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DOE OSTI2021

The Red Supergiant Content of M31 and M33

We identify red supergiants (RSGs) in our spiral neighbors M31 and M33 using near-IR (NIR) photometry complete to a luminosity limit of logL/L{sub ⊙}=4.0. Our archival survey data cover 5 deg{sup 2} of M31, and 3 deg{sup 2} for M33, and are likely spatially complete for these massive stars. Gaia is used to remove foreground stars, after which the RSGs can be separated from asymptotic giant branch (AGB) stars in the color–magnitude diagram. The photometry is used to derive effective temperatures and bolometric luminosities via MARCS stellar atmosphere models. The resulting H-R diagrams show superb agreement with the evolutionary tracks of the Geneva evolutionary group. Our census includes 6400 RSGs in M31 and 2850 RSGs in M33 within their Holmberg radii; by contrast, only a few hundred RSGs are known so far in the Milky Way. Our catalog serves as the basis for a study of the RSG binary frequency being published separately, as well as future studies relating to the evolution of massive stars. Here we use the matches between the NIR-selected RSGs and their optical counterparts to show that the apparent similarity in the reddening of OB stars in M31 and M33 is the result of Malmquist bias; the average extinction in M31 is likely higher than that of M33. As expected, the distribution of RSGs follows that of the spiral arms, while the much older AGB population is more uniformly spread across each galaxy’s disk.

47 OTHER INSTRUMENTATION↗

DOE OSTI2022

mie_scat

This is a standalone Fortran code (mie_scat) that calculates the mie scattering cross sections, absorption cross sections, and efficiency coefficients of dust grains. It includes a separate file (miegrn) that functions as a wrapper function between PHOENIX (a proprietary radiative transfer code to model stellar atmospheres) and the mie scattering calculations. Miegrn works to determine the input parameters for mie_scat and then feeds the resultant data back into PHOENIX.

Stangl, Sarah↗

DOE OSTI2022

Hydrogen Line Shape Uncertainties in White Dwarf Model Atmospheres

For isolated white dwarf (WD) stars, fits to their observed spectra provide the most precise estimates of their effective temperatures and surface gravities. Even so, recent studies have shown that systematic offsets exist between such spectroscopic parameter determinations and those based on broadband photometry. These large discrepancies (10% in T eff , 0.1 M ⊙ in mass) provide scientific motivation for reconsidering the atomic physics employed in the model atmospheres of these stars. Recent simulation work of ours suggests that the most important remaining uncertainties in simulation-based calculations of line shapes are the treatment of 1) the electric field distribution and 2) the occupation probability (OP) prescription. We review the work that has been done in these areas and outline possible avenues for progress.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

SPISEA: A Python-based Simple Stellar Population Synthesis Code for Star Clusters

We present Stellar Population Interface for Stellar Evolution and Atmospheres (SPISEA), an open-source Python package that simulates simple stellar populations. The strength of SPISEA is its modular interface which offers the user control of 13 input properties including (but not limited to) the initial mass function, stellar multiplicity, extinction law, and the metallicity-dependent stellar evolution and atmosphere model grids used. The user also has control over the initial–final mass relation in order to produce compact stellar remnants (black holes, neutron stars, and white dwarfs). We demonstrate several outputs produced by the code, including color–magnitude diagrams, HR-diagrams, luminosity functions, and mass functions. SPISEA is object-oriented and extensible, and we welcome contributions from the community. The code and documentation are available on GitHub (https://github.com/astropy/SPISEA) and ReadtheDocs (https://spisea.readthedocs.io/en/latest/), respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Improve the Search of Very Metal-poor Stars Using the Deep Learning Method

