arXiv subjects

Gwendolyn M. Eadie

Publications and source records attributed to Gwendolyn M. Eadie.

29 records · Page 2Linked to original sources

arXiv2023

The HERBAL model: A hierarchical errors-in-variables Bayesian lognormal hurdle model for galactic globular cluster populations

Galaxy stellar mass is known to be monotonically related to the size of the galaxy's globular cluster (GC) population for Milky Way sized and larger galaxies. However, the relation becomes ambiguous for dwarf galaxies, where there is some evidence for a downturn in GC population size at low galaxy masses. Smaller dwarfs are increasingly likely to have no GCs, and these zeros cannot be easily incorporated into linear models. We introduce the Hierarchical ERrors-in-variables Bayesian lognormAL hurdle (HERBAL) model to represent the relationship between dwarf galaxies and their GC populations, and apply it to the sample of Local Group galaxies where the luminosity range coverage is maximal. This bimodal model accurately represents the two populations of dwarf galaxies: those that have GCs and those that do not. Our model thoroughly accounts for all uncertainties, including measurement uncertainty, uncertainty in luminosity to stellar mass conversions, and intrinsic scatter. The hierarchical nature of our Bayesian model also allows us to estimate galaxy masses and individual mass-to-light ratios from luminosity data within the model. We find that 50% of galaxies are expected to host globular cluster populations at a stellar mass of $\log_{10}(M_*)=6.996$, and that the expected mass of GC populations remains linear down to the smallest galaxies. Our hierarchical model recovers an accurate estimate of the Milky Way stellar mass. Under our assumed error model, we find a non-zero intrinsic scatter of $0.59_{-0.21}^{+0.30}$ (95% credible interval) that should be accounted for in future models.

astro-ph.GA↗

arXiv2023

A CHIME/FRB study of burst rate and morphological evolution of the periodically repeating FRB 20180916B

FRB 20180916B is a repeating Fast Radio Burst (FRB) with a 16.3-day periodicity in its activity. In this study, we present morphological properties of 60 FRB 20180916B bursts detected by CHIME/FRB between 2018 August and 2021 December. We recorded raw voltage data for 45 of these bursts, enabling microseconds time resolution in some cases. We studied variation of spectro-temporal properties with time and activity phase. We find that the variation in Dispersion Measure (DM) is $\lesssim$1 pc cm$^{-3}$ and that there is burst-to-burst variation in scattering time estimates ranging from $\sim$0.16 to over 2 ms, with no discernible trend with activity phase for either property. Furthermore, we find no DM and scattering variability corresponding to the recent change in rotation measure from the source, which has implications for the immediate environment of the source. We find that FRB 20180916B has thus far shown no epochs of heightened activity as have been seen in other active repeaters by CHIME/FRB, with its burst count consistent with originating from a Poissonian process. We also observe no change in the value of the activity period over the duration of our observations and set a 1$σ$ upper limit of $1.5\times10^{-4}$ day day$^{-1}$ on the absolute period derivative. Finally, we discuss constraints on progenitor models yielded by our results, noting that our upper limits on changes in scattering and dispersion measure as a function of phase do not support models invoking a massive binary companion star as the origin of the 16.3-day periodicity.

astro-ph.HE↗

arXiv2023

Practical Guidance for Bayesian Inference in Astronomy

In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next, which can lead to confusion to both those learning and those familiar with Bayesian statistics. Moreover, the choice varies between the astronomy and statistics literature, too. In this paper, our goal is two-fold: (1) provide a reference that consolidates and clarifies terminology and notation across disciplines, and (2) outline practical guidance for Bayesian inference in astronomy. Highlighting both the astronomy and statistics literature, we cover topics such as notation, specification of the likelihood and prior distributions, inference using the posterior distribution, and posterior predictive checking. It is not our intention to introduce the entire field of Bayesian data analysis -- rather, we present a series of useful practices for astronomers who already have an understanding of the Bayesian "nuts and bolts" and wish to increase their expertise and extend their knowledge. Moreover, as the field of astrostatistics and astroinformatics continues to grow, we hope this paper will serve as both a helpful reference and as a jumping off point for deeper dives into the statistics and astrostatistics literature.

astro-ph.IM↗

arXiv2023

An FRB Sent Me a DM: Constraining the Electron Column of the Milky Way Halo with Fast Radio Burst Dispersion Measures from CHIME/FRB

