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J. Olivares

Publications and source records attributed to J. Olivares.

At least 37 records · Page 2Linked to original sources

Lithium depletion boundary, stellar associations, and Gaia

Stellar ages are key to improving our understanding of different astrophysical phenomena. However, many techniques to estimate stellar ages are highly model-dependent. The lithium depletion boundary (LDB), based on the presence or absence of lithium in low-mass stars, can be used to derive ages in stellar associations of between 20 and 500~Ma. The purpose of this work is to revise former LDB ages in stellar associations in a consistent way, taking advantage of the homogeneous \textit{Gaia} parallaxes as well as bolometric luminosity estimations that do not rely on monochromatic bolometric corrections. We studied nine open clusters and three moving groups characterised by a previous determination of the LDB age. We gathered all the available information from our data and the literature: membership, distances, photometric data, reddening, metallicity, and surface gravity. We re-assigned membership and calculated bolometric luminosities and effective temperatures using distances derived from Gaia DR2 and multi-wavelength photometry for individual objects around the former LDB. We located the LDB using a homogeneous method for all the stellar associations. Finally, we estimated the age by comparing it with different evolutionary models. We located the LDB for the twelve stellar associations and derived their ages using several theoretical evolutionary models. We compared the LDB ages among them, along with data obtained with other techniques, such as isochrone fitting, ultimately finding some discrepancies among the various approaches. Finally, we remark that the 32 Ori MG is likely to be composed of at least two populations of different ages.

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Structural parameters of 389 local Open Clusters

The distribution of member stars in the surroundings of an Open Cluster (OC) can shed light on the process of its formation, evolution and dissolution. The analysis of structural parameters of OCs as a function of their age and position in the Galaxy brings constraints on theoretical models of cluster evolution. The Gaia catalogue is very appropriate to find members of OCs at large distance from their centers. We aim at revisiting the membership lists of OCs from the solar vicinity, in particular by extending these membership lists to the peripheral areas thanks to Gaia EDR3. We used the clustering algorithm HDBSCAN on Gaia parallaxes and proper motions to systematically look for members up to 50 pc from the cluster centers. We fitted a King's function on the radial density profile of these clusters and a Gaussian Mixture Model on their two dimensional distribution of members. We also evaluated the degree of mass segregation of the clusters. Our methodology performs well on 389 clusters out of the 467 selected ones. We report the detection of vast coronae around almost all the clusters and the detection of 71 OCs with tidal tails, multiplying by more than four the number of such structures identified. We find the size of the cores to be on average smaller for old clusters than for young ones. Also, the overall size of the clusters seems to slightly increase with age while the fraction of stars in the halo seems to decrease. As expected the mass segregation is more pronounced in the oldest clusters but a clear trend with age is not seen. OCs are more extended than previously expected, regardless of their age. The decrease in the proportion of stars populating the clusters halos highlights the different cluster evaporation processes and the short timescales they need to affect the clusters. Reported parameters all depend on cluster ages but can not be described as single functions of time.

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$χ^{1}$ Fornacis cluster DANCe. Census of stars, structure, and kinematics of the cluster with Gaia-EDR3

Context: The $χ^{1}$ Fornacis cluster (Alessi 13) is one of a few open clusters of its age and distance in the Solar neighbourhood that ought to benefit from more attention as it can serve as a cornerstone for numerous future studies related to star and planet formation. Aims: We take advantage of the early installment of the third data release of the Gaia space mission in combination with archival data and our own observations, to expand the census of cluster members and revisit some properties of the cluster. Methods: We applied a probabilistic method to infer membership probabilities over a field of more than 1000 deg${^2}$ to select the most likely cluster members and derive the distances, spatial velocities, and physical properties of the stars in this sample. Results: We identify 164 high-probability cluster members (including 61 new members) covering the magnitude range from 5.1 to 19.6 mag in the G-band. Our sample of cluster members is complete down to 0.04 M$_{\odot}$. We derive the distance of $108.4\pm0.3$ pc from Bayesian inference and confirm that the cluster is comoving with the Tucana-Horologium, Columba, and Carina young stellar associations. We investigate the kinematics of the cluster from a subsample of stars with measured radial velocities and we do not detect any significant expansion or rotation effects in the cluster. Our results suggest that the cluster is somewhat younger (about 30 Myr) than previously thought. Based on spectroscopic observations, we argue that the cluster is mass-segregated and that the distribution of spectral types shows little variation compared to other young stellar groups. Conclusions: In this study, we deliver the most complete census of cluster members that can be done with Gaia data alone and we use this new sample to provide an updated picture on the 6D structure of the cluster.

