MCC PHS 142 M01 Astronomy Homework Ch.20-21      
Adj Prof Astronomy: Sam Wormley <>

Background Material

  Textbook - Read Chapters 20-21
  Textbook -
  Textbook -
      (take the Multiple Choice Quiz for for each chapter)

  Web - 
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White Dwarfs

Explanation: The circled stars in the picture above are from a class
that is hard to see in the cosmos: white dwarfs. The entire photo
covers a small region near the center of a globular cluster known as
M4. Researchers using the Hubble Space Telescope discovered a large
concentration of white dwarfs in M4. This was expected--low mass stars,
including the Sun, are known to evolved to the white dwarf stage. 

White dwarfs do not usually evolve further, they just gradually cool
down from their high temperatures. It is hoped that studying how these
stars cool could lead to a better understanding of their ages, of the
age of their parent globular cluster, and hopefully even the age of our

The Structure and Evolution of Hot White Dwarfs are among the oldest
objects in the galaxy and are the remnants of the earliest phases of
star formation. No bigger than the Earth, they are formed when a star
like our Sun ends its life. When white dwarfs are born the are
incredibly hot (about 200,000 degrees C) and then cool down slowly over
thousands of millions of years. Study of the distribution and physical
characteristics of the white dwarf population is an essential part of
understanding the early history of the galaxy. In addition, observing
white dwarfs allows us to address a number of problems concerning the
latter stages of stellar evolution, particularly those of mass loss and
cessation of nuclear fusion during the post Red Giant phases, and study
the behavior of matter under conditions of extreme temperature and
pressure which cannot be reproduced in a laboratory. As white dwarfs
cool, from time-to-time they become unstable and begin to "ring",
rather like an enormous church bell. We see this "ringing" as tiny
variations in the brightness of the star which, if measured very
accurately, can tell us how massive the star is, what it is made of and
how fast it is cooling. 

White Dwarfs form as the outer layers of a low-mass red giant star puff
out to make a planetary nebula. Since the lower mass stars make the
white dwarfs, this type of remnant is the most common endpoint for
stellar evolution. If the remaining mass of the core is less than 1.4
solar masses, the pressure from the degenerate electrons (called
electron degeneracy pressure) is enough to prevent further collapse.


O star (the fairest one in sight), 
We grant your loftiness the right 
To some obscurity of cloud- 
It will not do to say of night, 
Since dark is what brings out your 

Some mystery becomes the proud. 
But to be wholly taciturn 
In your reserve is not allowed.
Say something to us we can learn 
By heart and when alone repeat. 
Say something! And it says "I burn." 
But say with what degree of heat. 
Talk Fahrenheit, talk Centigrade. 
Use language we can comprehend. 
Tell us what elements you blend. 
It gives us strangely little aid,
But does tell something in the end. 

And steadfast as Keats Eremite, 
Not even stooping from its sphere, 
It asks a little of us here. 
It asks of us a certain height, 
So when at times the mob is swayed 
To carry praise or blame too far, 
We may choose something like a star 
To stay our minds on and be staid. 
                    -Robert Frost 
Frost knew that elements are synthesized in stars. He knew that we know
what we know about stars from measuring their light (determining their
temperature). He knew that in human lifetimes stars are steady and
stable--something we can count on. And you know that if you look long
enough, and far enough, that they all "blow themselves up or dim to a
dying cinder". 

You all have young eager minds. There is so much fascinating stuff to
learn and you only have a few score years and ten to fit everything in.
Several years ago, I had the privilege of seeing in Omaha, 50 pieces of
Rodin sculpture on tour from the Iris and B. Gerald Cantor Collection.
Quoting Eliot Nusbaum, of the Des Moines Register, August 4, 1996, and
I quote:

  There is a picture on the back wall of the gallery at the
  Joslyn Art Museum that shows Auguste Rodin's funeral. In
  the center of the image is a monumental version of his most
  famous work, "The Thinker".

  Forming a ring around the statue is a cordon of armed
  guards. Beyond the cordon is a huge crowd of mourners--the
  kind of crowd you expect for a head of state, not an

