In a series of three papers, Eadie et al. developed a hierarchical Bayesian method to estimate the Milky Way Galaxy's mass given a physical model for the potential, a measurement model, and kinematic data of test particles such as globular clusters (GCs) or halo stars in the Galaxy's halo. The Galaxy's virial mass was found to have a 95\% Bayesian credible region (c.r.) of $(0.67, 1.09) \times 10^{12} M_{\odot}$. In the present study, we test the hierarchical Bayesian method against simulated galaxies created in the McMaster Unbiased Galaxy Simulations 2 (MUGS2), for which the true mass is known. We estimate the masses of MUGS2 galaxies using GC analogs from the simulations as tracers. The analysis, completed as a blind test, recovers the true $M_{200}$ of the MUGS2 galaxies within 95\% Bayesian c.r. in 8 out of 18 cases. Of the 10 galaxy masses that were not recovered within the 95\% c.r., a large subset have posterior distributions that occupy extreme ends of the parameter space allowed by the priors. A few incorrect mass estimates are explained by the exceptional evolution history of the galaxies. We also find evidence that the model cannot describe both the galaxies' inner and outer structure simultaneously in some cases. After removing the GC analogs associated with the galactic disks, the true masses were found more reliably (13 out of 18 were predicted within the c.r.). Finally, we discuss how representative the GC analogs are of the real GC population in the Milky Way.
We develop a novel Bayesian methodology aimed at reliably and precisely inferring the distribution of dark matter within the Milky Way using rotation curve data. We identify a subset of the available rotation curve tracers that are mutually consistent with each other, thus eliminating data sets that might suffer from systematic bias. We investigate three different models for the mass distribution of the luminous (baryonic) component that bracket the range of likely morphologies. We demonstrate the statistical performance of our method on simulated data in terms of coverage, fractional distance…
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie, Harris, & Widrow (2015) and Eadie & Harris (2016) and builds upon the preliminary reports by Eadie et al (2015a,c). The method uses a distribution function $f(\mathcal{E},L)$ to model the galaxy and kinematic data from satellite objects such as globular clusters (GCs) to trace the Galaxy's gravitational potential. A major advantage of the method is that it not only includes complete and incomp…
We present BALRoGO: Bayesian Astrometric Likelihood Recovery of Galactic Objects, a public code to measure the centers, effective radii, and bulk proper motions of Milky Way globular clusters and Local Group dwarf spheroidals, whose data are mixed with Milky Way field stars. Our approach presents innovative methods such as surface density fits allowing for strong interloper contamination and proper motion fits using a Pearson VII distribution for interlopers, instead of classic Gaussian-mixture recipes. We also use non-parametric approaches to represent the color-magnitude diagram of such stel…
Chemical tagging has great promise as a technique to unveil our Galaxy's history. Grouping stars based on their similar chemistry can establish details of the star formation and merger history of the Milky Way. With precise measurements of stellar chemistry, chemical tagging may be able to group together stars born from the same gas cloud, regardless of their current positions and kinematics. Successfully tagging these birth clusters requires high quality chemical space information and a good cluster-finding algorithm. To test the feasibility of chemical tagging on data from current and upcomi…
This work investigates the vertical profile of the stars in the disk of the Milky Way. The models investigated are of the form $sech^{2/n}(nz/(2H))$ where, setting $α= 2/n$, the three functions of the sequence $α= 0,1,2$ correspond to exponential, $sech$, $sech^2$ functions. We consider symmetric models and asymmetric models, above and below the plane. The study uses the large sample of K and M stars of Ferguson et al. (2017) and applies the methods of Bayesian model comparison to discriminate between the 6 models. Two inconsistencies in Ferguson et al. (2017), concerning the vertical height c…
