Report: Physics of Galaxies – Key Discussion Questions & Solutions
1. Dark Matter Evidence: Rotation Curves
Question:
The observed rotation curves of spiral galaxies (velocity vs. radius) remain flat or even rise at large radii, while Keplerian motion predicts a decline ($v \propto r^-1/2$). Explain this discrepancy and show how it leads to the dark matter hypothesis.
6. Gravitational Lensing by Galaxies
Question:
A background galaxy at redshift $z_s=1$ is lensed by a foreground elliptical galaxy at $z_l=0.3$. The Einstein radius is measured to be $\theta_E = 2''$. Estimate the mass of the lens inside the Einstein radius.
Part 5: Recommended Reading Order for Discussion Questions
Not all chapters are created equal. To maximize your learning curve, tackle Physics Galaxy discussion questions in this specific order:
- Expected (Keplerian): If most mass were concentrated in the center (bulge/stars), for $r > r_\textmax$, $v(r) = \sqrt\fracGM(r)r$ with $M(r)$ constant → $v \propto 1/\sqrtr$.
- Observed: $v(r) \approx$ constant out to large $r$ → implies $M(r) \propto r$ (since $v^2 = GM(r)/r \Rightarrow M(r) = v^2 r / G$).
- Conclusion: Additional unseen mass – dark matter halo with $\rho(r) \propto r^-2$ (isothermal sphere profile) on large scales.
Discussion Question 1: What is the estimated age of the universe?
(Q_in = Q_12 + Q_23 = n C_v T_0 + 2P_0 V_0 \ln 2).
But (n C_v T_0 = \fracP_0 V_0\gamma - 1).
The study of the galaxy is an exciting and rapidly evolving field, with many open questions and mysteries waiting to be solved. By exploring these discussion questions and solutions, we gain a deeper understanding of the physics that governs the universe, from the behavior of dark matter and dark energy to the evolution of galaxies and the role of black holes. As we continue to explore and observe the galaxy, we may uncover even more secrets about the cosmos and our place within it.
