arXiv subjects

Paola Marigo

Publications and source records attributed to Paola Marigo.

At least 37 records · Page 2Linked to original sources

arXiv2022

Simulating the Legacy Survey of Space and Time stellar content with TRILEGAL

We describe a large simulation of the stars to be observed by the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). The simulation is based on the TRILEGAL code, which resorts to large databases of stellar evolutionary tracks, synthetic spectra, and pulsation models, added to simple prescriptions for the stellar density and star formation histories of the main structures of the Galaxy, to generate mock stellar samples through a population synthesis approach. The main bodies of the Magellanic Clouds are also included. A complete simulation is provided for single stars, down to the $r=27.5$ mag depth of the co-added wide-fast-deep survey images. A second simulation is provided for a fraction of the binaries, including the interacting ones, as derived with the BinaPSE module of TRILEGAL. We illustrate the main properties and numbers derived from these simulations, including: comparisons with real star counts; the expected numbers of Cepheids, long-period variables and eclipsing binaries; the crowding limits as a function of seeing and filter; the star-to-galaxy ratios, etc. Complete catalogs are accessible through the NOIRLab Astro Data Lab, while the stellar density maps are incorporated in the LSST metrics analysis framework (MAF).

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arXiv2022

The Initial-Final Mass Relation of White Dwarfs: A Tool to Calibrate the Third Dredge-up

The initial mass-final mass relationship (IFMR) of white dwarfs (WD) represents a crucial benchmark for stellar evolution models, especially for the efficiency of mixing episodes and mass loss during the asymptotic giant branch (AGB) phase. In this study, we argue that such relation offers the opportunity of constraining the third dredge-up (3DU), with important consequences for chemical yields. The results are discussed in light of recent studies that have identified a kink in the IFMR for initial masses close to $2\,M_{\odot}$. Adopting a physically-sound approach in which the efficiency $λ$ of the 3DU varies as a function of core and envelope masses, we calibrate $λ$ in solar-metallicity TP-AGB models in order to reproduce the final masses of their WD progeny, over a the range of initial masses $0.9 \le M_{\rm i}/M_{\odot} \le 6$. In particular, we find that in low-mass stars with $1.4 \le M_{\rm i}/M_{\odot} \le 2.0$ the efficiency is small, $λ\le 0.3$, it steeply rises to about $λ\simeq 0.65$ in intermediate-mass stars with $2.0 \le M_{\rm i}/M_{\odot} \le 4.0$, and then it drops in massive TP-AGB stars with $4.0 \le M_{\rm i}/M_{\odot} \le 6.0$. Our study also suggests that a second kink may show up in the IFMR at the transition between the most massive carbon stars and those that are dominated by hot-bottom burning.

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arXiv2021

A Fresh Look at AGB stars in Galactic Open Clusters with Gaia: Impact on Stellar Models and the Initial-Final Mass Relation

Benefiting from the GAIA second and early third releases of photometric and astrometric data we examine the population of asymptotic giant branch (AGB) stars that appear in the fields of intermediate-age and young open star clusters. We identify 49 AGB star candidates, brighter than the tip of the red giant branch, with a good-to-high cluster membership probability. Among them we find 19 TP-AGB stars with known spectral type: 4 M stars, 3 MS/S stars and 12 C stars. By combining observations, stellar models, and radiative transfer calculations that include the effect of circumstellar dust, we characterize each star in terms of initial mass, luminosity, mass-loss rate, core mass, period and mode of pulsation. The information collected helps us shed light on the TP-AGB evolution at solar-like metallicity, placing constraints on the third dredge-up process, the initial masses of carbon stars, stellar winds, and the initial-final mass relation (IFMR). In particular, we find that two bright carbon stars, MSB 75 and BM IV 90, members of the clusters NGC 7789 and NGC 2660 (with similar ages of $\simeq 1.2-1.6$ Gyr and initial masses $ 2.1 \ge M_{\rm i}/M_{\odot} \ge 1.9$), have unusually high core masses, $M_{\rm c} \approx 0.67-0.7\,M_{\odot}$. These results support the findings of a recent work (Marigo et al. 2020) that identified a kink in the IFMR, which interrupts its monotonic trend just at the same initial masses. Finally, we investigate two competing scenarios to explain the $M_{\rm c}$ data: the role of stellar winds in single-star evolution, and binary interactions through the blue-straggler channel.