Very metal-poor (VMP) stars have [Fe/H] < -2.0 dex. They are among the oldest stars in the universe, and their unique metallicity can help explore the enrichment mechanism and evolutionary history of the chemical elements of stars in the early universe. However, most current stellar parameter estimation methods do not perform well in determining the stellar parameters of VMP stars, which limits our ability to discover and exploit the properties of VMP stars. In this study, we propose a new model based on a convolutional neural network to determine the stellar atmospheric parameters of VMP stars. We tested our model on the LAMOST spectra; our model can determine the effective temperature (T {sub eff}), surface gravity (log g), metallicity ([Fe/H]), and carbon abundance ([C/Fe]) of the LAMOST spectra with precisions σ(T {sub eff}) = 134.82 K, σ(log g) = 0.33 dex, σ ([Fe/H]) = 0.20 dex, and σ([C/Fe]) = 0.35 dex. Furthermore, our model can distinguish VMP stars from normal stars with an accuracy of 88.65%. We also compared this model with other widely used methods, and found that this method performs better than other methods. It can be applied to the stellar parameter pipelines of upcoming large surveys such as 4MOST, WEAVES, and MOONS to search for VMP stars and identify carbon-enhanced metal-poor stars.

36 MATERIALS SCIENCE↗

DOE OSTI2026

MESA Isochrones and Stellar Tracks (MIST). III. The White Dwarf Cooling Sequence

We present a substantial update to the MESA Isochrones and Stellar Tracks (MIST) library, extending the MIST model grids and isochrones down the white dwarf (WD) cooling sequence with realistic physics for WD cooling timescales. This work provides a large grid of MESA models for carbon–oxygen core WDs with hydrogen atmospheres (spectral type DA/DC), descended from full prior stellar evolution calculations. The model tracks, isochrones, and WD cooling timescale contours are available on the MIST project website and at doi:10.5281/zenodo.15242047. Our WD models provide a very large, publicly available grid with detailed physics for WD cooling timescales: realistic interior and envelope compositions, with element diffusion and heavy-element sedimentation, nuclear burning at the base of the WD hydrogen envelope, core crystallization, and C/O phase separation. As a large grid of open-source stellar evolution models, these WD models provide both out-of-the-box model tracks for comparison with observations and a framework for building further WD models to investigate variations in WD physics.

Astronomy and AstroPhysics↗

DOE OSTI2021

ACCESS: An Optical Transmission Spectrum of the High-gravity Hot Jupiter HAT-P-23b

We present a new ground-based visible transmission spectrum of the high-gravity, hot Jupiter HAT-P-23b, obtained as part of the ACCESS project. We derive the spectrum from five transits observed between 2016 and 2018, with combined wavelength coverage between 5200 Å and 9269 Å in 200 Å bins, and with a median precision of 247 ppm per bin. HAT-P-23b’s relatively high surface gravity (g ≈ 30 m s{sup −2}), combined with updated stellar and planetary parameters from Gaia DR2, gives a five-scale-height signal of 384 ppm for a hydrogen-dominated atmosphere. Bayesian models favor a clear atmosphere for the planet with the tentative presence of TiO, after simultaneously modeling stellar contamination, using spots parameter constraints from photometry. If confirmed, HAT-P-23b would be the first example of a high-gravity gas giant with a clear atmosphere observed in transmission at optical/near-IR wavelengths; therefore, we recommend expanding observations to the UV and IR to confirm our results and further characterize this planet. This result demonstrates how combining transmission spectroscopy of exoplanet atmospheres with long-term photometric monitoring of the host stars can help disentangle the exoplanet and stellar activity signals.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

The DESI Y1 RR Lyrae catalog I: Empirical modeling of the cyclic variation of spectroscopic properties and a chemodynamical analysis of the outer halo

