1 / 20

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.

mshead
Download Presentation

Firmament Marathon: Exploring the Wonders of Stars

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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).

More Related