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arXiv2021

The VMC survey -- XLIII. The spatially resolved star formation history across the Large Magellanic Cloud

We derive the spatially-resolved star formation history (SFH) for a $96$ deg$^2$ area across the main body of the Large Magellanic Cloud (LMC), using the near-infrared photometry from the VISTA survey of the Magellanic Clouds (VMC). The data and analyses are characterised by a great degree of homogeneity and a low sensitivity to the interstellar extinction. 756 subregions of size $0.125$ deg$^2$ -- corresponding to projected sizes of about $296\times322\,\mathrm{pc}^{2}$ in the LMC -- are analysed. The resulting SFH maps, with typical resolution of $0.2$--$0.3$ dex in logarithm of age, reveal main features in the LMC disc at different ages: the patchy star formation at recent ages, the concentration of star formation on three spiral arms and on the Bar up to ages of $\sim\!1.6$ Gyr, and the wider and smoother distribution of older populations. The period of most intense star formation occurred roughly between 4 and 0.5 Gyr ago, at rates of $\sim\!0.3\,\mathrm{M}_{\odot}\mathrm{yr}^{-1}$. We compare young and old star formation rates with the observed numbers of RR Lyrae and Cepheids. We also derive a mean extinction and mean distance for every subregion, and the plane that best describes the spatial distribution of the mean distances. Our results cover an area about 50 per cent larger than the classical SFH maps derived from optical data by Harris & Zaritsky (2009). Main differences with respect to those maps are lower star formation rates at young ages, and a main peak of star formation being identified at ages slightly younger than $1$ Gyr.

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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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arXiv2020

Formation of GW190521 from stellar evolution: the impact of the hydrogen-rich envelope, dredge-up and $^{12}$C($α$, $γ$)$^{16}$O rate on the pair-instability black hole mass gap

Pair-instability (PI) is expected to open a gap in the mass spectrum of black holes (BHs) between $\approx{}40-65$ M$_\odot$ and $\approx{}120$ M$_\odot$. The existence of the mass gap is currently being challenged by the detection of GW190521, with a primary component mass of $85^{+21}_{-14}$ M$_{\odot}$. Here, we investigate the main uncertainties on the PI mass gap: the $^{12}$C($α$, $γ$)$^{16}$O reaction rate and the H-rich envelope collapse. With the standard $^{12}$C($α$, $γ$)$^{16}$O rate, the lower edge of the mass gap can be 70 M$_\odot$ if we allow for the collapse of the residual H-rich envelope at metallicity $Z\leq{}0.0003$. Adopting the uncertainties given by the STARLIB database, for models computed with the $^{12}$C($α$, $γ$)$^{16}$O rate $-1\, σ$, we find that the PI mass gap ranges between $\approx{}80$ M$_\odot$ and $\approx{}150$ M$_\odot$. Stars with $M_{\rm ZAMS}>110$ M$_\odot$ may experience a deep dredge-up episode during the core helium-burning phase, that extracts matter from the core enriching the envelope. As a consequence of the He-core mass reduction, a star with $M_{\rm ZAMS} =160$ M$_\odot$ may avoid the PI and produce a BH of 150 M$_\odot$. In the $-2\,{}σ$ case, the PI mass gap ranges from 92 M$_\odot$ to 110 M$_\odot$. Finally, in models computed with $^{12}$C($α$, $γ$)$^{16}$O $-3\,{}σ$, the mass gap is completely removed by the dredge-up effect. The onset of this dredge-up is particularly sensitive to the assumed model for convection and mixing. The combined effect of H-rich envelope collapse and low $^{12}$C($α$, $γ$)$^{16}$O rate can lead to the formation of BHs with masses consistent with the primary component of GW190521.

