Structure and Evolution of Stars

Course manual 2017/2018

Course content

Study materials

Literature

• Matthew Benacquista, 'An introduction to the evolution of single and binary stars', Springer.

Other

• Assignments and additional notes on Blackboard.

Objectives

The students will study the equations of stellar structure and evolution and learn to derive the basic properties of stars and their behaviour in time from them. Following this, they will learn how this changes when binary stars are considered, and how the outcomes of binary star evolution can be predicted from a combination of stellar evolution and orbital dynamics.

Learning outcomes by topic:

1. Measuring stellar properties

• Be able to explain how we measure basic properties such as luminosity, mass, radius, temperature, distance? (Blackbody physics, spectra – continuum and lines, basic properties of binaries, parallax....)
• Be able to explain what the mass-luminosity relation is, and how is it derived.
• Be able to specify the basic properties of the populations in the Hertzsprung-Russell diagram.

2. Stellar evolution equations

• Understand how to derive the equations for (1) mass distribution, (2) force balance, (3) energy, (4) composition.
• Local thermodynamic equilibrium – be able to define this concept and apply it.
• Virial theorem and total energy of star – be able to derive these equations and derive basic conclusions about stellar structure that arise from them.
• Timescales – dynamical, thermal, nuclear: know how to estimate these, and what they are.

3. Pressures

• The equation of state: know what this is for Ideal gases, degenerate systems (non-relativistic and relativistic limits), Partially degenerate systems, and Radiation.
• Be able to sketch out in a plot of temperature against density the regions where different pressures dominate.
• Be able to explain qualitatively the role of ionization in changing the adiabatic index.

4. Radiation and nuclear

• Energy transport: understand and be able to set up problems involving energy transport by radiation and convection (to come later). Be able to explain why conduction is usually neglected.
• Be able to derive and solve the radiative transport equation.
• Opacities: know different types that are most relevant in stars, and in what parameter ranges of temperature/density they are important. Be able to explain and apply the concept of the Kramers’ opacity and the Rosseland mean opacity.
• Understand, be able to explain the origin of, and apply the concept of the Eddington limit.
• Nuclear reactions in stars: know the dominant reactions (pp chain, CNO cycle, and triple-alpha reaction, r- process, s-process) , when they are important, and the temperature dependence of their reaction rates.

5. Simple models

• Be able to specify boundary conditions on stellar models (including concept of photosphere).
• You should be able to solve the stellar structure equations for (a) Polytropic models, (b) Homologous models.

6. Stability and convection

• Thermal stability – be able to show how star with ideal gas EOS responds to small changes in luminosity or nuclear energy generation rate.
• Thermal instability in degenerate stars: be able to outline in principle why this occurs.
• Thin shell instability: be able to show how this occurs.
• Dynamical instabilities: understand and be able to explain qualitatively the role of adiabatic index.
• Convection: Be familiar with the Schwarzschild instability criterion and Ledoux instability criterion, understand and be able to explain under what conditions convection is likely to occur, and what it does (energy transport, mixing, convective overshoot).

7. Stellar evolution: stellar birth, main sequence, post main sequence evolution and compact remnants

• You should be able to trace out the main route of a star of a given mass through the HR diagram, understand the main physical processes at work in setting the direction and timescale of the track.
• Stellar birth: Jeans condition for collapse (including lowest mass of stars that can form), isothermal nature of initial collapse due to efficient cooling by dust, core of protostar becoming optically thick, dissociation and ionization leading to core collapse, accretion of envelope, convection (role of opacity, Hayashi track, simple models of such stars), radiation resumes (Henyey track).
• Main sequence and post main sequence: ZAMS (nuclear reactions start in core when T high enough), Core burning vs shell burning processes and effect on star (giant branch, horizontal branch, AGB...), effects of degeneracy, differences between low and high mass stars, Chandrasekhar-Schonberg limit.
• End life of stars: Stellar winds and mass loss in different types of stars (OB stars, blue supergiants, red supergiants, Wolf-Rayet stars), Core collapse supernovae, cooling tracks of WDs, formation of NS (neutron degeneracy so polytropic models apply) and BH.
• Be able to read and interpret a Kippenhahn diagram.

