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Stellar Structure

Stellar Structure. Section 2: Dynamical Structure Lecture 2 – Hydrostatic equilibrium Mass conservation Dynamical timescale Is a star solid, liquid or gas? Boundary conditions Limit on central pressure

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Stellar Structure

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  1. Stellar Structure Section 2: Dynamical Structure Lecture 2 – Hydrostatic equilibrium Mass conservation Dynamical timescale Is a star solid, liquid or gas? Boundary conditions Limit on central pressure Gravitational potential energy

  2. Force balance • Hydrostatic equilibrium: balance between gravity and internal pressure (evidence: geological timescales) Horizontal pressure forces cancel. Balance net outwards pressure force against inward gravitational force. Spherical symmetry: Newton’s theorem allows replacement of mass distribution by equivalent mass at centre (just mass withinr). A δr r P(r), ρ(r) – pressure, density at r; M(r) – mass within r Hence (see blackboard): (2.1)

  3. Mass conservationDynamical timescale • Definition of M(r) yields (see blackboard) (2.2) • What happens if forces not in balance? • Find (see blackboard) departures from equilibrium on a very short timescale – the dynamical timescale, tD:

  4. Equation of state • Two equations, 3 variables (P, ρ, M) • Equation of state relates P, ρ – but introduces more variables (see blackboard) • Is a star solid, liquid or gaseous? • Mean density and surface temperature (see blackboard) suggest liquid. • But actually a plasma – highly ionised gas, so that particle size ~ nuclear radius << typical separation (~ atomic radius). • Hence stellar material behaves like an ideal gas(plus radiation pressure) – see blackboard

  5. Limits on conditions inside stars:pressure • Now have 3 equations, 5 variables (P, ρ, M, T, μ) – but can obtain some general results without more equations. • Boundary conditions: take P = ρ = 0 at the surface. • Can then find lower limit for the central pressure (Theorem I): • (for proof, see blackboard, and Handout). • For Sun, lower limit is ~450 million atmospheres. (2.11)

  6. Gravitational potential energy • Gravity is an attractive force – so the work done to bring matter from infinity to form a star is negative: positive work must be done to prevent the infall of material. • This means that the gravitational potential energy, Ω, is negative (see blackboard). • It is related to the internal pressure by Theorem II: (2.13) • (for proof, see blackboard, and Handout).

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