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arXiv2020

Modelling Long-Period Variables -- II. Fundamental mode pulsation in the nonlinear regime

Long-period variability in luminous red giants has several promising applications, all of which require models able to accurately predict pulsation periods. Linear pulsation models have proven successful in reproducing the observed periods of overtone modes in evolved red giants, but they fail to accurately predict their fundamental mode periods. Here, we use a 1D hydrodynamic code to investigate the long-period variability of M-type asymptotic giant branch stars in the nonlinear regime. We examine the period and stability of low-order radial pulsation modes as a function of mass and radius, and find overtone mode periods in complete agreement with predictions from linear pulsation models. In contrast, nonlinear models predict an earlier onset of dominant fundamental mode pulsation, and shorter periods at large radii. Both features lead to a substantially better agreement with observations, that we verify against OGLE and Gaia data for the Magellanic Clouds. We provide simple analytic relations describing the nonlinear fundamental mode period-mass-radius relation. Differences with respect to linear predictions originate from the readjustment of the envelope structure induced by large-amplitude pulsation. We investigate the impact of turbulent viscosity on linear and nonlinear pulsation, and probe possible effects of varying metallicity and carbon abundance.

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arXiv2020

Constraining the thermally pulsing asymptotic giant branch phase with resolved stellar populations in the Large Magellanic Cloud

Reliable models of the thermally pulsing asymptotic giant branch (TP-AGB) phase are of critical importance across astrophysics, including our interpretation of the spectral energy distribution of galaxies, cosmic dust production, and enrichment of the interstellar medium. With the aim of improving sets of stellar isochrones that include a detailed description of the TP-AGB phase, we extend our recent calibration of the AGB population in the Small Magellanic Cloud (SMC) to the more metal rich Large Magellanic Cloud (LMC). We model the LMC stellar populations with the TRILEGAL code, using the spatially-resolved star formation history derived from the VISTA survey. We characterize the efficiency of the third dredge-up by matching the star counts and the $K_{\rm s}$-band luminosity functions of the AGB stars identified in the LMC. In line with previous findings, we confirm that, compared to the SMC, the third dredge-up in AGB stars of the LMC is somewhat less efficient, as a consequence of the higher metallicity. The predicted range of initial mass of C-rich stars is between $M_{\rm i} \approx 1.7 - 3~\mathrm{M}_{\odot}$ at $Z_{\rm i} = 0.008$. We show how the inclusion of new opacity data in the carbon star spectra will improve the performance of our models. We discuss the predicted lifetimes, integrated luminosities and mass-loss rate distributions of the calibrated models. The results of our calibration are included in updated stellar isochrones publicly available.

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arXiv2020

PHAT XX. AGB stars and other cool giants in M31 star clusters

The presence of AGB stars in clusters provides key constraints for stellar models, as has been demonstrated with historical data from the Magellanic Clouds. In this work, we look for candidate AGB stars in M31 star clusters from the Panchromatic Hubble Andromeda Treasury (PHAT) survey. Our photometric criteria selects stars brighter than the tip of the red giant branch, which includes the bulk of the thermally-pulsing AGB stars as well as early-AGB stars and other luminous cool giants expected in young stellar populations (e.g. massive red supergiants, and intermediate-mass red helium-burning stars). The AGB stars can be differentiated, a posteriori, using the ages already estimated for our cluster sample. 937 candidates are found within the cluster aperture radii, half (450) of which are very likely cluster members. Cross-matching with additional databases reveals two carbon stars and ten secure variables among them. The field-corrected age distribution reveals the presence of young supergiants peaking at ages smaller than 100 Myr, followed by a long tail of AGB stars extending up to the oldest possible ages. This long tail reveals the general decrease in the numbers of AGB stars from initial values of 50e-6/Msun at 100 Myr down to 5e-6/Msun at 10 Gyr. Theoretical models of near-solar metallicity reproduce this general trend, although with localized discrepancies over some age intervals, whose origin is not yet identified. The entire catalogue is released together with finding charts to facilitate follow-up studies.