We present the catalog of RR Lyrae stars observed in the first year of operations of the Dark Energy Spectroscopic Instrument (DESI) survey. This catalog contains 6,240 RR Lyrae stars out to $\sim100$ kpc from the Galactic center and over 12,000 individual epochs with homogeneously-derived stellar atmospheric parameters. We introduce a novel methodology to model the cyclical variation of the spectroscopic properties of RR Lyrae from single-epoch measurements. We employ this method to infer the radial velocity and effective temperature variation of fundamental mode and first-overtone RR Lyrae stars and to determine their systemic velocities and mean temperatures. For fundamental mode pulsators, we obtain radial velocity curves with amplitudes of $\sim$30--50 km s$^{-1}$ and effective temperature curves with 300--1,000 K variations, whereas for first-overtone pulsators these amplitudes are $\sim20$ km s$^{-1}$ and $\sim 600$ K, respectively. We use our sample to study the metallicity distribution of the halo and its dependence on Galactocentric distance ($R_{\rm GC}$). Using a radius-dependent mixture model, we split the data into chemodynamically distinct components and find that our inner halo sample ($R_{\rm GC}\lesssim50$ kpc) is predominantly composed of stars with [Fe/H] $\sim-1.5$ dex and largely radial orbits (with an anisotropy parameter $\beta\sim0.94$), that we associate with the Gaia-Sausage-Enceladus merger event. Stars in the outer halo field exhibit a broader and more metal-poor [Fe/H] distribution with more circular orbits ($\beta\sim0.39$). The metallicity gradient of the metal-rich and the metal-poor components is found to be $0.005$ and $0.010$ dex kpc$^{-1}$, respectively. Our catalog highlights DESI's tantalizing potential for studying the Milky Way and the pulsation properties of RR Lyrae stars in the era of large spectroscopic surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Atmospheric Escape From TOI-700 d: Venus versus Earth Analogs

The recent discovery of an Earth-sized planet (TOI-700 d) in the habitable zone of an early-type M-dwarf by the Transiting Exoplanet Survey Satellite constitutes an important advance. In this Letter, we assess the feasibility of this planet to retain an atmosphere – one of the chief ingredients for surface habitability – over long timescales by employing state-of-the-art magnetohydrodynamic models to simulate the stellar wind and the associated rates of atmospheric escape. We take two major factors into consideration, namely, the planetary atmospheric composition and magnetic field. In all cases, we determine that the atmospheric ion escape rates are potentially a few orders of magnitude higher than the inner Solar system planets, but TOI-700 d is nevertheless capable of retaining a 1 bar atmosphere over gigayear timescales for certain regions of the parameter space. The simulations show that the unmagnetized TOI-700 d with a 1 bar Earth-like atmosphere could be stripped away rather quickly (< 1 gigayear), while the unmagnetized TOI-700 d with a 1 bar CO 2 -dominated atmosphere could persist for many billions of years; we find that the magnetized Earth-like case falls in between these two scenarios. We also discuss the prospects for detecting radio emission of the planet (thereby constraining its magnetic field) and discerning the presence of an atmosphere.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

SDSS-IV MaStar: [α/Fe] for the MaNGA Stellar Library from synthetic model spectra

ABSTRACT We calculate the α-enhancement ratio [α/Fe] for the Mapping Nearby Galaxies at APO (MaNGA) Stellar Library (MaStar) while also fitting for the fundamental atmospheric parameters effective temperature, surface gravity, and metallicity – Teff, log g, [Fe/H]. This approach builds upon a previous catalogue of stellar parameters, whereby only the fundamental atmospheric parameters are fit with solar-scaled models. Here, we use the same Markov Chain Monte Carlo method with the additional free parameter [α/Fe]. Using the full spectral fitting code pPXF, we are able to fit multiple lines sensitive to [α/Fe] for a more robust measurement. Quality flags based on the convergence of the sampler, errors in [α/Fe] and a cut in the χ2 of the model fit are used to clean the final catalogue, returning 17 214 spectra and values in the range of −0.25 < [α/Fe] < 0.48. Comparing our calculated [α/Fe] with literature values reveals a degeneracy in cool stars with log g ≥ ∼4; this comparison is then used to create an alternative and calibrated parameter set. We also plot the final catalogue in an [Fe/H] versus [α/Fe] diagram and recover the expected result of increasing [α/Fe] with decreasing [Fe/H] for Milky Way disc-halo stars. We apply our method to a subsample of spectra of uniform resolution and higher signal to noise that finds that our results are independent of this higher signal to noise. In the context of stellar population models, we are able to cover a parameter space for the creation of intermediate to old age models at solar-scaled [α/Fe], high [Fe/H] and enhanced [α/Fe], low [Fe/H].

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

The High-energy Radiation Environment around a 10 Gyr M Dwarf: Habitable at Last?

