arXiv subjects

Leo Girardi

Publications and source records attributed to Leo Girardi.

At least 19 recordsLinked to original sources

arXiv2026

A homogeneous view of asymptotic giant branch carbon stars as seen by Gaia

Carbon stars on the asymptotic giant branch are major contributors to galactic dust enrichment, with gas mass-loss rates up to 1e-4 Msun/yr. We present a homogeneous spectral energy distribution analysis of the Gaia DR3 Golden Sample of carbon stars in the Milky Way and Magellanic Clouds. Our dataset includes 14,747 sources with multi-band photometry from Gaia, 2MASS, and WISE, combined with recent distance and extinction estimates. For a subsample of 2,494 Mira variables, we model multi-band light curves to derive accurate mean magnitudes. Stellar and circumstellar parameters are obtained by fitting observations with a large grid of synthetic spectra computed with the DUSTY radiative transfer code using COMARCS atmospheres. We derive effective temperature, optical depth, and gas mass-loss rate for each source. The distributions peak around Teff = 3150 K, with mass-loss rates spanning 1e-11 to 1e-4 Msun/yr and inner dust temperatures near 1000 K. We find a correlation between variability amplitude and mass-loss rate. This framework provides a statistically robust view of carbon stars across environments with different metallicities. Apparent environmental dependencies are influenced by luminosity distributions and selection effects rather than purely intrinsic metallicity differences. The combined Gaia and WISE selection limits the detection of both highly obscured and faint Magellanic Cloud sources, but the observed trends remain significant within the sampled populations.

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arXiv2025

Enhanced Mass Loss of Very Massive Stars: Impact on the Evolution, Binary Processes, and Remnant Mass Spectrum

Very massive stars (VMS) play a fundamental role in astrophysics due to their winds and supernovae (SN), and their role as massive black hole (BH) progenitors. However, their origin and evolution remain a significant challenge. Recent theoretical work and observations suggest that VMS approaching the Eddington limit may experience mass loss above the standard wind predictions. This study investigates how enhanced winds influence single and binary VMS evolution, observable properties, and resulting BH populations. New stellar wind prescriptions, sensitive to the Eddington parameter ($Γ_e$) and the luminosity-to-mass ratio, were implemented into the stellar evolution code PARSEC v2.0. These updated single-star tracks (100 - 600 M$_{\odot}$ at Z=0.006) were used to model the VMS population in the Tarantula Nebula and integrated into the SEVN binary evolution code. The $Γ_e$-enhanced single-star tracks match observed VMS properties better than standard models. Explaining the most massive star, R136a1, through a single-star origin suggests a zero-age main sequence (ZAMS) mass limit of $<$ 400 M$_{\odot}$ regardless of the wind recipe used. However, binary stellar mergers also offer a suitable origin for R136a1 and other observed VMS, potentially lowering the upper ZAMS mass limit by ~100 M$_{\odot}$. In binaries, enhanced winds inhibit main-sequence stellar mergers and limit BH production above the pair-instability mass gap's lower edge (~50 M$_{\odot}$). Binary BHs merging in a Hubble time with enhanced winds yield more primary BHs above 30 M$_{\odot}$ and enable secondary BHs between 30-40 solar masses, a range not found with standard stellar winds at LMC metallicity. This study highlights the crucial role that stellar winds and binary interactions play in VMS evolution and offers predictions relevant for interpreting VMS observations and gravitational wave source origins.

