Introduction to Modern Astrophysics --
Physics 489
9:10 - 10:00 a.m.
MWF, Room 128A
Zachry [Spring
Semester, 2007]
This course is meant for
juniors and seniors. (The textbook was nominally written for juniors.)
Prerequisites: Mechanics
(Physics 218 or equivalent), electromagnetism (Physics 208 or equivalent), and
modern physics (Physics 309 or 222 or equivalent). [Introductory differential
and integral calculus is thus also implied.]
Introduction to Modern
Astrophysics was offered in the spring of 2006 for the first time in many years
(with 30 students enrolled). It should, however, find an enduring place in the
new astronomy program.
Instructor: Roland E. Allen
1-979-845-4341,
allen@tamu.edu, Room 519 Engineering/Physics Building
Office hours: 3:00 - 4:00 p.m.
Monday, Tuesday, and Thursday; or by appointment.
You will find interesting
information, and many interesting websites with astronomical images,
information, and news, at http://astronomy.tamu.edu/.
The textbook is An
Introduction to Modern Astrophysics,
Second Edition, by Bradley W. Carroll and Dale A. Ostlie (Addison-Wesley,
2007, ISBN 0-8053-0402-9).
Evaluation:
Homework 40%
2 exams 40%
final exam (one-half on last
part of course, one-half comprehensive) 20%
Homework is due at the
beginning of class each Wednesday.
Each homework set will
consist of about 5 problems from those at the end of the chapters in the
textbook. Homework late by < 48 hours, 1/2 credit. Homework late by > 48
hours, no credit.
The
exams will involve partial-credit problems (and questions), and will be based
on (i) what is covered in class, (ii) the additional reading assignments (see
below), and (iii) the homework sets (see below). The exams are a test of understanding. That is why you
should understand everything once as we proceed through the course. For
example, should you memorize a long formula based on the Boltzmann factor
e^(-E/kT)? No. But should you understand the Boltzmann factor and how it is
used? Yes. You should know the basic equations (example -- the expression for
centripetal force). The more complicated results either will be worked out as
you go through the exam or else will be given to you. Each exam will cover
everything we have done before the exam (including the homework that has just
been turned in and not yet returned graded, so you may want to keep a copy for
studying).
Exams will be on Fridays: March
2 and April 13
an Exam 1:
an Exam 2:
2 Final Exams:
An optional 10 minute talk can
be given for extra credit equal to one homework set.
Topics (taken from the
chapter headings in the textbook):
1. The Celestial Sphere
2. Celestial Mechanics
3. The Continuous Spectrum of
Light
4. The Theory of Special
Relativity
5. The Interaction of Light
with Matter
6. Telescopes [including
optical, radio, infrared, ultraviolet, and x-ray]
7. Binary Systems and Stellar
Parameters
8. The Classification of
Stellar Spectra
9. Stellar Atmospheres
10. The Interiors of Stars
11. The Sun
12. The Interstellar Medium
and Star Formation
13. Main Sequence and
Post-Main-Sequence Stellar Evolution
14. Stellar Pulsation
15. The Fate of Massive Stars
16. The Degenerate Remnants
of Stars
17. General Relativity and
Black Holes
18. Close Binary Star Systems
19. Physical Processes in the
Solar System
20. The Terrestrial Planets
21. The Realms of the Giant
Planets
22. Minor Bodies of the Solar
System
23. Formation of Planetary
Systems
22. The Milky Way Galaxy
23 The Nature of
Galaxies
24. Galactic Evolution
25. The Structure of the
Universe
26. Active Galaxies
27. Cosmology
28. The Early Universe
There are also very useful
appendices A-N, which even include computer codes. Those who are interested in
computational science can replace some of the homework problems by one or two
numerical problems in astrophysics, for which there are suggestions among the
homework problems in the textbook.
As mentioned above, it is
impossible to cover all this material in one semester. Fortunately the textbook
is well written, so anyone with a desire to learn everything can profitably
read the textbook, even though only the material covered in class, in the
reading assignments, or in the homework is required.
HOMEWORK ASSIGNMENTS
In doing each homework problem, you often need to read
the text near the equations that are cited. Below, in the hints, we use the
convention that a^{b} or a^b means a to the b power (or else a superscript),
and a_{b} or a_b means a subscript.
HW 1 due Wed., Jan. 24
1.1 (do for only circular motion), 1.8 (recall (1.2),
(1.3), (1.4), (1.8), (1.9)), 2.4, 2.7 (a) and (d) (use (2.32) and (2.35), of
course, plus Example 2.4), 2.8 (b).
