arXiv subjects

Paul G. Beck

Publications and source records attributed to Paul G. Beck.

At least 19 recordsLinked to original sources

arXiv2026

Magnetic Signatures in Merger Products

Asteroseismic estimates of the magnetic field strength in the radiative interior of red giant stars depend strongly on the internal stellar structure derived from models. Since red giant branch merger products have been shown to be able to possess a different core structure than single stars of the same mass, we investigate how a mass-gain history influences our estimates of an internal magnetic field strength. We construct stellar models with and without a mass-gain event after the onset of the RGB evolutionary phase with masses of $1.1\,M_\odot \le M \le 2\,M_\odot$. First, by assuming a weak magnetic field, we investigate the influence of a mass-gain event on the global sensitivity of the oscillation frequencies to the magnetic field. We find that mass-gain models can be several times more sensitive to the field than single-star models of identical total mass at masses above $1.6\,M_\odot$. Therefore, considering a mass-gain evolutionary history for merger candidates allows a significant correction to the magnetic field strength. In the presence of strong magnetic fields, we also show that the critical field strength needed to suppress mixed dipole modes is significantly lower if a mass-gain event has occurred (for stars with masses $M\gtrsim1.6\,M_\odot$). The massive end of the suppressed stars' distribution is therefore strongly favored by a merger origin. We conclude that properly constraining the stellar evolutionary history is essential when aiming to constrain internal field strength estimates from asteroseismic observations.

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arXiv2026

Symbiotic binaries in the Gaia data. II. Symbiotic candidates from general variability classification in DR3

We investigate the reliability of the symbiotic star class in the general variability classification of Gaia DR3 and search for new genuine symbiotic systems among the objects assigned to this category. The sample contains 649 sources, including 246 previously known symbiotic stars, 61 literature candidates, and 339 new candidates proposed by the Gaia variability pipeline. Diagnostics based on the Gaia colour-magnitude diagram, near-infrared photometry, and the pseudo-equivalent width of H$α$ indicate that a large fraction of the new candidates are likely contaminants, predominantly pulsating red giants. To quantify the contamination, we constructed a Random Forest classifier trained on confirmed symbiotic stars and on Mira and semi-regular variables, using Gaia photometry, variability parameters, H$α$ measurements from XP spectra, and infrared colours. The classifier reaches a balanced accuracy of $\approx$0.94 and efficiently separates most symbiotic binaries from single evolved stars, leaving only eight strong candidates among the 339 newly proposed objects. Follow-up spectroscopy confirms three new symbiotic stars through the presence of high-excitation emission lines, while several additional objects remain possible symbiotics. Our results show that the Gaia DR3 variability classification efficiently recovers known symbiotic stars but has low purity due to overlap with pulsating red giants. The small number of newly confirmed systems implies that the discrepancy between predicted and observed Galactic symbiotic populations remains unresolved, although Gaia provides a powerful basis for future searches combining variability, spectroscopic indicators, and multi-wavelength data.

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arXiv2026

K 1-6 is a photoionised ISM nebula shaped by a fast-moving hot white dwarf in a triple system

K 1-6 has long been classified as a planetary nebula (PN) hosting a binary central star, yet it has remained poorly studied due to its faintness. The central star exhibits pronounced photometric variability whose origin has so far been unclear. We aim to present a comprehensive characterisation of the K 1-6 system, including the physical properties of its stellar components and the nature of the surrounding nebulosity. We conducted a multi-wavelength analysis combining optical and UV spectroscopy obtained with the Gran Telescopio Canarias, the Telescopio Nazionale Galileo, the Nordic Optical Telescope, and the Hubble Space Telescope. We also present long-term multi-band ground- and space-based photometry, including high-cadence data from the Transiting Exoplanet Survey Satellite, narrow-band imaging, and the latest astrometric constraints from Gaia. Our results show that the nebula is not a remnant PN, but instead consists of interstellar medium photoionised by a hot white dwarf, which is relatively evolved. It has a cooling age of 1-2 Myr, implying that any original PN has long since dissipated. We further find that the central object is a hierarchical triple system, comprising an inner binary with an orbital period likely of the order of thousands of days and a distant tertiary companion on a timescale of tens of thousands of years. The optically dominant cool component of the inner binary is an inflated K-type star displaying extreme magnetic activity, including large-amplitude variability and flaring. Its properties resemble those of BY Dra-type binaries and Abell 35-type systems, and are difficult to reconcile with single-star evolution, pointing instead to a history of binary interaction.

