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--- un:modeling-a-star [2025/10/27 09:04] – asad
+++ un:modeling-a-star [2025/10/27 09:14] (current) – asad
@@ Line 2: / Line 2: @@
 The [[https://colab.research.google.com/drive/1PSfZbhlFeHRx0VLswMfXtmllTH6EHgIL?usp=sharing|StatStar Python program]] models the internal structure of a star using the four fundamental differential equations of stellar structure:
-  - hydrostatic equilibrium,
+  - hydrostatic equilibrium
-  - mass continuity,
+  - mass continuity
-  - energy generation, and
+  - energy generation
-  - energy transport.
+  - energy transport
 It integrates these equations inward from the stellar surface to the center, using physical laws of gas pressure, radiation, and nuclear energy generation.
@@ Line 11: / Line 11: @@
 When you run the program (**statstar_run()**), it first asks for:
-  - the stellar mass \( M_\odot \) in solar units
+  - the stellar mass \( M \) in solar units
-  - the luminosity \( L_\odot \) in solar units
+  - the luminosity \( L \) in solar units
   - the effective temperature \( T_{\rm eff} \) in kelvins
   - the chemical composition (fractions of hydrogen \( X \) and metals \( Z \))
@@ Line 41: / Line 41: @@
 The outermost shell (zone 1) is placed at \( r = R_s \), the surface radius.
 At the surface, the total mass \( M_r = M_s \) and luminosity \( L_r = L_s \) are known.
-Surface temperature and pressure are assumed small (\( T_0 = P_0 = 0 \)).
+The program uses \( T_0 = 0 \) and \( P_0 = 0 \) as mathematical boundary conditions at the outermost layer to simplify the integration start.
+However, this does **not** mean that the physical surface temperature is zero—the physical \( T_{\rm eff} \) provided by the user is already used earlier to determine the stellar radius through the Stefan–Boltzmann law.
+Thus, \( T_0 = 0 \) and \( P_0 = 0 \) simply mark the starting point of numerical integration, not real physical values.
 Because the structure equations become numerically unstable near the surface, the code uses approximate analytic expansions for the first few layers.