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arXiv2025

Discovery of a Weak CN Spectral Absorption Feature in Red Supergiant Stars in the Andromeda (M31) and Triangulum (M33) Galaxies

Using Keck DEIMOS spectra of stars in the Andromeda (M31) and Triangulum (M33) galaxies, selected from the large multi-band (near ultraviolet, visible light, and near infrared) Hubble Space Telescope surveys PHAT and PHATTER, respectively, we have identified a subset of stars that contain a previously unnoticed weak spectral absorption feature around 8000 Angstrom (0.8 micron). This absorption feature appears to be associated with the cyanogen (CN) molecule. Strong CN spectral absorption is a standard feature of carbon stars, which are thought to be intermediate mass (2-3 ~ M_sun) stars with C/O > 1 in the thermally-pulsating asymptotic giant branch phase of stellar evolution. However, the stars that are the focus of this paper are characterized by a weak version of this CN spectral absorption feature in a spectrum that is otherwise dominated by normal O-rich spectral absorption lines such as TiO and/or the Ca near infrared triplet. We have dubbed these stars "weak CN" stars. We present an automated method for identifying weak CN stars in M31 and M33, and examine their photometric properties in relation to model isochrones and stellar tracks. We find that weak CN stars tend to be fairly localized in color-magnitude space, and appear to be red supergiant stars with masses ranging from 5-10 M_sun, overall lifetimes of about 40-50 Myr, and currently in the core He burning phase of stellar evolution.

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arXiv2025

Strikingly high fraction of fast rotators in Magellanic Cloud star clusters

There has been growing evidence that the rich star clusters in the Magellanic Clouds contain significant fractions of rapidly rotating stars. In this work, we aim to constrain these fractions by studying the colour-magnitude diagrams of four star clusters, selected among those with the most striking signatures of fast rotators. Using isochrones derived from PARSEC v2.0 stellar tracks, we generate distinct stellar populations, each covering a limited interval of initial rotation rates $ω_\mathrm{i}$, referred to as 'Partial Models' (PMs). Using optimization algorithms and Monte Carlo Markov Chains, PMs are combined to create the final best-fitting model. In our analysis, we adopt two key assumptions: a uniform age and an isotropic distribution of stellar spin axes within each cluster. The solutions are allowed to explore the entire range of $ω_\mathrm{i}$, and different values of age, metallicity, distance and foreground extinction. We find that the rotational velocity distributions in all four clusters reveal a high fraction of stars with $ω_\mathrm{i}$ close to the break-up value, in all cases. Specifically, the fraction of stars with $ω_\mathrm{i}>0.7$ exceeds $80\%$ in the clusters NGC 419 of the Small Magellanic Cloud (SMC) and NGC 1831 and NGC 1866 of the Large Magellanic Cloud (LMC). For NGC 2203 of the LMC, this fraction is smaller, although it still exceeds $50\%$, confirming that also this cluster is mainly populated by fast-rotating stars.

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arXiv2024

Calibration of the JAGB method for the Magellanic Clouds and Milky Way from Gaia DR3, considering the role of oxygen-rich AGB stars

The JAGB method is a new way of measuring distances with use of AGB stars that are situated in a selected region in a J versus J-Ks CMD, using the fact that the absolute J magnitude is (nearly) constant. It is implicitly assumed in the method that the selected stars are carbon-rich AGB stars. However, as the sample selected to determine M_J is purely colour based there can also be contamination by oxygen-rich AGB stars. As the ratio of C to O-rich stars is known to depend on metallicity and initial mass, the star formation history and age-metallicity relation in a galaxy should influence the value of M_J. The aim of this paper is to look at mixed samples of O- and C-rich stars for the LMC, the SMC and Milky Way (MW), using the Gaia catalogue of long period variables as basis. We report the mean and median magnitudes and the results of fitting Gaussian and Lorentzian profiles to the luminosity function (LF) using different colour and magnitudes cuts. For the SMC and LMC we confirm the previous results in the literature. The LFs of the SMC and LMC JAGB stars are clearly different, yet the mean magnitude inside a selection box can be argued to agree at the 0.02~mag level. The analysis of the MW sample is less straightforward. The contamination by O-rich stars is substantial for a classical lower limit of (J-Ks)0= 1.3, and becomes less than 10% only for (J-Ks)0= 1.5. The sample of AGB stars is much smaller than for the MCs for two reasons. Nearby AGB stars tend to be absent as they saturate in the 2MASS catalogue, and the parallax errors of AGB stars tend to be larger compared to non-AGB stars. The mean and median magnitudes are fainter than for the MC samples by about 0.4~mag which is not predicted by theory. We do not confirm the claim in the literature that the absolute calibration of the JAGB method is independent of metallicity up to solar metallicity.