We present mass and mass profile estimates for the Milky Way Galaxy using the Bayesian analysis developed by Eadie et al (2015b) and using globular clusters (GCs) as tracers of the Galactic potential. The dark matter and GCs are assumed to follow different spatial distributions; we assume power-law model profiles and use the model distribution functions described in Evans et al. (1997); Deason et al (2011, 2012a). We explore the relationships between assumptions about model parameters and how these assumptions affect mass profile estimates. We also explore how using subsamples of the GC popula…
The exponential scale length ($L_d$) of the Milky Way's (MW's) disk is a critical parameter for describing the global physical size of our Galaxy, important both for interpreting other Galactic measurements and helping us to understand how our Galaxy fits into extragalactic contexts. Unfortunately, current estimates span a wide range of values and often are statistically incompatible with one another. Here, we perform a Bayesian meta-analysis to determine an improved, aggregate estimate for $L_d$, utilizing a mixture-model approach to account for the possibility that any one measurement has no…
We develop a Bayesian Machine Learning framework called BINGO (Bayesian INference for Galactic archaeOlogy) centred around a Bayesian neural network. After being trained on the APOGEE and \emph{Kepler} asteroseismic age data, BINGO is used to obtain precise relative stellar age estimates with uncertainties for the APOGEE stars. We carefully construct a training set to minimise bias and apply BINGO to a stellar population that is similar to our training set. We then select the 17,305 stars with ages from BINGO and reliable kinematic properties obtained from \textit{Gaia} DR2. By combining the a…
Space observatories like the Hubble Space Telescope and Gaia are providing unprecedented 6D phase space information of satellite galaxies. Such measurements can shed light on the structure and assembly history of the Local Group, but improved statistical methods are needed to use them efficiently. Here we illustrate such a method using analogs of the Local Group's two most massive satellite galaxies, the Large Magellanic Cloud (LMC) and Triangulum (M33), from the Illustris dark-matter-only cosmological simulation. We use a Bayesian inference scheme combining measurements of positions, velociti…
A Complete Spectroscopic Survey of the Milky Way satellite Segue 1: Dark matter content, stellar membership and binary properties from a Bayesian analysis
The vast quantity of strong galaxy-galaxy gravitational lenses expected by future large-scale surveys necessitates the development of automated methods to efficiently model their mass profiles. For this purpose, we train an approximate Bayesian convolutional neural network (CNN) to predict mass profile parameters and associated uncertainties, and compare its accuracy to that of conventional parametric modelling for a range of increasingly complex lensing systems. These include standard smooth parametric density profiles, hydrodynamical EAGLE galaxies and the inclusion of foreground mass struct…
We present new mass estimates and cumulative mass profiles (CMPs) with Bayesian credible regions for the Milky Way (MW) Galaxy, given the kinematic data of globular clusters as provided by (1) the $\textit{Gaia}$ DR2 collaboration and the HSTPROMO team, and (2) the new catalog in Vasiliev (2019). We use globular clusters beyond 15kpc to estimate the CMP of the MW, assuming a total gravitational potential model $Φ(r) = Φ_{\circ}r^{-γ}$, which approximates an NFW-type potential at large distances when $γ=0.5$. We compare the resulting CMPs given data sets (1) and (2), and find the results to be …
The mass of the Milky Way is a critical quantity which, despite decades of research, remains uncertain within a factor of two. Until recently, most studies have used dynamical tracers in the inner regions of the halo, relying on extrapolations to estimate the mass of the Milky Way. In this paper, we extend the hierarchical Bayesian model applied in Eadie & Jurić (2019) to study the mass distribution of the Milky Way halo; the new model allows for the use of all available 6D phase-space measurements. We use kinematic data of halo stars out to $142~{\rm kpc}$, obtained from the H3 Survey and $\t…