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arXiv2026

Hints of enhanced magnetic activity after the intermediate rotation period gap as traced by the chromospheric Ca ii infrared triplet

For low-mass stars (M < 1.4 Msun), the connection between stellar rotation and magnetic activity governs stellar spin-down, shapes the environments of their exoplanets, and provides an age-diagnostic via magneto-gyro-chronology. Recently, unexpected phenomena known as the intermediate rotation period gap and the rotational stalling have been discovered. These are likely due to internal angular momentum redistribution, and mark departures from a smooth spin-down evolution. These features have been shown to cause enhanced magnetic activity on the photosphere, as measured by the photometric index from light curves (Sph), in both cluster and field stars. However, their influence on other magnetic activity proxies, and particularly in field stars, remains poorly understood. In this work, we study the impact of the intermediate-period gap on chromospheric magnetic activity as traced by the Ca ii infrared triplet (IRT) index. We target the stars observed by the Kepler mission, as this is the largest and most reliable sample of field stars with measured rotation periods sensitive to the gap. We calculate the Ca ii IRT index for the Kepler stars using the spectroscopic information from the Gaia mission data release three (DR3). We study the rotation-activity relation as a function of spectral type, finding that K dwarfs are more active than G dwarfs, which in turn are more active than F dwarfs. For main-sequence stars, we find that chromospheric magnetic activity is also enhanced after the intermediate-period gap, mirroring its effect on the photospheric Sph index. Our work reveals that the intermediate-period gap marks a genuine transition in stellar magnetic behavior, not only at the photosphere but also at the chromosphere. This highlights the need to account for its signatures across activity proxies, as well as its impact on exoplanet habitability and the age-rotation-activity relation.

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arXiv2026

The PLATO Science Calibration and Validation Plan: Targets for the First Long-pointing Field

In order to meet the science goals of the PLATO space mission, an extensive science calibration and validation plan has been designed. This paper describes this plan, as well as the methodology adopted to select the science calibration and validation stars that have entered its input catalogue. This is the so-called {\tt scvPIC}, which is part of the general PLATO Input Catalogue (PIC) for the first selected long pointing field in the Southern Hemisphere known as LOPS2. While many of PLATO's science requirements needed dedicated stars as calibrators as discussed here, its most stringent requirement is the delivery of the age of the host stars of exoplanetary systems with an accuracy better than 10\% for a G0V star of {\it V} = 10 mag, i.e. a nearby Sun-like star. This is presently not within reach for large populations of dwarfs and subgiants in the Milky Way as it requires the models of their stellar interiors to be improved. We discuss how this ambitious age requirement led to the selection of tens of thousands of red giants, and of thousands of main-sequence early F-type gravity-mode pulsators in order to deduce their internal rotation profile across stellar evolution. This asteroseismic observable will then be imported as key information into improved models of dwarfs and subgiants in the Milky Way as optimal modelling tools for ever better age-dating of the exoplanet hosts as the PLATO mission moves along. Additional calibrators and validators included in the {\tt scvPIC} are a few thousands of binaries, a few hundreds of legacy and benchmark stars, a few hundred photometrically stable stars, and six transiting brown dwarfs.

