Background: Deepest and sharpest infrared image of the universe (galaxy cluster SMACS 0723). Webb telescope (July 2022)
ASTB23.   Astrophysics of Stars, Galaxies and the Universe

This page provides lecture notes, texts of home assignements and other material, such as the tutorial notes. Please note that this is the only sure source of information on ASTB23. Quercus is used for announcements and submission of assignments only.


Syllabus with dates of lectures and exams
Re-download syllabus every week, and any materials linked to the course page that you may need for exam preparation a week before exam (it's admittedly rare, but the access to planets.utsc server was once cut off just before final exam). In the syllabus there are two markers, one indicating where we stopped in the most recent lecture (####), and the other (^^^^) showing approximately up to which topic (or subsection of textbook) you should read before the next meeting.

Lectures, Tutorials, Office hours

Lectures (see syllabus for dates and times) follow the material in textbooks (before midterm) and mostly lecture notes after midterm. They contain extra material, comments, diagrams or equations outlined on the blackboard, and some explanations not found in the book. Informative web pages may (sparingly) appear during lectures as well; notes down keywords or URLs if you want to revisit them.

Tutorials are NOT meant for the explanation of Lectures - they deal with simple astrophysical calculations not discussed in lectures. If you want a good grade on the written parts of exams and the home assignments, please come to tutorials with some kind of calculating device and practice solving problems.
Office hours: an hour after lectures, half an hour after tutorial. I open to discussions about astrophysics, academic career, supercomputers, aerodynamics, or the meaning of life, universe and everything at quite irregular times, in my office. Please drop by and if I'm too busy then you can come later.

Email TA, visit the lecturer

Our TA is marker only, no contact hours, but may answer emails about grading. Contact him first (ASTB23 in subject): Abdur Khan (abdu.khan AT mail.utor...)
lecturer: Prof. Pawel Artymowicz (pronounced: PAvel ArtyMOvich). Office SW 506G, 5th floor (Physics & Astrophysics Group) in old Science Wing. Please email remarks and questions to: pawel AT, importantly with a subject line "ASTB23", or else it may be accidentally misplaced!


Book number 1 is definitely the most important for this course.
1. "What are the stars?" by G. Srinivasan, (Lec. Notes in Physics) Springer 2014 (avail. online from UofT lib)
2. "Life and death of stars" by G. Srinivasan, (Lec. Notes in Physics) Springer 2014, (avail. online from UofT lib)
3. "Galaxies in the Universe", 2nd ed. by L. Sparke and J. Gallagher, Cambridge U Press. Book 3 is optional. It may provide a differently worded explanation of material we cover in the last sections of the course, which are described in lectures, tutorials, and the files with their notes. Ways to find the books will be discussed in the 1st lecture.


Max. score: 100%
Midterm: 21% (10% problems + 11% quiz)
Final exam: 46% (22% problems + 24% quiz)
4 sets of home assignments: 30% (7.5% ea.)
Class activity/participation: 3%
Optional credit for reading an additional book: 4%

Class participation are a few points given not just for showing up, but for above-average activity: asking and answering questions in class, volunteering to solve tutorial problems. Those who are noticeably inactive, don't get activity points. Extra book reading is described in one of the subsections below.

Minimum percentage marks for letter grades (for orientation only; grades are reported as percentages):
A+ 90%, A 85%, A- 80%, B+ 77%, B 73%, B- 70%, C+ 67%, C 63%, C- 60%, D+ 57%, D 53%, D- 50%, F 49% or less.

Lecture notes

In September/Oct., we follow the Srinivasan textbooks closely (most of the 1st and parts of 2nd). You are supposed to read those books, and I'll discuss the contents in lectures, also showing the text on the screen but rarely reading the text -- mostly showing equations. There will normally be no separate slides, except for when we deviate from the book.

E.g., in the first introductory lecture we use Lecture 1 notes .
and in the 7th we use Lecture 7 notes .
This will change after the midterm, when we discuss galaxies and universe. (Notes below will be published just before our meetings.)
Lectures 13-14 notes , Lectures 15-16 notes , Lectures 17-18 notes , Lectures 19-20 notes , Lectures 21-22 notes , Lectures 23-24 notes

Tutorial and blackboard notes

As explained above, attending tutorials is important for written parts of the exams (half of the points for exams). Tutorials teach you how to approach and numerically solve problems. Many problems are listed and most are fully solved or at least outlined in detail in tutorial notes, which also serve as a preparation material for exams.

