Mass estimates from stellar proper motions: The mass of ω\omega Centauri

We lay out and apply methods to use proper motions of individual kinematic tracers for estimating the dynamical mass of star clusters. We first describe a simple projected mass estimator and then develop an approach that evaluates directly the likelihood of the discrete kinematic data given the model predictions. Those predictions may come from any dynamical modelling approach, and we implement an analytic King model, a spherical isotropic Jeans equation model and an axisymmetric, anisotropic Jeans equation model.We apply these approaches to the enigmatic globular cluster omega Centauri, combining the proper motion from van Leeuwen et al (2000) with improved photometric cluster membership probabilities. We show that all mass estimates based on spherical isotropic models yield $(4.55\pm 0.1) \times 10^6 M_{\odot} [D/5.5 \pm 0.2 kpc]^3$, where our modelling allows us to show how the statistical precision of this estimate improves as more proper motion data of lower signal-to-noise are included. MLM predictions, based on an anisotropic axisymmetric Jeans model, indicate for $\omega$ Cen that the inclusion of anisotropies is not important for the mass estimates, but that accounting for the flattening is: flattened models imply $(4.05\pm 0.1) \times 10^6 M_{\odot} [D/5.5 \pm 0.2 kpc]^3$, 10% lower than when restricting the analysis to a spherical model. The best current distance estimates imply an additional uncertainty in the mass estimate of 12%.Comment: Accepted for publication in MNRA

The Milky Way's Stellar Disk

A suite of vast stellar surveys mapping the Milky Way, culminating in the Gaia mission, is revolutionizing the empirical information about the distribution and properties of stars in the Galactic stellar disk. We review and lay out what analysis and modeling machinery needs to be in place to test mechanisms of disk galaxy evolution and to stringently constrain the Galactic gravitational potential, using such Galactic star-by-star measurements. We stress the crucial role of stellar survey selection functions in any such modeling; and we advocate the utility of viewing the Galactic stellar disk as made up from `mono-abundance populations' (MAPs), both for dynamical modeling and for constraining the Milky Way's evolutionary processes. We review recent work on the spatial and kinematical distribution of MAPs, and lay out how further study of MAPs in the Gaia era should lead to a decisively clearer picture of the Milky Way's dark matter distribution and formation history.Comment: Astron. Astrophys. Rev., in pres

Chempy\mathit{Chempy}: A flexible chemical evolution model for abundance fitting - Do the Sun's abundances alone constrain chemical evolution models?

Elemental abundances of stars are the result of the complex enrichment history of their galaxy. Interpretation of observed abundances requires flexible modeling tools to explore and quantify the information about Galactic chemical evolution (GCE) stored in such data. Here we present Chempy, a newly developed code for GCE modeling, representing a parametrized open one-zone model within a Bayesian framework. A Chempy model is specified by a set of 5-10 parameters that describe the effective galaxy evolution along with the stellar and star-formation physics: e.g. the star-formation history, the feedback efficiency, the stellar initial mass function (IMF) and the incidence of supernova type Ia (SN Ia). Unlike established approaches, Chempy can sample the posterior probability distribution in the full model parameter space and test data-model matches for different nucleosynthetic yield sets. We extend Chempy to a multi-zone scheme. As an illustrative application, we show that interesting parameter constraints result from only the ages and elemental abundances of Sun, Arcturus and the present-day interstellar medium (ISM). For the first time, we use such information to infer IMF parameter via GCE modeling, where we properly marginalize over nuisance parameters and account for different yield sets. We find that of the IMF $11.6_{-1.6}^{+2.1}$ % explodes as core-collapse SN, compatible with Salpeter 1955. We also constrain the incidence of SN Ia per 10^3 Msun to 0.5-1.4. At the same time, this Chempy application shows persistent discrepancies between predicted and observed abundances for some elements, irrespective of the chosen yield set. These cannot be remedied by any variations of Chempy's parameters and could be an indication for missing nucleosynthetic channels. Chempy should be a powerful tool to confront predictions from stellar nucleosynthesis with far more complex abundance data sets.Comment: 19 pages, 17 figures, accepted for publication in A&A, python code: https://github.com/jan-rybizki/Chemp