arXiv subjects

G. Valle

Publications and source records attributed to G. Valle.

At least 19 recordsLinked to original sources

arXiv2026

A critical analysis of main-sequence fitting in open clusters to derive the helium-to-metal enrichment ratio $ΔY/ΔZ$

We aim to investigate the feasibility of accurately determining the helium-to-metal enrichment ratio $ΔY/ΔZ$ for open clusters using Gaia DR3 photometry. To test the reliability of this calibration, we performed a theoretical investigation using mock open clusters. We generated synthetic photometric data from isochrones calculated by five different stellar evolution codes (FRANEC, PARSEC 1.2s, PARSEC 2.0, BASTI, and MIST), for which the true $ΔY/ΔZ$ is known. We then fitted these mock clusters with two sets of isochrones calculated with the FRANEC code, differing only in the implementation of bolometric corrections (BCs). The analysis focused on the G-band absolute magnitude range (4.3 to 6.5 mag) to minimise the impact of poorly constrained physics. Synthetic clusters were generated at [Fe/H] values from 0.0 to 0.15 dex, for different numbers of populating stars and different levels of photometric uncertainties. The Monte Carlo experiments revealed significant and code-dependent biases. Unbiased results were achieved only when the stellar models used for synthetic-cluster generation and fitting were identical. Using identical FRANEC stellar models but different BCs introduced a significant bias of up to 0.6. Furthermore, using different stellar models for synthetic cluster generations resulted in even larger biases: $ΔY/ΔZ$ was underestimated by up to 0.8 for PARSEC target isochrones, while it was overestimated for BASTI and MIST isochrones by up to 0.6 and 1.5, respectively. The magnitude and the inconsistency of these biases strongly suggest that the photometric calibration of $ΔY/ΔZ$ using open clusters is not reliably robust.

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arXiv2025

Constraining the helium-to-metal enrichment ratio $ΔY/ΔZ$ from nearby field stars using Gaia DR3 photometry

We investigate the feasibility of accurately determining the helium-to-metal enrichment ratio, $ΔY/ΔZ$, from Gaia DR3 photometry for nearby low-mass main sequence field stars. We selected a sample of 2770 nearby MS stars from the Gaia DR3 catalogue, covering a Gaia $M_G$ absolute magnitude range of 6.0 to 6.8 mag. We computed a dense grid of isochrones, with $ΔY/ΔZ$ varying from 0.4 to 3.2. These models were then used to fit the observations using the SCEPtER pipeline. The fitted values indicated that $ΔY/ΔZ$ values of $1.5 \pm 0.5$ were dequate for most stars. However, several clues suggested caution ought to be taken in interpreting this result. Chief among these concerns is the trend of decreasing $ΔY/ΔZ$ with increasing $M_G$ magnitude, as well as the discrepancy between the red and blue parts of the observations. This result is further supported by our additional analysis of mock data, which were sampled and fitted from the same isochrone grid. In the mock data, no such trend emerged, while the uncertainty remained as large as 0.7. The robustness of our conclusions was confirmed by repeating the estimation using isochrones with Gaia magnitudes derived from different atmospheric models and by adopting a different stellar evolution code for stellar model computation. In both cases, the results changed drastically, clustering at $ΔY/ΔZ \approx 0.4$, which is at the lower end of the allowed values. Considering the current uncertainties affecting stellar model computations, it appears that adopting field stars for calibration is not a viable approach, even when adopting precise Gaia photometry.

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arXiv2025

Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and {\it Gaia} DR3 parallaxes. III. Main-sequence stars

