arXiv subjects

Saskia Hekker

Publications and source records attributed to Saskia Hekker.

At least 19 recordsLinked to original sources

arXiv2026

The Twentieth Data Release of the Sloan Digital Sky Survey: First All-Sky BOSS Spectra, eROSITA-SDSS-V Mapper Coordinated Observations, and a Preview of the Local Volume Mapper

This paper presents the twentieth data release (DR20) from the Sloan Digital Sky Survey, the third data release of its fifth generation (SDSS-V). SDSS-V is a panoptic spectroscopy survey that is mapping the stars, gas, and galaxies through three scientific programs: the Milky Way Mapper (MWM), the Local Volume Mapper (LVM), and the Black Hole Mapper (BHM). DR20 presents the first optical (BOSS) SDSS-V spectra from southern hemisphere for the MWM and BHM surveys; new optical MWM and BHM data from the northern hemisphere are also available, for a total over 3 million spectra of 1.5 million stars and half a million galaxies and quasars, with galactic and extragalactic x-ray targets coordinate with eROSITA DR2. DR20 includes integral field spectroscopy maps from LVM of six targets and 169 tiles, spanning Galactic HII regions, planetary nebulae, and nearby galaxies. Additionally, eighteen value added catalogs are also released with DR20, based on SDSS-V MWM and BHM data, and we present a new LVM visualization tool including an RGB HiPS map as a value added product.

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arXiv2026

Oscillations of red giant stars with magnetic damping in the core. II. Mixed mode visibilities on the red-giant branch

Mode visibilities can be estimated from observed power spectra or from theory by making assumptions about the damping processes occurring in the star. However, a quantitative comparison between the two approaches was so far not feasible due to observational biases. The biases arise from the fact that in observations, the power spectrum is divided into frequency segments in which modes of a certain spherical degree are expected to dominate. In this work, we used synthetic power spectra to calculate the visibility as it has been done in observations and compare it with published observed visibilities to quantify the influence of the biases. We find that, taking the biases into account, the observed spatial response of the dipole modes is 1.47, which is closer to the theoretical value than previous estimates. In particular, we predict that the normalized dipole mode visibility of late red-giant branch (RGB) stars might be overestimated by up to 20% in published observations. For stars with depressed dipole modes, we find that the normalized dipole mode visibilities estimated in observational studies might be overestimated by 20% throughout their entire evolution on the RGB. The quadrupole mode visibility, on the other hand, appears to be largely unaffected by the biases, expect on the late RGB. In addition, we investigated the evolution of the visibility and detectability of the mixed mode signature while testing different prescriptions for the energy loss caused by a strong internal magnetic field in the stellar core. We argue that taking into account the inner turning point of the g-mode cavity could allow a portion of the mode energy to be preserved when interacting with a strong magnetic field. We further show that such partial dissipation allows the mixed mode signature to be both present or absent in the observable power spectra, which is consistent with observations.

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arXiv2026

Hidden oscillations in plain sight: identification of seismically unresolved red-giant asteroseismic binary candidates

Light curves of oscillating stars provide valuable insights into the stellar interiors. When oscillations from a pair of stars are captured within a single photometric aperture, they can be considered as potential asteroseismic binaries (ABs). If the two stars oscillate at similar frequency ranges, the superpositioned oscillation patterns appear as if from a single star, leading to inaccurate asteroseismic parameters. We investigate seismically unresolved AB candidates consisting of two red-giant stars observed by Kepler. We directly compare the power density spectra (PDSs) of blended and separated oscillations from both stars, and examine the impact of oscillations from two stars on asteroseismic and stellar parameters. We selected APOKASC3 stars with at least one neighboring source within 20 arcsec and show oscillations in similar frequency ranges. We focus on the systems where the light curves from each star in AB candidates are available or can be extracted with a custom mask. We identified 6 seismically unresolved AB candidates whose PDS morphologies change noticeably across light curves extracted with different apertures. Oscillations from two stars in a PDS cause inaccurate mode identification and bias the seismic parameters. These biases propagate into stellar properties: masses and radii for the 6 AB candidates differ by up to about 3 and 2 times relative to the individual stars, respectively. For the AB candidate with the most complex PDS, core properties become unreliable, with the coupling factor often being overestimated. We checked that all 6 AB candidates are chance alignments. Our results indicate that the inconsistencies in asteroseismic and stellar parameters across different studies can be explained by potential seismically unresolved ABs. We highlight the importance of identifying and accurately accounting for such systems in asteroseismic analysis.