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Miec: A Bayesian hierarchical model for the analysis of nearby young open clusters

Context. The analysis of luminosity and mass distributions of young stellar clusters is essential to understanding the star-formation process. However, the gas and dust left over by this process extinct the light of the newborn stars and can severely bias both the census of cluster members and its luminosity distribution. Aims. We aim to develop a Bayesian methodology to infer, with minimal biases due to photometric extinction, the candidate members and magnitude distributions of embedded young stellar clusters. Methods. We improve a previously published methodology and extend its application to embedded stellar clusters. We validate the method using synthetically extincted data sets of the Pleiades cluster with varying degrees of extinction. Results. Our methodology can recover members from data sets extincted up to Av ~ 6 mag with accuracies, true positive, and contamination rates that are better than 99%, 80%, and 9%, respectively. Missing values hamper our methodology by introducing contaminants and artifacts into the magnitude distributions. Nonetheless, these artifacts vanish through the use of informative priors in the distribution of the proper motions. Conclusions. The methodology presented here recovers, with minimal biases, the members and distributions of embedded stellar clusters from data sets with a high percentage of sources with missing values (>96%).

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Dynamical traceback age of the $β$ Pictoris moving group

Context: The $β$ Pictoris moving group is one of the most well-known young associations in the solar neighbourhood and several members are known to host circumstellar discs, planets, and comets. Measuring its age with precision is basic to study several astrophysical processes such as planet formation and disc evolution which are strongly age dependent. Aims: We aim to determine a precise and accurate dynamical traceback age for the $β$ Pictoris moving group. Methods: Our sample combines the extremely precise Gaia DR2 astrometry with ground-based radial velocities measured in an homogeneous manner. We use an updated version of our algorithm to determine dynamical ages. The new approach takes into account a robust estimate of the spatial and kinematic covariance matrices of the association to improve the sample selection process and to perform the traceback analysis. Results: We estimate a dynamical age of $18.5_{-2.4}^{+2.0}$ Myr for the $β$ Pictoris moving group. We investigated the spatial substructure of the association at birth time and we propose the existence of a core of stars more concentrated. We also provide precise radial velocity measurements for 81 members of $β$ Pic, including ten stars with the first determination of their radial velocities. Conclusions: Our dynamical traceback age is three times more precise than previous traceback age estimates and, more important, for the first time, reconciles the traceback age with the most recent estimates of other dynamical, lithium depletion boundary, and isochronal ages. This has been possible thanks to the excellent astrometric and spectroscopic precisions, the homogeneity of our sample, and the detailed analysis of binaries and membership.

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Chamaeleon DANCe. Revisiting the stellar populations of Chamaeleon I and Chamaeleon II with Gaia-DR2 data

Context: Chamaeleon is the southernmost low-mass star-forming complex within 200 pc from the Sun. Its stellar population has been extensively studied in the past, but the current census of the stellar content is not complete yet and deserves further investigation. Aims: We take advantage of the second data release of the \textit{Gaia} space mission to expand the census of stars in Chamaeleon and to revisit the properties of the stellar populations associated to the Chamaeleon I (Cha I) and Chamaeleon II (Cha II) dark clouds. Methods: We perform a membership analysis of the sources in the \textit{Gaia} catalogue over a field of 100 deg$^{2}$ encompassing the Chamaeleon clouds, and use this new census of cluster members to investigate the 6D structure of the complex. Results: We identify 188 and 41 high-probability members of the stellar populations in Cha I and Cha II, respectively, including 19 and 7 new members. Our sample covers the magnitude range from $G=6$ to $G=20$ mag in Cha I, and from $G=12$ to $G=18$ mag in Cha II. We confirm that the northern and southern subgroups of Cha I are located at different distances ($191.4^{+0.8}_{-0.8}$ pc and $186.7^{+1.0}_{-1.0}$ pc), but they exhibit the same space motion within the reported uncertainties. Cha II is located at a distance of $197.5^{+1.0}_{-0.9}$ pc and exhibits a space motion that is consistent with Cha I within the admittedly large uncertainties on the spatial velocities of the stars that come from radial velocity data. The median age of the stars derived from the Hertzsprung-Russell diagram (HRD) and stellar models is about 1-2 Myr, suggesting that they are somewhat younger than previously thought. We do not detect significant age differences between the Chamaeleon subgroups, but we show that Cha II exhibits a higher fraction of disc-bearing stars compared to Cha I.