We compare the radii derived from the asteroseismic scaling relations with those from surface brightness-colour relations (SBCRs) combined with the Gaia DR3 parallaxes for main-sequence (MS) stars. The atmospheric and asteroseismic parameters were sourced from the recently released KEYSTONE catalogue and matched to Gaia DR3 and TESS Input Catalog v8.2. We computed SBCR-based radii using two different SBCRs, and estimated their relative differences with respect to radius estimates from asteroseismic grid-based methods. We find a good agreement between SBCR and asteroseismic radii, with mean relative differences in radii ($E_g$) in the range 2% to 3% and a standard deviation of about 3%. We find no dependence on parallax, and a mild dependence on [Fe/H] for one of the SBCRs tested. We find a negative correlation between $E_g$ and the stellar mass, with a slope varying from $-0.051\pm0.016$ to $-0.039\pm0.014$ per solar mass. This change in slope led to a roughly 1.5% larger discrepancy in the $E_g$ estimates for stars with masses below 1.0 $M_{\odot}$. This larger discrepancy at the low-mass end supports conclusions drawn from giant star studies. This result is independently corroborated by the LEGACY sample, which uses Kepler photometry. For the LEGACY sample we measure a mean relative offset in $E_g$ of -1.4% with a standard deviation of 2.3%, and a dependence of $E_g$ on mass with a slope of $-0.052\pm0.011$ per mass unit, both fully consistent with the KEYSTONE analysis. The [...] apparent mass dependence still requires closer examination. This result is reassuring as it demonstrates the great accuracy and reliability of the radius estimates obtained through SBCRs, which, moreover, offer the significant advantage of being applicable to a large sample of stars with substantially lower time and costs compared to what is required by asteroseismology.

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arXiv2025

The role of stellar model input in correcting the asteroseismic scaling relations. Red giant branch models

This study investigates the variability of the theoretical correction factor, $f_{Δν}$, used in red giant branch (RGB) scaling relations, arising from different assumptions in stellar model computations. Adopting a commonly used framework, we focused on a 1.0 $M_{\odot}$ star and systematically varied seven input parameters: the reference solar mixture, the initial helium abundance, the inclusion of microscopic diffusion and mass loss, the method for calculating atmospheric opacity, the mixing-length parameter, and the boundary conditions. Each parameter was tested using two distinct but physically plausible values to mimic possible choices of different evolutionary codes. For each resulting stellar model, we computed the oscillation frequencies along the RGB and derived the large frequency spacing, $Δν_0$. The correction factor $f_{Δν}$ was then calculated by comparing the derived $Δν_0$ with that predicted by the uncorrected scaling relations. We found substantial variability in $f_{Δν}$ across the different models. The variation ranged from approximately 1.3% in the lower RGB to about 3% at $\log g = 1.4$. This level of variability is significant, as it corresponds to roughly half the values typically quoted in the literature and leads to a systematic change in derived masses from 5% to more than 10%. The most significant contribution to this variability came from the choice of atmospheric opacity calculation (approximately 1.2%), with a smaller contribution from the inclusion of microscopic diffusion (approximately 0.4%). These results indicate that the choice of the reference stellar model has a non-negligible impact on the calculation of correction factors applied to RGB star scaling relations.

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arXiv2025

Tests and calibrations of stellar models with two triply eclipsing triple systems

We investigated the possibility of using two recently characterised triply eclipsing triple systems to constrain stellar model parameters. We specifically focused on evaluating the influence of the underlying astrophysical assumptions employed in the characterisation of the system to fix absolute values of the radii, effective temperatures, and metallicity. We used dense grids of pre-computed stellar models to fit the data for the triply eclipsing systems with a modified version of the SCEPtER pipeline. We achieve an excellent agreement with observational data for TIC 650024463, which comprises three low-mass main-sequence (MS) stars. We find it has an age of $9.0^{+1.4}_{-1.1}$ Gyr and a multimodal posterior density. Characterising TIC 323486857 proved more challenging. This system comprises two intermediate-mass MS stars and a slightly more massive tertiary in the red giant branch phase. For this last system we tested alternative scenarios for convective core overshooting. When all stars were assumed to have the same overshooting efficiency, significant discrepancies arose with the observed data for the tertiary star. This discrepancy may arise from the different assumptions regarding overshooting efficiency made for the observational characterisation of the system, in which an increasing overshooting efficiency with stellar mass was adopted. By allowing independent overshooting efficiencies for all stars, we recovered a solution close to that adopted in the system observational characterisation. Encouragingly, despite the relevant differences between the adopted stellar models and those used for the observational characterisation, we found a system age of $2.33^{+0.18}_{-0.16}$ Gyr in all the tested scenarios, and this age is in agreement with independent determinations.