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arXiv2026

Asymptotic power spectra and visibilities of damped mixed modes

Recent observational studies of red giant stars have estimated the visibility of their mixed oscillation modes, which is a proxy of the average energy of these modes. Among other things, they demonstrated that although the damping rate of the oscillations in the core of many red giants appears to be negligible, other red giants exhibit high core damping rates that are sometimes consistent with the infinite value limit. Up until now, it has not been possible to link the mixed mode visibilities to core damping rates in a quantitative way. In this study, we use the progressive wave picture to derive an analytical function expressing the approximate resonance pattern of red giants up to a proportionality factor. This function can model the influence of the damping on the oscillations, as well as take into account other effects such as mode asymmetries. In particular, this expression can be used to obtain a quantitative estimate for the visibility of mixed modes and to predict the detectability of mixed mode and multiplet signatures under different core damping rates. Here, we conduct a parameter study to investigate how the damping processes affect these aspects. We find that the visibility approaches the value expected for an infinite core damping rate already at finite values. Furthermore, we find that both the mixed mode and the multiplet signatures disappear at finite core damping rates. This implies that the observational characteristics of red giants with finite core damping rates can appear as if their core damping rate were infinite, providing an explanation for the observed populations. Moreover, we have used our method to quantitatively estimate the core damping rates of red giants with unusually low mixed mode amplitudes from their observed visibilities.

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arXiv2025

Ensemble seismic study of the properties of the core of Red Clump stars

Red clump stars still pose open questions regarding several physical processes, such as the mixing around the core, or the nuclear reactions, which are ill-constrained by theory and experiments. The oscillations of red clump stars, which are of mixed gravito-acoustic nature, allow us to directly investigate the interior of these stars and thereby better understand their physics. In particular, the measurement of their period spacing is a good probe of the structure around the core. We aim to explain the distribution of period spacings in red clump stars observed by Kepler by testing different prescriptions of core-boundary mixing and nuclear reaction rate. Using the MESA stellar evolution code, we computed several grids of core-helium burning tracks, with varying masses and metallicities. Each of these grids have been computed assuming a certain core boundary mixing scheme, or carbon-alpha reaction rate. We then sampled these grids, in a Monte-Carlo fashion, using observational spectroscopic metallicities and seismic masses priors, in order to retrieve a period spacing distribution that we compared to the observations. We found that the best fitting distribution was obtained when using a "maximal overshoot" core-boundary scheme, which has similar seismic properties as a model whose modes are trapped outside a semi-convective region, and which does not exhibit core breathing pulses at the end of the core-helium burning phase. If no mode trapping is assumed, then no core boundary mixing scheme is compatible with the observations. Moreover, we found that extending the core with overshoot worsens the fit. Additionally, reducing the carbon-alpha reaction rate (by around 15%) improves the fit to the observed distribution. Finally, we noted that an overpopulation of early red clump stars with period spacing values around 250s is predicted by the models but not found in the observations.

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arXiv2025

Red giant asteroseismic binaries in the Kepler field

Systems in which two oscillating stars are observed in the same light curve, so-called asteroseismic binaries (ABs), arise from either chance alignments or gravitationally bound stars. In the latter case, ABs offer a novel way to find binary systems and combine asteroseismology and orbital dynamics to determine precise stellar parameters for both stars. Such systems provide valuable tests to stellar models and scaling relations. While population synthesis studies predict approximately 200 ABs in the Kepler long-cadence data, only a few have been detected to date. In this work, we aim to (1) expand the sample of ABs in Kepler data, (2) estimate global asteroseismic parameters for both stars in each AB, and (3) assess whether these pairs are gravitationally bound. We analysed 40 well-resolved ABs identified in Kepler long-cadence data, and matched these solar-like oscillators with Gaia DR3 sources using spectroscopic estimates of $ν_{\rm max}$. To assess whether each pair is gravitationally bound, we checked their projected separation and parallax consistency, and compared observed total orbital velocity differences from astrometry with theoretical predictions from Keplerian orbits. We find that most ABs appear to be chance alignments. However, two systems, KIC 6501237 and KIC 10094545, show orbital velocities, seismic masses, and evolutionary stages consistent with a wide binary configuration, with probabilities of ~50% and ~25%, respectively. Furthermore, eleven ABs are likely spatially unresolved binaries based on Gaia multiplicity indicators. Our findings suggest that most seismically resolved ABs in the Kepler field are not gravitationally bound, in contrast to earlier population synthesis predictions. Remarkably, the two wide binary candidates identified here are promising benchmarks for asteroseismic calibration. Spectroscopic follow-up is necessary to confirm their binary nature.

