Autumn PS119a 2006 Lecture 17 November 03, 2006 Opening music: Symphony No. 5 in C Minor, by Beethoven (1770-1827), first performed in Vienna in 1804. Dalton was measuring the masses of different elements at this time, experiments that were the precursors of modern particle physics. The actual origins of the elements, and in fact the organization of the periodic table, were unknown at the time of his experiments and most of the elements in the periodic table were not identified. Opening art: (repeat Frieda, from last lecture). Closing music: Three Penny Opera, by Kurt Weill (1900-1950), first performed in 1929, between the formulation of the Hertzsprung-Russell diagram (1923) and the detection of the neutron as a free particle by Chadwick (1932) Earlier, in 1920, Rutherford had suggested the name "proton" for the charged nucleus of the H atom. Closing Art: The Scream, by Edvard Munch (1863-1944), a fitting reminder of the horrors released by atomic energy. First shown in 1893, a few years before the discovery of radioactivity that opened the nuclear age. This painting was recently in the news because it was stolen from a European museum. It then came to light that there were actually several copies of the same piece of art (which I am sure made some museum owners look like the face in the painting.) They were found in the last year. (Bart Simpson version, as well.)
I.
The Death of Stars a) White Dwarfs
We know empirically that stars at this stage lose a shell of mass if they are solar mass like stars. The central star gets very hot, under gravitational collapse, and becomes a white dwarf. Radiation from this hot star ionizes the gas in the expanding shell (known as a "planetary nebula" because the color is greenish, similar to that of some outer planets, according to one naming story.) This glowing nebula lasts as long as there is ionizing radiation, then burns out. There are a few hundred of these objects in the galaxy, implying that the stars are rare (the progenitors, solar-like stars on the main sequence, are numerous: there are hundreds of millions of them, implying that, on the main sequence, stars are stable and last for a long time. The longer a star lasts in a given state, the better our chances of seeing it in that state during our very short lifetime as humans.
Eventually, the star collapses (no more fuel left) to a white dwarf. Any state of matter has an ultimate limit to its compressibility set by the Pauli exclusion principle, that no two particles can be in the same quantum state and position in real space, at the same time. In the case of white dwarfs, the plasma of protons and electrons has an ultimate compressibility generally termed "electron degeneracy". A one solar mass white dwarf is about the size of the Earth but one million times as dense. b) Neutron Stars Chandrashekar, a professor at the University of Chicago for some 60 years, discovered in 1933 that there is a mass limit to white dwarfs. If they are more massive than 1.4 solar masses, gravity overcomes the pressure of electron degeneracy and the star transitions to another state, where the size of the star is set by neutron degeneracy. Basically, electrons are forced directly into protons, making neutrons, and the neutrons are as packed together as they can possibly be. On a later homework, you will show that such objects have mean densities of 1015 g/cm3, much higher than the density of main sequence stars or of white dwarfs. (A spoon full, on the surface of Earth, would weigh billions of tons.) A white dwarf, on the other hand, is about the size of the Earth, has a density of one million grams/cm3. A spoon full of white dwarf matter, on Earth, would weigh less than the same amount of neutron star matter by a factor of one billion. As we will discuss later, neutron stars have masses of 4 solar masses. Eventually, if the mass of the star is too high, the remnant of the star is so massive that a neutron star would be crushed and the remnant becomes a black hole. Stars that leave stellar remnants of neutron stars or black holes are thought to be dramatic supernovae in their last few minutes. Stars must either have initial masses less than 1.4 Solar masses (the Chandrasekar limit) to become white dwarfs, or they must lose enough mass in the planetary nebula stage to get down below that limit. If, by the time all the nuclear fuel is expended, a star is above the limit, it will become a neutron star. Neutron stars were postulated in the early 1930's as the state to which stars were transitioning when a supernova occurs (Zwicky, Baade). They were finally discovered in 1967/1968 when Hewish and a graduate student, Jocelyn Bell, found pulsing radio sources with periods of
milliseconds (pulsars). Thomas Gold, of Cornell, immediately understood that the periodic radio radiation could be due to pulsations, in which a star gets periodically brighter and fainter (as if you blew into a balloon, released the air, inflated it again, etc.) or to a rotating bright spot on the surface of a star (think of a person on a darkened merry-go-round at night, holding a flashlight and pointing it steadily along a radius of the merry-go-round, pointing at eye level). An observer might not see the darkened merry-goround, but every time the beam of light rotates into view, the observer would see a "pulse".) The question at the time of the discovery of pulsars was, what were properties the of a star that could pulsate or rotate so fast? As the objects could not be seen in visible light, they must be very faint in visible light, hence they had to be very small. At the time, only three known stable configurations of faint stars were known: very cool, red stars on the main sequence; white dwarfs; and the neutron stars: until 1968 , neutron stars were not known to actually exist: they were predicted but unconfirmed. A quick calculation (see homework 6) shows that a spot on a rotating white dwarf (which has a radius similar to that of Earth) would have to be moving faster than the speed of light to create millisecond, apparent pulses, which is impossible by the theory of special relativity (Einstein, 1905). Likewise for cool red stars on the main sequence. This conclusion, therefore, left only neutron stars as possible, by elimination. One could also imagine something in orbit around a small body and use Newton's version of Kepler's law to compute the radius of the orbit, assuming that the period of the pulses of radio radiation corresponded to an orbital period. The result is bigger than neutron star and smaller than a white dwarf, and the velocity is less than the speed of light. (See the related homework problem.) As for possible pulsating stars, if something is used to strike a body, the frequency of emitted sound, for instance, is related to the density of the material. An object of a given density has a unique, characteristic frequency. (Denser objects have a higher pitch when struck than less dense objects.) If the proportionality constant is "a", then =a 1/2. (In class, I stated this inversely: the time scale for collapse of a body is 1/ (G)1/2.) For instance, RR Lyr stars, on the horizontal branch of HR diagrams of globular clusters, have a density such that they pulsate (expand and contract) every 0.5 days, or so. This pulsational period can be used to identify RR Lyr stars in other galaxies by virtue of the fact that the intensity
of light from these stars changes as the star expands and contracts. The densities are of the order of 1 g/cm3. For a white dwarf, with a density of 106 g/cm3, the associated pulsations would have periods of 1-2 minutes, compared to the millisecond periods of the observed pulsars. A neutron star, with densities of 1015 g/cm3, would, on the other hand, have a natural frequency less than that of a white dwarf by a factor of (1015/106)1/2, or 30,000. 1.5 minutes is about 100 sec, so the natural frequency would be 0.003 seconds, or 3 milliseconds. Evidently, a neutron star is a possible source of the radio pulses observed by Bell and Hewish. The actual source of the light is believed to be nearby particles focused by an very intense magnetic field, which configuration generates light from a spot on the surface of a neutron star, just as described for the flashlight held by the merry-go-round rider, above. Thus, the discovery of pulsars proved to be confirmation of the existence of neutron stars, even though the physical mechanism was not exactly understood. c) Black Holes If a stellar remnant exceeds 4 Solar masses, it is believed to become a black hole. A black hole is an object with mass but with no other characteristics that we understand, excep...