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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

AESOPUS 2.1: Low-Temperature Opacities Extended to High Pressure

We address the critical need for accurate Rosseland mean gas opacities in high-pressure environments, spanning temperatures from 100 K to 32000 K. Current opacity tables from Wichita State University and AESOPUS 2.0 are limited to $\log(R) \le 1$, where $R=ρ\, T_6^{-3}$ in units of $\mathrm{g}\,\mathrm{cm}^{-3}(10^6\mathrm{K})^{-3}$. This is insufficient for modeling very low-mass stars, brown dwarfs, and planets with atmospheres exhibiting higher densities and pressures ($\log(R) > 1$). Leveraging extensive databases such as ExoMol, ExoMolOP, MoLLIST, and HITEMP, we focus on expanding the AESOPUS opacity calculations to cover a broad range of pressure and density conditions ($-8 \leq \log(R) \leq +6$). We incorporate the thermal Doppler mechanism and micro-turbulence velocity. Pressure broadening effects on molecular transitions, leading to Lorentzian or Voigt profiles, are explored in the context of atmospheric profiles for exoplanets, brown dwarfs, and low-mass stars. We also delve into the impact of electron degeneracy and non-ideal effects such as ionization potential depression under high-density conditions, emphasizing its notable influence on Rosseland mean opacities at temperatures exceeding $10,000$ K. As a result, this study expands AESOPUS public web interface for customized gas chemical mixtures, promoting flexibility in opacity calculations based on specific research needs. Additionally, pre-computed opacity tables, inclusive of condensates, are provided. We present a preliminary application to evolutionary models for very low-mass stars.

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arXiv2024

The JWST Resolved Stellar Populations Early Release Science Program V. DOLPHOT Stellar Photometry for NIRCam and NIRISS

We present NIRCam and NIRISS modules for DOLPHOT, a widely-used crowded field stellar photometry package. We describe details of the modules including pixel masking, astrometric alignment, star finding, photometry, catalog creation, and artificial star tests (ASTs). We tested these modules using NIRCam and NIRISS images of M92 (a Milky Way globular cluster), Draco II (an ultra-faint dwarf galaxy), and WLM (a star-forming dwarf galaxy). DOLPHOT's photometry is highly precise and the color-magnitude diagrams are deeper and have better definition than anticipated during original program design in 2017. The primary systematic uncertainties in DOLPHOT's photometry arise from mismatches in the model and observed point spread functions (PSFs) and aperture corrections, each contributing $\lesssim0.01$ mag to the photometric error budget. Version 1.2 of WebbPSF models, which include charge diffusion and interpixel capacitance effects, significantly reduced PSF-related uncertainties. We also observed minor ($\lesssim0.05$ mag) chip-to-chip variations in NIRCam's zero points, which will be addressed by the JWST flux calibration program. Globular cluster observations are crucial for photometric calibration. Temporal variations in the photometry are generally $\lesssim0.01$ mag, although rare large misalignment events can introduce errors up to 0.08 mag. We provide recommended DOLPHOT parameters, guidelines for photometric reduction, and advice for improved observing strategies. Our ERS DOLPHOT data products are available on MAST, complemented by comprehensive online documentation and tutorials for using DOLPHOT with JWST imaging data.

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arXiv2023

Discovery of astrometric accelerations by dark companions in the globular cluster $ω$ Centauri

We present results from the search for astrometric accelerations of stars in $ω$ Centauri using 13 years of regularly-scheduled {\it Hubble Space Telescope} WFC3/UVIS calibration observations in the cluster core. The high-precision astrometry of $\sim$160\,000 sources was searched for significant deviations from linear proper motion. This led to the discovery of four cluster members and one foreground field star with compelling acceleration patterns. We interpret them as the result of the gravitational pull by an invisible companion and determined preliminary Keplerian orbit parameters, including the companion's mass. {For the cluster members} our analysis suggests periods ranging from 8.8 to 19+ years and dark companions in the mass range of $\sim$0.7 to $\sim$1.4$M_\mathrm{sun}$. At least one companion could exceed the upper mass-boundary of white dwarfs and can be classified as a neutron-star candidate.