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arXiv2025

The Nineteenth Data Release of the Sloan Digital Sky Survey

Mapping the local and distant Universe is key to our understanding of it. For decades, the Sloan Digital Sky Survey (SDSS) has made a concerted effort to map millions of celestial objects to constrain the physical processes that govern our Universe. The most recent and fifth generation of SDSS (SDSS-V) is organized into three scientific ``mappers". Milky Way Mapper (MWM) that aims to chart the various components of the Milky Way and constrain its formation and assembly, Black Hole Mapper (BHM), which focuses on understanding supermassive black holes in distant galaxies across the Universe, and Local Volume Mapper (LVM), which uses integral field spectroscopy to map the ionized interstellar medium in the local group. This paper describes and outlines the scope and content for the nineteenth data release (DR19) of SDSS and the most substantial to date in SDSS-V. DR19 is the first to contain data from all three mappers. Additionally, we also describe nine value added catalogs (VACs) that enhance the science that can be conducted with the SDSS-V data. Finally, we discuss how to access SDSS DR19 and provide illustrative examples and tutorials.

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arXiv2025

Linearity of Structure Kernels in Main-sequence and Subgiant Solar-like Oscillators

Seismic structure inversions have been used to study the solar interior for decades. With the high-precision frequencies obtained using data from the Kepler mission, it has now become possible to study other solar-like oscillators using structure inversions, including both main-sequence and subgiant stars. Subgiant stars are particularly interesting because they exhibit modes of mixed acoustic-buoyancy nature, which provide the opportunity to probe the deeper region of stellar cores. This work examines whether the structure inversion techniques developed for the pure acoustic modes of the Sun and other main-sequence stars are still valid for mixed modes observed in subgiant stars. We construct two grids of models: one of main-sequence stars and one of early subgiant stars. Using these grids, we examine two different parts of the inversion procedure. First, we examine what we call the "kernel errors", which measure how well the mode sensitivity functions can recover known frequency differences between two models. Second, we test how these kernel errors affect the ability of an inversion to infer known structure differences. On the main sequence, we find that reliable structure inversion results can be obtained across the entire range of masses and large frequency separations we consider. On the subgiant branch, however, the rapid evolution of mixed modes leads to large kernel errors and hence difficulty recovering known structure differences. Our tests show that using mixed modes to infer the structure of subgiant stars reliably will require improvements to current fitting approaches and modifications to the structure inversion techniques.

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arXiv2025

The efficiency of mixed modes for angular momentum transport

Core rotation rates of red-giant stars inferred from asteroseismic observations are substantially lower than predicted by current stellar models. This indicates the lack of an efficient angular momentum transport mechanism in radiative interiors. Mixed pressure-gravity modes are a promising candidate to extract angular momentum from the core of red giants. We focus on determining the effect of mixed modes on the rotation rates of stars evolving along the red giant branch (RGB). We developed a post-processing code that computes the angular momentum transport by meridional currents, shear-induced turbulence and mixed modes. Rotation rates were computed for models along the RGB with different stellar masses and different initial rotation profiles. We find that the mixed modes can explain some of the spin down observed in red giant stars, however, the values of non-radial mode amplitudes strongly affect the efficiency of this mechanism. Rotation rates from models neglecting radiative damping on the mixed mode amplitudes overlap with observations and produce a localised spin down around the hydrogen-burning shell, whereas the inclusion of radiative damping strongly suppresses and delays this spin down. We also show that including an additional viscosity term with values in the range $10^3-10^4$ cm$^2$s$^{-1}$ redistributes the localised spin down due to the mixed modes, enhancing their efficiency. Our results reveal that the mixed mode amplitudes need to be constraint to precisely quantify the spin down of red giant cores. Nevertheless, the mixed mode mechanism by itself cannot explain the full spread in observed core rotation rates along the RGB. This will only be possible with an additional mechanism for angular momentum transport.

