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Register a new userThe seven sisters DANCe IV. Bayesian hierarchical model
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Aims. We develop, test and characterise of a new statistical tool (intelligent system) for the sifting and analysis of nearby young open cluster (NYOC) populations. Methods. Using a Bayesian formalism, this statistical tool is able to obtain the posterior distributions of parameters governing the cluster model. It also uses hierarchical bayesian models to establish weakly informative priors, and incorporates the treatment of missing values and non-homogeneous (heteroscedastic) observational uncertainties. Results. From simulations, we estimate that this statistical tool renders kinematic (proper motion) and photometric (luminosity) distributions of the cluster population with a contamination rate of $5.8 pm 0.2$ %. The luminosity distributions and present day mass function agree with the ones found by Bouy et al. (2015b) on the completeness interval of the survey. At the probability threshold of maximum accuracy, the classifier recovers $sim$ 90% of Bouy et al. (2015b) candidate members and finds 10% of new ones. Conclusions. A new statistical tool for the analysis of NYOC is introduced, tested and characterised. Its comprehensive modelling of the data properties allows it to get rid of the biases present in previous works. In particular, those resulting from the use of only completely observed (non-missing) data and the assumption of homoskedastic uncertainties. Also, its Bayesian framework allows it to properly propagate observational uncertainties into membership probabilities and cluster velocity and luminosity distributions. Our results are in a general agreement with those from the literature, although we provide the most up-to-date and extended list of candidate members of the Pleiades cluster.
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Methods. We compute Bayesian evidences and Bayes Factors for a set of variations of the classical radial models by King (1962), Elson et al. (1987) and Lauer et al. (1995). The variations incorporate different degrees of model freedom and complexity, amongst which we include biaxial (elliptical) symmetry, and luminosity segregation. As a by-product of the model comparison, we obtain posterior distributions and maximum a posteriori estimates for each set of model parameters. Results. We find that the model comparison results depend on the spatial extent of the region used for the analysis. For a circle of 11.5 parsecs around the cluster centre (the most homogeneous and complete region), we find no compelling reason to abandon Kings model, although the Generalised King model, introduced in this work, has slightly better fitting properties. Furthermore, we find strong evidence against radially symmetric models when compared to the elliptic extensions. Finally, we find that including mass segregation in the form of luminosity segregation in the J band, is strongly supported in all our models. Conclusions. We have put the question of the projected spatial distribution of the Pleiades cluster on a solid probabilistic framework, and inferred its properties using the most exhaustive and least contaminated list of Pleiades candidate members available to date. Our results suggest however that this sample may still lack about 20% of the expected number of cluster members. Therefore, this study should be revised when the completeness and homogeneity of the data can be extended beyond the 11.5 parsecs limit. Such study will allow a more precise determination of the Pleiades spatial distribution, its tidal radius, ellipticity, number of objects and total mass.
The DANCe survey provides photometric and astrometric (position and proper motion) measurements for approximately 2 millions unique sources in a region encompassing $approx$80deg$^{2}$ centered around the Pleiades cluster. We aim at deriving a complete census of the Pleiades, and measure the mass and luminosity function of the cluster. Using the probabilistic selection method described in Sarro+2014, we identify high probability members in the DANCe ($ige$14mag) and Tycho-2 ($Vlesssim$12mag) catalogues, and study the properties of the cluster over the corresponding luminosity range. We find a total of 2109 high probability members, of which 812 are new, making it the most extensive and complete census of the cluster to date. The luminosity and mass functions of the cluster are computed from the most massive members down to $approx$0.025M$_{odot}$. The size, sensitivity and quality of the sample result in the most precise luminosity and mass functions observed to date for a cluster. Our census supersedes previous studies of the Pleiades cluster populations, both in terms of sensitivity and accuracy.
There are two puzzles surrounding the Pleiades, or Seven Sisters. First, why are the mythological stories surrounding them, typically involving seven young girls being chased by a man associated with the constellation Orion, so similar in vastly separated cultures, such as the Australian Aboriginal cultures and Greek mythology? Second, why do most cultures call them Seven Sisters even though most people with good eyesight see only six stars? Here we show that both these puzzles may be explained by a combination of the great antiquity of the stories combined with the proper motion of the stars, and that these stories may predate the departure of most modern humans out of Africa around 100,000 BC.
Inter-survey calibration remains an important systematic uncertainty in cosmological studies using type Ia supernova (SNe Ia). Ideally, each survey would measure its system throughputs, for instance with bandpass measurements combined with observations of well-characterized spectrophotometric standard stars; however, many important nearby-SN surveys have not done this. We recalibrate these surveys by tying their tertiary survey stars to Pan-STARRS1 g, r, and i, and SDSS/CSP u. This improves upon previous recalibration efforts by taking the spatially variable zeropoints of each telescope/camera into account, and applying improved color transformations in the surveys natural instrumental photometric systems. Our analysis uses a global hierarchical model of the data which produces a covariance matrix of magnitude offsets and bandpass shifts, quantifying and reducing the systematic uncertainties in the calibration. We call our method CROSS-CALIBration with a Uniform Reanalysis (X-CALIBUR). This approach gains not only from a sophisticated analysis, but also from simply tying our calibration to more color calibrators, rather than just the one color calibrator (BD+17 4708) as many previous efforts have done. The results presented here have the potential to help understand and improve calibration uncertainties upcoming SN Ia cosmological analyses.
Extremely metal-poor stars provide us with indirect information on the first generations of massive stars. The TOPoS survey has been designed to increase the census of these stars and to provide a chemical inventory that is as detailed as possible. Seven of the most iron-poor stars have been observed with the UVES spectrograph at the ESO VLT Kueyen 8.2m telescope to refine their chemical composition. We analysed the spectra based on 1D LTE model atmospheres, but also used 3D hydrodynamical simulations of stellar atmospheres. We measured carbon in six of the seven stars: all are carbon-enhanced and belong to the low-carbon band, defined in the TOPoS II paper. We measured lithium (A(Li)=1.9) in the most iron-poor star (SDSS J1035+0641, [Fe/H] < -5.2 ). We were also able to measure Li in three stars at [Fe/H]~ -4.0, two of which lie on the Spite plateau. We confirm that SDSS J1349+1407 is extremely rich in Mg, but not in Ca. It is also very rich in Na. Several of our stars are characterised by low alpha-to-iron ratios. The lack of high-carbon band stars at low metallicity can be understood in terms of evolutionary timescales of binary systems. The detection of Li in SDSS J1035+0641 places a strong constraint on theories that aim at solving the cosmological lithium problem. The Li abundance of the two warmer stars at [Fe/H]~ -4.0 places them on the Spite plateau, while the third, cooler star, lies below. We argue that this suggests that the temperature at which Li depletion begins increases with decreasing [Fe/H]. SDSS J1349+1407 may belong to a class of Mg-rich EMP stars. We cannot assess if there is a scatter in alpha-to-iron ratios among the EMP stars or if there are several discrete populations. However, the existence of stars with low alpha-to-iron ratios is supported by our observations.
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