The Mass of the Milky Way Using Globular Cluster Kinematics

Transcription

1 The Mass of the Milky Way Using Globular Cluster Kinematics Gwendolyn Eadie, PhD Candidate PhD Supervisor: William Harris Collaborators: Aaron Springford (Stats, Queen s Univ.) Postgraduate Scholarships-Doctoral Program eadiegm@mcmaster.ca

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5 Cartoon Model of the Galaxy and a Globular Cluster r

6 Cartoon Model of the Galaxy and a Globular Cluster v r r

7 Cartoon Model of the Galaxy and a Globular Cluster v t v r r

8 Cartoon Model of the Galaxy and a Globular Cluster v t v r r Galactocentric

9 Cartoon Model of the Galaxy and a Globular Cluster v t μ v los v r r Heliocentric

10 Cartoon Model of the Galaxy and a Globular Cluster v los μ v r Heliocentric v t r solar motion rotation of disk Position of GC distance Galactocentric

11 Cartoon Model of the Galaxy and a Globular Cluster Not always measured! μ Heliocentric solar motion rotation of disk Position of GC distance Galactocentric

12 Cartoon Model of the Galaxy and a Globular Cluster Not always measured! v t v los μ r v r? Heliocentric solar motion rotation of disk Position of GC distance Galactocentric

13 Some of the challenges Mixture of incomplete and complete data v los v los? μ

14 Some of the challenges Different types of orbits

15 Some of the challenges Difficult to compare masses

16 Some of the challenges Measurement uncertainties True but unknown value

17 Some of the challenges Small sample (157 globular clusters)

18 Some of the challenges Mixture of incomplete and complete data Different types of orbits Difficult to compare masses Measurement uncertainties Small sample (157 globular clusters)

19 We have overcome some challenges Mixture of incomplete and complete data Different types of orbits Difficult to compare masses Measurement uncertainties Small sample (89/157 globular clusters)

20 Eadie & Harris (2016), ApJ 829, 108 Mass within ~200 kpc: 6.8 x M sun 95% credible region (4.7, 9.2) x M sun

21 Only used 89/157 GCs Can we do better? And what about uncertainties?

22 Only used 89/157 GCs Can we do better? And what about uncertainties? Use a Hierarchical Bayesian Model

23 Basics of the Hierarchical Bayesian Model Measurement Model (Likelihood) Physical Model (Prior) Model for the Galaxy Model for the Globular Cluster Populations Constraints on Model Parameters (HyperPriors)

24 We have overcome many challenges! Mixture of incomplete and complete data Different types of orbits Difficult to compare masses Measurement uncertainties Small sample (143/157 globular clusters)

25 Mass Before Uncertainties No uncertainties, 89 GCs Mass within ~200 kpc: 6.8 (4.7, 9.2) x M sun

26 Mass Profile No uncertainties, 89 GCs Mass within ~200 kpc: 6.8 (4.7, 9.2) x M sun With uncertainties, 143 GCs Mass within ~200 kpc: 6.2 (4.8, 7.8) x M sun (Eadie, Springford, and Harris 2016, ApJ, in press)

27 Future Work More proper motions New classes of objects Dwarf galaxies, halo stars (Gaia!), Planetary Nebulae Analyze simulated data (Eadie et al, in prep) Beyond the MW M31, dwarf galaxies, galaxy clusters, brightest cluster galaxies

28 Galaxy s mass within ~200 kpc between x M eadiegm@mcmaster.ca Thank you! Eadie, Harris, & Springford, ApJ (in press) Eadie & Harris (2016), ApJ 829, 108. Eadie, Harris, Widrow (2015), ApJ 806, 54. Eadie, Harris, Widrow & Springford (2015), IAU Proc., Symposium 317. Eadie, Harris, Springford (2015), JSM Proc., SPES.

29 Group 1

30 Group 2 Eadie & Harris (2016), ApJ

31 Eadie & Harris (2016), ApJ 829, 108

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33 Sensitivity analysis - limiting the sample r cut Eadie, Harris, and Springford (2016), ApJ, in press

34 Sensitivity analysis - limiting the sample

35 Eadie, Harris, and Springford (2016), ApJ, in press Sensitivity analysis - removing inner GCs

36 Number of GCs Number with proper motions Eadie, Harris, and Springford (2016), ApJ, in press Sensitivity analysis - removing inner GCs

37 Setting up the Hierarchical Bayesian Model Data Parameter Uncertainty (fixed)

38 Setting up the Hierarchical Bayesian Model distance line-of-sight velocity proper motion (DEC) proper motion (RA)

39 Setting up the Hierarchical Bayesian Model Likelihood (measurement model) Prior (physical model) Hyperpriors (for model parameters)

40 Hierarchical Bayesian Model Likelihood x Prior x Hyperprior

41 157 Globular Clusters in the catalog

42 157 Globular Clusters in the catalog 14 don t have any velocity measurements

43 157 Globular Clusters in the catalog 14 don t have any velocity measurements 143 GCs left

44 157 Globular Clusters in the catalog 14 don t have any velocity measurements 143 GCs left 85 have proper motion measurements

45 157 Globular Clusters in the catalog 14 don t have any velocity measurements 143 GCs left 85 have proper motion measurements 72 have usable proper motion measurements

46 157 Globular Clusters in the catalog 14 don t have any velocity measurements 143 GCs left 85 have proper motion measurements 72 have usable proper motion measurements +17

47 Gain a few GCs by using a geometric approximation v los v r ɣ treat unknown v t s as nuisance parameters

48 89 / 157 GCs, Galactocentric Frame 72 are complete data 17 are incomplete data treat unknown v t s as nuisance parameters This method: Eadie & Harris (2016), ApJ 829, 108. Eadie, Harris, & Widrow (2015), ApJ 806, 54. Eadie, G. 2014, JSM Proceedings, ASA, Section 175. Eadie, G. MSc Thesis, Queen s University (2013).