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arXiv2025

Power density spectra morphologies of seismically unresolved red-giant asteroseismic binaries

Asteroseismic binaries are two oscillating stars detected in a single light curve. These systems provide robust constraints on stellar models from the combination of dynamical and asteroseismical stellar parameters. Predictions suggested that approximately 200 asteroseismic binaries may exist among the Kepler long-cadence data, and the majority of them consist of two red-clump stars. However, detecting these systems is challenging when the binary components exhibit oscillations at similar frequencies that are indistinguishable. In this study, we predict the morphologies of power density spectra (PDS) of seismically unresolved red-giant asteroseismic binaries to provide examples that can be used to identify among observed stars. We created 5,000 artificial asteroseismic binary (AAB) systems by combining the KASOC light curves of red giants with oscillations at similar frequency ranges. To quantify the complexity of the oscillation patterns, we used the maximum signal-to-noise ratio of the background-normalized PDS and Shannon entropy. Additionally, we identified the radial and quadrupole mode pairs for the individual binary components and determined their impact on the PDS morphologies of AABs. Our results reveal that the majority of AABs consist of the two red-clump stars. The PDS of AABs generally exhibits increased entropy and decreased oscillation power compared to individual components. We focused on the AABs whose stellar components have similar brightness and classified them into four distinct morphologies: single star-like PDS, aligned, partially aligned, and misaligned. Most AABs with detectable oscillations from both components show complex oscillation patterns. Therefore, unresolved asteroseismic binaries with low oscillation power and complex oscillation patterns as characterized by high entropy offer a potential explanation to understand the observed stars with complex PDS.

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arXiv2025

Enhanced magnetic activity in rapidly rotating binary stars

Stellar activity is fundamental to stellar evolution and the formation and habitability of exoplanets. The interaction between convective motions and rotation in cool stars results in a dynamo process that drives magnetic surface activity. In single stars, activity increases with rotation rate until it saturates for stars with rotation periods Prot < 3 - 10 d. However, the mechanism responsible for saturation remains unclear. Observations indicate that red giants in binary systems that are in spin-orbit resonance exhibit stronger chromospheric activity than single stars with similar rotation rates, suggesting that tidal flows can influence surface activity. Here, we investigate the chromospheric activity of main-sequence binary stars to understand the impact of tidal forces on saturation phenomena. For binaries with 0.5 < Prot/d < 1, mainly contact binaries that share a common thermal envelope, we find enhanced activity rather than saturation. This result supports theoretical predictions that a large-scale $α$ - $ω$ dynamo during common-envelope evolution can generate strong magnetic fields. We also observe supersaturation in chromospheric activity, a phenomenon tentatively noted previously in coronal activity, where activity levels fall below saturation and decrease with shorter rotation periods. Our findings emphasise the importance of studying stellar activity in stars with extreme properties compared to the Sun's.

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arXiv2025

Asteroseismic Structure Inversions of Main-Sequence Solar-like Oscillators with Convective Cores

Asteroseismic inferences of main-sequence solar-like oscillators often rely on best-fit models. However, these models cannot fully reproduce the observed mode frequencies, suggesting that the internal structure of the model does not fully match that of the star. Asteroseismic structure inversions provide a way to test the interior of our stellar models. Recently, structure inversion techniques were used to study 12 stars with radiative cores. In this work, we extend that analysis to 43 main-sequence stars with convective cores observed by Kepler to look for differences in the sound speed profiles in the inner 30% of the star by radius. For around half of our stars, the structure inversions show that our models reproduce the internal structure of the star, where the inversions are sensitive, within the observational uncertainties. For the stars where our inversions reveal significant differences, we find cases where our model sound speed is too high and cases where our model sound speed is too low. We use the star with the most significant differences to explore several changes to the physics of our model in an attempt to resolve the inferred differences. These changes include using a different overshoot prescription and including the effects of diffusion, gravitational settling, and radiative levitation. We find that the resulting changes to the model structure are too small to resolve the differences shown in our inversions.