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arXiv2026

Tales of stellar and binary co-evolution, told by stellar oscillations -- Binary demographics and their impact on stellar mass, orbits, and age estimates in main-sequence and red-giant stars

Red giants are increasingly used as stellar population tracers due to their well-understood evolution and the availability of asteroseismic observables. However, stellar binarity can alter observable properties and introduce strong biases. We aim to provide a holistic picture of the binary population and its evolution in the red giant phase by characterizing a sample of binaries hosting oscillating red giants from a combination of extensive asteroseismic, spectroscopic, and astrometric surveys. We investigate the binary properties of evolved stars in the APOKASC3 and APO-K2 catalogs, leveraging asteroseismic constraints and Gaia DR3 non-single-star solutions. We explore the mass distribution of red-giant binary systems and analyze the evolution of their binary fraction. For stars with M$\leq$1.8M$_\odot$, we find binary fractions $\sim$31% and $\sim$41% for oscillating and non-oscillating solar-like stars on the main-sequence (MS). By the power excess ($ν_\mathrm{max}$) as luminosity proxy, we detect a binary attrition of $\sim$69% and $\sim$81% on the low- and high-luminosity red-giant branch (RGB) and an additional $\sim$38% to the red clump (RC), with respect to the MS. Binaries hosting RC and secondary clump stars (2RC) stars are largely depleted at $P_\mathrm{orb}\lesssim$500 and $\lesssim$200 days, respectively. Mass-dependent differences in binary fractions and orbital properties point to more substantial binary attrition for stars with M $\leq$1.8 M$_\odot$. The distinct mass distributions and the depletion of short-period binaries during the red-giant phase underscore the impact of stellar expansion and binary interactions on stellar evolution. RC systems with $P_\mathrm{orb}\lesssim$800 to 1,000 days are likely shaped by past interactions, such as mass transfer or loss, which can lead to significantly biased age estimates if not accounted for.

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arXiv2026

On the contradictory case of the binary system HD 81809 hosting two pulsating solar-like stars observed by TESS

We present a new comprehensive study of HD81809, a nearby binary system of two solar-like stars showing high-amplitude X-ray emission and a well-defined 8-year solar-like magnetic cycle. By analyzing high-resolution spectroscopy, alongside DR3 Gaia astrometry, and bolometric fluxes, we derive updated fundamental parameters for both components. In particular, we uncover a significant chemical difference: the primary is metal-poor ([Fe/H]$ \simeq - 0.57$), while the secondary shows solar-like metallicity ([Fe/H]$=0.00$). This suggests that the system originated in a mildly metal-poor environment, consistent with the Galactic thick disk population, and that the secondary's surface composition has been altered by a recent accretion event. Using multi-sector TESS photometry, we detected solar-like oscillations in both components, deriving global asteroseismic parameters $Δν= 43.32 \pm 3.91 μ$Hz, $ν_{\rm max} = 708.74^{+3.23}_{-3.74} μ$Hz for HD81809 A, and $Δν= 97.75 \pm 4.49~μ$Hz, $ν_{\rm max} = 2098.07^{+3.07}_{-2.83} μ$Hz for HD81809 B. By combining all the observational constraints with stellar evolutionary models computed using CLES and MESA codes, we reconstructed the evolutionary scenario of the system. Our results indicate that HD 81809 is an old system with an age of $\sim 10 \mathrm{Gyr}$, composed of a subgiant primary with mass $\sim 0.87M_{\odot}$ and radius $\sim1.96R_{\odot}$ - likely responsible for the reactivated dynamo cycle - and a main sequence secondary with mass $ M=0.85M_{\odot}$ and radius $R=1.10R_{\odot}$. This system represents a benchmark for studying stellar evolution, magnetic activity, and the physics of old, metal-poor stars in the Galactic thick disk.

