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--- courses:ast301:3 [2024/03/15 07:20] – [2. Modeling a star] asad
+++ courses:ast301:3 [2024/03/15 13:19] (current) – [3. HR diagram] asad
@@ Line 161: / Line 161: @@
 {{:courses:ast301:starzones.webp?nolink&700|}}
-The models also provide the information about the radiative and convective zones inside a star. The lowest mass stars are completely convective and the size of central radiative zone increases with mass. In a solar-mass star only the outer envelope (30%) is convective, but a star becomes completely radiative if its mass is 1.5 solar mass. Stars with mass $> 2$ $M_\odot$ develop a radiative zone at the core and the central radiative zone keeps increasing in size with mass. So lightweight stars produce nuclear energy at the radiative core whereas heavyweight stars do that in their convective core.
+The models also provide the information about the radiative and convective zones inside a star. The lowest mass stars are completely convective and the size of central radiative zone increases with mass. In a solar-mass star only the outer envelope (30%) is convective, but a star becomes completely radiative if its mass is 1.5 solar mass. Stars more than two times heavier than the sun develop a convective zone at the core and the central convective zone keeps increasing in size with mass. So lightweight stars produce nuclear energy at the radiative core whereas heavyweight stars do that in their convective core.
 ===== - HR diagram =====
+HR ([[wp>Ejnar_Hertzsprung|Hertzsprung]]-[[wp>Henry_Norris_Russell|Russell]]) diagram related the luminosity and temperature of stars. These two quantities are linked to the radius via the equation of flux we introduced before: $\mathscr{F}=\sigma T_e^4=L/(4\pi R^2)$ where $T_e$ is the **effective temperature**.
+$$ R = \frac{\sqrt{L}}{\sqrt{4\pi\sigma}T^2} = \frac{\sqrt{L/L_\odot}}{(T/T_\odot)^2} \ R_\odot $$
+which means there are diagonal constant-radius lines in the HR diagram. HR diagram can be shown using either $T$-$L$ or the corresponding observable quantities color index and absolute magnitude. Both temperature-luminosity and color-magnitude versions are shown below.
+[[https://astro.unl.edu/naap/hr/animations/hr.html|{{:courses:ast301:hrd.webp?nolink|}}]]
+B-V color index is the difference between apparent magnitudes in the blue and visual or yellow bands, i. e. $m_B-m_V$. The absolute magnitude on the $y$-axis is the yellow magnitude $M_V$. A negative B-V index means the $m_B<m_V$ and, hence, the brightness in blue wavelengths is greater than in the visual band. Note that $M_V\propto - \log L$ and $(m_B-m_V)\propto -\log T$ which will be evident if you compare the axes of the two panels.
+The green patch in the HR diagram is the main sequence where a star stays during its stable period. Before the birth a star is to the lower right hand side of the main sequence. When the equilibrium of the star is broken, it moves to the upper right hand side of the main sequence toward the giant (light red) or supergiant (blue) branches. After death stars move to the lower left hand side of the main sequence near the white dwarf patch (grey). Some massive stars oscillate periodically and they are found in the instability strip (dark red). On the main sequence the heavier stars are found in the upper part, and vice versa.
 ===== - Main sequence and giant branch =====