Prob. 1.2, 1.3, 2.2, 2.3, 2.4
Prob. 2.5, 2.6, 2.9, 2.10b, 2.11
Prob. 2.12, 2.13, 2.14
(b) From Fig. 2.12, measure (estimate) the power, α, of the relation R ∝ Mα for the ZAMS curve for two regimes: M < 1.3 MSun and M > 1.3 MSun.
(c) Now re-write τth/τnuc as a function of mass for the two regimes.
(d) Does this ratio increase or decrease with increasing mass? Comment as to why this might be the case.
Prob. 5. Refer to the figure handed out in class showing the secular behaviour of a number of properties of the center of the Sun with time, namely: XH, κ, T, ε, L, P, and ρ. By `secular', I mean
Prob. Set 4: Assigned Thurs. Oct. 26, Due Mon. Nov. 6
Prob. 4.1, 4.2, 4.3, 4.4, and 5.1
(a) Write expressions for (i) the total number of stars, N, between mass, M1 and M2; (ii) the total luminosity of all stars, L, between M1 and M2; and (iii) the total mass, M, of all stars between M1 and M2.
M should be expressed in units of MSun and L in LSun.
(b) Evaluate N, L, and M for the range, 0.1 < M/MSun < 0.5, and for the range 10 < M/MSun < 10.4. (Call them Nhigh, Nlow etc).
(c) Evaluate the ratios: Nhigh/Nlow, Lhigh/Llow, and Mhigh/Mlow, and comment on your results.
(d) Suppose 25 million years pass. How would you expect these ratios to change, if at all?
(a) Plot Pic as a function of Ric. Show the plot over a reasonable range.
(b) What is the value of Ric for this star? Explain.
(a) Derive an expressive for the age, t, of a WD as a function of its initial interior temperature, Tc0 and its current interior temperature, Tc. Let t = 0 when Tc = Tc0. Note that dU/dt = -L.
(b) Reasonable values of the constants for a one solar mass star are C1 = 2 x 1040 and C2 = 9.3 x 105 in cgs units. If a 1 Msun white dwarf starts with an interior temperature of 107 K, what would its interior temperature be after 13.7 billion years?