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New radial velocity observations of AH Her: evidence for material outside the tidal radius

Spectroscopic observations of AH Herculis during a deep quiescent state are put forward. We found the object in a rare long minima, allowing us to derive accurately the semi-amplitudes: $K_1 =121 \pm \, 4$ \kms\ and $K_2 =152 \pm 2$ \kms\ and its mass functions $M_W{ \sin }^{ 3 }i=0.30 \pm 0.01$ M$_{\odot}$ and $M_R{ \sin }^{ 3 }i=0.24 \pm 0.02$ M$_{\odot}$, while its binary separation is given by $a \sin i =1.39 \pm 0.02$~R$_{\odot}$. The orbital period $P_{orb}$~=~ 0.25812~$\pm~0.00032$~days was found from a power spectrum analysis of the radial velocities of the secondary star. These values are consistent with those determined by \citet{Horne:1986}. Our observations indicate that K5 is the most likely spectral type of the secondary. We discuss why we favour the assumption that the donor in AH Her is a slightly evolved star, in which case we find that the best solution for the inclination yields $i = 48^\circ \pm 2^\circ$. Nonetheless, should the donor be a ZAMS star, we obtain that the inclination is between $ i = 43^\circ$ and $i = 44^\circ$. We also present Doppler tomography of H$α$ and H$β$, and found that the emission in both lines is concentrated in a large asymmetric region at low velocities, but at an opposite position to the secondary star, outside the tidal radius and therefore at an unstable position. We also analyse the H$α$ and H$β$ line profiles, which show a single broad peak and compare it with the previous quiescent state study which shows a double-peaked profile, providing evidence for its transient nature.

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Kalkayotl: A cluster distance inference code

Context: Stellar clusters are benchmarks for theories of star formation and evolution. The high precision parallax data of the Gaia mission allows significant improvements in the distance determination to stellar clusters and its stars. In order to have accurate and precise distance determinations, systematics like the parallax spatial correlations need to be accounted for, especially for stars in small sky regions. Aims: Provide the astrophysical community with a free and open code designed to simultaneously infer cluster parameters (i.e. distance and size) and the distances to its stars using Gaia parallax measurements. It includes cluster oriented prior families and is specifically designed to deal with the Gaia parallax spatial correlations. Methods: A Bayesian hierarchical model is created to allow the inference of both the cluster parameters and distances to its stars. Results: Using synthetic data that mimics Gaia parallax uncertainties and spatial correlations, we observe that our cluster oriented prior families result in distance estimates with smaller errors than those obtained with an exponentially decreasing space density prior. In addition, the treatment of the parallax spatial correlations minimizes errors in the estimated cluster size and stellar distances and avoids the underestimation of uncertainties. Although neglecting the parallax spatial correlations has no impact on the accuracy of cluster distance determinations, it underestimates the uncertainties and may result in measurements that are incompatible with the true value. Conclusions: The combination of prior knowledge with the treatment of Gaia parallax spatial correlations produces accurate (error <10%) and trustworthy estimates (i.e. true values contained within the 2$σ$ uncertainties) of clusters distances for clusters up to ~5 kpc, and cluster sizes for clusters up to ~1 kpc.

astro-ph.IM↗

Lupus DANCe. Census of stars and 6D structure with Gaia-DR2 data

Context: Lupus is recognised as one of the closest star-forming regions, but the lack of trigonometric parallaxes in the pre-Gaia era hampered many studies on the kinematic properties of this region and led to incomplete censuses of its stellar population. Aims: We use the second data release of the Gaia space mission combined with published ancillary radial velocity data to revise the census of stars and investigate the 6D structure of the Lupus complex. Methods: We performed a new membership analysis of the Lupus association based on astrometric and photometric data over a field of 160 deg2 around the main molecular clouds of the complex and compared the properties of the various subgroups in this region. Results: We identified 137 high-probability members of the Lupus association of young stars, including 47 stars that had never been reported as members before. Many of the historically known stars associated with the Lupus region identified in previous studies are more likely to be field stars or members of the adjacent Scorpius-Centaurus association. Our new sample of members covers the magnitude and mass range from G=8 to G=18 mag and from 0.03 to 2.4Msun, respectively. We compared the kinematic properties of the stars projected towards the molecular clouds Lupus 1 to 6 and showed that these subgroups are located at roughly the same distance (about 160~pc) and move with the same spatial velocity. Our age estimates inferred from stellar models show that the Lupus subgroups are coeval (with median ages ranging from about 1 to 3 Myr). The Lupus association appears to be younger than the population of young stars in the Corona-Australis star-forming region recently investigated by our team using a similar methodology. The initial mass function of the Lupus association inferred from the distribution of spectral types shows little variation compared to other star-forming regions.