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arXiv2020

Carbon star formation as seen through the non-monotonic initial-final mass relation

The initial-final mass relation (IFMR) links the birth mass of a star to the mass of the compact remnant left at its death. While the relevance of the IFMR across astrophysics is universally acknowledged, not all of its fine details have yet been resolved. A new analysis of a few carbon-oxygen white dwarfs in old open clusters of the Milky Way led us to identify a kink in the IFMR, located over a range of initial masses, $1.65 \lesssim M_{\rm i}/M_{\odot} \lesssim 2.10$. The kink's peak in WD mass of $\approx 0.70-0.75 \, M_{\odot}$ is produced by stars with $M_{\rm i} \simeq 1.8 - 1.9 \, M_{\odot}$, corresponding to ages of about $1.8 - 1.7 $ Gyr. Interestingly, this peak coincides with the initial mass limit between low-mass stars that develop a degenerate helium core after central hydrogen exhaustion, and intermediate-mass stars that avoid electron degeneracy. We interpret the IFMR kink as the signature of carbon star formation in the Milky Way. This finding is critical to constraining the evolution and chemical enrichment of low-mass stars, and their impact on the spectrophotometric properties of galaxies.

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arXiv2019

YBC, a stellar bolometric corrections database with variable extinction coefficients: an application to PARSEC isochrones

We present the \texttt{YBC} database of stellar bolometric corrections (BCs), available at \url{http://stev.oapd.inaf.it/YBC}. We homogenize widely-used theoretical stellar spectral libraries and provide BCs for many popular photometric systems, including the Gaia filters. The database can be easily extended to additional photometric systems and stellar spectral libraries. The web interface allows users to transform their catalogue of theoretical stellar parameters into magnitudes and colours of selected filter sets. The BC tables can be downloaded or also be implemented into large simulation projects using the interpolation code provided with the database. We compute extinction coefficients on a star-by-star basis, hence taking into account the effects of spectral type and non-linearity dependency on the total extinction. We illustrate the use of these BCs in \texttt{PARSEC} isochrones. We show that using spectral-type dependent extinction coefficients is quite necessary for Gaia filters whenever $\Av\gtrsim 0.5$\,mag. BC tables for rotating stars and tables of limb-darkening coefficients are also provided.

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arXiv2019

Multiple stellar populations in NGC 1866. New clues from Cepheids and Colour-Magnitude Diagram

We perform a comprehensive study of the stellar populations in the young Large Magellanic Cloud cluster NGC 1866, combining the analysis of its best-studied Cepheids with that of a very accurate colour-magnitude diagram (CMD) obtained from the most recent Hubble Space Telescope photometry. We use a Bayesian method based on new PARSEC stellar evolutionary tracks with overshooting and rotation to obtain ages and initial rotation velocities of five well-studied Cepheids of the cluster. We find that four of the five Cepheids belong to an initially slowly rotating young population (of $ 176 \pm 5$ Myr), while the fifth one is significantly older, either $ 288 \pm 20$ Myr for models with high initial rotational velocity ($ω_\mathrm{i} \sim 0.9$), or $ 202 \pm 5$ Myr for slowly rotating models. The complementary analysis of the CMD rules out the latter solution while strongly supporting the presence of two distinct populations of $\sim$176 Myr and $\sim$288 Myr, respectively. Moreover, the observed multiple main sequences and the turn-offs indicate that the younger population is mainly made of slowly rotating stars, as is the case of the four younger Cepheids, while the older population is made mainly of initially fast rotating stars, as is the case of the fifth Cepheid. Our study not only reinforces the notion that some young clusters like NGC 1866 harbor multiple populations, but gives also hints that the first population, the older, may inherit the angular momentum from the parent cloud while stars of the second one, the younger, do not.

