Ay 123
Structure and Evolution of Stars
(Fall Term 2016)

Class Logistics

the final is out - please see gita patel in cahill 244 to pick it up

Professor: Lynne Hillenbrand (lah@astro)
Graduate Teaching Assistant: Ivanna Escala (ie@astro)

Purpose: This is the graduate "stars" class at Caltech, taken by all first-year graduate students in Ay. Other graduate students in e.g. Ph or PS often enroll, as do senior undergraduates from these three options.

- Monday 1 pm (Cahill 219)
- Wednesday 1 pm (Cahill 219)
- Friday 11 am (Cahill 312 - third floor, front hallway between the two cross-stitches of the building)

Reading: Self-study is highly recommended. See the syllabus below for recommended weekly reading.

Problem Sets: To develop your understanding of course material, you will be asked roughly weekly to complete analytic work and/or coding, plotting and analysis relevant to stellar structure and evolution concepts. See below.

Exams: The mid-term assessment will be an oral evaluation of your conceptual understanding, rather than problem solving ability. The final exam will be a three-hour closed book exam that will test both problem solving and conceptual understanding.


Ultimately you are responsible for your graduate education.
Please make an initial pass through the problems on your own.
Discussion and collaboration with your peers on problem sets, and consultation with the TA, is permitted in the conceptual phase of working an assigment.
After all, the goal is to improve your understanding of the underlying physics.
However, students are expected to work out the final solutions themselves.
You may not acquire or use previous solution sets from this or any other stars-related course.
Several of the problem sets will require use of computers for calculations and plotting of results.

Grading will be based on the weekly assignments (~55% with the lowest score dropped), the mid-term exam (~15%), and the final exam (~30%).

If you have either constructive feedback or complaints about this course, please come see me. You may also use the (anonymous if you like) feedback form to provide input.

Syllabus and Reading

Ay 123 syllabus and weekly reading assignments

We aim to cover:

  • basic physics of stellar interiors and atmospheres (e.g. equilibrium conditions, thermodynamics, equations of state, opacity, convection, radiative transfer, nuclear reactions)
  • analytic, heuristic, and real stellar models
  • stellar evolution from the Hayashi limit to compact remnants, for high to low mass stars.

    Advanced topics beyond the typical undergraduate curriculum you may have already experienced include:

  • stellar pulsations / oscillations
  • stellar rotation
  • binary star evolution.


    There is an enormous range of topics and an extensive depth to which they deserve to be covered - more than can be legitimately expected in our mere 30 hours of class time over the term.


    Please acquire a copy of:

  • Kippenhahn, Weigert, & Weiss Stellar Structure and Evolution

    There is an e-book version available through the Caltech library that can be read by one student at a time. Please be courteous to your fellow students and close out the computer access when you are done.

    If you are looking for supplemental material, there are many many books on stellar physics.
    Please consult the following to deepen and broaden your understanding of various topics in stars.

    For the graduate level:

  • Iben, Stellar Evolution Physics, 2013 (two enormous but complete volumes)
    1. Physical Processes in Stellar Interiors
    2. Advanced Evolution of Single Stars
  • Hansen, Kawaler, & Trimble, Stellar Interiors, 2004 (2nd edition)
  • Rutten, Radiative Transfer in Stellar Atmospheres , 2003
  • Gray, The Observation and Analysis of Stellar Photospheres, 2005 (3rd edition)
  • Hubeny and Mihalas Theory of Stellar Atmospheres, 2015
  • Collins, Fundamentals of Stellar Astrophysics, 1989
  • Clayton, Principles of Stellar Evolution and Nucleosynthesis
  • Christensen-Dalsgaard, Lecture Notes on Stellar Oscillations , 2003
  • Shapiro and Teukolsky, Black holes, white dwarfs, and neutron stars
  • Padmanabhan, Theoretical Astrophysics, Vol2: Stars and Stellar Systems

    For undergraduate level review:

  • Bohm-Vitense, Stellar Astrophysics Vol. 2: Stellar Atmospheres, 1989
  • Bohm-Vitense, Stellar Astrophysics Vol. 3: Stellar Structure and Evolution, 1989
  • Prialnik, An Introduction to the Theory of Stellar Structure and Evolution, 2000
  • Phillips, The Physics of Stars, 1999
  • Bowers & Deeming, Astrophysics Vol. 1: Stars, 1984

    The above should all be on reserve for this course, in our own astrophysics reading room / library.
    Note that some Caltech course reserves can be in SFL.


  • Choi et al. 2016 paper on MESA grid which is recommending reading/skimming -- describes the real deal behind modern stellar modelling.
  • Christensen-Dalsgaard 2002 review article on stellar seismology
  • Stahler 1988 Understanding Young Stars: A History
  • Palla 2012 short paper with more on the Hayashi tracks

    On-Line Visualizations of Ay123 concepts

  • NIST Atomic database with wavelengths, energy levels, transition probabilities
  • X, Y, Z Calculator for detailed element abundance input

  • The famous rho-T diagrams - same plane, many ways to look at it
  • Hydrogen Fusion Simulator
  • Helium Fusion Simulator
  • Zoomable and clickable Table of Nuclides

  • Pulsations spherical harmonics nomenclature

  • Polytropic model and Lane-Emden applet
  • Polytrope calculator

  • "EZ" Stellar Evolution input/output details and movies
  • More sophisticated, but still easy-to-use MESA-Web and some movies from pre-main sequence to helium burning
  • Full-up MESA - a state-of-the-art high-level code/interface covering everything we need; worth having but somewhat complex to install!

  • Synthetic spectral libraries

    Besides your regular course reading/studying and class attendance, a quick (daily) visit to the Astronomy Picture of the Day might broaden your astronomical horizons.

    Class Slides

  • part 1 -- overview, basic stellar interiors
  • part 2 -- opacity, energy transport
  • part 3 -- states of matter, stellar seismology
  • part 4 -- energy generation
  • part 5 -- stellar models, numeric and analytic
  • part 6 -- star formation and pre-main sequence evolution
  • part 7 -- low-mass and intermediate-mass post-main sequence evolution
  • part 8 -- high-mass post-main sequence evolution and evolution wrap-up
  • part 9 -- stellar atmospheres

    Problem Sets

  • ps1 due 7 October

  • ps2 due 14 October

  • ps3 due 21 October

  • ps4 due 28 October

  • ps5 due 4 November

  • ps6 due 11 November
    note the gap

  • ps7 due 2 December

    Left: Experimental convection moving top-to-bottom [from http://www.solarviews.com/eng/edu/convect.htm]
    Right: Oberved convection moving bottom-to-top [viewed from my office during the 2009 Station Fire]

    Last Revised: 23 October 2016 by LAH