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Corona-Australis DANCe. I. Revisiting the census of stars with Gaia-DR2 data

Corona-Australis is one of the nearest regions to the Sun with recent and ongoing star formation, but the current picture of its stellar (and substellar) content is not complete yet. We take advantage of the second data release of the Gaia space mission to revisit the stellar census and search for additional members of the young stellar association in Corona-Australis. We applied a probabilistic method to infer membership probabilities based on a multidimensional astrometric and photometric data set over a field of 128 deg$^{2}$ around the dark clouds of the region. We identify 313 high-probability candidate members to the Corona-Australis association, 262 of which had never been reported as members before. Our sample of members covers the magnitude range between $G\gtrsim5$ mag and $G\lesssim20$ mag, and it reveals the existence of two kinematically and spatially distinct subgroups. There is a distributed `off-cloud' population of stars located in the north of the dark clouds that is twice as numerous as the historically known `on-cloud' population that is concentrated around the densest cores. By comparing the location of the stars in the HR-diagram with evolutionary models, we show that these two populations are younger than 10 Myr. Based on their infrared excess emission, we identify 28 Class II and 215 Class III stars among the sources with available infrared photometry, and we conclude that the frequency of Class II stars (i.e. `disc-bearing' stars) in the on-cloud region is twice as large as compared to the off-cloud population. The distance derived for the Corona-Australis region based on this updated census is $d=149.4^{+0.4}_{-0.4}$ pc, which exceeds previous estimates by about 20 pc.In this paper we provide the most complete census of stars in Corona-Australis available to date that can be confirmed with Gaia data.

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Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry

Aims:We take advantage of the second data release of the Gaia space mission and the state-of-the-art astrometry delivered from very long baseline interferometry observations to revisit the structure and kinematics of the nearby Taurus star-forming region. Methods: We apply a hierarchical clustering algorithm for partitioning the stars in our sample into groups (i.e., clusters) that are associated with the various molecular clouds of the complex, and derive the distance and spatial velocity of individual stars and their corresponding molecular clouds. Results: We show that the molecular clouds are located at different distances and confirm the existence of important depth effects in this region reported in previous studies. For example, we find that the L 1495 molecular cloud is located at $d=129.9^{+0.4}_{-0.3}$ pc, while the filamentary structure connected to it (in the plane of the sky) is at $d=160.0^{+1.2}_{-1.2}$ pc. We report B 215 and L 1558 as the closest ($d=128.5^{+1.6}_{-1.6}$ pc) and most remote ($d=198.1^{+2.5}_{-2.5}$ pc) substructures of the complex, respectively. The median inter-cloud distance is 25 pc and the relative motion of the subgroups is on the order of a few km/s. We find no clear evidence for expansion (or contraction) of the Taurus complex, but signs of the potential effects of a global rotation. Finally, we compare the radial velocity of the stars with the velocity of the underlying $^{13}$CO molecular gas and report a mean difference of $0.04\pm0.12$ km/s (with r.m.s. of 0.63 km/s) confirming that the stars and the gas are tightly coupled.

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IC 4665 DANCe I. Members, empirical isochrones, magnitude distributions, present-day system mass function, and spatial distribution

Context. The study of star formation is extremely challenging due to the lack of complete and clean samples of young, nearby clusters, and star forming regions. The recent Gaia DR2 catalogue complemented with the deep, ground based COSMIC DANCe catalogue offers a new database of unprecedented accuracy to revisit the membership of clusters and star forming regions. The 30 Myr open cluster IC 4665 is one of the few well-known clusters of this age and it is an excellent target where to test evolutionary models and study planetary formation. Aims. We aim to provide a comprehensive membership analysis of IC 4665 and to study the following properties: empirical isochrones, distance, magnitude distribution, present-day system mass function, and spatial distribution. Methods. We use the Gaia DR2 catalogue together with the DANCe catalogue to look for members using a probabilistic model of the distribution of the observable quantities in both the cluster and background populations. Results. We obtain a final list of 819 candidate members which cover a 12.4 magnitude range (7 < J < 19.4). We find that 50% are new candidates, and we estimate a conservative contamination rate of 20%. This unique sample of members allows us to obtain a present-day system mass function in the range of 0.02-6 Msun, which reveals a number of details not seen in previous studies. In addition, they favour a spherically symmetric spatial distribution for this young open cluster. Conclusions. Our membership analysis represents a significant increase in the quantity and quality (low-contamination) with respect to previous studies. As such, it offers an excellent opportunity to revisit other fundamental parameters such as the age.