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arXiv2023

The JWST Resolved Stellar Populations Early Release Science Program IV: The Star Formation History of the Local Group Galaxy WLM

We present the first star formation history (SFH) and age-metallicity relation (AMR) derived from resolved stellar populations imaged with the JWST NIRCam instrument. The target is the Local Group star-forming galaxy WLM at 970 kpc. The depth of the color-magnitude diagram (CMD) reaches below the oldest main sequence turn-off with a SNR=10 at M_F090W=+4.6 mag; this is the deepest CMD for any galaxy that is not a satellite of the Milky Way. We use Hubble Space Telescope (HST) optical imaging that overlaps with the NIRCam observations to directly evaluate the SFHs derived based on data from the two great observatories. The JWST and HST-based SFHs are in excellent agreement. We use the metallicity distribution function measured from stellar spectra to confirm the trends in the AMRs based on the JWST data. Together, these results confirm the efficacy of recovering a SFH and AMR with the NIRCam F090W-F150W filter combination and provide validation of the sensitivity and accuracy of stellar evolution libraries in the near-infrared relative to the optical for SFH recovery work. From the JWST data, WLM shows an early onset to star formation, followed by an extended pause post-reionization before star formation re-ignites, which is qualitatively similar to what has been observed in the isolated galaxies Leo~A and Aquarius. Quantitatively, 15% of the stellar mass formed in the first Gyr, while only 10% formed over the next ~5 Gyr; the stellar mass then rapidly doubled in ~2.5 Gyr, followed by constant star formation over the last ~5 Gyr.

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arXiv2023

The Panchromatic Hubble Andromeda Treasury XXI. The Legacy Resolved Stellar Photometry Catalog

We present the final legacy version of stellar photometry for the Panchromatic Hubble Andromeda Treasury (PHAT) survey. We have reprocessed all of the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS) near ultraviolet (F275W, F336W), optical (F475W, F814W), and near infrared (F110W, F160W) imaging from the PHAT survey using an improved method that optimized the survey depth and chip gap coverage by including all overlapping exposures in all bands in the photometry. An additional improvement was gained through the use of charge transfer efficiency (CTE) corrected input images, which provide more complete star finding as well as more reliable photometry for the NUV bands, which had no CTE correction in the previous version of the PHAT photometry. While this method requires significantly more computing resources and time than earlier versions where the photometry was performed on individual pointings, it results in smaller systematic instrumental completeness variations as demonstrated by cleaner maps in stellar density, and it results in optimal constraints on stellar fluxes in all bands from the survey data. Our resulting catalog has 138 million stars, 18% more than the previous catalog, with lower density regions gaining as much as 40% more stars. The new catalog produces nearly seamless population maps which show relatively well-mixed distributions for populations associated with ages older than 1-2 Gyr, and highly structured distributions for the younger populations.

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arXiv2023

Investigating Gaia EDR3 parallax systematics using asteroseismology of Cool Giant Stars observed by Kepler, K2, and TESS I. Asteroseismic distances to 12,500 red-giant stars

Gaia EDR3 has provided unprecedented data that generate a lot of interest in the astrophysical community, despite the fact that systematics affect the reported parallaxes at the level of ~ 10 muas. Independent distance measurements are available from asteroseismology of red-giant stars with measurable parallaxes, whose magnitude and colour ranges more closely reflect those of other stars of interest. In this paper, we determine distances to nearly 12,500 red-giant branch and red clump stars observed by Kepler, K2, and TESS. This is done via a grid-based modelling method, where global asteroseismic observables, constraints on the photospheric chemical composition, and on the unreddened photometry are used as observational inputs. This large catalogue of asteroseismic distances allows us to provide a first comparison with Gaia EDR3 parallaxes. Offset values estimated with asteroseismology show no clear trend with ecliptic latitude or magnitude, and the trend whereby they increase (in absolute terms) as we move towards redder colours is dominated by the brightest stars. The correction model proposed by Lindegren et al. (2021) is not suitable for all the fields considered in this study. We find a good agreement between asteroseismic results and model predictions of the red clump magnitude. We discuss possible trends with the Gaia scan law statistics, and show that two magnitude regimes exist where either asteroseismology or Gaia provides the best precision in parallax.