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arXiv2024

Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and {\it Gaia} DR3 parallaxes. II. Red giants and red clump stars from the {\it Kepler} catalogue

A recent investigation highlighted peculiar trends between the radii derived from surface brightness-colour relations (SBCRs) combined with Gaia DR3 parallaxes with respect to asteroseismic scaling relation radii from K2 data. [...] We investigated on the robustness of the results based on Kepler data. We cross-matched asteroseismic and astrometric data for over 12,000 red giant branch and red clump stars from the end-of-mission Kepler catalogue with the Gaia DR3 and TIC v8.2 to obtain precise parallaxes, V- and K-band magnitudes, and E(B - V) colour excesses. Two well-tested SBCRs from the literature were adopted to estimate stellar radii. The analysis confirmed that SBCR and asteroseismic radii agree very well. The overall differences are only 1-2% depending on the adopted SBCR. The dispersion of 7% was about two-thirds of what was found for K2-based data. As a difference from the K2-based investigation, the ratio of SBCRs-to-asteroseismic radii did not depend on the metallicity [Fe/H]. Moreover, the intriguing decreasing trend with [$α$/Fe] of the radius ratio for massive stars that was observed in K2 data was absent in Kepler data. The SBCR radii are systematically higher than asteroseismic estimates by 5% for stars with masses below 1.0 $M_{\odot}$. The SBCRs have proven to be a highly effective tool for estimating radii with a precision comparable to that obtained from asteroseismology, but at a significantly lower observational cost. Moreover, the superior concordance of Kepler-derived radii with SBCR measurements and the absence of the discrepancies observed in the K2-derived radii suggest the existence of underlying systematic errors that impact specific mass and metallicity regimes within the K2 dataset.

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arXiv2024

Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and Gaia DR3 parallaxes. Red giants and red clump stars

We compared stellar radii derived from asteroseismic scaling relations with those estimated using two independent surface brightness-colour relations (SBCRs) and Gaia DR3 parallaxes. We cross-matched asteroseismic and astrometric data for over 6,400 RGB and RC stars from the APO-K2 catalogue with the TESS Input Catalogue v8.2 to obtain precise V band magnitudes and E(B-V) colour excesses. We then adopted two different SBCRs from the literature to derive stellar radius estimates, denoted as $R^a$ and $R^b$, respectively. We analysed the ratio of these SBCR-derived radii to the asteroseismic radius estimates, $R$, provided in the APO-K2 catalogue. Both SBCRs exhibited good agreement with asteroseismic radius estimates. On average, $R^a$ was overestimated by 1.2% with respect to $R$, while $R^b$ was underestimated by 2.5%. For stars larger than 20 $R_{\odot}$, SBCR radii are systematically lower than asteroseismic ones. The agreement with asteroseismic radii shows a strong dependence on the parallax. The dispersion is halved for stars with a parallax greater than 2.5 mas. In this subsample, $R^b$ showed perfect agreement with $R$, while $R^a$ remained slightly overestimated by 3%. A trend with [Fe/H] of 4% to 6% per dex was found. For stars less massive than about 0.95 $M_{\odot}$, SBCR radii were significantly higher than asteroseismic ones, by about 6%. This overestimation correlated with the presence of extended helium cores in these stars' structures relative to their envelopes. Furthermore, radius ratios showed a dichotomous behaviour at higher masses, mainly due to the presence of several RC stars with SBCR radii significantly lower with respect to asteroseismology. This behaviour originates from a different response of asteroseismic scaling relations and SBCR to [$α$/Fe] abundance ratios for massive stars, both in RGB and RC phases, which is reported here for the first time.

