The mass of our Milky Way

Abstract: We perform an extensive review of the numerous studies and methods used to determine the total mass of the Milky Way. We group the various methods into seven broad classes, including: i) estimating Galactic escape velocity using high velocity objects; ii) measuring the rotation curve through terminal and circular velocities; iii) modeling halo stars, globular clusters and satellite galaxies with the Spherical Jeans equation and iv) with phase-space distribution functions; v) simulating and modeling the dynamics of stellar streams and their progenitors; vi) modeling the motion of the Milky Way, M31 and other distant satellites under the framework of Local Group timing argument; and vii) measurements made by linking the brightest Galactic satellites to their counterparts in simulations. For each class of methods, we introduce their theoretical and observational background, the method itself, the sample of available tracer objects, model assumptions, uncertainties, limits and the corresponding measurements that have been achieved in the past. Both the measured total masses within the radial range probed by tracer objects and the extrapolated virial masses are discussed and quoted. We also discuss the role of modern numerical simulations in terms of helping to validate model assumptions, understanding systematic uncertainties and calibrating the measurements. While measurements in the last two decades show a factor of two scatters, recent measurements using \textit{Gaia} DR2 data are approaching a higher precision. We end with a detailed discussion of future developments, especially as the size and quality of the observational data will increase tremendously with current and future surveys. In such cases, the systematic uncertainties will be dominant and thus will necessitate a much more rigorous testing and characterization of the various mass determination methods.

• The paper presents an extensive review of seven methods for estimating the Milky Way’s mass, emphasizing Gaia data enhancements.
• It details various approaches such as escape velocity analysis, rotation curves, and stellar stream modeling to infer mass distribution.
• The study underscores that advanced dynamical modeling and simulations are crucial for reducing uncertainties and refining mass estimates.

Analysis of Techniques for Estimating the Mass of the Milky Way Galaxy

The paper "The mass of our Milky Way" provides an extensive review of the methodologies employed in calculating the total mass of the Milky Way galaxy, categorized into seven primary modeling approaches. These methods reflect the diversity and complexity of astronomical techniques used to tackle this problem, demonstrating both the evolution of methodologies over time and the implications brought by new datasets and theoretical advancements.

Summary of Methodologies

1. Galactic Escape Velocity Analysis: This method utilizes high-velocity objects within the galaxy to estimate escape velocities and thus infer the mass distribution. Notably, this approach has been enhanced significantly by data from the Gaia mission, which has yielded more precise measurements.
2. Rotation Curve Measurements: By analyzing the rotation curve through the terminal and circular velocities, researchers can provide estimates of mass distribution within the Milky Way. Recent studies incorporating Gaia data have improved reliability and expanded the radial range of these measurements.
3. Spherical Jeans Equation (SJE): This equation uses the dynamics of different tracers like halo stars and satellite galaxies to infer mass distribution, though subject to assumptions about isotropy which can introduce significant uncertainties.
4. Phase-Space Distribution Functions: These are formulated using integrals of motion and allow for fitting models to observed velocity distributions, though they depend heavily on assumptions regarding the functional form of the distribution functions used.
5. Stellar Streams and Tidal Debris Modelling: By analyzing the dynamics of stellar streams formed from disrupted satellites, modelers can extract the underlying gravitational potential. However, this requires addressing the complexities of dynamical friction and incomplete phase information.
6. Local Group Timing Argument: This method involves reconstructing the historical dynamics of the Milky Way and M31 galaxies, under certain cosmological assumptions, to place constraints on the mass of the Local Group and its components.
7. Simulations and Empirical Subhalo Distribution: Utilizing numerical simulations helps correlate observed satellite properties with host halo masses. This includes using the inferred orbital parameters of satellites within simulations to set empirical constraints.

Numerical Results and Implications

The paper compares numerous studies and their resulting mass estimates, finding a consensus range for the Milky Way's total mass to be between $0.5 \times 10^{12} M_{\odot}$ and $2.0 \times 10^{12} M_{\odot}$. Discrepancies often arise from systematic uncertainties intrinsic to each approach, highlighting the importance of choosing appropriate model assumptions and considering tracer completeness.

The application of Gaia DR2 data has notably refined these estimates by providing high-precision proper motion measurements, decreasing observational uncertainties and allowing for more accurate dynamical modeling. This represents a significant leap towards achieving consensus, as it reduces reliance on assumptions that previously hindered accuracy.

Theoretical and Practical Implications

The continuous advancements in observational techniques, notably through upcoming telescopes and missions, promise to refine mass estimates further by increasing the depth and breadth of data coverage, especially in the outer regions of the Milky Way. This will enable more detailed gravitational modeling, which is crucial for:

• Understanding galaxy formation within the context of $\Lambda$CDM cosmology.
• Refining models of dark matter distribution.
• Exploring the influence of dynamical processes on galactic evolution.

Future directions entail integrating advanced simulation techniques to better match the unique formation history of the Milky Way, improving potential model selections, and accounting for non-equilibrium dynamics introduced by massive accretions like the Large Magellanic Cloud.

In conclusion, the methodologies reviewed in this paper highlight not only the complexity of modeling the Milky Way's mass but also the promising trajectory of research driven by robust data and innovative techniques. By bridging theoretical models with high-fidelity observations, the pursuit of understanding our galaxy's mass continues to occupy a pivotal role in extragalactic astronomy.