Recent work has demonstrated that high levels of X-ray and UV activity on young M dwarfs may drive rapid atmospheric escape on temperate, terrestrial planets orbiting within the habitable zone. However, secondary atmospheres on planets orbiting older, less active M dwarfs may be stable and present more promising candidates for biomarker searches. In order to evaluate the potential habitability of Earth-like planets around old, inactive M dwarfs, we present new Hubble Space Telescope and Chandra X-ray Observatory observations of Barnard’s Star (GJ 699), a 10 Gyr old M3.5 dwarf, acquired as part of the Mega-MUSCLES program. Despite the old age and long rotation period of Barnard’s Star, we observe two FUV (δ 130 ≈ 5000 s; E 130 ≈ 10 29.5 erg each) and one X-ray (E X ≈ 10 29.2 erg) flares, and we estimate a high-energy flare duty cycle (defined here as the fraction of the time the star is in a flare state) of ~25%. A publicly available 5 Å to 10 μm spectral energy distribution of GJ 699 is created and used to evaluate the atmospheric stability of a hypothetical, unmagnetized terrestrial planet in the habitable zone (r HZ ~ 0.1 au). Both thermal and nonthermal escape modeling indicate (1) the quiescent stellar XUV flux does not lead to strong atmospheric escape: atmospheric heating rates are comparable to periods of high solar activity on modern Earth, and (2) the flare environment could drive the atmosphere into a hydrodynamic loss regime at the observed flare duty cycle: sustained exposure to the flare environment of GJ 699 results in the loss of ≈87 Earth atmospheres Gyr -1 through thermal processes and ≈3 Earth atmospheres Gyr -1 through ion loss processes. These results suggest that if rocky planet atmospheres can survive the initial ~5 Gyr of high stellar activity, or if a second-generation atmosphere can be formed or acquired, the flare duty cycle may be the controlling stellar parameter for the stability of Earth-like atmospheres around old M stars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

HD 143811 AB b: A Directly Imaged Planet Orbiting a Spectroscopic Binary in Sco-Cen

We present confirmation of HD 143811 AB b, a substellar companion to spectroscopic binary HD 143811 AB through direct imaging with the Gemini Planet Imager (GPI) and Keck NIRC2. HD 143811 AB was observed as a part of the GPI Exoplanet Survey in 2016 and 2019 and is a member of the Sco-Cen star formation region. The exoplanet is detected ∼430 mas from the host star by GPI. With two GPI epochs and one from Keck/NIRC2 in 2022, we confirm through common proper motion analysis that the object is bound to its host star. We derive an orbit with a semimajor axis of $64^{+32}_{-14}$ au and eccentricity $0.23^{+0.24}_{-0.16}$. Spectral analysis of the GPI H-band spectrum and NIRC2 L′ photometry provides additional proof that this object is a substellar companion. We compare the spectrum of HD 143811 AB b to PHOENIX stellar models and Exo-Radioactive-Convective Equilibrium Model (REM) exoplanet atmosphere models and find that Exo-REM models provide the best fits to the data. From the Exo-REM models, we derive an effective temperature of $1042^{+178}_{-132}$ K for the planet and translate the derived luminosity of the planet to a mass of 5.6 ± 1.1 M Jup assuming hot-start evolutionary models. HD 143811 AB b is the first directly imaged planet around a binary that is not on an ultrawide orbit. Future characterization of this object will shed light on the formation of planets around binary star systems.

Astronomy and AstroPhysics↗

DOE OSTI2024

Carbon- and Oxygen-rich stars in MaStar: identification and classification

ABSTRACT Carbon- and Oxygen-rich stars populating the Thermally Pulsing Asymptotic Giant Branch (TP-AGB) phase of stellar evolution are relevant contributors to the spectra of ∼1 Gyr old populations. Atmosphere models for these types are uncertain, due to complex molecules and mass-loss effects. Empirical spectra are then crucial, but samples are small due to the short (∼3 Myr) TP-AGB lifetime. Here we exploit the vastness of the MaNGA Stellar library MaStar (∼60 000 spectra) to identify C and O-rich type stars. We define an optical colour selection with cuts of (g − r) > 2 and (g − i) < 1.55(g − r) − 0.07, calibrated with known C- and O-rich spectra. This identifies C- and O-rich stars along clean, separated sequences. An analogue selection is found in V, R, I bands. Our equation identifies C-rich and O-rich spectra with predictive performance metric F1-scores of 0.72 and 0.74 (over 1), respectively. We finally identify 41 C- and 87 O-rich type AGB stars in MaStar, 5 and 49 of which do not have a SIMBAD counterpart. We also detect a sample of non-AGB, dwarf C-stars. We further design a fitting procedure to classify the spectra into broad spectral types, by using as fitting templates empirical C- and O-rich spectra. We find remarkably good fits for the majority of candidates and categorize them into C- and O-rich bins following existing classifications, which correlate to effective temperature. Our selection models can be applied to large photometric surveys (e.g. Euclid, Rubin). The classified spectra will facilitate future evolutionary population synthesis models.