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arXiv2024

Stellar model tests and age determination for RGB stars from the APO-K2 catalogue

By adopting the recently empirically derived dependence of $α$-elements on $[α/{\rm Fe}]$ instead of the conventionally applied uniform one, we tested the agreement between stellar model predictions and observations for red giant branch (RGB) stars in the APO-K2 catalogue. We particularly focused on the biases in effective temperature scales and on the robustness of age estimations. We computed a grid of stellar models relying on the empirical scaling of $α$-elements, investigating the offset in effective temperature $ΔT$ between these models and observations, using univariate analyses for both metallicity [Fe/H] and $[α/{\rm Fe}]$. To account for potential confounding factors, we then employed a multivariate generalised additive model to study the dependence of $ΔT$ on [Fe/H], $[α/{\rm Fe}]$, $\log g$, and stellar mass. The initial analysis revealed a negligible trend of $ΔT$ with [Fe/H], in contrast with previous works in the literature. A slight $ΔT$ difference of 25 K was detected between stars with high and low $α$-enhancement. Our multivariate analysis reveals a dependence of $ΔT$ on both [Fe/H] and $[α/{\rm Fe}]$, and highlights a significant dependence on stellar mass. This suggests a discrepancy in how effective temperature scales with stellar mass in the models compared to observations. Despite differences in assumed chemical composition, our analysis, through a fortunate cancellation effect, yields ages that are largely consistent with recent studies of the same sample. Notably, our analysis identifies a 6% fraction of stars younger than 4 Ga within the high-$α$ population. However, our analysis of the [C/N] ratio supports the possible origin of the these stars as a result of mergers or mass transfer events.

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arXiv2024

Element abundances of galactic RGB stars in the APO-K2 catalogue. Dissimilarity in the scaling with [$α$/Fe]

We conducted an investigation on the chemical abundances of 4,316 stars in the red giant branch (RGB) phase from the recently released APO-K2 catalogue. Our aim was to characterize the abundance trends of the single elements with [$α$/Fe], mainly focusing on C, N, and O, which are the most relevant for the estimation of stellar ages. The chemical analysis of the RGB sample involved cross-matching data from the APO-K2 catalogue with individual element abundances from APOGEE DR17. The analysis detected a statistically significant difference in the [(C+N+O)/Fe] - [$α$/Fe] trend with respect to the simple $α$-enhancement scenario. This difference remained robust across different choices for the reference solar mixture and potential zero-point calibrations of C and N abundances. The primary discrepancy was a steeper increase in [O/Fe] with [$α$/Fe], reaching a 0.1 dex difference at [$α$/Fe] = 0.3. Notably, the impact on the evolutionary timescale of such oxygen over-abundance with respect to the commonly adopted uniform $α$-enhancement is rather limited. We verified that stellar models computed using an ad hoc O-rich mixture sped up the evolution by only 1% at [$α$/Fe] = 0.3, due to the counterbalancing effects of O enrichment on both the evolutionary timescale and the Z-to-[Fe/H] relationship.

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arXiv2024

Constraining the helium-to-metal enrichment ratio $ΔY/ΔZ$ from main sequence binary stars. Theoretical analysis of the accuracy and precision of the age and helium abundance estimates

We investigated the theoretical possibility of accurately determining the helium-to-metal enrichment ratio $ΔY/ΔZ$ from precise observations of double lined eclipsing binary systems. Using Monte Carlo simulations, we drew synthetic binary systems with masses between 0.85 and 1.00 $M_{\odot}$ from a grid of stellar models with $ΔY/ΔZ = 2.0$ [...]. Subsequently, a broader grid with $ΔY/ΔZ$ from 1.0 to 3.0 was used in the fitting process. To account for observational uncertainties, two scenarios were explored: S1 with realistic uncertainties of 100 K in temperature and 0.1 dex in [Fe/H], and S2 with halved uncertainties. We repeated the simulation at two baseline metallicities: [Fe/H] = 0.0 and -0.3. The posterior distributions of $ΔY/ΔZ$ were severely biased towards the edge of the allowable range in the S1 errors scenario. The situation only marginally improved when considering the S2 scenario. The effect is due to the impact of changing $ΔY/ΔZ$ in the stellar effective temperature and its interplay with [Fe/H] observational error, and it is therefore not restricted to the specific fitting method. Despite the presence of these systematic discrepancies, the age of the systems were recovered unbiased with 10% precision. Our findings indicate that the observational uncertainty in effective temperature and metallicity significantly hinders the accurate determination of the $ΔY/ΔZ$ parameter from main sequence binary systems.

