Classifying Globular Clusters and Applying them to Estimate the mass of the Milky Way

We combine the kinematics of 159 globular clusters(GCs) provided by the Gaia Early Data Release 3(EDR3) with other observational data to classify the GCs,and to estimate the mass of the Milky Way(MW).We use the agemetallicity relation,integrals of motion,action space and the GC orbits to identify the GCs as either formed in situ(Bulge and Disk) or ex situ(via accretion).We find that 45.3% have formed in situ,while 38.4% may be related to known merger events:Gaia-Sausage-Enceladus,the Sagittarius dwarf galaxy,the Helmi streams,the Sequoia galaxy and the Kraken galaxy.We also further identify three new sub-structures associated with the Gaia-Sausage-Enceladus.The remaining 16.3% of GCs are unrelated to the known mergers and thought to be from small accretion events.We select 46 GCs which have radii 8.0 <r<37.3 kpc and obtain the anisotropy parameter β=0.315_(-0.049)^(+0.055),which is lower than the recent result using the sample of GCs in Gaia Data Release 2,but still in agreement with it by considering the error bar.By using the same sample,we obtain the MW mass inside the outermost GC as M(<37.3 kpc)=0.423_(-0.02)^(+0.02)×10^(12)M_(⊙),and the corresponding M_(200)=1.11_(-0.18)^(+0.25)×10^(12)M_(⊙).The estimated mass is consistent with the results in many recent studies.We also find that the estimated β and mass depend on the selected sample of GCs.However,it is difficult to determine whether a GC fully traces the potential of the MW.

Stellar Dynamical Modeling—Counting Conserved Quantities

Knowing the conserved quantities that a galaxy’s stellar orbits conform to is important in helping us understand the stellar distribution and structures within the galaxy.Isolating integrals of motion and resonances are particularly important,non-isolating integrals less so.We compare the behavior and results of two methods for counting the number of conserved quantities,one based on the correlation integral approach and the other a more recent method using machine learning.Both methods use stellar orbit trajectories in phase space as their only input,and we create such trajectories from theoretical spherical,axisymmetric,and triaxial model galaxies.The orbits have known isolating integrals and resonances.We find that neither method is fully effective in recovering the numbers of these quantities,nor in determining the number of non-isolating integrals.From a computer performance perspective,we find the correlation integral approach to be the faster.Determining the algebraic formulae of(multiple)conserved quantities from the trajectories has not been possible due to the lack of an appropriate symbolic regression capability.Notwithstanding the shortcomings we have noted,it may be that the methods are usable as part of a trajectory analysis tool kit.

Stellar dynamical modeling-accuracy of 3D density estimation for edge-on axisymmetric galaxies

From Rybicki’s analysis using the Fourier slice theorem,mathematically it is possible to reproduce uniquely an edge-on axisymmetric galaxy’s 3D light distribution from its 2D surface brightness.Utilizing galaxies from a cosmological simulation,we examine the ability of Syer and Tremaine’s madeto-measure method and Schwarzschild’s method for stellar dynamical modeling to do so for edge-on oblate axisymmetric galaxies.Overall,we find that the methods do not accurately recover the 3D distributions,with the made-to-measure method producing more accurate estimates than Schwarzschild’s method.Our results have implications broader than just luminosity density,and affect other luminosity-weighted distributions within galaxies,for example,age and metallicity.