Hill, Lewis (ORCID:0000000180528080)↗

DOE OSTI2021

Exosphere Modeling of Proxima b: A Case Study of Photochemical Escape with a Venus-like Atmosphere

Exoplanets orbiting M dwarfs within habitable zones are exposed to stellar environments more extreme than that terrestrial planets experience in our solar system, which can significantly impact the atmospheres of the exoplanets and affect their habitability and sustainability. This study provides the first prediction of hot oxygen corona structure and the associated photochemical loss from a 1 bar CO 2 -dominated atmosphere of a Venus-like rocky exoplanet, where dissociative recombination of O 2 + ions is assumed to be the major source reaction for the escape of neutral O atoms and formation of the hot O corona (or exospheres) as on Mars and Venus. We employ a 3D Monte Carlo code to simulate the exosphere of Proxima Centauri b (PCb) based on the ionosphere simulated by a 3D magnetohydrodynamic model. Our simulation results show that variability of the stellar wind dynamic pressure over one orbital period of PCb does not affect the overall spatial structure of the hot O corona but contributes to the change in the global hot O escape rate that varies by an order of magnitude. The escape increases dramatically when the planet possesses its intrinsic magnetic fields as the ionosphere becomes more extended with the presence of a global magnetic field. Furthermore, the extended hot O corona may lead to a more extended H exosphere through collisions between thermal H and hot O, which exemplifies the importance of considering nonthermal populations in exospheres to interpret future observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Investigating the architecture and internal structure of the TOI-561 system planets with CHEOPS, HARPS-N, and TESS

ABSTRACT We present a precise characterization of the TOI-561 planetary system obtained by combining previously published data with TESS and CHEOPS photometry, and a new set of 62 HARPS-N radial velocities (RVs). Our joint analysis confirms the presence of four transiting planets, namely TOI-561 b (P = 0.45 d, R = 1.42 R⊕, M = 2.0 M⊕), c (P = 10.78 d, R = 2.91 R⊕, M = 5.4 M⊕), d (P = 25.7 d, R = 2.82 R⊕, M = 13.2 M⊕), and e (P = 77 d, R = 2.55 R⊕, M = 12.6 R⊕). Moreover, we identify an additional, long-period signal (>450 d) in the RVs, which could be due to either an external planetary companion or to stellar magnetic activity. The precise masses and radii obtained for the four planets allowed us to conduct interior structure and atmospheric escape modelling. TOI-561 b is confirmed to be the lowest density (ρb = 3.8 ± 0.5 g cm−3) ultra-short period (USP) planet known to date, and the low metallicity of the host star makes it consistent with the general bulk density-stellar metallicity trend. According to our interior structure modelling, planet b has basically no gas envelope, and it could host a certain amount of water. In contrast, TOI-561 c, d, and e likely retained an H/He envelope, in addition to a possibly large water layer. The inferred planetary compositions suggest different atmospheric evolutionary paths, with planets b and c having experienced significant gas loss, and planets d and e showing an atmospheric content consistent with the original one. The uniqueness of the USP planet, the presence of the long-period planet TOI-561 e, and the complex architecture make this system an appealing target for follow-up studies.