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arXiv2026

Testing Red Clump Models with the Asteroseismic Binary KIC 10841730

Binaries in which both stars are pulsating are rare but extremely valuable. We present the first study of an asteroseismic binary system consisting of a core helium-burning red clump (RC) star and a red giant branch (RGB) star. The Kepler target KIC 10841730 is a wide binary (period $2917 \pm 8$ d) that provides ideal conditions to test the accuracy of RC models. While prior studies of RC stars have revealed discrepancies in modelling the period spacings of mixed modes, other model parameters remain largely untested. We perform a detailed modelling analysis using individual mode frequencies and cover a large parameter space in mass, metallicity, He-abundance, mixing length, overshooting, and mass-loss, and we also explore different methods to correct for surface effects. We find two possible results for the red clump models. One solution requires introducing an unexpected offset of the phase shift in the red clump model, yielding an age consistent with the companion star and current masses of $1.01 \pm 0.06$ and $1.08 \pm 0.06$ M$_\odot$ for the RC and RGB star, respectively. Alternatively, we find that excluding the identification of two questionable radial modes resolves the phase-shift offset issue but results in a higher mass and thus a much younger age for the red clump star, contradicting the age obtained from its companion. We conclude that uncertainties in red clump models affect not only the g-mode period spacings but also the properties of the p modes. We show the power of asteroseismic binaries in validating and constraining stellar models and highlight the need for refining red-clump models.

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arXiv2025

Is the Symbiotic Recurrent Nova T CrB Late? Recent Photometric Evolution and Comparison with Past Pre-Outburst Behaviour

T CrB is a symbiotic recurrent nova that last erupted in 1946. Given its recurrence timescale of approximately 80 years, the next outburst is eagerly anticipated by the astronomical community. In this work, we analyse the optical light curves of T CrB, comparing recent photometric evolution with historical data to evaluate potential predictive indicators of nova eruptions. Although the "super-active" phases preceding both the 1946 and anticipated eruptions are strikingly similar, the subsequent photometric behaviour differs. We find that the decline in brightness observed in 2023, interpreted by some as a "pre-eruption dip", deviates from the deep minimum recorded prior to the 1946 event and does not reliably predict the eruption timing. Recent photometric and spectroscopic observations indicate that the system is returning to a high-accretion state. Given this, an eruption may be imminent, even without distinct precursors. While the next eruption of T CrB will be a major scientific event, its expected peak brightness of $V \sim 2$ mag highlights the importance of setting realistic public expectations for what will be a visually modest, yet astrophysically very significant, celestial event.

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arXiv2025

Magnetic activity evolution of solar-like stars: II. $S_{\rm ph}$-Ro evolution of Kepler main-sequence targets

There is now a large sample of stars observed by the Kepler satellite with measured rotation periods and photometric activity index $S_{\rm ph}$. We use this data, in conjunction with stellar interiors models, to explore the interplay of magnetism, rotation, and convection. Stellar activity proxies other than $S_{\rm ph}$ are correlated with the Rossby number, $Ro$, or ratio of rotation period to convective overturn timescale. We compute the latter using the Yale Rotating Evolution Code stellar models. We observe different $S_{\rm ph}$-$Ro$ relationships for different stellar spectral types. Though the overall trend of decreasing magnetic activity versus $Ro$ is recovered, we find a localized dip in $S_{\rm ph}$ around $Ro/Ro_{\odot} \sim$\,0.3 for the G and K dwarfs. F dwarfs show little to no dependence of $S_{\rm ph}$ on $Ro$ due to their shallow convective zones; further accentuated as $T_{\rm eff}$ increases. The dip in activity for the G and K dwarfs corresponds to the intermediate rotation period gap, suggesting that the dip in $S_{\rm ph}$ could be associated with the redistribution of angular momentum between the core and convective envelope inside stars. For G-type stars, we observe enhanced magnetic activity above solar $Ro$. Compared to other Sun-like stars with similar effective temperature and metallicity, we find that the Sun's current level of magnetic activity is comparable to its peers and lies near the transition to increasing magnetic activity at high $Ro$. We confirm that metal-rich stars have a systematically larger $S_{\rm ph}$ level than metal-poor stars, which is likely a consequence of their deeper convective zones.

