arXiv subjects

Rene A. Mendez

Publications and source records attributed to Rene A. Mendez.

At least 37 records · Page 2Linked to original sources

arXiv2021

Bayes-based orbital elements estimation in triple hierarchical stellar systems

Under certain rather prevalent conditions (driven by dynamical orbital evolution), a hierarchical triple stellar system can be well approximated, from the standpoint of orbital parameter estimation, as two binary star systems combined. Even under this simplifying approximation, the inference of orbital elements is a challenging technical problem because of the high dimensionality of the parameter space, and the complex relationships between those parameters and the observations (astrometry and radial velocity). In this work we propose a new methodology for the study of triple hierarchical systems using a Bayesian Markov-Chain Monte Carlo-based framework. In particular, graphical models are introduced to describe the probabilistic relationship between parameters and observations in a dynamically self-consistent way. As information sources we consider the cases of isolated astrometry, isolated radial velocity, as well as the joint case with both types of measurements. Graphical models provide a novel way of performing a factorization of the joint distribution (of parameter and observations) in terms of conditional independent components (factors), so that the estimation can be performed in a two-stage process that combines different observations sequentially. Our framework is tested against three well-studied benchmark cases of triple systems, where we determine the inner and outer orbital elements, coupled with the mutual inclination of the orbits, and the individual stellar masses, along with posterior probability (density) distributions for all these parameters. Our results are found to be consistent with previous studies. We also provide a mathematical formalism to reduce the dimensionality in the parameter space for triple hierarchical stellar systems in general.

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arXiv2021

Orbits and masses of binaries from Speckle Interferometry at SOAR

We present results from Speckle inteferometric observations of fifteen visual binaries and one double-line spectroscopic binary, carried out with the HRCam Speckle camera of the SOAR 4.1 m telescope. These systems were observed as a part of an on-going survey to characterize the binary population in the solar vicinity, out to a distance of 250 parsec. We obtained orbital elements and mass sums for our sample of visual binaries. The orbits were computed using a Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate their uncertainty. Their periods cover a range from 5 yr to more than 500 yr; and their spectral types go from early A to mid M - implying total system masses from slightly more than 4 MSun down to 0.2 MSun. They are located at distances between approximately 12 and 200 pc, mostly at low Galactic latitude. For the double-line spectroscopic binary YSC8 we present the first combined astrometric/radial velocity orbit resulting from a self-consistent fit, leading to individual component masses of 0.897 +/- 0.027 MSun and 0.857 +/- 0.026 MSun; and an orbital parallax of 26.61 +/- 0.29 mas, which compares very well with the Gaia DR2 trigonometric parallax (26.55 +/- 0.27 mas). In combination with published photometry and trigonometric parallaxes, we place our objects on an H-R diagram and discuss their evolutionary status. We also present a thorough analysis of the precision and consistency of the photometry available for them.

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arXiv2021

Exploring the Galactic Anticenter substructure with LAMOST & Gaia DR2

We characterize the kinematic and chemical properties of 589 Galactic Anticenter Substructure Stars (GASS) with K-/M- giants in Integrals-of-Motion space. These stars likely include members of previously identified substructures such as Monoceros, A13, and the Triangulum-Andromeda cloud (TriAnd). We show that these stars are on nearly circular orbits on both sides of the Galactic plane. We can see velocity($V_{Z}$) gradient along Y-axis especially for the south GASS members. Our GASS members have similar energy and angular momentum distributions to thin disk stars. Their location in [$α$/M] vs. [M/H] space is more metal poor than typical thin disk stars, with [$α$/M] \textbf{lower} than the thick disk. We infer that our GASS members are part of the outer metal-poor disk stars, and the outer-disk extends to 30 kpc. Considering the distance range and $α$-abundance features, GASS could be formed after the thick disk was formed due to the molecular cloud density decreased in the outer disk where the SFR might be less efficient than the inner disk.

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arXiv2020

Speckle interferometry at SOAR in 2019

The results of speckle interferometric observations at the 4.1 m Southern Astrophysical Research Telescope (SOAR) in 2019 are given, totaling 2555 measurements of 1972 resolved pairs with separations from 15 mas (median 0.21") and magnitude difference up to 6 mag, and non-resolutions of 684 targets. We resolved for the first time 90 new pairs or subsystems in known binaries. This work continues our long-term speckle program. Its main goal is to monitor orbital motion of close binaries, including members of high-order hierarchies and Hipparcos pairs in the solar neighborhood. We give a list of 127 orbits computed using our latest measurements. Their quality varies from excellent (25 orbits of grades 1 and 2) to provisional (47 orbits of grades 4 and 5).