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arXiv2025

Pushing the boundaries of asteroseismic individual frequency modelling: unveiling two evolved very-low metallicity red giants

Metal-poor stars are key to understanding the first stellar generation in the Galaxy. Asteroseismic characterisation of red giants has traditionally relied on global seismic parameters, not the full spectrum of individual oscillation modes. Here, we present the first characterisation of two evolved very metal-poor stars, including the detailed mixed-mode patterns. We demonstrate that incorporating individual frequencies into grid-based modelling of red-giant stars enhances its precision, enabling detailed studies of these ancient stars and allowing us to infer the stellar properties of two $[\mathrm{Fe}/\mathrm{H}]{\sim}{-}2.5$ dex Kepler stars: KIC 4671239 and KIC 7693833. Recent developments in both observational and theoretical asteroseismology allows for detailed studies of the complex oscillation pattern of evolved giants. We employ Kepler time series and surface properties from high-resolution spectroscopic data to asteroseismically characterise the two stars using the BAyesian STellar Algorithm, BASTA. Both stars show agreement between constraints from seismic and classical observables; an overlap unrecoverable when purely considering the global seismic parameters. KIC 4671239 and KIC 7693833 were determined to have masses of $0.78^{+0.04}_{-0.03}$ and $0.83^{+0.03}_{-0.01} M_{\odot}$ with ages of $12.1^{+1.6}_{-1.5}$ and $10.3^{+0.6}_{-1.4}$ Gyr, respectively. A $\sim10$% discrepancy between observed and modelled $ν_{\mathrm{max}}$ suggests a metallicity dependence of its scaling relation, leading to overestimated masses and incorrect age inferences for metal-poor stars. Utilising the full spectrum of individual oscillation modes, we circumvent the dependence on the asteroseismic scaling relations, providing direct constraints on the stars themselves, pushing the boundaries of state-of-the-art detailed modelling of evolved stars at metallicities far different from solar.

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arXiv2025

Oscillations of red giant stars with magnetic damping in the core. I. Dissipation of mode energy in dipole-like magnetic fields

Strong magnetic fields in the core of red-giant branch stars are expected to suppress the amplitudes of the multipole modes. This occurs when the strength of the internal magnetic field approaches the critical field strength, at which the magnetic forces become comparable to the buoyancy. We performed Hamiltonian ray tracing simulations of magneto-gravity waves to investigate the suppression of the multipole modes in the presence of an internal dipole-like magnetic field. We took into account different stellar masses, metallicities, and ages, as well as various oscillation frequencies and spherical degrees. In particular, we estimated the trapped fraction, a measure of multipole mode suppression, which quantifies the fraction of mode energy in the core that is dissipated by the interaction with the magnetic field. Our results indicate that the trapped fraction can be described by a simple expression, which smoothly connects the regime without multipole mode suppression with the regime with complete suppression of the multipole modes. Crucially, the trapped fraction depends only on the ratio between the strength of the internal magnetic field and the critical field strength. Therefore, our expression for the trapped fraction provides a flexible tool that can be used, for example, to estimate the amount of multipole mode suppression as a star ascends the red-giant branch or to investigate the onset of the suppression in observed power spectral densities.

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arXiv2024

APOKASC-3: The Third Joint Spectroscopic and Asteroseismic catalog for Evolved Stars in the Kepler Fields

In the third APOKASC catalog, we present data for the complete sample of 15,808 evolved stars with APOGEE spectroscopic parameters and Kepler asteroseismology. We used ten independent asteroseismic analysis techniques and anchor our system on fundamental radii derived from Gaia $L$ and spectroscopic $T_{\rm eff}$. We provide evolutionary state, asteroseismic surface gravity, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them for 12,418 stars. This includes 10,036 exceptionally precise measurements, with median fractional uncertainties in \nmax, \dnu, mass, radius and age of 0.6\%, 0.6\%, 3.8\%, 1.8\%, and 11.1\% respectively. We provide more limited data for 1,624 additional stars which either have lower quality data or are outside of our primary calibration domain. Using lower red giant branch (RGB) stars, we find a median age for the chemical thick disk of $9.14 \pm 0.05 ({\rm ran}) \pm 0.9 ({\rm sys})$ Gyr with an age dispersion of 1.1 Gyr, consistent with our error model. We calibrate our red clump (RC) mass loss to derive an age consistent with the lower RGB and provide asymptotic GB and RGB ages for luminous stars. We also find a sharp upper age boundary in the chemical thin disk. We find that scaling relations are precise and accurate on the lower RGB and RC, but they become more model dependent for more luminous giants and break down at the tip of the RGB. We recommend the usage of multiple methods, calibration to a fundamental scale, and the usage of stellar models to interpret frequency spacings.

