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--- un:hr-diagram [2025/10/27 12:01] – asad
+++ un:hr-diagram [2025/10/27 12:05] (current) – asad
@@ Line 26: / Line 26: @@
 Astronomers often plot **absolute magnitude** \(M_V\) instead of luminosity, and **color index** \(B - V\) instead of temperature.
-The color index is defined as the difference between the apparent magnitudes in the \(B\) (blue) and \(V\) (visual) filters:
+The color index is defined as the difference between the apparent [[magnitude]]s in the \(B\) (blue) and \(V\) (visual) filters:
 $$
@@ Line 43: / Line 43: @@
 The position of a star on the H-R diagram reflects its **mass** and **evolutionary stage**:
-* **Main-sequence stars** — Hydrogen-burning stars in equilibrium between gravity and radiation pressure.
+  * **Main-sequence stars** — Hydrogen-burning stars in equilibrium between gravity and radiation pressure.
-* **Giants and supergiants** — Evolved stars that have exhausted hydrogen in their cores and expanded in radius.
+  * **Giants and supergiants** — Evolved stars that have exhausted hydrogen in their cores and expanded in radius.
-* **White dwarfs** — Compact remnants of low-mass stars, very hot but low in luminosity.
+  * **White dwarfs** — Compact remnants of low-mass stars, very hot but low in luminosity.
 High-mass stars are found toward the upper left (high \(T_{\text{eff}}\), high \(L\)), while low-mass stars lie at the lower right (low \(T_{\text{eff}}\), low \(L\)).
@@ Line 54: / Line 54: @@
 ===== Insights =====
-* The H-R diagram unifies stellar structure and evolution by connecting observable quantities (\(M_V\), \(B - V\)) to intrinsic properties (\(L\), \(T_{\text{eff}}\), \(R\)).
+  * The H-R diagram unifies stellar structure and evolution by connecting observable quantities (\(M_V\), \(B - V\)) to intrinsic properties (\(L\), \(T_{\text{eff}}\), \(R\)).
-* The slope of the main sequence corresponds to the **mass–luminosity relation**, approximately \(L \propto M^{3.5}\).
+  * The slope of the main sequence corresponds to the **mass–luminosity relation**, approximately \(L \propto M^{3.5}\).
-* The diagram reveals both the temperature sequence and evolutionary status of stars, from main sequence to giants and dwarfs.
+  * The diagram reveals both the temperature sequence and evolutionary status of stars, from main sequence to giants and dwarfs.
-* The Sun is located roughly in the middle of the main sequence, near \(T_{\text{eff}} = 5800~\text{K}\) and \(M_V = +4.8\).
+  * The Sun is located roughly in the middle of the main sequence, near \(T_{\text{eff}} = 5800~\text{K}\) and \(M_V = +4.8\).
 ===== Inquiries =====
- - Derive the relation \(L = 4\pi R^2 \sigma T_{\text{eff}}^4\) and explain how stellar radius can be inferred from it.
+  - Derive the relation \(L = 4\pi R^2 \sigma T_{\text{eff}}^4\) and explain how stellar radius can be inferred from it.
- - Explain why stars with low \(B - V\) values are hotter than those with high \(B - V\).
+  - Explain why stars with low \(B - V\) values are hotter than those with high \(B - V\).
- - How can the H-R diagram of a globular cluster be used to estimate its age?
+  - How can the H-R diagram of a globular cluster be used to estimate its age?
- - Discuss why white dwarfs are located at the lower left of the H-R diagram.
+  - Discuss why white dwarfs are located at the lower left of the H-R diagram.
- - If two stars have the same temperature but different luminosities, what can be inferred about their radii?
+  - If two stars have the same temperature but different luminosities, what can be inferred about their radii?
- - Why is the main sequence diagonal rather than horizontal or vertical?
+  - Why is the main sequence diagonal rather than horizontal or vertical?
- - Describe how interstellar reddening can distort the position of stars in an H-R diagram.
+  - Describe how interstellar reddening can distort the position of stars in an H-R diagram.