Problem sets

Solutions to problems are to be submitted in ***legibly*** handwritten or in printed form (not required). You will scan or photograph your work and submit it to the Assignments section of ASTB23 Quercus page. Marker of your work will put comments on Quercus & we'll make those visible to you. Please put your student# at the top of the first page of your solution, for our convenience while marking.
Use your words, don't just write a stream of symbols - it is up to you to be understood correctly by a TA or lecturer.

Assignments are meant to be doable in 7 days, but will be published more than a week before the deadline, usually 9 days before. If you have a letter from AcessAbility office, then even somewhat earlier.

If a link to something current (apparently due so on) doesn't work, please let me know asap. But if you see an inactive link to far-off assignments, lectures or exams (>10 day in advance), that's normal. Wait for the link to be activated.

Some assignments may look like something existing on internet. Using such resources is counterproductive & dangerous, as I am known to change some hard-to-notice details of assignments every year (a few students were caught this way - plagiarism is a serious offense).

Except in emergencies, there is no grace period (no late submissions of assignments), because I will sometimes post & discuss solutions on the due day, before you forget what the assignment was all about. [If you have an emergency preventing you from obeying the deadline, state the nature of the emergency in an email to the lecturer. You will be considered for exception of due date if the delay is short, or for transfer of points otherwise. If you encounter sudden medical issues, see a doctor a.s.a.p. and get a notice; this is required to successfully ask for transfer of points to final exam, if you miss the midterm exam for medical reasons.]

Set #1. Due: 28 Sep

problem set #1, ~~ problem set #1 with hints and solutions , please re-download, the solutions have been updated.

Set #2. Due: 19 Oct

This set of problems will be part of your preparation for the written part of the midterm. Check the solutions:
problem set #2 ~~ problem set #2 with solutions

Set #3. Due: 16 Nov

problem set #3 , ~~ problem set #3 with solutions ,

Set #4. Due: 30 Nov

[Please include 3 last digits of your student number in the names of submitted files]
problem set #4 , ~~ problem set #4 with solutions ,

Midterm exam preparation: 26 Oct during tutorial

2 double-sided hand-written (not printed or photocopied) sheets of own notes are allowed at midterm. Calculators are required. Otherwise, phones, electronic devices and books are not allowed.

You solve the quiz by marking Y or N in front of a supplied question, not on a separate sheet (no scantrons) and not in the examination booklet, and return the exam sheets. WARNING: circle at least one word or number that is wrong, in case you decide the statement in the quiz is wrong (N). Otherwise it will be considered that you guessed an answer and you will not get a credit for that particular sentence in the quiz.

How does one prepare best? There will be one written problem, very similar to the assignments, and some of the tutorial problems, so please review all those (tutorial notes section).
The standards of description in your solution of the problem are the same as for home assignment - cf. the top of tutorial notes. If you don't describe the steps in a solution in words and only include mathematical doodles, you run a risk of not being fully understood and appreciated.

The quiz should take you less than 20 minutes. It will contain ~27 Y/N questions similar to the ones listed in the practice files provided below; you can divide the hour however you like between quiz and the problems.

The material is our textbook 1 up to and INCLUDING Chapter 5, plus Lectures. One example of things we dealt with is the definition and usage of optical depth τ, which was not discussed much in the textbook. So there could be a question about it in Quiz or the writtem part.


I list here the those sections (whole subsections, only beginning pages are quoted) that may be interesting per se, but will not be required at exam:

Introduction by Lord Rees (Dr Rees was made a baron by our former Queen for achievements in astrophysics).
Preface by the author (page numbers are Roman numerals).
Box on p. 32
Chapter 4, i.e. the details of how to set up the inequality for beta (gas pressure to total pressure ratio) and what the solutions are - it's not important for us.
Probably also:
Pages 110-115
Global Networks and Solar Observatories in Space subsections p.127
Subsection Effect of a Magnetic (..) p.136
Rotational Splitting section p. 138
Mass states and Flavour (...) p. 160
Quantum Oscillations p. 165

The quiz is sampling your understanding of concepts and knowledge of facts from both the lecture notes and the textbooks. You won't be tested on precise dates of historic events, although it's a good idea to know what happened in which century, or which concepts preceded some later concepts. Knowledge of what a key figure did (Eddington or Fraunhoffer, for instance) is required, their detailed biographies not.