We test a Yukawa correction to the Newtonian potential, making use of our own Galaxy - the Milky Way - as a testbed. We include as free parameter the Yukawa strength and range and the dark matter profile parameters, and compare several morphologies for the bulge, gas, and disk components, also using Bayesian model selection criteria. We employ up-to-date datasets for both the visible (baryonic) component of the Milky Way, and for the tracers of the gravitational potential (the Rotation Curve). We find that the data are consistent with the Newtonian potential, and constrain the Yukawa coupling …
We employ our Bayesian Machine Learning framework BINGO (Bayesian INference for Galactic archaeOlogy) to obtain high-quality stellar age estimates for 68,360 red giant and red clump stars present in the 17th data release of the Sloan Digital Sky Survey, the APOGEE-2 high-resolution spectroscopic survey. By examining the denoised age-metallicity relationship of the Galactic disc stars, we identify a drop in metallicity with an increase in [Mg/Fe] at an early epoch, followed by a chemical enrichment episode with increasing [Fe/H] and decreasing [Mg/Fe]. This result is congruent with the chemical…
We present a new estimate of the mass of the Milky Way, inferred via a Bayesian approach by making use of tracers of the circular velocity in the disk plane and stars in the stellar halo, as from the publicly available {\tt galkin} compilation. We use the rotation curve method to determine the dark matter distribution and total mass under different assumptions for the dark matter profile, while the total stellar mass is constrained by surface stellar density and microlensing measurements. We also include uncertainties on the baryonic morphology via Bayesian model averaging, thus converting a p…
Estimating a distance by inverting a parallax is only valid in the absence of noise. As most stars in the Gaia catalogue will have non-negligible fractional parallax errors, we must treat distance estimation as a constrained inference problem. Here we investigate the performance of various priors for estimating distances, using a simulated Gaia catalogue of one billion stars. We use three minimalist, isotropic priors, as well an anisotropic prior derived from the observability of stars in a Milky Way model. The two priors that assume a uniform distribution of stars--either in distance or in sp…
Forward-modelling Milky Way Cepheids: selection effects and physical priors in the Gaia-HST calibration
University of Oxford（牛津大学）；Space Telescope Science Institute（太空望远镜科学研究所）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of Portsmouth（朴茨茅斯大学）；CNRS & Sorbonne Université（法国国家科学研究中心与索邦大学）；Duke University（杜克大学）
The stellar velocity distribution in the Solar Neighbourhood displays kinematic substructures, which are possibly signatures of the bar and spiral arms of the Milky Way and of previous accretion events. These kinematic substructures -- moving groups -- can be thought of as continuous manifolds in the 6D phase space, and the ridges in the $V_ϕ-R$ and arches in the $V_ϕ-V_R$ plane, discovered with the Gaia mission, as projections of these manifolds. We develop and apply a methodology to perform a blind search for substructure in the Gaia EDR3 6D data, and obtain a sampling of the manifolds. The …
Selection functions are vital for understanding the observational biases of spectroscopic surveys. With the wide variety of multi-object spectrographs currently in operation and becoming available soon, we require easily generalisable methods for determining the selection functions of these surveys. Previous work, however, has largely been focused on generating individual, tailored selection functions for every data release of each survey. Moreover, no methods for combining these selection functions to be used for joint catalogues have been developed. We have developed a Poisson likelihood est…
We report 1,656 new star clusters found in the Galactic disk (|b|<20 degrees) beyond 1.2 kpc, using Gaia EDR3 data. Based on an unsupervised machine learning algorithm, DBSCAN, and followed our previous studies, we utilized a unique method to do the data preparation and obtained the clustering coefficients, which proved to be an effective way to search blindly for star clusters. We tabulated the physical parameters and member stars of the new clusters, and presented some interesting examples, including a globular cluster candidate. The cluster parameters and member stars are available at CDS v…