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arXiv2024

The PLATO Mission

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

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arXiv2024

The IACOB project XII. A new grid of northern standards for the spectral classification of B-type stars

With the advent of large spectroscopic surveys, automated stellar parameter determination has become commonplace. Nevertheless, spectral classification still offers a quick and useful alternative for obtaining parameter estimates for large samples of spectra of varying quality. We present a new atlas of stellar spectra covering the B-type range, with the intention of providing detailed classification criteria valid for modern spectra and improving the grid of reliable standards. This new grid will be used in future works to provide classification criteria beyond the classical classification range and addressing, in particular, the use of Gaia/RVS spectra. We analysed historical standards by means of multiple high-resolution spectra, marking out problematic cases and complementing the grid with a new set of reliable comparators. We then elaborated on a new set of classification criteria based on high-quality R=4000 spectra. Our new classification grid is much thicker than any previous set of standards, presenting a high degree of self-consistency. Although it is based entirely on morphological criteria, the grid demonstrates a much better correlation with different physical parameters. The new grid can be used to study classification criteria in other spectral ranges, providing a valuable tool for the study of B-type stars that covers a very wide range of temperatures, luminosities, and stellar masses. The very process of classification also offers valuable insights into stellar evolution.

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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

TOI-1408: Discovery and Photodynamical Modeling of a Small Inner Companion to a Hot Jupiter Revealed by TTVs

We report the discovery and characterization of a small planet, TOI-1408 c, on a 2.2-day orbit located interior to a previously known hot Jupiter, TOI-1408 b ($P=4.42$ d, $M=1.86\pm0.02\,M_\mathrm{Jup}$, $R=2.4\pm0.5\,R_\mathrm{Jup}$) that exhibits grazing transits. The two planets are near 2:1 period commensurability, resulting in significant transit timing variations (TTVs) for both planets and transit duration variations (TDVs) for the inner planet. The TTV amplitude for TOI-1408 c is 15% of the planet's orbital period, marking the largest TTV amplitude relative to the orbital period measured to date. Photodynamical modeling of ground-based radial velocity (RV) observations and transit light curves obtained with the Transiting Exoplanet Survey Satellite (TESS) and ground-based facilities leads to an inner planet radius of $2.22\pm0.06\,R_\oplus$ and mass of $7.6\pm0.2\,M_\oplus$ that locates the planet into the Sub-Neptune regime. The proximity to the 2:1 period commensurability leads to the libration of the resonant argument of the inner planet. The RV measurements support the existence of a third body with an orbital period of several thousand days. This discovery places the system among the rare systems featuring a hot Jupiter accompanied by an inner low-mass planet.

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arXiv2023

Spectroscopic identification of rapidly rotating red giant stars in APOKASC-3 and APOGEE DR16

Rapidly rotating red giant stars are astrophysically interesting but rare. In this paper we present a catalog of 3217 active red giant candidates in the APOGEE DR16 survey. We use a control sample in the well-studied Kepler fields to demonstrate a strong relationship between rotation and anomalies in the spectroscopic solution relative to typical giants. Stars in the full survey with similar solutions are identified as candidates. We use vsin\textiti measurements to confirm 50+/- 1.2% of our candidates as definite rapid rotators, compared to 4.9+/-0.2% in the Kepler control sample. In both the Kepler control sample and a control sample from DR16, we find that there are 3-4 times as many giants rotating with 5 < vsini < 10 km s$^{-1}$ compared to vsini > 10 km s$^{-1}$, the traditional threshold for anomalous rotation for red giants. The vast majority of intermediate rotators are not spectroscopically anomalous. We use binary diagnostics from APOGEE and \textit{Gaia} to infer a binary fraction of 73+/-2.4%. We identify a significant bias in the reported metallicity for candidates with complete spectroscopic solutions, with median offsets of 0.37 dex in [M/H] from a control sample. As such, up to 10% of stars with reported [M/H]<-1 are not truly metal poor. Finally, we use Gaia data to identify a sub-population of main sequence photometric binaries erroneously classified as giants.

