Reading:

*Chapter 16-1, 16-2* (ZG4)

Notes:

*pages 46 - 51*

Key Question: | How is Energy Transported in a Star? | |
---|---|---|

Key Principle: | Radiation Pressure and Convection | |

Key Problem: | Find the Main-Sequence Mass-Luminosity Relation |

- Equations of State
- What is an
*equation of state*? - What is the equation of state of an ideal gas?
- What the relation between dP/dr and dP/drho?
- Why do we parameterize P=P0*rho^gamma?

- What is an
- Energy Generation and Radiative Transport
- What is the luminosity dL generated in a shell of mass dM?
- What is dL/dr in a spherical star?
- For radiative transport of energy, what is dP_rad/dr in terms of dT/dr?
- What is dP_rad/dr in terms of L(r)?
- What is the
*radiative temperature gradient*dT/dr in a star? - How does this depend on the opacity, density, T and L(r) at the shell?

- Convective Energy Transport
- What is the expected scale of convection (ie. the pressure scale height in the interior) in the Sun?
- How does
*convection*transport energy? - For an ideal gas P=nkT, what is dP/dr in terms of dT/dr and dn/dr (for number density n)?
- What is a
*polytropic equation of state*? - What is the convective temperature gradient dT/dr for a pressure gradient dP/dr?
- When is a gas stable against convection?
- Where might you expect energy to be carried by convection in a star?

- Main Sequence Scaling Relations
- How does the mean density scale with mass and radius?
- How does the central pressure scale with mass and radius?
- How does the central temperature scale with mass and radius?
- How does the luminosity scale with mass and opacity?
- Why does this relation depend on the opacity but not the energy generation?
- What is the
*Kramer's Opacity Law*for bound-free and free-free opacity? - What is
*electron scattering*cross section and opacity?

- Stellar Structure continued...
- The mass-luminosity relation (L/Lsun) = (M/Msun)^3.5 is an approximation to the solution of the equations of stellar structure for a star of mass close to that of the Sun. The actual exponent ranges from 2.5 to over 4 over the main sequence, and of course does not obey anything like this off the main sequence.
- It turns out that the stellar structure that you find depends only upon the mass M of the star! If the energy is produced by fusion as given by E(r)=E(T(r),rho(r)), then the star falls on the main sequence and the surface temperature T, and luminosity L depend on the mass M such that they increase as you increase the mass.
- Because higher mass stars are much more luminous, they burn their
fuel faster, and have shorter lifetimes on the main sequence.
Note that the lifetime t is proportional to M/L (fuel/rate of burning)
and for stars of mass near the Sun's:
t/tsun = (M/Msun)/(L/Lsun) = M/M^3.5 = 1/M^2.5 Thus, a star of twice the mass of the Sun would live only 18% of the life span of the Sun. A star of 0.5 Msun would live 5.6 times longer. - The most massive stars live only a few millions of years! (Short by cosmic standards.)

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*smyers@nrao.edu*
*Steven T. Myers*