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arXiv2023

A Multiwavelength Classification and Study of Red Supergiant Candidates in NGC 6946

We have combined resolved stellar photometry from Hubble Space Telescope (\emph{HST}), \emph{Spitzer}, and \emph{Gaia} to identify red supergiant (RSG) candidates in NGC~6946, based on their colors, proper motions, visual morphologies, and spectral energy distributions. We start with a large sample of 17,865 RSG candidates based solely on \emph{HST} near-infrared photometry. We then chose a small sample of 385 of these candidates with Spitzer matches for more detailed study. Using evolutionary models and isochrones, we isolate a space where RSGs would be found in our photometry catalogs. We then visually inspect each candidate and compare to Gaia catalogs to identify and remove foreground stars. As a result, we classify 95 potential RSGs, with 40 of these being in our highest-quality sample. We fit the photometry of the populations of stars in the regions surrounding the RSGs to infer their ages. Placing our best candidate RSG stars into three age bins between 1 and 30 Myr, we find 27.5\% of the candidates falling between 1-10 Myr, 37.5\% between 10-20 Myr, and 35\% 20-30 Myr. A comparison of our results to the models of massive star evolution shows some agreement between model luminosities and the luminosities of our candidates for each age. Three of our candidates appear significantly more consistent with binary models than single-star evolution models.

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arXiv2023

The JWST Resolved Stellar Populations Early Release Science Program II. Survey Overview

We present the JWST Resolved Stellar Populations Early Release Science (ERS) science program. We obtained 27.5 hours of NIRCam and NIRISS imaging of three targets in the Local Group (Milky Way globular cluster M92, ultra-faint dwarf galaxy Draco II, star-forming dwarf galaxy WLM), which span factors of $\sim10^5$ in luminosity, $\sim10^4$ in distance, and $\sim10^5$ in surface brightness. We describe the survey strategy, scientific and technical goals, implementation details, present select NIRCam color-magnitude diagrams (CMDs), and validate the NIRCam exposure time calculator (ETC). Our CMDs are among the deepest in existence for each class of target. They touch the theoretical hydrogen burning limit in M92 ($<0.08$ $M_{\odot}$; SNR $\sim5$ at $m_{F090W}\sim28.2$; $M_{F090W}\sim+13.6$), include the lowest-mass stars observed outside the Milky Way in Draco II (0.09 $M_{\odot}$; SNR $=10$ at $m_{F090W}\sim29$; $M_{F090W}\sim+12.1$), and reach $\sim1.5$ magnitudes below the oldest main sequence turnoff in WLM (SNR $=10$ at $m_{F090W}\sim29.5$; $M_{F090W}\sim+4.6$). The PARSEC stellar models provide a good qualitative match to the NIRCam CMDs, though are $\sim0.05$ mag too blue compared to M92 F090W$-$F150W data. The NIRCam ETC (v2.0) matches the SNRs based on photon noise from DOLPHOT stellar photometry in uncrowded fields, but the ETC may not be accurate in more crowded fields, similar to what is known for HST. We release beta versions of DOLPHOT NIRCam and NIRISS modules to the community. Results from this ERS program will establish JWST as the premier instrument for resolved stellar populations studies for decades to come.