  Such was the stature of the great French artist, and
  deservedly so. Walking through a gallery of his work nearly
  80 years after his death, is so exciting you just can't
  help but be astonished, amazed and thrilled... 
Viewing Rodin's work evokes such emotion in me, that I was exhausted after three hours and found it was "too much". Now that reminds of something Max V. Exner... said to me some years ago. Max, long retired now, was ISU's Extension 4-H Music Specialist. I met Max while in high school, at a summer 4-H music camp. As an undergraduate student at Iowa State, I was privileged to be part of a choir that Max directed, taking us to Chicago to cut the National 4-H Record. Some years later, during a visit to Max's office in ISU's Morrell Hall, I was intrigued by some visual material Max had created depicting the back-and-forth, give-and-take structure of the first theme in Brahms Symphony No.4.... a favorite of mine from childhood. As it turns out, that Brahms Symphony was performed in C.Y. Stephens some years back... by one of the world famous orchestras that we are so privileged to have perform in Ames. The final piece performed that evening was the Brahms, which was superb. Max Exner was sitting in the row ahead of me... I made some comment... He replied that it was "too much". He knew Brahms intimately from his work in music. I, being an amateur scholar of Rodin, know some of Rodin's work intimately. Now I know what Max meant when he said it was "too much". There are many many beautiful things in life, music, sculpture, paintings, literature, nature and on and on. Knowledge is one of those things. Knowledge will help you get a better job. Knowledge will enrich your life. This astronomy class will help you appreciate the nature around you. You are learning part of the history of how we have come to know who we are and our place in the Universe. I sincerely hope that each of you will go on and learn all you can about "what's out there" in the Universe. Review of the Final States of Stars Star are born and stars die... just like us. The big massive stars have but short lives, a few millions of years. Stars like our sun last for a good 10 billions of years, and the little red stars like Barnard's Star might last for 100 billion years. How long stars live, is determined by their mass (which must be at least 80 Jupiter masses to sustain thermonuclear fusion of hydrogen). There are four (4) fates for the end of stars depending on their masses and the masses of their cores: Red/Brown Dwarfs - less than 0.076 Ms <== Main Sequence 0.076-0.8 Ms Stars less than about 0.6 solar masses, when nuclear fuel is used up, gravitational collapse shrinks the star, but no more than the gas temperature-pressure-volume laws of classical physics allow. We have not found any white dwarf less massive than 0.6 solar masses. Part of the answer is that the universe may not be old enough for lower mass stars to have evolved off the main sequence. White Dwarfs - 0.08 and 1.44 Ms <== Main Sequence 0.8-8 Ms Stars with core masses between 0.08 and 1.44 solar masses are destined to become white dwarfs. White dwarfs are degenerate matter. Further collapse is halted by electron degeneracy pressure. See pages 456-459 in your textbook. The vast majority of stars are in this mass range and are destined to become white dwarfs. Neutron Stars - 1.44 and 2.9 Ms <== Main Sequence 8-30 Ms Core masses between 1.44 and 2.9 solar masses overcome electron degeneracy pressure and collapse to form neutron stars, a star that is essentially one gigantic nucleus. Further collapse is halted by neutron degeneracy pressure. Black Holes - 3 or more Ms <== Main Sequence > 30 Ms But for cores with mass of 3 or more solar masses, neutron degeneracy pressure does not stop the collapse and the star becomes a black hole with zero physical size, but with all the mass. Gravity really wins! In each case, gravity eventually wins. But, to what extent is determined by the mass and the relative pressures of the quantum mechanical forces, electron and neutron degeneracy pressure. See: Homework Problems Note the answers to the odd (Conceptual Questions, Problems and Figure-Based Questions) are in the back of your textbook. It is strongly suggested that you do some of those in every chapter so you have immediate feedback as how well you are understanding the material. There are online multiple choice quizzes for each chapter of your textbook. Goto then click on Your book Student Edition Choose a chapter Multiple Choice Quiz You are expected to do all of your own homework. Statistical patterns showing copying or collaboration will result in no credit for the homework assignment for all participants involved. The Code of Academic Conduct for Iowa Valley Community College District is found in the Student Handbook. Physical Science classes require the use of mathematics. If you don't know algebra, you sould NOT be taking this class. If you need to review, look at Introduction to Algebra WolframAlpha is way faster than a scientific calculator. There is little excuse for turning homework in late. You have a whole week between classes to read the chapters and do the homework. Homework one week late - half credit. Two or more weeks late - no credit. Do the homework during the week, not in class! You got homework questions, email me 24/7. Even if you don't have a homework question, email me anyway! Problem 1: Binary stars are often plotted as though the smaller star orbits the stationary more massive star. We know that the two binary stars orbit their common center of gravity, the barycenter. In the case of the Earth and Moon the barycenter is about a quarter of the way to the center of the Earth, beneath the surface. Still such binary star diagrams are very useful tools for observers of binary stars, allowing an easy calculation of separation and phase angle. Determine from the diagram below the separation in arcseconds of Sirius, the "Dog Star" and the Pup when you are 60 years old. Hint: Copy the 5" (5 arc second) scale from the diagram onto a separate piece of paper to help measure angular distances. Problem 2: Using your starwheel (planisphere), set the Dog Star, Sirius so that it is due South. From the planisphere determine the Right Ascension (RA) and Declination (Dec) of the Dog Star, Sirius. Problem 3: M87 is a huge elliptical galaxy with a 2-3 billion solar mass black hole in its heart. The equatorial coordinates are: Right Ascension: 12:30.8 (hours:minutes) Declination: +12:24 (degrees:minutes) Using your starwheel (planisphere), determine what constellation M87 is found. Problem 4: A 2-Solar Mass core of a star contracts after using its nuclear fuels. Explain why we can be sure that the star will not become a white dwarf. Problem 5: What is the difference between the spectra of Type I supernovae and those of Type II supernovae? Problem 6: Why don't we see any pulsars with periods longer than a few seconds? Problem 7: Note the space-time diagrams in Figures 20.22-23. Why can't an object move "horizontally" in a space-time diagram? Problem 8: Assume that a white dwarf has a radius that is 0.67 Earth radii. Use Figure 20.3 to find the mass of the star. Problem 9: Use Figure 20.9 to find the brightness (relative to its maximum brightness) of a Type II supernova 100 days after the time of maximum light. Problem 10: What would happen to the distance between Jupiter and the Sun, if the Sun shed mass onto Jupiter? Problem 11: What is the ultimate source of energy emitted by accretion disks in binary systems? Problem 12: In a nova, why is the shell of hydrogen on the white dwarf consumed explosively rather than steadily?