HW 2 due Wed., Jan. 31
2.8, 2.3 (take the
derivative of r in (2.29) with respect to time to get v_r ( in terms of d
theta/dt), and then use the expression on p. 46 for d theta/dt in terms of
v_theta to write v_r in terms of v_theta (and theta)), 2.9 (transform from t to
theta within the integral, using the result for d theta/dt that follows from
the equations on p. 46; also substitute
Kepler's third law expression for period outside the integral); 3.7,
3.9.
HW 3 due Wed., Feb. 7
3.12 (get u=5(1-e^{-u}),
where u= hc/lambda kT; then solve
by iteration with an initial u=5), 3.14 (the u= hc/lambda kT substitution
within the integral brings T^4 out in front), 3.15, 4.9, 4.11 (show that (Delta
s')^2= (Delta s)^2; the proper time is the time in the coordinate system where Delta x = 0, with the same
for y and z).
HW 4 due Wed., Feb. 14
4.14 (rule for derivative of product also works with
vectors, and v^2=v dot v with v = velocity vector; for this problem, just show
that the given solution for a
works), 4.15 (the formula for the acceleration becomes very simple for 1d
motion, and you may use an integral table to solve the differential equation
du/(1-u^2)^(3/2) = (F/mc)dt); 5.1 (see Example 5.1.1), 5.4 (see (5.4) of
course), 5.14.
HW 5 due Wed., Feb. 21
6.8 (see p. 148); 7.1 (let r, r_1, and r_2 be position
vectors here; (2.23) and (2.24) show that these three vectors are proportional
to one another at any given time, so the masses m_1, m_2, and mu trace out
ellipses with exactly the same shape -- i.e., eccentricity e; this implies that
r_a/a =1+e (by (2.6)) is the same in each case; then Fig. 2.11 demonstrates
that a = a_1 + a_2); 8.10, 8.13; 9.11 (use Rosseland mean opacity as the
opacity kappa of p. 242).
HW 6 due Wed., Feb. 28
9.25 (delta lambda is approximately delta E/|dE/d
lambda|, and we want the total delta E), 10.4 (see (8.3), and kinetic energy
must exceed (10.26) x Boltzmann constant), 10.13 (E=mc^2, 1 MeV=10^6 eV, see
inside front cover for constants), 10.14 (lepton number on pp. 308-309 = +1 for
electron or neutrino, -1 for their antiparticles), 11.3 (see p. 248 for
ionization energy of H-, (8.9) for appropriate form of Saha equation, and
inside front cover as usual).
EXAM 1 ON FRIDAY MARCH 2
HW 7 due Wed., Mar. 7
HW 8 due Wed., Mar. 21
16.1 (long but worthwhile --
see pp. 58, 62, 183-184, 220, 558, 569-570), 16.6, 16.7 (see pp. 569-570, and
recall that rho=mass/volume), 16.19 ((a+ delta a)^n=a^n(1+delta a/a)^n or
approximately a^n(1+n delta a/a), with e.g. n = 2 or -1), 16.22.
HW 9 due Wed., Mar. 28
16.23, 16.25 (sin theta is
approximately theta, in radians), 17.8 (see (4.27) and (4.29)), 17.9, 17.12.
HW 10 due Wed., Apr. 4
14.3 (see (14.1) and (12.1)
with m = V, as on p. 75), 14.5 (Fig. 14.7, p. 488, and p. A-11; give as
approximate % of equilibrium radius), 14.6 (gamma = 5/3 for monatomic gas),
14.7 (here and in following problem, use d log(), and delta Y = delta X
(dY/dX)), 14.8.
HW 11 due Wed., Apr. 11
17.14 (see (17.22), (17.27),
and text below (17.28); you are integrating over the usual angular coordinates
theta and phi, with dr=0),17.17,17.18,17.20,17.22.
HW 12 due Wed., Apr. 18
17.23 (integrate ()dM =()dt of course), 18.2 (see Fig. 18.1, (18.4), and (18.7); use (18.3) and (18.5) x r_2 + (18.6) x r_1 to get r), 20.16 (see (19.4), and Appendix C for Earth-Moon distance), 21.7 (recall (2.17)), 22.6.