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arXiv2024

Impact of $α$ enhancement on the asteroseismic age determination of field stars. Application to the APO-K2 catalogue

We investigated the theoretical biases affecting the asteroseismic grid-based estimates of stellar parameters in the presence of a mismatch between the heavy element mixture of observed stars and stellar models. We performed a controlled simulation adopting effective temperature, [Fe/H], average large frequency spacing, and frequency of maximum oscillation power as observational constraints. Synthetic stars were sampled from grids of stellar models computed with different [alpha/Fe] values from 0.0 to 0.4. The mass, radius, and age of these objects were then estimated by adopting a grid of models with a fixed [alpha/Fe] value of 0.0. The experiment was repeated assuming different sets of observational uncertainties. In the reference scenario, we adopted an uncertainty of 1.5% in seismic parameters, 50 K in effective temperature, and 0.05 dex in [Fe/H]. A higher uncertainty in the atmospheric constraints was also adopted in order to explore the impact on the precision of the observations of the estimated stellar parameters. Our simulations showed that estimated parameters are biased up to 3% in mass, 1.5% in radius, and 4% in age when the reference uncertainty scenario was adopted. These values correspond to 45%, 48%, and 16% of the estimated uncertainty in the stellar parameters. These biases in mass and radius disappear when adopting larger observational uncertainties because of the possibility of the fitting algorithm exploring a wider range of possible solutions. However, in this scenario, the age is significantly biased by -8%. Finally, we verified that the stellar mass, radius, and age can be estimated with a high accuracy by adopting a grid with the incorrect value of [alpha/Fe] if the metallicity [Fe/H] of the target is adjusted to match the Z in the fitting grid. In this scenario, the maximum bias in the age was reduced to 1.5%.

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arXiv2023

Seismic and spectroscopic analysis of 9 bright red giants observed by Kepler

Photometric time series gathered by space telescopes such as CoRoT and Kepler allow to detect solar-like oscillations in red-giant stars and to measure their global seismic constraints, which can be used to infer global stellar properties (e.g. masses, radii, evolutionary states). Combining such precise constraints with photospheric abundances provides a means of testing mixing processes that occur inside red-giant stars. In this work, we conduct a detailed spectroscopic and seismic analysis of nine nearby (d < 200 pc) red-giant stars observed by Kepler. Both seismic constraints and grid-based modelling approaches are used to determine precise fundamental parameters for those evolved stars. We compare distances and radii derived from Gaia Data Release 3 parallaxes with those inferred by a combination of seismic, spectroscopic and photometric constraints. We find no deviations within errorsbars, however the small sample size and the associated uncertainties are a limiting factor for such comparison. We use the period spacing of mixed modes to distinguish between ascending red-giants and red-clump stars. Based on the evolutionary status, we apply corrections to the values of $Δν$ for some stars, resulting in a slight improvement to the agreement between seismic and photometric distances. Finally, we couple constraints on detailed chemical abundances with the inferred masses, radii and evolutionary states. Our results corroborate previous studies that show that observed abundances of lithium and carbon isotopic ratio are in contrast with predictions from standard models, giving robust evidence for the occurrence of additional mixing during the red-giant phase.

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arXiv2023

Impact of the uncertainties of $3 α$ and $^{12}{\rm C}(α,γ)^{16}{\rm O}$ reactions on the He-burning phases of low- and intermediate-mass stars

We estimate the impact on the stellar evolution of the uncertainties in the $3α$ and the $^{12}{\rm C}(α,γ)^{16}{\rm O}$ reaction rates [...]. We calculated models of low- and intermediate-mass stars for different values of the rates. The $3α$ reaction rate was varied up to $\pm 24\%$, while the $^{12}{\rm C}(α,γ)^{16}{\rm O}$ reaction rate was varied by up to $\pm 35\%$. The models were calculated for two different initial chemical compositions to represent different stellar populations. A $M = 0.67$ $M_{\odot}$ model was chosen as representative of the halo ancient stars, while for disk stars, the $M=1.5$ $M_{\odot}$ and $M=2.5$ $M_{\odot}$ models were considered. The impact of the two reaction rates on the central He-burning lifetime and the asymptotic giant branch (AGB) lifetime, as well as the mass of the C/O core at the central He exhaustion and the internal C and O abundances, was investigated. A variation of the $^{12}{\rm C}(α,γ)^{16}{\rm O}$ reaction rates resulted in marginal differences in the analysed features among the three considered stellar masses, except for the C/O abundances. The central He-burning lifetime changed by less than 4%, while the AGB lifetime was affected only at the 1% level. The internal C and O abundances showed greater variation, with a change of about 15%. The uncertainty in the $3α$ reaction rate mainly influences the C and O central abundances (up to 10%) for all the models considered, and the AGB lifetime for intermediate mass stars (up to 5%). Most of the investigated features were affected by less than 2%. The current uncertainty in the two reaction rates has a negligible effect on the predicted evolutionary time scale with respect to other uncertainty sources. The variability in the chemical profile at the end of the shell He-burning phase is still relevant.

