**Prob. Set 1: Assigned Monday. Sept. 17, Due Wed. Sept. 26:**

Do problems: 1.3, 1.5, 2.4b, 2.7, 3.1, and 3.2. For the last question, you may find it useful to read Sect. 3.9 in LeBlanc

Do problems: 1.3, 1.5, 2.4b, 2.7, 3.1, and 3.2. For the last question, you may find it useful to read Sect. 3.9 in LeBlanc

**For problem 3.2, it should be to plot log(kappa_R) against log(T) -- not log(R)**

**Prob. Set 2: Assigned Wed. Sept. 26, Due Thurs. Oct. 4**

Do problems: 3.5 (for part c, use a pressure scale height of 0.063 Rsun), 3.8, 3.10, 3.11, and 3.12 (the Sun's thermal timescale is about 32 million years)

Do problems: 3.5 (for part c, use a pressure scale height of 0.063 Rsun), 3.8, 3.10, 3.11, and 3.12 (the Sun's thermal timescale is about 32 million years)

**Prob. Set 3: Assigned Thurs. Oct. 4, Due Monday. Oct. 15**

**Prob. Set 4: Assigned Wed. Oct. 17, Due Wed. Oct. 31**

More questions handed out in class.

**Prob. Set 5: Assigned Wed. Oct. 31, Due Thurs. Nov. 8**Questions handed out in class.

**Prob. Set 6: Assigned Thurs. Nov. 8, Due Mon. Nov. 19**

1. Consider a 1 Msun star that has left the main sequence and is in the subgiant phase with an inert isothermal He core. The core has the following parameters: M

(a) Plot P

(b) What is the value of R

κ = -(1/v) (∂v/∂P)|

where v is the specific volume (cm

(a) Rewrite κ in terms of the density, ρ.

(b) Find an expression for κ(ρ) for a non-relativistic and relativistic C/O white dwarf with constants evaluated.

(c) Evaluate κ for a typical non-relativistic and relativistic C/O white dwarf. Look up κ for the hardest substance on Earth that you can find and compare. 3. Although the pressure of a white dwarf is produced by electron degeneracy, the internal energy, U, depends on the ion temperature such that U = C

(a) Derive an expression for the age, t, of a white dwarf as a function of its initial interior temperature, T

(b) Reasonable values of the constants for a 1 M

_{ic}= 0.08 M_{sun}and T_{ic}=19.1 x 10^{6}K.(a) Plot P

_{ic}as a function of R_{ic}. Ensure that you plot over a sufficient range of R_{ic}to show the behaviour of the function.(b) What is the value of R

_{ic}of this star? Explain. 2. The isothermal compressibility of an object is defined as:κ = -(1/v) (∂v/∂P)|

_{T}where v is the specific volume (cm

^{3}/g) and P is the pressure.(a) Rewrite κ in terms of the density, ρ.

(b) Find an expression for κ(ρ) for a non-relativistic and relativistic C/O white dwarf with constants evaluated.

(c) Evaluate κ for a typical non-relativistic and relativistic C/O white dwarf. Look up κ for the hardest substance on Earth that you can find and compare. 3. Although the pressure of a white dwarf is produced by electron degeneracy, the internal energy, U, depends on the ion temperature such that U = C

_{1}T_{int}, where T_{int}is the internal (isothermal) temperature and C_{1}is a constant. The luminosity of a white dwarf departs somewhat from the Stefan-Boltzmann law when it is related to the internal temperature, i.e. L = C_{2}T_{int}^{7/2}, where C_{2}is another constant.(a) Derive an expression for the age, t, of a white dwarf as a function of its initial interior temperature, T

_{int0}and its current interior temperature, T_{int}. Let t = 0 when T_{int}= T_{int0}and note that dU/dt = -L.(b) Reasonable values of the constants for a 1 M

_{sun}star are C_{1}= 2 x 10^{40}and C_{2}= 9.3 x 10^{5}(cgs). If a 1 M_{sun}white dwarf starts with an interior temperature of 10^{7}K, what would be its interior temperature after 13.7 billion years? Comment on the length of time it would take for a white dwarf to cool to a `cinder'. 4. Estimate the time it takes for the iron core of a 25 M_{sun}star to collapse to a neutron star.