8. Binaries

• Understand and be able to solve simple problems involving the following concepts:Orbital mechanics of non-interacting binaries.
  •  
  • Effect of tidal forces on non-interacting binaries: binaries become coplanar, corotating, and circular.
  • Roche lobe overflow
  • Effect of conservative mass transfer on orbital separation (depends on which star is the donor).
  • Stability of mass transfer (depends on adjustment rate of stellar radius and Roche lobe radius), in general mass transfer is unstable once donor mass: accretor mass exceeds a certain ratio.
  • Non-conservative mass transfer, mass loss, and disruption of binaries: common envelope evolution, effect of supernovae,
  • The concept of the Eddington accretion rate for compact object binaries.
• Types of binaries: Be able to describe basic properties of the following types of system: MS/post MS binaries (Algol systems, Wolf-Rayet/O-star binaries), White dwarf binaries (Close detatched WD binaries, Double core planetary nebulae, Double WD binaries, Cataclysmic variables – including dwarf and classical novae, Supersoft X-ray sources, Symbiotic binaries), Neutron star and Black hole binaries (High mass X-ray binaries, Low mass X-ray binaries, binary radio pulsars).
• Clusters: effect of dynamical interactions on binary evolution.
• Be able to read and understand typical binary evolution graphics tracing out evolutionary paths.

Teaching methods

• Lecture
• Seminar

The teaching will consist of lectures, in which the basic concepts will be explained, and tutorial classes where the students will work through homework assignments with the Teaching Assistant. 

Homework problems will be set each week. They are intended to help you to become familiar with the
theory and practice of stellar physics, and to practice for the exam. For this reason they are not graded.
You are, however, expected to do them before each tutorial section. You are expected to participate in the
tutorial section and be absent only rarely, and randomly selected students will be asked to demonstrate
(parts of) their solution on the blackboard as a starter for discussion. Since the goal of the problem sets
is to get practice and stimulate discussion and not to get grades, it is OK to work on them in teams.
It is your own responsibility to be an active participant in such a team, so that you learn enough to
understand the material and pass the exam. I will hand out fully-worked solutions after the fact, both
to ensure that the discussion can focus on the essentials of the solution rather than all the nitty gritty
of the algebra, and so that you have an example solution for your exam preparation. There will be 8
problem sets in total, with 8 tutorials.

Learning activities

Attendance

Requirements concerning attendance (OER-B).

Assessment

Students must achieve a minimum grade of 5 on all three of the assessed elements, and a 6 overall.

Assignments

Computational assignment

• Computational stellar structure assignment

Essay

• An essay on a classic paper in stellar evolution.

Assignment deadlines are *hard* deadlines. Late = zero credit.

Computer assignment

It is essential in modern natural science to be able to go beyond analytic solutions: many of the problems
that can be solved with a piece (or stack) of paper and a pencil have been done, so often the set of equations
you have translated your astrophysics problem into can only be solved numerically. This should not stop
you from solving it. Stellar astrophysics presents many such problems: most of the physics is known, so
we can phrase the problem in the form of a set of equations to solve. These equations are sometimes
simple enough to estimate what the solution must be approximately, even to solve them. But we know
that stars have very rich and diverse behaviour even though the equations describing their evolution fit
on a few lines; apparently the solution to the equations can also be very non-trivial. We will do a computer assignment: it will require you to write a program to analyse a problem, using numerical libraries, and to present the solution in the form of some numbers and some graphs, as well as a copy of the code. The preferred language is Python; if you want to use another coding language, discuss this with me first.

Essay

The second assignment will involve you picking a seminal paper in stellar astrophysics from a list (to
be provided). You will write a 4-6 page essay, explaining what you have learnt, and discussing the paper's
relevance to and influence on the field. The essay should summarize the motivation for the work and the context in which it was done, the  main results of the paper and then discuss these critically, in the light of more recent work, explaining its impact on the field (hint: look at subsequent papers that cite it!). Reading the paper, finding more relevant literature, and writing up your essay should not take more than 3 days. Please also try to write in decent English (spelling and style).

Both assignments are graded and thus must be done individually.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Additional information

Recommended prior knowledge: Elementary radiative transfer.

Contact information

Coordinator

• dr. A.L. Watts