Nathan Stein

Inverting Color-Magnitude Diagrams to Access Precise Star Cluster Parameters: A Bayesian Approach*

We demonstrate a new Bayesian technique to invert color-magnitude diagrams of main-sequence and white dwarf stars to reveal the underlying cluster properties of age, distance, metallicity, and line-of-sight absorption, as well as individual stellar masses. The advantages our technique has over traditional analyses of color-magnitude diagrams are objectivity, precision, and explicit dependence on prior knowledge of cluster parameters. Within the confines of a given set of often-used models of stellar evolution, a single mapping of initial to final masses, and white dwarf cooling, and assuming photometric errors that one could reasonably achieve with the Hubble Space Telescope, our technique yields exceptional precision for even modest numbers of cluster stars. For clusters with 50-400 members and one to a few dozen white dwarfs, we find typical internal errors of σ([Fe/H]) ≤ 0.03 dex, σ(m - MV) ≤ 0.02 mag, and σ(AV) ≤ 0.01 mag. We derive cluster white dwarf ages with internal errors of typically only 10% for clusters with only three white dwarfs and almost always ≤5% with 10 white dwarfs. These exceptional precisions will allow us to test white dwarf cooling models and standard stellar evolution models through observations of white dwarfs in open and globular clusters.

Inverting Color–Magnitude Diagrams to Access Precise Star Cluster Parameters: A New White Dwarf Age for the Hyades

We have extended our Bayesian modeling of stellar clusters—which uses main-sequence stellar evolution models, a mapping between initial masses and white dwarf (WD) masses, WD cooling models, and WD atmospheres—to include binary stars, field stars, and two additional main-sequence stellar evolution models. As a critical test of our Bayesian modeling technique, we apply it to Hyades UBV photometry, with membership priors based on proper motions and radial velocities, where available. Under the assumption of a particular set of WD cooling models and atmosphere models, we estimate the age of the Hyades based on cooling WDs to be 648 ± 45 Myr, consistent with the best prior analysis of the cluster main-sequence turnoff (MSTO) age by Perryman et al. Since the faintest WDs have most likely evaporated from the Hyades, prior work provided only a lower limit to the cluster’s WD age. Our result demonstrates the power of the bright WD technique for deriving ages and further demonstrates complete age consistency between WD cooling and MSTO ages for seven out of seven clusters analyzed to date, ranging from 150 Myr to 4 Gyr.

STATISTICAL ANALYSIS OF STELLAR EVOLUTION

Color-Magnitude Diagrams (CMDs) are plots that compare the magnitudes (luminosities) of stars in different wavelengths of light (colors). High nonlinear correlations among the mass, color, and surface temperature of newly formed stars induce a long narrow curved point cloud in a CMD known as the main sequence. Aging stars form new CMD groups of red giants and white dwarfs. The physical processes that govern this evolution can be described with mathematical models and explored using complex computer models. These calculations are designed to predict the plotted magnitudes as a function of parameters of scientific interest, such as stellar age, mass, and metallicity. Here, we describe how we use the computer models as a component of a complex likelihood function in a Bayesian analysis that requires sophisticated computing, corrects for contamination of the data by field stars, accounts for complications caused by unresolved binary-star systems, and aims to compare competing physics-based computer models of stellar evolution.

New Techniques to Determine Ages of Open Clusters Using White Dwarfs

Currently there are two main techniques for independently determining the ages of stellar populations: main-sequence evolution theory (via cluster isochrones) and white dwarf cooling theory. Open clusters provide the ideal environment for the calibration of these two clocks. Because current techniques to derive cluster ages from white dwarfs are observationally challenging, we discuss the feasibility of determining white dwarf ages from the brighter white dwarfs alone. This would eliminate the requirement of observing the coolest (i.e., faintest) white dwarfs. We discuss our method for testing this new idea, as well as the required photometric precision and prior constraints on metallicity, distance, and reddening. We employ a new Bayesian statistical technique to obtain and interpret results.

Combining computer models to account for mass loss in stellar evolution

Intricate computer models can be used to describe complex physical processes in astronomy such as the evolution of stars. Like a sampling distribution, these models typically predict observed quantities as a function of a number of unknown parameters. Including them as components of a statistical model, however, leads to significant modeling, inferential, and computational challenges. In this article, we tackle these challenges in the study of the mass loss that stars experience as they age. We have developed a new Bayesian technique for inferring the so-called initial–final mass relation (IFMR), the relationship between the initial mass of a Sun-like star and its final mass as a white dwarf. Our model incorporates several separate computer models for various phases of stellar evolution. We bridge these computer models with a parameterized IFMR in order to embed them into a statistical model. This strategy allows us to apply the full force of powerful statistical tools to build, fit, check, and improve the statistical models and their computer model components. In contrast to traditional techniques for inferring the IFMR, which tend to be quite ad hoc, we can estimate the uncertainty in our fit and ensure that our model components are internally coherent. We analyze data from three star clusters: NGC 2477, the Hyades, and M35 (NGC 2168). The results from NGC 2477 and M35 suggest different conclusions about the IFMR in the mid- to high-mass range, raising questions for further astronomical work. We also compare the results from two different models for the primary hydrogen-burning stage of stellar evolution. We show through simulations that misspecification at this stage of modeling can sometimes have a severe effect on inferred white dwarf masses. Nonetheless, when working with observed data, our inferences are not particularly sensitive to the choice of model for this stage of evolution.

BAYESIAN ANALYSIS OF TWO STELLAR POPULATIONS IN GALACTIC GLOBULAR CLUSTERS. I. STATISTICAL AND COMPUTATIONAL METHODS

We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations (vanDyk et al. 2009, Stein et al. 2013). Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties---age, metallicity, helium abundance, distance, absorption, and initial mass---are common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and also show model misspecification can potentially be identified. As a proof of concept, we analyze the two stellar populations of globular cluster NGC 5272 using our model and methods. (BASE-9 is available from GitHub: this https URL).

Bayesian analysis of two stellar populations in Galactic globular clusters– III. Analysis of 30 clusters

We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of 30 Galactic Globular Clusters to characterize two distinct stellar populations. A sophisticated Bayesian technique is employed to simultaneously sample the joint posterior distribution of age, distance, and extinction for each cluster, as well as unique helium values for two populations within each cluster and the relative proportion of those populations. We find the helium differences among the two populations in the clusters fall in the range of ~0.04 to 0.11. Because adequate models varying in CNO are not presently available, we view these spreads as upper limits and present them with statistical rather than observational uncertainties. Evidence supports previous studies suggesting an increase in helium content concurrent with increasing mass of the cluster and also find that the proportion of the first population of stars increases with mass as well. Our results are examined in the context of proposed globular cluster formation scenarios. Additionally, we leverage our Bayesian technique to shed light on inconsistencies between the theoretical models and the observed data.

Bayesian Analysis of Two Stellar Populations in Galactic Globular Clusters. II. NGC 5024, NGC 5272, and NGC 6352

We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of Galactic Globular Clusters to find and characterize two stellar populations in NGC 5024 (M53), NGC 5272 (M3), and NGC 6352. For these three clusters, both single and double-population analyses are used to determine a best fit isochrone(s). We employ a sophisticated Bayesian analysis technique to simultaneously fit the cluster parameters (age, distance, absorption, and metallicity) that characterize each cluster. For the two-population analysis, unique population level helium values are also fit to each distinct population of the cluster and the relative proportions of the populations are determined. We find differences in helium ranging from

Detecting Relativistic X-ray Jets in High-Redshift Quasars

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Detecting Unspecified Structure in Low-Count Images

0.05 to 0.11 for these three clusters. Model grids with solar