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Unformatted text preview: Physics 160: Stellar Astrophysics Homework #6 Due Tuesday November 15th at 5pm in SERF 340 Reading: Carroll & Ostlie chapters 12 & 13
Exercise [75 pts]:
(1) [25 pts] Losing the Sun
(a) [5 pts] How many hydrogen atoms are converted into helium per
second in the core of the Sun, assuming all of the Sun’s luminosity is
produced through the pp chain?
(b) [5 pts] Based on part (a), how long would it take for the Sun to
fuse 10%, 50% and 100% of its hydrogen into helium at the current
luminosity? Why is the last number probably not realistic?
(c) [5 pts] What is the mass loss rate of the Sun due to fusion in M/yr
at the current luminosity? How long would it take for the Sun to
shrink to zero mass?
(d) [5 pts] Is the mass loss rate due to the solar wind larger or smaller
than the mass loss rate due to fusion?
(e) [5 pts] The Main Sequence lifetime of the Sun is 1010 yr. What
fraction of hydrogen is converted into helium, and what percentage of
mass is lost by the Sun over this period from fusion and solar wind?
(2) [20 pts] The H ion is formed when a second electron becomes weakly
bound to a neutral hydrogen atom. The ionization potential of this extra
electron is 0.75 eV.
(a) [10 pts] Using the Saha equation and assuming a temperature of
5800 K, determine the fraction of all H atoms that are H ions in the
Sun’s photosphere. You can assume that most neutral H atoms are in
the ground state.
(b) [10 pts] What is the relative number of H ions to neutral H atoms
in the n=3 state (the initial state for Hα emission)? (3) [30 pts] Playing with the Standard Solar Model
On the Physics 160 website, download the “Bahcall et al. 2005 Solar Model”
file, which contains the numerical structure model for the Sun based on an
update to the Bahcall et al. (2001) paper mentioned in class. Specifically,
this file contains a table of enclosed mass, radius, temperature, density,
pressure, enclosed luminosity, and then 1H, 4He, 3He, 12C, 14N and 16O mass
fractions. You will use these data to explore the Solar interior.
(a) [10 pts] Reproduce Figure 11.3 by plotting the mass fractions of 1H,
4
He and 3He as a function of radius (you will need to scale the 3He by
100x to see it). Explain the variations you see, and verify the
inversion in the H/He abundance at the center of the Sun. What
causes this inversion?
(b) [10 pts] Plot the mass fractions of 4He, 12C and 16O relative to their
photospheric mass fractions (i.e., mass fractions at the last radius
point) as a function of radius. Describe and explain the origin of any
variations (or not) present in the core, radiative zone and convection
zone.
(c) [10 pts] Reproduce Figure 11.5. You can calculate the derivative
dLr/dr numerically (ignoring i=0 and i=max): dL r
dr =
i 1
2 Li − Li−1
Li+1 − Li
+
ri+1 − ri
ri − ri−1 Where is the maximum of this curve? Why is that maximum at that
point? Also calculate and plot the energy production rate ε as a
function of radius using Equation 10.36 and verify that it is maximum
at the core (be careful at r=0?). ...
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This note was uploaded on 02/26/2012 for the course PHYS 160 taught by Professor Norman,m during the Fall '08 term at UCSD.
 Fall '08
 Norman,M
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