Undergrad Sun and hydrostatic equilibrium

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SUMMARY

The discussion focuses on estimating the pressure of the Sun's photosphere using hydrostatic equilibrium equations. The correct formula involves the relationship between surface gravity (g) and the opacity (κ) of the solar photosphere, specifically expressed as pressure = g / κ. The opacity is determined by the cross section per gram of the solar material, which is essential for calculating the mass per area of the gas in a single mean-free path of an optical photon. Understanding these parameters is crucial for accurate modeling of solar atmospheric conditions.

PREREQUISITES
  • Understanding of hydrostatic equilibrium principles
  • Familiarity with solar physics and the structure of the Sun
  • Knowledge of optical properties, specifically mean-free path and opacity
  • Basic grasp of gravitational forces in astrophysics
NEXT STEPS
  • Research the specific values of solar surface gravity (g) and opacity (κ) in the solar photosphere
  • Study the derivation and applications of the hydrostatic equilibrium equation in astrophysics
  • Explore the concept of mean-free path in the context of stellar atmospheres
  • Investigate the methods for measuring and calculating opacity in astrophysical contexts
USEFUL FOR

Astronomers, astrophysicists, and students studying stellar structure and dynamics will benefit from this discussion, particularly those focused on solar physics and hydrostatic equilibrium modeling.

Andreas C
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I've been trying to make an estimate for the pressure of the sun's photosphere using some sort of hydrostatic equilibrium equation, but I can't seem to get one that even comes close to agreeing with observations. Does anyone know what the right formula is and what the right way to approach the problem is?
 
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Yeah, I don't think the formula I used is the right one, and I CAN'T seem to find the right one, so does anyone know which one it is?
 
The photosphere is where you see through a single mean-free path of an optical photon. So you need to know the opacity there, to know how much stuff is in a single mean-free path. So look up the cross section per gram in the solar photosphere, then know that the weight per area of the gas you are seeing through, to see the photosphere, is the surface gravity times the mass per area, where the mass per area is 1 over the cross section per gram. So that's the pressure-- g over kappa, where g is the acceleration of gravity at the solar surface, and kappa is the cross section per gram there. Think of that as g times the mass per area that you are seeing through.
 

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