2023 quiz preparation exercises:
Many answers are provided. Please start the preparation by solving the questions from the first file, without answers, and only then check your answers. The sample questions indicate the format of the quiz and some of the most important topics that will be tested. Few of these questions will be found in the actual test. This set is thus not sufficient to prepare for the midterm - you need to study from the book and your notes. [Let me repeat, so nobody gets that part wrong: You will have to circle at least one word or formula which makes the sentence wrong, if you mark it as wrong. Not doing so will result in zero points, even if the sentence indeed is false.]
Questions only
Question and many answers

The 2023 midterm: PDF with solutions

Final Exam Preparation

Exam place, time and allowed materials

Up to 8 hand written pages on either 4 or 8 sheets of paper (not printed or photocopied) of *own* notes are allowed.
Calculator is required. Phones are not allowed at your desk, there will be a plastic bag to put them (and laptop) in, seal, and place under the chair. You can also leave them in your bag in front of the exam room. Exam booklets and candidate forms will be provided. Please bring picture ID. The official rules state that you can't leave the room in the first 30 min. and nobody can come after anybody leaves the room, so don't be late. Thank you for observing the rules.


About 1/3 of the final exam will be questions from the 1st part of the course, 2/3 from the post-midterm material (galaxies and universe). Normally 2 out of a total of 3 written problems are about galaxies and stellar systems.

As to the mathematical prereqs, please make sure that you know how to do full derivatives, for example if $z=2 c x^3$, and $c$ does not depend on $t$, then $dz/dt = 6 c x^2 \,dx/dt$, not just $dz/dt = 6 c x^2$. Know the method of separation of variables for the simple 1st order ODEs. As an example, the ODE $dy/dt = -t y/2 $ with initial condition $y(0)= e = 2.718..$ would be solved by the following steps: $dy/y = x^2 \,dx$, $\int dy/y = -(1/2)\int t \,dt$, $ln y +const. = -t^2$. In order to satisfy init. cond., $const. = -1$. Solution: $y(t) = e^{1-t^2}$.

Astronomical prerequisites include, among others, the familiariy with the parallax method of distance determination, magnitude brightness scale ($ m = -2.5\, \log I + const. = -2.5 \log (L/4\pi r^2) + const.), and the use of Hubble's law.

First, please review the whole material for midterm preparation mentioned above, including the textbook no. 1 for the quiz, as well as tutorial notes. Pay attention to the proper method to solve written problems, presented at the top of that page.

For white dwarfs and other degenerate objects, in textbook 2 read Chapters 3,5,6, and 7 up to page 91, omitting anything that was clearly and and repeatedly indicated in lectures to be not required, mainly the degenrate pressure in case of non-negligible temperature (fuzzy Fermi ball in velocity space, while we only studied sharp Fermi sphere of cold degenerate gas). Learn stellar evolution from Lecture notes, chapters later than 7 in book 2 are not required.

For galaxies and universe - study the lecture notes closely. Familiarity with textbook 3 if not mentioned explicitly in the lecture notes is not required, in the sense that I won't ask questions that are only described in the Sparke+Gallagher book but not mentioned in Lectures. If you are not sure how certain things work and want to check the book on a subject discussed concisely in the lectures, that would be a very good idea. For written problems, don't forget to consult the tutorial notes page, as well as all the assignment sets and solutions.

The format of the final examination will be exactly he same as that of the midterm, only longer (almost 3 hrs instead of 1). No Scantron sheets, you will return the Y or N circled in front of the question + circle the wrong word(s), if any. In the materials below, most stellar topics will not be repeated, though in the final exam they'll be present (up to 40 percent of the final exam).
Preparation to the final exam's quiz is given here in this TXT file.
The version of this file with partial answers is present here.

Preparation for the final exam's written problem (in addition to the sources listed above) are here: Problems with many hints or solutions

Please read the relevant parts of textbooks and pay close attention to lecture notes. In fact, only textbook 1 is very important, textbooks 2 is less important, texbook 3 is completely optional. (The second part of the course was based on lecture notes with just a few encouragements to look at book chapters in case those notes were not clear.)