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arXiv2024

The radial modes of stars with suppressed dipole modes

The Kepler space mission provided high-quality light curves for more than 16 000 red giants. The global stellar oscillations extracted from these light curves carry information about the interior of the stars. Several hundred red giants were found to have low amplitudes in their dipole modes (i.e. they are suppressed dipole-mode stars). A number of hypotheses (involving e.g. a magnetic field, binarity, or resonant mode coupling) have been proposed to explain the suppression of the modes, yet none has been confirmed. We aim to gain insight into the mechanism at play in suppressed dipole-mode stars by investigating the mode properties (linewidths, heights, and amplitudes) of the radial oscillation modes of red giants with suppressed dipole modes. We selected from the literature suppressed dipole-mode stars and compared the radial-mode properties of these stars to the radial-mode properties of stars in two control samples of stars with typical (i.e. non-suppressed) dipole modes. We find that the radial-mode properties of the suppressed dipole-mode stars are consistent with the ones in our control samples, and hence not affected by the suppression mechanism. From this we conclude that (1) the balance between the excitation and damping in radial modes is unaffected by the suppression, and by extrapolation the excitation of the non-radial modes is not affected either; and (2) the damping of the radial modes induced by the suppression mechanism is significantly less than the damping from turbulent convective motion, suggesting that the additional damping originates from the more central non-convective regions of the star, to which the radial modes are least sensitive.

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arXiv2024

Merger seismology: distinguishing massive merger products from genuine single stars using asteroseismology

Products of stellar mergers are predicted to be common in stellar populations and can potentially explain stars with peculiar properties. When the merger occurs after the initially more massive star has evolved into the Hertzsprung gap (HG), the merger product may remain in the blue part of the Hertzsprung-Russell diagram (HRD) for millions of years. Such objects could, therefore, explain the overabundance of observed blue stars, such as blue supergiants. However, it is currently not straightforward to distinguish merger products from genuine single stars. We make detailed asteroseismic comparisons between models of massive post-main-sequence merger products and genuine single stars to identify which asteroseismic diagnostics can be used to distinguish them. In doing so, we develop tools for the relatively young field of merger seismology. Genuine single stars in the HG are fully radiative, while merger products have a convective He-burning core and convective H-burning shell while occupying similar locations in the HRD. These structural differences are reflected in lower asymptotic period spacing values for merger products and the appearance of deep dips in their period spacing patterns. Our genuine single-star models with masses above roughly 11.4 solar masses develop short-lived intermediate convective zones during their HG evolution. This also leads to deep dips in their period spacing patterns. Because of the lack of a convective core, merger products and genuine single stars can be distinguished based on their asymptotic period spacing value in this mass range. We perform the comparisons with and without the effects of slow rotation included in the pulsation equations and conclude that the two types of stars are seismically distinguishable in both cases. The observability of the distinguishing asteroseismic features of merger products can now be assessed and exploited in practice.

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arXiv2024

The K2 Asteroseismic KEYSTONE sample of Dwarf and Subgiant Solar-Like Oscillators. I: Data and Asteroseismic parameters

The KEYSTONE project aims to enhance our understanding of solar-like oscillators by delivering a catalogue of global asteroseismic parameters (${Δν}$ and ${ν_{\rm max}}$) for 173 stars, comprising mainly dwarfs and subgiants, observed by the K2 mission in its short-cadence mode during campaigns 6-19. We derive atmospheric parameters and luminosities using spectroscopic data from TRES, astrometric data from $\textit{Gaia}$, and the infrared flux method (IRFM) for a comprehensive stellar characterisation. Asteroseismic parameters are robustly extracted using three independent methods, complemented by an iterative refinement of the spectroscopic analyses using seismic ${\log g}$ values to enhance parameter accuracy. Our analysis identifies new detections of solar-like oscillations in 159 stars, providing an important complement to already published results from previous campaigns. The catalogue provides homogeneously derived atmospheric parameters and luminosities for the majority of the sample. Comparison between spectroscopic ${T_{\rm eff}}$ and those obtained from the IRFM demonstrates excellent agreement. The iterative approach to spectroscopic analysis significantly enhances the accuracy of the stellar properties derived.

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