints on the hypotheses that have appeared in the literature concerning the occulting elements. The star's magnetism, if existing, is not extreme. The spots on the surface, if present, would occupy 0.02% of the area, at most. The chromosphere, irrespective of the epoch of observation, is hotter than the values expected from radiative equilibrium, meaning that the star has some degree of activity. We find no clear evidence of the interstellar medium nor exocoments being responsible for the dimmings of the light curve. However, we detect at 1-2 sigma level, a decrease of the radial velocity of the star during the first dip recorded after the \emph{\emph{Kepler}} observations. We claim the presence of an optically thick object with likely inclined and high impact parameter orbits that produces the observed Rossiter-McLaughlin effect.

The Misaligned Orbit of the Earth-sized Planet Kepler-408b

Abstract Kepler-408 is one of the 33 planet-hosting Kepler stars for which asteroseismology has been used to investigate the orientation of the stellar rotation axis relative to the planetary orbital plane. The transiting hot Earth, Kepler-408b, has an orbital period of 2.5 days and a radius of 0.86 R ⊕, making it much smaller than the planets for which spin–orbit alignment has been studied using the Rossiter–McLaughlin effect. Because conflicting asteroseismic results have been reported in the literature, we undertake a thorough re-appraisal of this system and perform numerous checks for consistency and robustness. We find that the conflicting results are due to the different models for the low-frequency noise in the power spectrum. A careful treatment of the background noise resolves these conflicts, and shows that the stellar inclination is degrees. Kepler-408b is, by far, the smallest planet known to have a significantly misaligned orbit.

Role of the Rossiter-McLaughlin effect in the study of close binaries

This paper is devoted to binary stars belonging to the class of eclipsing-variable systems. Photometric and spectroscopic analysis of eclipses allows us to determine geometric parameters of the orbit and physical characteristics of stellar components as well as inclinations of stellar equators to the orbital plane. Estimations of inclinations can be obtained from measurement of the Rossiter-McLaughlin effect, which is discussed using examples of some eccentric binaries with an anomalous apsidal effect. Our task is to find the complete spectrum of solutions of the equation of apsidal motion, depending on the inclinations of the polar axes of the components to the orbital one for these systems, based on their individual spectroscopic and photometric observational data. The matrix of solutions allows us to select those pairs of polar inclinations that provide agreement with the observational apsidal period.

Accurate Computation of Light Curves and the Rossiter–McLaughlin Effect in Multibody Eclipsing Systems

Abstract We present an efficient method for computing the visible flux for each body during a multibody eclipsing event for all commonly used limb-darkening laws. Our approach follows the idea put forth by Pál to apply Green’s theorem on the limb-darkening integral, thus transforming the two-dimensional flux integral over the visible disk into a one-dimensional integral over the visible boundary. We implement this idea through an iterative process that combines a fast method for describing the visible boundary of each body with a fast numerical integration scheme to compute the integrals. For the two-body case, our method compares well in speed with both that of Mandel & Agol and that of Giménez. The strength of the method is that it works for any number of spherical bodies with a computational accuracy that is adjustable through the use of a tolerance parameter. Most significantly, the method offers two main advantages over previously used techniques: (i) it can employ a multitude of limb-darkening laws, including all of the commonly used ones; and (ii) it can compute the Rossiter–McLaughlin effect for rigid-body rotation with an arbitrary orientation of the rotation axis using any of these limb-darkening laws. In addition, we can compute the Rossiter–McLaughlin effect for stars exhibiting differential rotation using the quadratic limb-darkening law. We provide the mathematical background for the method and explain in detail how to implement the technique with the help of several examples and codes that we make available.

Activity induced variation in spin-orbit angles as derived from Rossiter–McLaughlin measurements

One of the most powerful methods used to estimate sky-projected spin-orbit angles of exoplanetary systems is through a spectroscopic transit observation known as the RossiterMcLaughlin (RM) effect. So far mostly single RM observations have been used to estimate the spin-orbit angle, and thus there have been no studies regarding the variation of estimated spin-orbit angle from transit to transit. Stellar activity can alter the shape of photometric transit light curves and in a similar way they can deform the RM signal. In this paper we present several RM observations, obtained using the HARPS spectrograph, of known transiting planets that all transit extremely active stars, and by analyzing them individually we assess the variation in the estimated spin-orbit angle. Our results reveal that the estimated spin-orbit angle can vary significantly (up to ~42°) from transit to transit, due to variation in the configuration of stellar active regions over different nights. This finding is almost two times larger than the expected variation predicted from simulations. We could not identify any meaningful correlation between the variation of estimated spin-orbit angles and the stellar magnetic activity indicators. We also investigated two possible approaches to mitigate the stellar activity influence on RM observations. The first strategy was based on obtaining several RM observations and folding them to reduce the stellar activity noise. Our results demonstrated that this is a feasible and robust way to overcome this issue. The second approach is based on acquiring simultaneous high-precision short-cadence photometric transit light curves using TRAPPIST/SPECULOOS telescopes, which provide more information about the stellar active region’s properties and allow a better RM modeling.