Using action-based distribution function for the dynamical model of the Milky Way we have estimated its total mass and its density profile. Constraints are coming from the globular cluster proper motions from Gaia EDR3, from the rotation curve based on Gaia DR2 data, and from the vertical force data. We use Bayesian Markov chain Monte Carlo method to explore the parameters, for which the globular cluster distribution function and the Galactic potential are fully constrained. Numerical simulations are used to study the uncertainties on the potential constraint if considering a possible massive …
We construct a model for the Galactic globular cluster system based on a realistic gravitational potential and a distribution function (DF) analytic in the action integrals. The DF comprises disc and halo components whose functional forms resemble those recently used to describe the stellar discs and stellar halo. We determine the posterior distribution of our model parameters using a Bayesian approach. This gives us an understanding of how well the globular cluster data constrain our model. The favoured parameter values of the disc and halo DFs are similar to values previously obtained from f…
In this paper, we have investigated one of the alternative theories to dark matter named MOdified Gravity (MOG) by testing its ability to describe the local dynamics of the Milky Way in vertical and transverse directions with the baryonic matter. MOG is designed to interpret the dynamics of galaxies and cluster of galaxies without the need for dark matter. We use local observational data such as the vertical dispersion, rotation curve, surface density and number density of stars in the Milky Way to obtained the parameters of MOG and the baryonic component of MW by implementing a Bayesian appro…
The Halo Assembly in Lambda-CDM: Observations in 7 Dimensions (HALO7D) dataset consists of Keck II/DEIMOS spectroscopy and Hubble Space Telescope-measured proper motions of Milky Way halo main sequence turnoff stars in the CANDELS fields. In this paper, we present the spectroscopic component of this dataset, and discuss target selection, observing strategy, and survey properties. We present a new method of measuring line-of-sight (LOS) velocities by combining multiple spectroscopic observations of a given star, utilizing Bayesian hierarchical modeling. We present the LOS velocity distributions…
White dwarf stars are a well-established tool for studying Galactic stellar populations. Two white dwarfs in a tight binary system offer us an additional messenger - gravitational waves - for exploring the Milky Way and its immediate surroundings. Gravitational waves produced by double white dwarf (DWD) binaries can be detected by the future Laser Interferometer Space Antenna (LISA). Numerous and widespread DWDs have the potential to probe shapes, masses and formation histories of the stellar populations in the Galactic neighbourhood. In this work we outline a method for estimating the total s…
Princeton University（普林斯顿大学）；New York University（纽约大学）；Flatiron Institute（熨斗研究所）
We demonstrate an algorithm for learning a flexible color-magnitude diagram from noisy parallax and photometry measurements using a normalizing flow, a deep neural network capable of learning an arbitrary multi-dimensional probability distribution. We present a catalog of 640M photometric distance posteriors to nearby stars derived from this data-driven model using Gaia DR2 photometry and parallaxes. Dust estimation and dereddening is done iteratively inside the model and without prior distance information, using the Bayestar map. The signal-to-noise (precision) of distance measurements improv…
Recent submillimeter and far-infrared wavelength observations of absorption in the rotational ground-state lines of various simple molecules against distant Galactic continuum sources have opened the possibility of studying the chemistry of diffuse molecular clouds throughout the Milky Way. In order to calculate abundances, the column densities of molecular and atomic hydrogen, HI, must be known. We aim at determining the atomic hydrogen column densities for diffuse clouds located on the sight lines toward a sample of prominent high-mass star-forming regions that were intensely studied with th…
We exploit the [Mg/Mn]-[Al/Fe] chemical abundance plane to help identify nearby halo stars in the 14th data release from the APOGEE survey that have been accreted on to the Milky Way. Applying a Gaussian Mixture Model, we find a `blob' of 856 likely accreted stars, with a low disc contamination rate of ~7%. Cross-matching the sample with the second data release from Gaia gives us access to parallaxes and apparent magnitudes, which place constraints on distances and intrinsic luminosities. Using a Bayesian isochrone pipeline, this enables us to estimate new ages for the accreted stars, with typ…