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arXiv2019

Value-added catalogs of M type stars in LAMOST DR5

In this work, we present new catalogs of M giant and M dwarf stars from the LAMOST DR5. In total, 39,796 M giants and 501,152 M dwarfs are identified from the classification pipeline. The template-fitting results contain M giants with 7 temperature subtypes from M0 to M6, M dwarfs with 18 temperature subtypes from K7.0 to M8.5 and 12 metallicity subclasses from dMr to usdMp. We cross-matched our M-type catalog with the 2MASS and WISE catalog to obtain infrared magnitude and colors. Adopting the distances derived from the parallaxes in \gaia{} DR2, the M_G vs. (G_bp-G_rp)_0 diagram shows that there are also early-type stars and white dwarf-M dwarf binaries included in our M type stars sample, with a contamination rate of about 4.6% for M giants and 0.48% for M dwarfs. We found that CaH spectral indices are an efficient selection criteria for carbon stars. A total of 289 carbon stars were identified from the M giants sample, and further confirmed by LAMOST spectra.

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arXiv2019

Speckle interferometry at SOAR in 2018

The results of speckle interferometric observations at the 4.1 m Southern Astrophysical Research Telescope (SOAR) in 2018 are given, totaling 3097 measurements of 2427 resolved pairs with separations from 11 mas to 5.9" (median 0.15", magnitude difference up to 7 mag) and non-resolutions of 624 targets. This work continues our long-term speckle program. Its main goal is to monitor orbital motion of close binaries, including members of high-order hierarchies and Hipparcos pairs in the solar neighborhood. Also, pre-main-sequence stars in the Orion OB1 association were surveyed, resolving 26 out of 118 targets. In addition, we report discovery of 35 new companions among field visual multiples (some of which are likely optical) and first-time resolutions of another 31 pairs. By combining the measurements given here with the published ones, we computed 76 orbits for the first time and updated orbital elements of 34 visual binaries. Their periods range from 0.65 to 1100 years, and their quality varies from first tentative solutions of grade 5 to accurate elements of grades 1 and 2. Finally, a list of 53 spurious pairs discovered by various techniques and unresolved at SOAR

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arXiv2019

Visual binary stars with partially missing data: Introducing multiple imputation in astrometric analysis

Partial measurements of relative position are a relatively common event during the observation of visual binary stars. However, these observations are typically discarded when estimating the orbit of a visual pair. In this article we present a novel framework to characterize the orbits from a Bayesian standpoint, including partial observations of relative position as an input for the estimation of orbital parameters. Our aim is to formally incorporate the information contained in those partial measurements in a systematic way into the final inference. In the statistical literature, an imputation is defined as the replacement of a missing quantity with a plausible value. To compute posterior distributions of orbital parameters with partial observations, we propose a technique based on Markov chain Monte Carlo with multiple imputation. We present the methodology and test the algorithm with both synthetic and real observations, studying the effect of incorporating partial measurements in the parameter estimation. Our results suggest that the inclusion of partial measurements into the characterization of visual binaries may lead to a reduction in the uncertainty associated to each orbital element, in terms of a decrease in dispersion measures (such as the interquartile range) of the posterior distribution of relevant orbital parameters. The extent to which the uncertainty decreases after the incorporation of new data (either complete or partial) depends on how informative those newly-incorporated measurements are. Quantifying the information contained in each measurement remains an open issue.

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arXiv2018

The Origins of Young Stars in the Direction of the Leading Arm of the Magellanic Stream: Abundances, Kinematics, and Orbits

We explore the origins of the young B-type stars found by Casetti-Dinescu et al.(2014) at the outskirts of the Milky-Way disk in the sky region of Leading Arm of the Magellanic Stream. High-resolution spectroscopic observations made with the MIKE instrument on the Magellan Clay 6.5m telescope for nine stars are added to the previous sample analyzed by Zhang et al. (2017). We compile a sample of fifteen young stars with well-determined stellar types, ages, abundances and kinematics. With proper motions from Gaia DR2 we also derive orbits in a realistic Milky-Way potential. We find that our previous radial-velocity selected LA candidates have substantial orbital angular momentum. The substantial amount of rotational component for these stars is in contrast with the near-polar Magellanic orbit, thus rendering these stars unlikely members of the LA. There are four large orbital-energy stars in our sample. The highest orbital-energy one has an age shorter than the time to disk crossing, with a birthplace $z=2.5$~kpc and $R_{\rm GC}\sim 28$~kpc. Therefore, the origin of this star is uncertain. The remaining three stars have disk runaway origin with birthplaces between 12 and 25 kpc from the Galactic center. Also, the most energetic stars are more metal poor ([Mg/H] =$-0.50\pm0.07$) and with larger He scatter ($σ_{\rm [He/H]} = 0.72$) than the inner disk ones ([Mg/H] $=0.12\pm0.36$, $σ_{\rm [He/H]} = 0.15$). While the former group's abundance is compatible with that of the Large Magellanic Cloud, it could also reflect the metallicity gradient of the MW disk and their runaway status via different runaway mechanisms.