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arXiv2022

Low-Temperature Gas Opacities with AESOPUS 2.0

This work introduces new low-temperature gas opacities, in the range 3.2 <= log(T/K) <= 4.5, computed with the AESOPUS code under the assumption of thermodynamic equilibrium (Marigo &_Aringer_2009). In comparison to the previous version AESOPUS 1.0, we updated and expanded molecular absorption to include 80 species, mostly using the recommended line lists currently available from the ExoMol and HITRAN databases. Furthermore, in light of a recent study, we revised the H- photodetachment cross section, added the free-free absorption of other negative ions of atoms and molecules, and updated the collision-induced absorption due to H2/H2, H2/H, H2/He, and H/He pairs. Using the new input physics, we computed tables of Rosseland mean opacities for several scaled-solar chemical compositions, including Magg et al. (2022)'s most recent one, as well as alpha-enhanced mixtures. The differences in opacity between the new AESOPUS 2.0 and the original AESOPUS 1.0 versions, as well as other sets of calculations, are discussed. The new opacities are released to the community via a dedicated web-page that includes both pre-computed tables for widely used chemical compositions, and a web-interface for calculating opacities on-the-fly for any abundance distribution.

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arXiv2021

A Census of Thermally-Pulsing AGB stars in the Andromeda Galaxy and a First Estimate of their Contribution to the Global Dust Budget

We present a near-complete catalog of the metal-rich population of Thermally-Pulsing Asymptotic Giant Branch stars in the northwest quadrant of M31. This metal-rich sample complements the equally complete metal-poor Magellanic Cloud AGB catalogs produced by the SAGE program. Our catalog includes HST wide-band photometry from the Panchromatic Hubble Andromeda Treasury survey, HST medium-band photometry used to chemically classify a subset of the sample, and Spitzer mid- and far-IR photometry that we have used to isolate dust-producing AGB stars. We have detected 346,623 AGB stars; these include 4,802 AGB candidates producing considerable dust, and 1,356 AGB candidates that lie within clusters with measured ages, and in some cases metallicities. Using the Spitzer data and chemical classifications made with the medium-band data, we have identified both carbon- and oxygen-rich AGB candidates producing significant dust. We have applied color--mass-loss relations based on dusty AGB stars from the LMC to estimate the dust injection by AGB stars in the PHAT footprint. Applying our color relations to a subset of the chemically-classified stars producing the bulk of the dust, we find that ~97.8% of the dust is oxygen-rich. Using several scenarios for the dust lifetime, we have estimated the contribution of AGB stars to the global dust budget of M31 to be 0.9-35.5%, which is in line with previous estimates in the Magellanic Clouds. Follow-up observations of the M31 AGB candidates with the JWST will allow us to further constrain stellar and chemical evolutionary models, and the feedback and dust production of metal-rich evolved stars.

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arXiv2021

Dissecting the Gaia HR diagram within 200 pc

We analyse the high-quality Hertzsprung-Russell diagram (HRD) derived from Gaia data release 2 for the Solar Neighbourhood. We start building an almost-complete sample within 200 pc and for |b|>25 deg, so as to limit the impact of known errors and artefacts in the Gaia catalog. Particular effort is then put into improving the modelling of population of binaries, which produce two marked features in the HRD: the sequence of near-equal mass binaries along the lower main sequence, and the isolated group of hot subdwarfs. We describe a new tool, BinaPSE, to follow the evolution of interacting binaries in a way that improves the consistency with PARSEC evolutionary tracks for single stars. BinaPSE is implemented into the TRILEGAL code for the generation of "partial models" for both single and binary stellar populations, taking into account the presence of resolved and unresolved binaries. We then fit the Gaia HRD via MCMC methods that search for the star formation history (SFH) and initial binary fraction (by mass) that maximise the likelihood. The main results are (i) the binary fraction derived from the lower main sequence is close to 0.4, while twice larger values are favoured when the upper part of the HRD is fitted; (ii) present models predict the observed numbers of hot subdwarfs to within a factor of 2; (iii) irrespective of the prescription for the binaries, the star formation rate peaks at values 1.5e-4 Msun/yr at ages slightly above 2 Gyr, and then decreases to 0.8e-4 Msun/yr at very old ages.

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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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