Lacedelli, G. (ORCID:0000000241977374)↗

DOE OSTI2021

SDSS-IV MaStar: theoretical atmospheric parameters for the MaNGA stellar library

ABSTRACT We calculate the fundamental stellar parameters effective temperature, surface gravity, and iron abundance – Teff, log g, [Fe/H] – for the final release of the Mapping Nearby Galaxies at APO (MaNGA) Stellar Library (MaStar), containing 59 266 per-visit-spectra for 24 290 unique stars at intermediate resolution (R ∼ 1800) and high S/N (median = 96). We fit theoretical spectra from model atmospheres by both MARCS and BOSZ-ATLAS9 to the observed MaStar spectra, using the full spectral fitting code pPXF. We further employ a Bayesian approach, using a Markov Chain Monte Carlo (MCMC) technique to map the parameter space and obtain uncertainties. Originally in this paper, we cross match MaStar observations with Gaia photometry, which enable us to set reliable priors and identify outliers according to stellar evolution. In parallel to the parameter determination, we calculate corresponding stellar population models to test the reliability of the parameters for each stellar evolutionary phase. We further assess our procedure by determining parameters for standard stars such as the Sun and Vega and by comparing our parameters with those determined in the literature from high-resolution spectroscopy (APOGEE and SEGUE) and from lower resolution matching template (LAMOST). The comparisons, considering the different methodologies and S/N of the literature surveys, are favourable in all cases. Our final parameter catalogue for MaStar cover the following ranges: 2592 ≤ Teff ≤ 32 983 K; −0.7 ≤ log g ≤ 5.4 dex; −2.9 ≤ [Fe/H] ≤ 1.0 dex and will be available with the last SDSS-IV Data Release, in 2021 December.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Measurements of ion-electron energy-transfer cross section in high-energy-density plasmas

Here, we report on measurements of the ion-electron energy-transfer cross section utilizing low-velocity ion stopping in high-energy-density plasmas at the OMEGA laser facility. These measurements utilize a technique that leverages the close relationship between low-velocity ion stopping and ion-electron equilibration. Shock-driven implosions of capsules filled with D 3 He gas doped with a trace amount of argon are used to generate densities and temperatures in ranges from 1 × 10 23 to 2 × 10 24 cm –3 and from 1.4 to 2.5 keV, respectively. The energy loss of 1-MeV DD tritons and 3.7-MeV D 3 He alphas that have velocities lower than the average velocity of the thermal electrons is measured. The energy loss of these ions is used to determine the ion-electron energy-transfer cross section, which is found to be in excellent agreement with quantum-mechanical calculations in the first Born approximation. This result provides an experimental constraint on ion-electron energy transfer in high-energy-density plasmas, which impacts the modeling of alpha heating in inertial confinement fusion implosions, magnetic-field advection in stellar atmospheres, and energy balance in supernova shocks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

J-PLUS: Support vector regression to measure stellar parameters

Stellar parameters are among the most important characteristics in studies of stars which, in traditional methods, are based on atmosphere models. However, time, cost, and brightness limits restrain the efficiency of spectral observations. The Javalambre Photometric Local Universe Survey (J-PLUS) is an observational campaign that aims to obtain photometry in 12 bands. Owing to its characteristics, J-PLUS data have become a valuable resource for studies of stars. Machine learning provides powerful tools for efficiently analyzing large data sets, such as the one from J-PLUS, and enables us to expand the research domain to stellar parameters. The main goal of this study is to construct a support vector regression (SVR) algorithm to estimate stellar parameters of the stars in the first data release of the J-PLUS observational campaign. The training data for the parameter's regressions are featured with 12-waveband photometry from J-PLUS and are crossidentified with spectrum-based catalogs. These catalogs are from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, the Apache Point Observatory Galactic Evolution Experiment, and the Sloan Extension for Galactic Understanding and Exploration. We then label them with the stellar effective temperature, the surface gravity, and the metallicity. Ten percent of the sample is held out to apply a blind test. We develop a new method, a multi-model approach, in order to fully take into account, the uncertainties of both the magnitudes and the stellar parameters. The method utilizes more than 200 models to apply the uncertainty analysis. We present a catalog of 2 493 424 stars with the root mean square error of 160 K in the effective temperature regression, 0.35 in the surface gravity regression, and 0.25 in the metallicity regression. We also discuss the advantages of this multi-model approach and compare it to other machine-learning methods.

79 ASTRONOMY AND ASTROPHYSICS↗