(Stefan-Boltzmann constant sigma = pi^2 k^4 / 60 hbar^3 c^2)
HW 13 due Wed., Apr. 25
29.18 (see (29.4), (29.58),
(29.60)), 29.33 (rho_{B,0} in (29.17); e.g., take ln() to get R=[function of
T+(3/2) ln R]/constant, and solve by iteration), 29.34 (see (29.92), (29.20,
and (27.15)), 29.31 (p. 1178 for t(10^9 K); (29.17) and (29.58); baryon density
falls as 1/R^3; kinetic energy is approximately kT)), 30.1 (a=4 sigma/c).
Optional: 29.42* and 29.52* for extra credit.
Optional 10 minute talk:
Tuesday, May 1 at 7:00 p.m.
READING ASSIGNMENTS
These reading assignments are in addition to, and
complementary to, the material that we cover in class. I.e., the course
consists of (i) the material covered in class, (ii) the material in the reading
assignments below, and (iii) the homework above.
PLEASE PAY PARTICULAR ATTENTION TO THE QUANTITATIVE
PARTS, INCLUDING EXAMPLES AND DERIVATIONS (AND REACTIONS). You should
understand each step and idea as you read. You may want to read the surrounding
material for further enlightenment and enrichment, even though it is not
required. Note that reading assignments (2) - (4) proceed in inverse order
through the textbook, so that finally all quantities like optical depth (tau),
mean free path (l), and cross section (sigma) should be understood.
(0) Saha equation and its applications, and
Hertzsprung-Russell diagram and its meaning, pp. 211-224, with emphasis on the
examples. Also look at Fig. 8.16 to get the flavor of the H-R diagram.
(1) "The Jeans Criterion", pp. 412-413. Also
p. 419, just assuming Eq. (12.26) and equation at bottom of p. 418.
_____________________________
(2) "The Random Walk", pp. 252-253.
(3) "Continuum Opacity and the H- Ion", p.
248.
(4) Mean free path, "The Definition of
Opacity", and "Optical Depth", pp. 240-243.
_____________________________
(5) "Processes That Broaden Spectral Lines",
pp. 268-271, ending with Example 9.5.3.
(6) "The Nuclear Timescale" and "Quantum
Mechanical Tunneling", pp. 298-302, ending just below (10.27).
(7) "Stellar Nucleosynthesis and Conservation
Laws" through "The Binding Energy per Nucleon", pp. 308 - 315,
ending just above middle of page. [You should understand but not memorize the
reactions here and elsewhere.]
_______________________________________________
PLEASE READ TO HERE, (0) - (7), BEFORE EXAM 1.
EXAM 1 ON FRIDAY MARCH 2
_______________________________________________
PLEASE READ THE REMAINDER, (8) - (20), BEFORE EXAM 2.
(8) "The Solar Interior", pp. 349-352.
(9) "The Solar Neutrino Problem" and
"The Solar Atmosphere", pp. 356-366 (except last 2 lines).
(10) Figs. 11.23 and 11.24, and p. 373.
(11) "The Hydrodynamic Nature of the Upper Solar
Atmosphere", pp. 376-379.
(12) "The Solar Cycle", pp. 381-384, and
Figs. 11.35, 11.36, and 11.38.
(13) "21-cm Radiation of Hydrogen", pp.
405-406.
(14) "Interstellar Chemistry" and "The
Heating and Cooling of the ISM", pp. 409-411.
(15) "H II Regions", pp. 431-432.
(16) "Late Stages of Stellar Evolution", pp.
457-464 (just getting the basic qualitative ideas).
(17) "Core-Collapse Supernovae", pp. 529-537,
ending with the second paragraph.
(18) "s-Process and r-Process
Nucleosynthesis" and "Gamma-Ray Bursts", pp. 542-543.
(19) Figs. 20.7-20.15 [on the Earth]
(20) "Double Neutron Star Binaries" and
"Short-Hard Gamma Ray Bursts", pp. 703-705.
(21) "Big Bang Nucleosynthesis", pp.
1177-1179.
Some useful tips from previous
astrophysics students:
From
Anonymous: You can evaluate many integrals by going to http://integrals.wolfram.com/index.jspand entering the function that you want to integrate.
From
Alex Cook: The computer codes which are in the book's appendices are easily
found online from the book's publisher: http://departments.weber.edu/astrophysics/Codes.html. There are the FORTRAN codes as well as some executables and sources in a few
other languages.
From
Tyler Morrison: I ran across a wonderful open source computer program called
Stellarium. According to the
website, "Stellarium is a free open source planetarium for your computer.
It shows a realistic sky in 3D, just like what you see with the naked eye,
binoculars, or a telescope."
I've installed it and am now running it on my desktop. I must say that it is absolutely
beautiful and has a very nice user interface. http://stellarium.sourceforge.net/is the website.