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arXiv2023

Stellar model calibrations with the Ai Phe binary system. Open questions about the robustness of the fit

We explore the robustness of the calibration of stellar models achievable with Ai Phe binary system. By means of the SCEPtER pipeline, we investigated the impact of different assumptions about the surface efficiency of microscopic diffusion. In the reference scenario, we allowed modification of the surface metallicity due to microscopic diffusion, while in the alternative scenario we assumed that competing mixing from other sources cancels out this effect. Due to the fact that the primary star has already experienced the first dredge-up while the secondary has not, the tested scenarios show interesting differences. While the estimated age is quite robust ($4.70^{+0.13}_{-0.14}$ Gyr and $4.62^{+0.13}_{-0.06}$ Gyr), the calibration of the convective core overshooting parameter $β$ reveals noticeable differences. The reference scenario suggests a wide multi-modal range of possible values of $β$ around 0.10; the alternative scenario computations point towards a sharp and lower $β$, around 0.04. The impossibility to obtain an unambiguous fit confirms the difficulty in achieving a sensible calibration of the free parameters of stellar models using binary systems, even when very accurate masses and radii are available.

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arXiv2023

Age and convective core overshooting calibrations in CPD-54 810 binary system. Statistical investigation on the solution robustness

Relying on precise observations for the CPD-54 810 binary system, we investigate the robustness of the estimated age and convective core overshooting for a system with both stars on the main sequence (MS). [...] We adopt the SCEPtER pipeline, based on grids of stellar models computed for a different initial chemical composition and convective core overshooting efficiency. The base fit suggests a common age of $3.02 \pm 0.15$ Gyr, in agreement with recent literature. This estimated convective core overshooting parameter is $β= 0.09 \pm 0.01$, with a corresponding convective core mass $M_c = 0.059^{+0.017}_{-0.021}$ $M_{\odot}$. The robustness of these estimates were tested assuming a narrow constraint on the helium-to-metal enrichment ratio. The chemical solution of the system changes, but the age and the overshooting parameter are almost unchanged ($3.08^{+0.17}_{-0.14}$ Gyr and $0.09 \pm 0.01$). In a further test, we halved the uncertainty as to the effective temperature of both stars and again the estimated parameter shows only small variations ($3.02 \pm 0.12$ Gyr and $0.09 \pm 0.01$). This low variability suggests that the age of the system with both stars in the MS can be reliably estimated at a 5\% level, but it also indicates that the power of the investigation is probably low. [...] Despite the great increase in the observational constraints' precision, the results support the conclusions of previous theoretical works on the stellar parameter calibration with double MS star binary systems.

