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Firmament Marathon: Exploring the Wonders of Stars

Join this six-week course to learn about stars, their structure, energy generation, and evolution. Discover the equations and physics behind stellar structure and explore the observable characteristics of different stars.

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Firmament Marathon: Exploring the Wonders of Stars

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  1. PHYS377:A six week marathon through the firmament by Orsola De Marco orsola@science.mq.edu.au Office: E7A 316 Phone: 9850 4241 Week 1.5, April 26-29, 2010

  2. Overview of the course • Where and what are the stars. How we perceive them, how we measure them. • (Almost) 8 things about stars: stellar structure equations. • The stellar furnace. • Stars that lose themselves and stars that lose it: stellar mass loss and explosions. • Stellar death: stellar remnants. • When it takes two to tango: binaries and binary interactions.

  3. Things about stars • Stars are held together by gravitation. • Collapse is resisted by internal thermal pressure. • These two forces play a key role in stellar structure – for the star to be stable they must be in balance. • Starsradiate energy into space. For stability they need to also generate energy. It follows that sometime stars run out of equilibrium and change, or evolve. • To describe stars (to make a model) we need to know how energy is produced and how it is transported to the surface. Inspired by S. Smartt lectures – Queens University, Belfast

  4. A stellar model • Determine the variables that define a star, e.g., L, P(r), r(r). • Using physics, establish an equal number of equations that relate the variables. Using boundary conditions, these equations can be solved exactly and uniquely. • Observe some of the boundary conditions, e.g. L, R…. and use the eqns to determine all other variables. You have the stellar structure. • Over time, energy generation decreases, the star needs to readjust. You can determine the new, post-change configurations using the equations: you are evolving the star. • Finally, determine the observable characteristics of the changed star and see if you can observe a star like it!

  5. Equations of stellar structure For a star that is static, spherical, and isolated there are several equations to fully describe it: • The Equation of Hydrostatic Equilibrium. • The Equation of Mass Conservation. • The Equation of Energy Conservation. • The Equation of Energy Transport. • Equation of State. • Equation of Energy Generation. • Opacity. • Gravitational Acceleration

  6. Stellar Equilibrium Net gravity force is “inward”: g = GM/r2 Pressure gradient “outward”

  7. 1. Equations of hydrostatic equilibriumBalance between gravity and internal pressure Mass of element where (r)=density at r. Forces acting in radial direction: • Outward force: pressure exerted by stellar material on the lower face: 2. Inward force: pressure exerted by stellar material on the upper face, and gravitational attraction of all stellar material lying within r

  8. In hydrostatic equilibrium: If we consider an infinitesimal element, we write for r0 Hence rearranging above we get The equation of hydrostatic support

  9. The central pressure in the Sun • Just using hydrostatic equilibrium and some approximations we can determine the pressure at the centre of the Sun.

  10. Dynamical Timescale (board proof) tdyn = √ ( R3/GM ) It is the time it takes a star to react/readjust to changes from Hydrostatic equilibrium.It is also called the free-fall time.

  11. 2. Equation of mass conservation Consider a thin shell inside the star with radius rand outer radius r+r This tells us that the total mass of a spherical star is the sum of the masses of infinitesimally small spherical shells. It also tells us the relation between M(r), the mass enclosed within radius r and r(r) the local mass density at r. In the limit where r  0

  12. Two equations in three unknowns

  13. 3. Equation of State Where m, the mean molecular weight, is a function of composition and ionization, and we can assume it to beconstant in a stellar atmosphere (≈0.6 for the Sun).

  14. Three equations in four unknowns

  15. Radiation transport • Conduction: Energy transport by bumping. Dominant in opaque solids. • Convection: Energy transport by matter bulk motion. Dominant in opaque liquids and gasses. • Radiation: Energy transport by photons. Dominant in transparent media.

  16. Equation of radiative energy transport

  17. The Solar Luminosity

  18. Convection • If k rises, dT/dr needs to rise to, till it is very high. High gradients lead to instability. What happens then? • Imagine a small parcel of gas rising fast (i.e. adiabatically – no heat change). Its P and r will change. P will equalise with the environment. • If rp < rsurr. the parcel keeps rising. • So if the density gradient in the star is small compared to that experienced by the (adiabatically) rising parcel, the star is stable against convection.

  19. Giant star: convection simulation Simulation by Matthias Steffen

  20. Equation of Energy Conservation This equation does not assume knowledge of what powers a star (i.e., the origin of e).

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