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arXiv2019

On the photometric signature of fast rotators

Rapidly rotating stars have been recently recognized as having a major role in the interpretation of colour-magnitude diagrams of young and intermediate-age star clusters in the Magellanic Clouds and in the Milky Way. In this work, we evaluate the distinctive spectra and distributions in colour-colour space that follow from the presence of a substantial range in effective temperatures across the surface of fast rotators. The calculations are inserted in a formalism similar to the one usually adopted for non-rotating stars, which allows us to derive tables of bolometric corrections as a function not only of a reference effective temperature, surface gravity and metallicity, but also of the rotational speed with respect to the break-up value, $ω$, and the inclination angle, $i$. We find that only very fast rotators ($ω>0.95$) observed nearly equator-on ($i>45^\circ$) present sizable deviations from the colour-colour relations of non-rotating stars. In light of these results, we discuss the photometry of the $\sim$ 200-Myr-old cluster NGC 1866 and its split main sequence, which has been attributed to the simultaneous presence of slow and fast rotators. The small dispersion of its stars in colour-colour diagrams allow us to conclude that fast rotators in this cluster either have rotational velocities $ω<0.95$, or are all observed nearly pole-on. Such geometric colour-colour effects, although small, might be potentially detectable in the huge, high-quality photometric samples in the post-Gaia era, in addition to the evolutionary effects caused by rotation-induced mixing.

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arXiv2019

Carbon stars with increased oxygen and nitrogen abundances: hydrostatic dust-free model atmospheres

We have computed a grid of hydrostatic spherical COMARCS models for C stars covering metallicities from [Z/H]=0 to -2 and values of the carbon excess [C-O] from 6.41 to 9.15, plus some temperature sequences, where the amount of oxygen and nitrogen is increased relative to a scaled solar element mixture. Such abundance variations may appear during the late stages of stellar evolution. Our study covers changes of [O/Z] and [N/Z] going up to +0.5. Based on the atmospheric structures we have calculated synthetic spectra and photometry for all of the models in a consistent way. The sequences with changed [O/Z] and [N/Z] can be used to derive correction terms, which are applied to the colours predicted for a certain combination of effective temperature, surface gravity, metallicity and carbon excess. If one neglects these shifts in case of a variable oxygen amount, taking [C-O] instead of C/O gives much better results, since the first quantity dominates the formation of many important molecular species. For the warmer C giants with weaker pulsation it is in principle possible to determine [C-O], [O/Z] or [N/Z] from high resolution spectra, when the opacities in the radiative transfer calculations for the models and observable properties are treated consistently. The corresponding changes due to the abundances often become significantly larger than the deviations caused by uncertainties of the stellar parameters or by a optically thin dust shell. Photometric data and low or medium resolution spectra are not sufficient to derive the mentioned quantities.

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arXiv2019

Constraining the thermally-pulsing asymptotic giant branch phase with resolved stellar populations in the Small Magellanic Cloud

The thermally-pulsing asymptotic giant branch (TP-AGB) experienced by low- and intermediate-mass stars is one of the most uncertain phases of stellar evolution and the models need to be calibrated with the aid of observations. To this purpose, we couple high-quality observations of resolved stars in the Small Magellanic Cloud (SMC) with detailed stellar population synthesis simulations computed with the TRILEGAL code. The strength of our approach relies on the detailed spatially-resolved star formation history of the SMC, derived from the deep near-infrared photometry of the VISTA survey of the Magellanic Clouds, as well as on the capability to quickly and accurately explore a wide variety of parameters and effects with the COLIBRI code for the TP-AGB evolution. Adopting a well-characterized set of observations -- star counts and luminosity functions -- we set up a calibration cycle along which we iteratively change a few key parameters of the TP-AGB models until we eventually reach a good fit to the observations. Our work leads to identify two best-fitting models that mainly differ in the efficiencies of the third dredge-up and mass loss in TP-AGB stars with initial masses larger than about 3 M$_{\odot}$. On the basis of these calibrated models we provide a full characterization of the TP-AGB stellar population in the SMC in terms of stellar parameters (initial masses, C/O ratios, carbon excess, mass-loss rates). Extensive tables of isochrones including these improved models are publicly available.

