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Chapter 10 The Interiors of Stars Most Basic Observations Of Sun Sun has maintained (i) its size, (ii) energy it emits every second, (iii) its surface temperature all this while. • Sun is a self-gravitating objects − each part of the sun exerts force on each other part of the sun. • Gravity always attracts There must be other kinds of forces acting against Gravity to prevent the sun from collapsing onto itself. These inward and outward forces must be in perfect balance! Hydrostatic Equilibrium • Sun is radiating the same amount of energy every second − 3 x 1026 Joule It must be generating the right amount of energy every second. Energy Generation Rate It must be making sure that each of its layer transports just the right amount of energy to maintain this energy output. Energy Transport Rate • Sun is maintaining the temperature of its surface, and is also maintaining some fixed temperature at each of its radial distance from the Sun. Since the transfer of fixed (energy) radiation from the center to the surface in each layer would depend crucially on how temperature in each layer varies, it must maintain the required temperature gradient in all layers. Temperature Gradient • Mass conservation Stellar Structure Equations Hydrostatic Equilibrium Mass Conservation Energy Transport Hydrostatic Equilibrium Ex. 10.1.1 Make a crude estimate of the pressure at the center of the Sun using the Hydrostatic Equilibrium. Rigorous calculation shows the pressure is ( ) Pressure Equation of State Completely neutral gas, Completely ionized gas, In terms of mass fractions, for a neutral gas In terms of mass fractions, for a completely ionized gas Go through P. 293 Ex. 10.1.2 Make an estimate of the temperature at the center of the Sun using the Gas pressure term alone and using the value for pressure we derived in the previous example. Stellar Energy Sources Mid-Sem Syllabus up to here! Gravitational Energy Kelvin-Helmholtz Timescale Assuming a spherical star of Radius R and M, the gravitational potential energy of the star, Nuclear Time Scale Total Mass of four (4) Hydrogen atoms Mass of one Helium atom Gamow Peak