The CHIME/FRB project has detected hundreds of fast radio bursts (FRBs), providing an unparalleled population to probe statistically the foreground media that they illuminate. One such foreground medium is the ionized halo of the Milky Way (MW). We estimate the total Galactic electron column density from FRB dispersion measures (DMs) as a function of Galactic latitude using four different estimators, including ones that assume spherical symmetry of the ionized MW halo and ones that imply more latitudinal-variation in density. Our observation-based constraints of the total Galactic DM contribution for $|b|\geq 30^\circ$, depending on the Galactic latitude and selected model, span 87.8 - 141 pc cm^-3. This constraint implies upper limits on the MW halo DM contribution that range over 52-111 pc cm^-3. We discuss the viability of various gas density profiles for the MW halo that have been used to estimate the halo's contribution to DMs of extragalactic sources. Several models overestimate the DM contribution, especially when assuming higher halo gas masses (~ 3.5 x 10^12 solar masses). Some halo models predict a higher MW halo DM contribution than can be supported by our observations unless the effect of feedback is increased within them, highlighting the impact of feedback processes in galaxy formation.

astro-ph.GA↗

arXiv2022

Light from the Darkness: Detecting Ultra-Diffuse Galaxies in the Perseus Cluster through Over-densities of Globular Clusters with a Log-Gaussian Cox Process

We introduce a new method for detecting ultra-diffuse galaxies by searching for over-densities in intergalactic globular cluster populations. Our approach is based on an application of the log-Gaussian Cox process, which is a commonly used model in the spatial statistics literature but rarely used in astronomy. This method is applied to the globular cluster data obtained from the PIPER survey, a \textit{Hubble Space Telescope} imaging program targeting the Perseus cluster. We successfully detect all confirmed ultra-diffuse galaxies with known globular cluster populations in the survey. We also identify a potential galaxy that has no detected diffuse stellar content. Preliminary analysis shows that it is unlikely to be merely an accidental clump of globular clusters or other objects. If confirmed, this system would be the first of its kind. Simulations are used to assess how the physical parameters of the globular cluster systems within ultra-diffuse galaxies affect their detectability using our method. We quantify the correlation of the detection probability with the total number of globular clusters in the galaxy and the anti-correlation with increasing half-number radius of the globular cluster system. The Sérsic index of the globular cluster distribution has little impact on detectability.

astro-ph.GA↗

arXiv2021

The Mass of the Milky Way from the H3 Survey

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 $\textit{Gaia}$ EDR3, to infer the mass of the Galaxy. Inference is carried out with the No-U-Turn sampler, a fast and scalable extension of Hamiltonian Monte Carlo. We report a median mass enclosed within $100~{\rm kpc}$ of $\rm M(<100 \; kpc) = 0.69_{-0.04}^{+0.05} \times 10^{12} \; M_\odot$ (68% Bayesian credible interval), or a virial mass of $\rm M_{200} = M(<216.2_{-7.5}^{+7.5} \; kpc) = 1.08_{-0.11}^{+0.12} \times 10^{12} \; M_\odot$, in good agreement with other recent estimates. We analyze our results using posterior predictive checks and find limitations in the model's ability to describe the data. In particular, we find sensitivity with respect to substructure in the halo, which limits the precision of our mass estimates to $\sim 15\%$.

astro-ph.GA↗

arXiv2021

Clearing the hurdle: The mass of globular cluster systems as a function of host galaxy mass

Current observational evidence suggests that all large galaxies contain globular clusters (GCs), while the smallest galaxies do not. Over what galaxy mass range does the transition from GCs to no GCs occur? We investigate this question using galaxies in the Local Group, nearby dwarf galaxies, and galaxies in the Virgo Cluster Survey. We consider four types of statistical models: (1) logistic regression to model the probability that a galaxy of stellar mass $M_{\star}$ has any number of GCs; (2) Poisson regression to model the number of GCs versus $M_{\star}$, (3) linear regression to model the relation between GC system mass ($\log{M_{gcs}}$) and host galaxy mass ($\log{M_{\star}}$), and (4) a Bayesian lognormal hurdle model of the GC system mass as a function of galaxy stellar mass for the entire data sample. From the logistic regression, we find that the 50% probability point for a galaxy to contain GCs is $M_{\star}=10^{6.8}M_{\odot}$. From post-fit diagnostics, we find that Poisson regression is an inappropriate description of the data. Ultimately, we find that the Bayesian lognormal hurdle model, which is able to describe how the mass of the GC system varies with $M_{\star}$ even in the presence of many galaxies with no GCs, is the most appropriate model over the range of our data. In an Appendix, we also present photometry for the little-known GC in the Local Group dwarf Ursa Major II.