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arXiv2022

A Radial Velocity Study of the Planetary System of Pi Mensae: Improved Planet Parameters for PI Mensae c and a Third Planet on a 125-d Orbit

Pi Men hosts a transiting planet detected by the TESS space mission and an outer planet in a 5.7-yr orbit discovered by RV surveys. We studied this system using new radial velocity (RV) measurements taken with the HARPS spectrograph on ESO's 3.6-m telescope as well as archival data. We constrain the stellar RV semi-amplitude due to the transiting planet, Pi Men c, as K_c = 1.21 +/- 0.12 m/s resulting in a planet mass of M_c = 3.63 +/- 0.38 M_Earth. A planet radius of R_c= 2.145 +/- 0.015 R_Earth yields a bulk density of rho = 2.03 +/- 0.22 g/cm^{-3}. The precisely determined density of this planet and the brightness of the host star make Pi Men c an excellent laboratory for internal structure and atmospheric characterization studies. Our HARPS RV measurements also reveal compelling evidence for a third body, PI Men d, with a minimum mass M sin i = 13.38 +/- 1.35 M_Earth orbiting with a period of P_d = 125 d on an eccentric orbit (e = 0.22). A simple dynamical analysis indicates that the orbit of Pi Men d is stable on timescales of at least 20 Myrs. Given the mutual inclination between the outer gaseous giant and the inner rocky planet and the presence of a third body at 125 d, Pi Men is an important planetary system for dynamical and formation studies.

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arXiv2022

Planet Hunters TESS IV: A massive, compact hierarchical triple star system TIC 470710327

We report the discovery and analysis of a massive, compact, hierarchical triple system (TIC 470710327) initially identified by citizen scientists in data obtained by NASA's Transiting Exoplanet Survey Satellite (TESS). Spectroscopic follow-up observations obtained with the HERMES spectrograph, combined with eclipse timing variations (ETVs), confirm that the system is comprised of three OB stars, with a compact 1.10 d eclipsing binary and a non-eclipsing tertiary on a 52.04 d orbit. Dynamical modelling of the system (from radial velocity and ETVs) reveal a rare configuration wherein the tertiary star (O9.5-B0.5V; 14-17 M$_{\odot}$) is more massive than the combined mass of the inner binary (10.9-13.2 M$_{\odot}$). Given the high mass of the tertiary, we predict that this system will undergo multiple phases of mass transfer in the future, and likely end up as a double neutron star gravitational wave progenitor or an exotic Thorne-Zytkow object. Further observational characterisation of this system promises constraints on both formation scenarios of massive stars as well as their exotic evolutionary end-products.

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arXiv2021

Weighing stars from birth to death: mass determination methods across the HRD

The mass of a star is the most fundamental parameter for its structure, evolution, and final fate. It is particularly important for any kind of stellar archaeology and characterization of exoplanets. There exists a variety of methods in astronomy to estimate or determine it. In this review we present a significant number of such methods, beginning with the most direct and model-independent approach using detached eclipsing binaries. We then move to more indirect and model-dependent methods, such as the quite commonly used isochrone or stellar track fitting. The arrival of quantitative asteroseismology has opened a completely new approach to determine stellar masses and to complement and improve the accuracy of other methods. We include methods for different evolutionary stages, from the pre-main sequence to evolved (super)giants and final remnants. For all methods uncertainties and restrictions will be discussed. We provide lists of altogether more than 200 benchmark stars with relative mass accuracies between $[0.3,2]\%$ for the covered mass range of $M\in [0.1,16]\,\msun$, $75\%$ of which are stars burning hydrogen in their core and the other $25\%$ covering all other evolved stages. We close with a recommendation how to combine various methods to arrive at a "mass-ladder" for stars.

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