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Ruprecht 147 DANCe I. Members, empirical isochrone, luminosity and mass distributions

Context. Ruprecht 147 is the oldest (2.5 Gyr) open cluster in the solar vicinity (< 300 pc), making it an important target for stellar evolution studies and exoplanet searches. Aims. Derive a census of members and the luminosity, mass, and spatial distributions of the cluster. Methods. We use an astro-photometric data set including all available information from the literature together with our own observations. We process the data with an updated version of an existent membership selection methodology. Results. We identify 259 high-probability candidate members, including 58 previously unreported. All these candidates cover the luminosity interval between G > 6 mag to i< 21 mag. The cluster luminosity and mass distributions are derived with an unprecedented level of details allowing us to recognize, among other features, the Wielen dip. The mass distribution in the low-mass regime drops sharply at 0.4 $M_{\odot}$ even though our data are sensitive to stellar masses down to 0.1 $M_{\odot}$, suggesting that most very-low-mass members left the cluster as the result of its dynamical evolution. In addition, the cluster is highly elongated (ellipticity $\sim$ 0.5) towards the galactic plane, and mass segregated. Conclusions. Our combined Gaia+DANCe data set allows us to obtain an extended list of cluster candidate members, and to derive luminosity, mass and projected spatial distributions in the oldest open cluster of the solar vicinity.

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A non-perturbative theory of effective Hamiltonians: example of moiré materials

We demonstrate that there exists a continuum Hamiltonian $H(\bf{r},\bf{p})$ that is formally the operator equivalent of the general tight-binding method, inheriting the associativity and Hermiticity of the latter operator. This provides a powerful and controlled method of obtaining effective Hamiltonians via Taylor expansion with respect to momentum and, optionally, deformation fields. In particular, for fundamentally non-perturbative defects, such as twist faults and partial dislocations, the method allows the deformation field to be retained to all orders, providing an efficient scheme for the generation of transparent and compact Hamiltonians for such defects. We apply the method to a survey of incommensurate physics in twist bilayers of graphene, graphdiyne, MoS$_2$, and phosphorene. For graphene we are able to reproduce the `reflected Dirac cones' of the $30^\circ$ quasi-crystalline bilayer found in a recent ARPES experiment, and show it is an example of a more general phenomena of coupling by the moiré momentum. We show that incommensurate physics is governed by the decay of the interlayer interaction on the scale of the single layer reciprocal lattices, and demonstrate that if this is slow incommensurate scattering effects lead to very rapid broadening of band manifolds as the twist angle is tuned through commensurate values.

cond-mat.mtrl-sci↗

Extensive Photometry of V1838 Aql during the 2013 Superoutburst

We present an in-depth photometric study of the 2013 superoutburst of the recently discovered cataclysmic variable V1838 Aql and subsequent photometry near its quiescent state. A careful examination of the development of the superhumps is presented. Our best determination of the orbital period is Porb = 0.05698(9) days, based on the periodicity of early superhumps. Comparing the superhump periods at stages A and B with the early superhump value we derive a period excess of ε = 0.024(2) and a mass ratio of q = 0.10(1). We suggest that V1838 Aql is approaching the orbital period minimum and thus has a low-mass star as a donor instead of a sub-stellar object.

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The seven sisters DANCe IV. Bayesian hierarchical model

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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The Seven Sisters DANCe III: Projected spatial distribution

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.

astro-ph.GA↗

A revised moving cluster distance to the Pleiades open cluster

Aims: We provide a new distance estimate for the Pleiades based on the moving cluster method, which will be useful to further discuss the so-called Pleiades distance controversy and compare it with the very precise parallaxes from the Gaia space mission. Methods: We apply a refurbished implementation of the convergent point search method to an updated census of Pleiades stars to calculate the convergent point position of the cluster from stellar proper motions. Then, we derive individual parallaxes for 64 cluster members using radial velocities compiled from the literature, and approximate parallaxes for another 1146 stars based on the spatial velocity of the cluster. This represents the largest sample of Pleiades stars with individual distances to date. Results: The parallaxes derived in this work are in good agreement with previous results obtained in different studies (excluding Hipparcos) for individual stars in the cluster. We report a mean parallax of $7.44\pm 0.08$~mas and distance of $134.4^{+2.9}_{-2.8}$pc that is consistent with the weighted mean of $135.0\pm 0.6$pc obtained from the non-Hipparcos results in the literature. Conclusions: Our result for the distance to the Pleiades open cluster is not consistent with the Hipparcos catalog, but favors the recent and more precise distance determination of $136.2\pm 1.2$pc obtained from Very Long Baseline Interferometry observations. It is also in good agreement with the mean distance of $133\pm 5$pc obtained from the first trigonometric parallaxes delivered by the Gaia satellite for the brightest cluster members in common with our sample.

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