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arXiv2018

In-Situ Star Formation in the Outskirts of the Large Magellanic Cloud: Gaia DR2 Confirmation

We explore the Gaia DR2 proper motions of six young, main-sequence stars, members of the Large Magellanic Cloud (LMC) reported by Moni Bidin et al. (2017). These stars are located in the outskirts of the disk, between 7 and 13 degrees from the LMC's center where there is very low H I content. Gaia DR2 proper motions confirm that four stars formed locally, in situ, while two are consistent with being expelled via dynamical interactions from inner, more gas-rich regions of the LMC. This finding establishes that recent star formation occurred in the periphery of the LMC, where thus far only old populations are known.

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arXiv2018

Optimality of the Maximum Likelihood estimator in Astrometry

The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on a CCD-like detector using commonly adopted estimators such as the weighted least squares and the maximum likelihood. Novel technical results are presented to determine the performance of an estimator that corresponds to the solution of an optimization problem in the context of astrometry. Using these results we are able to place stringent bounds on the bias and the variance of the estimators in close form as a function of the data. We confirm these results through comparisons to numerical simulations under a broad range of realistic observing conditions. The maximum likelihood and the weighted least square estimators are analyzed. We confirm the sub-optimality of the weighted least squares scheme from medium to high signal-to-noise found in an earlier study for the (unweighted) least squares method. We find that the maximum likelihood estimator achieves optimal performance limits across a wide range of relevant observational conditions. Furthermore, from our results, we provide concrete insights for adopting an adaptive weighted least square estimator that can be regarded as a computationally efficient alternative to the optimal maximum likelihood solution. We provide, for the first time, close-form analytical expressions that bound the bias and the variance of the weighted least square and maximum likelihood implicit estimators for astrometry using a Poisson-driven detector. These expressions can be used to formally assess the precision attainable by these estimators in comparison with the minimum variance bound.

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arXiv2018

Speckle interferometry at SOAR in 2016 and 2017

The results of speckle interferometric observations at the 4.1 m SOAR telescope in 2016 and 2017 are given, totaling 2483 measurements of 1570 resolved pairs and 609 non-resolutions. We describe briefly recent changes in the instrument and observing method and quantify the accuracy of the pixel scale and position angle calibration. Comments are given on 44 pairs resolved here for the first time. Orbital motion of the newly resolved subsystem BU~83 Aa,Ab roughly agrees with its 36 year astrometric orbit proposed by J.~Dommanget. Most Tycho binaries examined here turned out to be spurious.

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arXiv2017

Orbits for eighteen visual binaries and two double-line spectroscopic binaries observed with HRCAM on the CTIO SOAR 4m telescope, using a new Bayesian orbit code based on Markov Chain Monte Carlo

We present orbital elements and mass sums for eighteen visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two double-line spectroscopic binaries with no previous orbits, the individual component masses, using combined astrometric and radial velocity data, have a formal uncertainty of ~0.1 MSun. Adopting published photometry, and trigonometric parallaxes, plus our own measurements, we place these objects on an H-R diagram, and discuss their evolutionary status. These objects are part of a survey to characterize the binary population of stars in the Southern Hemisphere, using the SOAR 4m telescope+HRCAM at CTIO. Orbital elements are computed using a newly developed Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate the uncertainty of our derived parameters in a robust way. For spectroscopic binaries, using our approach, it is possible to derive a self-consistent parallax for the system from the combined astrometric plus radial velocity data ("orbital parallax"), which compares well with the trigonometric parallaxes. We also present a mathematical formalism that allows a dimensionality reduction of the feature space from seven to three search parameters (or from ten to seven dimensions - including parallax - in the case of spectroscopic binaries with astrometric data), which makes it possible to explore a smaller number of parameters in each case, improving the computational efficiency of our Markov Chain Monte Carlo code.

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arXiv2016

Analysis of the Bayesian Cramer-Rao lower bound in astrometry: Studying the impact of prior information in the location of an object

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims. We analyse bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (i.e., the position is a random variable) from observations that are statistically dependent on the position. Methods. We characterize the Bayesian Cramer-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results. We quantify and analyse the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.

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arXiv2016

Speckle interferometry at SOAR in 2015

The results of speckle interferometric observations at the SOAR telescope in 2015 are given, totalling 1303 measurements of 924 resolved binary and multiple stars and non-resolutions of 260 targets. The separations range from 12 mas to 3.37" (median 0.17"); the maximum measured magnitude difference is 6.7 mag. We resolved 27 pairs for the first time, including 10 as inner or outer subsystems in previously known binaries, e.g. the 50-mas pair in Epsilon Cha. Newly resolved pairs are commented upon. We discuss three apparently non-hierarchical systems discovered in this series, arguing that their unusual configuration results from projection. The resolved quadruple system HIP 71510 is studied as well.