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arXiv2023

Uncertainties in asteroseismic grid-based estimates of the ages of halo stars

[...] The aim of this paper is to study the precision and theoretical biases in the age determinations of halo stars adopting both asteroseismic and classic observational constraints. [...] We adopt the well-tested SCEPtER pipeline, covering evolutionary phases up to the red giant branch (RGB). The fitting grids contain stars with mass in the range of [0.7; 1.0] $M_{\odot}$ and metallicity [Fe/H] from -2.5 to -0.5. We investigate several scenarios characterised by different adopted observational uncertainties. We also assess the impact of systematic discrepancies between the recovery grid models and target stars by computing several synthetic grids of stellar models with perturbed input physics. In our reference scenario, we recover ages for stars in the main sequence (MS) or subgiant branch (SGB) with a typical 10\%--20\% precision, while we recover those of RGB stars with a precision of about 60\%. However, adopting tighter constraints on asteroseismic parameters, the age precision in RGB improved to 20\%, while few modifications occur in the other analysed evolutionary phases. A systematic discrepancies between grid models and target stars shows that a mismatch in the mixing-length parameter value leads to significant bias in the age estimations for MS stars (about 10\%), but this bias is smaller for SGB and RGB stars. Neglecting the microscopic diffusion effect in the recovery grid leads to a typical 40\% bias in age estimates for stars on the MS. Finally, we applied the technique to stars in globular clusters. We find a precision in age estimates of around 20\% for MS stars and up to 40\% for RGB stars, greater than those obtained with classical methods. We demonstrate the method on stars of the cluster M4, obtaining a cluster age of $11.9 \pm 1.5$ Gyr and a mass at the turn-of off $0.86 \pm 0.04$ $M_{\odot}$, which are in good agreement with literature results.

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arXiv2021

Robust statistical tools for identifying multiple stellar populations in globular clusters in the presence of measurement errors. A case study: NGC 2808

The finding of multiple stellar populations (MP), defined by patterns in the stellar element abundances, is nowadays considered a distinctive feature of globular clusters. However, while data availability and quality improved in last decades, this is not always true for the techniques adopted to their analysis, rising problems of objectivity of the claims and reproducibility. Using NGC 2808 as test case we show the use of well established statistical clustering methods. We focus the analysis to the RGB phase, where two data sets are available from recent literature for low- and high-resolution spectroscopy. We adopt both hierarchical clustering and partition methods. We explicitly address the usually neglected problem of measurement errors. The results of the clustering algorithms were subjected to silhouette width analysis to compare the performance of the split into different number of MP. For both data sets the results are at odd with those reported in the literature. Two MP are detected for both data sets, while the literature reports five and four MP from high- and low-resolution spectroscopy respectively. The silhouette analysis suggests that the population sub-structure is reliable for high-resolution spectroscopy data, while the actual existence of MP is questionable for the low-resolution spectroscopy data. The discrepancy with literature claims is explainable due to the difference of methods adopted to MP characterisation. By means of Monte Carlo simulations and multimodality statistical tests we show that the often adopted study of the histogram of the differences in some key elements is prone to multiple false positive findings. The adoption of statistically grounded methods, which adopt all the available information to subset the data and explicitly address the problem of data uncertainty, is of paramount importance to present more robust and reproducible researches.

astro-ph.GA↗

arXiv2021

Goodness-of-fit test for isochrone fitting in the Gaia era. Statistical assessment of the error distribution

[...] This paper presents a rigorous derivation of a goodness-of-fit statistics for colour-magnitude diagrams (CMD). We discuss the reliability of the underlying assumptions and their validity. We derived the distribution of the sum of squared Mahalanobis distances of stellar data and theoretical isochrone for a generic set of data and models. We applied this to the case of synthetic CMDs constructed to mimic real data of open clusters in the GAIA sample. We analysed the capability of distinguishing among different sets of input physics and parameters that were used to compute the stellar models. We generated synthetic clusters from isochrones computed with these perturbed quantities, and we evaluated the goodness-of-fit with respect to the unperturbed isochrone. We show that when $r$ magnitudes are available for each of the $N$ observational objects and $p$ hyperparameters are estimated in the fit, the error distribution follows a $χ^2$ distribution with $(r-1)N - p$ degrees of freedom. We show that the linearisation of the isochrone causes negligible deviation from this result. We investigated the possibility of detecting the effects on stellar models that are induced when varying convective core overshooting efficiency, $^{14}$N$(p,γ)^{15}$O reaction rate, microscopic diffusion velocities, outer BCs, and colour transformation. The results suggest that it is possible to detect the effect induced by only some of the perturbed quantities. [...] A variation in the convective core overshooting efficiency was detectable only for photometric errors of 0.003 mag and only for the 1 Gyr case. The effects induced by the outer boundary conditions and the bolometric corrections are the largest. [...] As a last exercise, we addressed the validity of the goodness-of-fit statistics for real-world open cluster CMDs, contaminated by field stars or unresolved binaries. [...]

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