2023 final exam with solutions

is in this file.

Getting the points for additional reading

The extra book reading ends with a conversation about the book with the lecturer (reserve time by email in advance before the final exam; you can come during office hours). The book is your choice, you can for instance go to the library and browse but needs to be pre-approved by the lecturer to assure the book's level and scope are ok. Also, look at our secret page where I placed some book suggestions. Ask for suggestions during tutorial. When you come to talk about the book, bring it with you.

I'll give you one more chance to come and talk about the book (on a 1st-come-1st-served basis) during the exam session. Come to my office SW506G on Thu 14 Dec, 3-5pm.

Your results

See this file and report any discrepancies by email.

Additional topics

Our sun

For a model of the sun's interior based on the equations of stellar structure from the lectures, see this plot., made by this IDL (or GDL) script.,

Electromagnetic and gravitational waves from a distant cataclysm

On 16 Oct 2017, a momentous astronomical discovery was announced. As a necessary byproduct of a merger of two orbiting neutron stars (mass range 0.8-2.6 solar masses) located in a relatively nearby galaxy 130 million light-years away, a wave-train of millisecond-period gravitational waves of more than 100 s duration was caught by LIGO/Virgo gravitational wave observatory. LIGO team alerted 70 other teams around the globe to comb the sky area covering 30 square degrees, to find and closely follow the resulting explosion (named kilonova or macronova explosion) in gamma rays, optical, infrared, X-ray and radio range - across the whole electromagnetic spectrum. All such efforts succeeded. This was the first neutron star merger ever detected, and the scale of follow-up campaigns was unprecedented. More than one thousand researchers from all the countries contributed to the effort. After collision, the neutron stars likely formed a new black hole in a lenticular galaxy NGC 4993, discovered by William Herschel in 1789. Although some specific questions remain at present time, the observations generally followed very closely the prior theoretical predictions of the process of merger, the accompanying explosion (in which 2 percent of exotic neutron matter manages to escape) and the aftermath. According to both theory and observations, similar cataclysms produced and dispersed most of the elements heavier than iron (the so-called r-process elements, lanthanides), including gold and platinum found on Earth.
There are many press releases and stories like this one.. See the external links to short Youtube presentations on this page , also an article in UCSC magazine, and a remarkable (and unusual in many respects) research paper here. If you wondered about UofT participation - see this link (prof. Pfeiffer's group at CITA simulated mergers on cluster systems including GPUs).

Great moments of astronomy

For those who would like to read about the history of astronomical discoveries from antiquity to the 19. century (age of spectroscopy), here as some links to lecture notes from ASTB03. This material is completely optional and won't be tested in our exams.
file 1 ,   file 2 ,   file 3 ,   file 4 ,   file 5 ,   file 6 ,   file 7 ,   file 8 .  

Webpage of book 3 (Sparke & Gallagher)

is available at

Links for reference and enjoyment: The Great Debate: The Shapley-Curtis Debate in 1920 Hubble Types of Galaxies as illustrated by the Messier galaxies Galaxy Classification NASA eyes up supermassive BH and NS Eta Carinae Multiwavelength Milky Way Maps Galaxies and the Universe - WWW graduate-level Course Notes 360-degree Milky Way Panorama Atlas of the Universe The Milky Way Galaxy - Yahoo links Andromeda Galaxy Supermassive Black Holes The 2dF Galaxy Redshift Survey 2 Micron All Sky Survey (2MASS) Boomerang backs flat universe About a newly found midium-sized black hole in Omega Centauri a huge 12 Gyr-old globular cluster (maybe a core of a dwarf galaxy that the Milky Way has encountered and swallowed) WMAP, launched in 2001, still working at the L2 point of Sun-Earth system. Precise measurement of the age and curvature of our world (universe), among others. WMAP and the Parameters of Cosmology A good online book about cosmology and early universe Alpher, Gamow, and the prediction of the CMBR And GamoW said, let there be a hot universe Boomerang in 1998 determined the geometry of the Universe to be flat, supporting the supernova evidence for the existence of dark energy. Gravitational wave and gamma ray burst + optical burst in NGC 4993 - two neutron stars collided!

home page of Pawel Artymowicz
last modified: Nov 2023