The high cosmological precision offered by the next generation of galaxy surveys hinges on improved corrections for Galactic dust extinction. We explore the possibility of estimating both the dust extinction and large-scale structure from a single photometric galaxy survey, making use of the predictable manner in which Milky Way dust affects the measured brightness and colors of galaxies in a given sky location in several redshift bins. To test our method, we use a synthetic catalog from a cosmological simulation designed to model the Vera C. Rubin Observatory Legacy Survey of Space and Time. …
The Milky Way's (MW) satellite population is a powerful probe of warm dark matter (WDM) models as the abundance of small substructures is very sensitive to the properties of the WDM particle. However, only a partial census of the MW's complement of satellite galaxies exists because surveys of the MW's close environs are incomplete both in depth and in sky coverage. We present a new Bayesian analysis that combines the sample of satellites recently discovered by the Dark Energy Survey (DES) with those found in the Sloan Digital Sky Survey (SDSS) to estimate the total satellite galaxy luminosity …
Chemo-dynamical reconstruction of Milky Way globular cluster progenitors: Age-metallicity relations and the universality of multiple stellar populations
Dipartimento di Fisica e Astronomia “Augusto Righi”–Università di Bologna（博洛尼亚大学）；INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚天文与空间科学观测站）；Berkeley Center for Cosmological Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校）；ICC, University of Barcelona（巴塞罗那大学）；ICREA（加泰罗尼亚高级研究学院）
We used adaptive mesh refinement hydrodynamic cosmological simulations of a $z=1$ Milky Way-type galaxy and a $z=0$ Dwarf galaxy and generated synthetic quasar absorption-line spectra of their circumgalactic medium (CGM). Our goal is to assess whether standard observational spectroscopic analysis methods accurately reproduce intrinsic column densities, metallicities [Si/H], and hydrogen densities $n_{H}$, in simulated absorption-line systems. Without knowledge of the intrinsic simulated properties (blind study), we analysed synthetic COS and HIRES spectra with fixed $S/N=30$ to determine the c…
In this thesis, the field star Initial Mass Function (IMF) and chemical evolution parameters for the Milky Way (MW) are derived using a forward modelling technique in combination with Bayesian statistics. Starting from a local MM disc model, observations of stellar samples in the Solar Neighbourhood are synthesised and compared to the corresponding volume-complete observational samples of Hipparcos stars. The resulting IMF, derived from observations in the range from 0.5 to 8Msun, is a two-slope broken power law with powers of -1.49 +- 0.08 and -3.02 +- 0.06 for the low-mass slope and the high…
Modeling the Milky Way wind: Supernova-driven outflows accelerate HI clouds near the Galactic center
Università di Firenze（佛罗伦萨大学）；INAF - Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所阿切特里天文台）；Research School of Astronomy and Astrophysics, The Australian National University（澳大利亚国立大学天文学与天体物理学研究学院）
Chemically tagging groups of stars born in the same birth cluster is a major goal of spectroscopic surveys. To investigate the feasibility of such strong chemical tagging, we perform a blind chemical tagging experiment on abundances measured from APOGEE survey spectra. We apply a density-based clustering algorithm to the eight dimensional chemical space defined by [Mg/Fe], [Al/Fe], [Si/Fe], [K/Fe], [Ti/Fe], [Mn/Fe], [Fe/H], and [Ni/Fe], abundances ratios which together span multiple nucleosynthetic channels. In a high quality sample of 182,538 giant stars, we detect twenty-one candidate cluste…
We estimate the Milky Way (MW) halo properties using satellite kinematic data including the latest measurements from Gaia DR2. With a simulation-based 6D phase-space distribution function (DF) of satellite kinematics, we can infer halo properties efficiently and without bias, and handle the selection function and measurement errors rigorously in the Bayesian framework. Applying our DF from the EAGLE simulation to 28 satellites, we obtain an MW halo mass of $M=1.23_{-0.18}^{+0.21}\times 10^{12} M_\odot$ and a concentration of $c=9.4_{ -2.1}^{ +2.8}$ with the prior based on the $M$-$c$ relation.…