astro-ph.GA↗

arXiv2021

Bayesian Inference of Globular Cluster Properties Using Distribution Functions

We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of sizes and concentrations are generated from lowered isothermal dynamical models, from which we test the reliability of the Bayesian method to estimate model parameters through repeated statistical simulation. We find that given unbiased star samples, we are able to reconstruct the cluster parameters used to generate the mock cluster and the cluster's cumulative mass and mean velocity squared profiles with good accuracy. We further explore how strongly biased sampling, which could be the result of observing constraints, may affect this approach. Our tests indicate that if we instead have biased samples, then our estimates can be off in certain ways that are dependent on cluster morphology. Overall, our findings motivate obtaining samples of stars that are as unbiased as possible. This may be achieved by combining information from multiple telescopes (e.g., Hubble and Gaia), but will require careful modeling of the measurement uncertainties through a hierarchical model, which we plan to pursue in future work.

astro-ph.GA↗

arXiv2018

Estimating the Milky Way's Mass via Hierarchical Bayes: A Blind Test on MUGS2 Simulated Galaxies

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.

astro-ph.GA↗

arXiv2016

Bayesian Mass Estimates of the Milky Way II: The dark and light sides of parameter assumptions

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 population beyond certain radii affect mass estimates. After exploring the posterior distributions of different parameter assumption scenarios, we conclude that a conservative estimate of the Galaxy's mass within 125kpc is $5.22\times10^{11} M_{\odot}$, with a $50\%$ probability region of $(4.79, 5.63) \times10^{11} M_{\odot}$. Extrapolating out to the virial radius, we obtain a virial mass for the Milky Way of $6.82\times10^{11} M_{\odot}$ with $50\%$ credible region of $(6.06, 7.53) \times 10^{11} M_{\odot}$ ($r_{vir}=185^{+7}_{-7}$kpc). If we consider only the GCs beyond 10kpc, then the virial mass is $9.02~(5.69, 10.86) \times 10^{11} M_{\odot}$ ($r_{vir}=198^{+19}_{-24}$kpc). We also arrive at an estimate of the velocity anisotropy parameter $β$ of the GC population, which is $β=0.28$ with a $50\%$ credible region (0.21, 0.35). Interestingly, the mass estimates are sensitive to both the dark matter halo potential and visible matter tracer parameters, but are not very sensitive to the anisotropy parameter.

astro-ph.GA↗

arXiv2015

Estimating the Galactic Mass Profile in the Presence of Incomplete Data

A powerful method to measure the mass profile of a galaxy is through the velocities of tracer particles distributed through its halo. Transforming this kind of data accurately to a mass profile M(r), however, is not a trivial problem. In particular, limited or incomplete data may substantially affect the analysis. In this paper we develop a Bayesian method to deal with incomplete data effectively; we have a hybrid-Gibbs sampler that treats the unknown velocity components of tracers as parameters in the model. We explore the effectiveness of our model using simulated data, and then apply our method to the Milky Way using velocity and position data from globular clusters and dwarf galaxies. We find that in general, missing velocity components have little effect on the total mass estimate. However, the results are quite sensitive to the outer globular cluster Pal 3. Using a basic Hernquist model with an isotropic velocity dispersion, we obtain credible regions for the cumulative mass profile M(r) of the Milky Way, and provide estimates for the model parameters with 95 percent Bayesian credible intervals. The mass contained within 260 kpc is 1.37x10^12 solar masses, with a 95 percent credible interval of (1.27,1.51)x10^12 solar masses. The Hernquist parameters for the total mass and scale radius are 1.55 (+0.18/-0.13)x10^12 solar masses and 16.9 (+4.8/-4.1) kpc, where the uncertainties span the 95 percent credible intervals. The code we developed for this work, Galactic Mass Estimator (GME), will be available as an open source package in the R Project for Statistical Computing.

astro-ph.GA↗