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arXiv2015

Performance analysis of the Least-Squares estimator in Astrometry

We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not offer a closed-form expression, but a new result is presented (Theorem 1) where both the bias and the mean-square-error of the least-squares estimator are bounded and approximated analytically, in the latter case in terms of a nominal value and an interval around it. From the predicted nominal value we analyze how efficient is the least-squares estimator in comparison with the minimum variance Cramer-Rao bound. Based on our results, we show that, for the high signal-to-noise ratio regime, the performance of the least-squares estimator is significantly poorer than the Cramer-Rao bound, and we characterize this gap analytically. On the positive side, we show that for the challenging low signal-to-noise regime (attributed to either a weak astronomical signal or a noise-dominated condition) the least-squares estimator is near optimal, as its performance asymptotically approaches the Cramer-Rao bound. However, we also demonstrate that, in general, there is no unbiased estimator for the astrometric position that can precisely reach the Cramer-Rao bound. We validate our theoretical analysis through simulated digital-detector observations under typical observing conditions. We show that the nominal value for the mean-square-error of the least-squares estimator (obtained from our theorem) can be used as a benchmark indicator of the expected statistical performance of the least-squares method under a wide range of conditions. Our results are valid for an idealized linear (one-dimensional) array detector where intra-pixel response changes are neglected, and where flat-fielding is achieved with very high accuracy.

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arXiv2015

Speckle interferometry at SOAR in 2014

The results of speckle interferometric observations at the SOAR telescope in 2014 are given. A total of 1641 observations were taken, yielding 1636 measurements of 1218 resolved binary and multiple stars and 577 non-resolutions of 441 targets. We resolved for the first time 56 pairs, including some nearby astrometric or spectroscopic binaries and ten new subsystems in previously known visual binaries. The calibration of the data is checked by linear fits to the positions of 41 wide binaries observed at SOAR over several seasons. The typical calibration accuracy is 0.1deg in angle and 0.3% in pixel scale, while the measurement errors are on the order of 3mas. The new data are used here to compute 194 binary-star orbits, 148 of which are improvements on previous orbital solutions and 46 are first-time orbits.

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arXiv2014

Analysis of the Cramer-Rao lower uncertainty bound in the joint estimation of astrometry and photometry

In this paper we use the Cramer-Rao lower uncertainty bound to estimate the maximum precision that could be achieved on the joint simultaneous (or 2D) estimation of photometry and astrometry of a point source measured by a linear CCD detector array. We develop exact expressions for the Fisher matrix elements required to compute the Cramer-Rao bound in the case of a source with a Gaussian light profile. From these expressions we predict the behavior of the Cramer-Rao astrometric and photometric precision as a function of the signal and the noise of the observations, and compare them to actual observations - finding a good correspondence between them. We show that the astrometric Cramer-Rao bound goes as $(S/N)^{-1}$ (similar to the photometric bound) but, additionally, we find that this bound is quite sensitive to the value of the background - suppressing the background can greatly enhance the astrometric accuracy. We present a systematic analysis of the elements of the Fisher matrix in the case when the detector adequately samples the source (oversampling regime), leading to closed-form analytical expressions for the Cramer-Rao bound. We show that, in this regime, the joint parametric determination of photometry and astrometry for the source become decoupled from each other, and furthermore, it is possible to write down expressions (approximate to first order in the small quantities F/B or B/F) for the expected minimum uncertainty in flux and position. These expressions are shown to be quite resilient to the oversampling condition, and become thus very valuable benchmark tools to estimate the approximate behavior of the maximum photometric and astrometric precision attainable under pre-specified observing conditions and detector properties.

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arXiv2014

WISEP J061135.13-041024.0AB: A J-Band Flux Reversal Binary at the L/T Transition

We present Keck II laser guide star adaptive optics observations of the brown dwarf WISEP J061135.13-041024.0 showing it is a binary with a component separation of 0.4". This system is one of the six known resolved binaries in which the magnitude differences between the components show a reversal in sign between the Y/J band and the H/K bands. Deconvolution of the composite spectrum results in a best fit binary solution with L9 and T1.5 components. We also present a preliminary parallax placing the system at a distance of 21.2+/-1.3 pc. Using the distance and resolved magnitudes we are able to place WISEP J061135.13-041024.0AB on a color-absolute magnitude diagram, showing that this system contributes to the well-known "J-band bump" and the components' properties appear similar to other late-type L and early-type T dwarfs. Fitting our data to a set of cloudy atmosphere models suggests the system has an age >1 Gyr with WISEP J061135.13-041024.0A having an effective temperature (Teff) of 1275-1325 K and mass of 64-65 M_Jup, and WISEP J061135.13-041024.0B having Teff = 1075-1115 K and mass 40-65 M_Jup.

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