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arXiv2019

Mixing by overshooting and rotation in intermediate mass stars

Double-line eclipsing binaries (DLEBs) have been recently used to constrain the amount of central mixing as a function of stellar mass, with contrasting results. In this work, we reanalyze the DLEB sample by Claret & Torres, using a Bayesian method and new PARSEC tracks that account for both convective core overshooting and rotational mixing. Using overshooting alone we obtain that, for masses larger than about 1.9 M$_{\odot}$, the distribution of the overshooting parameter, $λ_\mathrm{ov}$, has a wide dispersion between 0.3 and 0.8, with essentially no values below $λ_\mathrm{ov}=$ 0.3 - 0.4. While the lower limit supports a mild convective overshooting efficiency, the large dispersion derived is difficult to explain in the framework of current models of that process, which leave little room for large randomness. We suggest that a simple interpretation of our results can be rotational mixing: different initial rotational velocities, in addition to a fixed amount of overshooting, could reproduce the high dispersion derived for intermediate-mass stars. After a reanalysis of the data, we find good agreement with models computed with fixed overshooting parameter, $λ_\mathrm{ov}=0.4$, and initial rotational rates, $ω$, uniformly distributed in a wide range between $0$ and $0.8$ times the break-up value, at varying initial mass. We also find that our best-fitting models for the components of $α$ Aurigae and TZ Fornacis, agree with their observed rotational velocities, thus providing independent support to our hypothesis. We conclude that a constant efficiency of overshooting in concurrence with a star-to-star variation in the rotational mixing, might be crucial in the interpretation of such data.

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arXiv2018

Modelling Long-Period Variables - I. A new grid of O-rich and C-rich pulsation models

We present a new grid of non-adiabatic, linear pulsation models of Long-Period Variables (LPVs), including periods and growth rates for radial modes from the fundamental to the fourth overtone. The models span a wide range in mass, luminosity, metallicity, C/O ratio and helium abundance, effectively covering the whole thermally-pulsing asymptotic giant branch (TP-AGB) evolution, and representing a significant update with respect to previous works. The main improvement is the inclusion of detailed atomic and molecular opacities, consistent with the models chemical mixture, that makes the present set of models the first to systematically account for variability in C-stars. We examine periods and growth rates in the models, and find that, while the fundamental mode is affected by the structure of the envelope, overtones are less sensitive to the interior and largely determined by the global properties. In the models, the frequency of the overtone with the largest degree of excitation is found to scale with the acoustic cut-off frequency at the stellar surface, a behaviour similar to that observed for the frequency of maximum oscillation power for solar-like oscillations in less evolved red giants. This allows us to provide a simple analytic prescription to predict the most-likely dominant mode as a function of stellar parameters. Best-fit relations for periods are also provided. By applying results of pulsation models to evolutionary tracks, we present a general picture of the evolution of long-period variability during the TP-AGB, that we find consistent with observations. Models are made public through a dedicated web interface.

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arXiv2018

The VMC survey - XXXI. The spatially resolved star formation history of the main body of the Small Magellanic Cloud

We recover the spatially resolved star formation history across the entire main body and Wing of the Small Magellanic Cloud (SMC), using fourteen deep tile images from the VISTA survey of the Magellanic Clouds (VMC), in the YJKs filters. The analysis is performed on 168 subregions of size 0.143 deg2, covering a total contiguous area of 23.57 deg2. We apply a colour-magnitude diagram (CMD) reconstruction method that returns the best-fitting star formation rate SFR(t), age--metallicity relation, distance and mean reddening, together with their confidence intervals, for each subregion. With respect to previous analyses, we use a far larger set of VMC data, updated stellar models, and fit the two available CMDs (Y-Ks versus Ks and J-Ks versus Ks) independently. The results allow us to derive a more complete and more reliable picture of how the mean distances, extinction values, star formation rate, and metallicities vary across the SMC, and provide a better description of the populations that form its Bar and Wing. We conclude that the SMC has formed a total mass of (5.31+-0.05)x10^8 Msun in stars over its lifetime. About two thirds of this mass is expected to be still locked in stars and stellar remnants. 50 per cent of the mass was formed prior to an age of 6.3 Gyr, and 80 per cent was formed between 8 and 3.5 Gyr ago. We also illustrate the likely distribution of stellar ages and metallicities in different parts of the CMD, to aid the interpretation of data from future astrometric and spectroscopic surveys of the SMC.

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