Lecture Notes on Dark Matter and the Milky Way \n \n## Introduction \n- Focus on two main topics: \n - The Milky Way \n - Dark matter \n \n## Dark Matter \n- One of the biggest mysteries in astronomy. \n- Comprises more matter than visible matter in the universe. \n- Every galaxy is believed to sit within a dark matter halo. \n- Evidence for dark matter halos in galaxy clusters. \n- Hierarchical structure seen in the universe requires dark matter for proper explanation. \n- Current knowledge about dark matter: \n - Unknown subatomic particle type. \n - Uncertain spatial distribution in galaxies. \n \n## Estimating the Mass of the Milky Way \n- The mass of the Milky Way is dominated by its dark matter halo. \n- Previous mass estimates show significant discrepancies. \n - Different methods and assumptions lead to varied results. \n- Kinematic tracers used to estimate mass: \n - Objects orbiting the galaxy (e.g., globular clusters). \n - Challenges with kinematic tracers: \n - Our position in the galaxy affects measurements (heliocentric vs. galactocentric). \n - Incomplete data complicates transformations. \n - Measurement uncertainties can skew results. \n - Assumptions about orbital dynamics (e.g., isotropy vs. anisotropy) can affect outcomes. \n \n## Bayesian Approach to Mass Estimation \n- Utilizes Bayes' theorem to refine mass estimations. \n- Teaching method using M&Ms to illustrate Bayesian analysis. \n- The posterior distribution is derived from the likelihood and prior distributions. \n- Encourages using complete data sets to improve estimates. \n \n## Mass Estimation Results \n- Used hierarchical methods to account for uncertainties and incomplete data. \n- Results show a mass estimate of 0.87 × 10^12 solar masses for the Milky Way. \n- Cumulative mass profiles can be derived and compared with other studies. \n - Highlighted discrepancies in mass estimates at varying distances from the galaxy's center. \n \n## Future Directions \n- Interested in assessing masses of dwarf galaxies using similar methods. \n- Importance of applying these Bayesian techniques to different data types. \n- Collaboration with other researchers to improve the understanding of dark matter and galaxy evolution. \n \n## Stellar Seismology \n- Transition to discussing stellar seismology and its relevance. \n- Stars like our Sun create standing waves, providing insight into stellar interiors. \n- G modes and pressure mode oscillations can inform us about the internal structure of stars. \n \n## Power Spectrum Analysis \n- Discussed challenges of measuring stars far away, including noise and resolution issues. \n- Explained the power spectrum and its importance in understanding stellar properties. \n- Issues with classical methods (e.g., periodogram) for estimating power spectra. \n \n## Multi-Taper Method \n- Overview of multi-taper method for more accurate spectral estimation. \n- Comparison of different tapers and their performance. \n- Importance of reducing spectral leakage in power spectrum estimation. \n \n## Application to Astronomy \n- Potential applications of multi-taper methods in various astronomical contexts. \n- Importance of robust methodologies for future astronomical surveys. \n \n## Conclusion \n- Emphasized collaborative opportunities between statisticians and astronomers. \n- Potential to enhance methods and lead to new astronomical discoveries.