1. 16 October 2001Astronomy 102, Fall 20011 The remnant of supernova 1987A in the Large Magellanic Cloud, seen by the Hubble Space Telescope in 1995 (NASA/STScI). Today in Astronomy 102: neutron degeneracy pressure and neutron stars  The relativity of mass  Neutron stars and the Oppenheimer maximum mass.  Collapse of burned-out stars, the formation of neutron stars, and supernovae.  Pulsars are neutron stars.  When is black-hole formation inevitable?

2. 16 October 2001Astronomy 102, Fall 20012 The maximum mass and the speed-of-light limit Why is the speed of light the maximum speed that can be reached by any moving body? (Remember, this was not part of the two original axioms from which Einstein started…)  Because of the relativity of mass : if a body with rest mass m 0 moves at speed V with respect to an observer, the observer will measure a mass for the body. (Another result of the Special Theory.)  Note similarity to the formula for time dilation: in particular, that the denominator approaches 0, and thus m approaches infinity, if V approaches c.

3. 16 October 2001Astronomy 102, Fall 20013 The maximum mass and the speed-of-light limit (continued) So, suppose you have a body moving at very nearly the speed of light, and you want it to exceed the speed of light. What can you do?  It needs to accelerate for its speed to increase.  You need to exert a force on it in order to make it accelerate.  The force required is, essentially, proportional to the product of mass and acceleration in your reference frame. (Nonrelativistic version of this statement is Newton’s second law: force = mass times acceleration.)  But the mass approaches infinity as V approaches c, and thus an infinite force is required to accelerate it further. There’s no such thing as an infinite force, so c is the ultimate speed limit.

4. 16 October 2001Astronomy 102, Fall 20014 Final collapse of burned-out stars Electron degeneracy pressure can hold up a star of mass 1.4 M  or less against its weight, and do so indefinitely. Stellar cores in this mass range at death become white dwarfs. For heavier stars: gravity overwhelms electron degeneracy pressure, and the collapse doesn’t stop with the star at planet size.  As the star is crushed past a circumference of 10 4 cm or so, all the electrons and protons in the star are squeezed together so closely that they rapidly combine to form neutrons:  Eventually, then, the collapse might be stopped by the onset of neutron degeneracy pressure.  A star whose weight is held up by neutron degeneracy pressure is called a neutron star.

5. 16 October 2001Astronomy 102, Fall 20015 Oppenheimer’s theory of neutron stars Neutron stars were first proposed to exist, and to cause supernovae by their formation, by Zwicky and Baade (1934). First calculations of their sizes: Landau (1938).  Neutron stars are analogous to white dwarfs, but the calculations are much more difficult, since the strong nuclear force and general relativity must be taken into account. (For white dwarfs, special relativity suffices because the gravity of these stars is not strong enough to make general relativistic effects substantial.)  As such, they may also be expected to have a maximum mass, as white dwarfs do. For stars more massive than this maximum, neutron degeneracy pressure will not prevent the formation of black holes.

6. 16 October 2001Astronomy 102, Fall 20016 Albert Einstein and J. Robert Oppenheimer at Caltech in 1939. They probably were, at that moment, discussing the prevention of black holes by neutron-star formation. Oppenheimer’s theory of neutron stars (cont’d) First calculation of maximum mass: Oppenheimer and Volkoff (1939). They got 0.7 M  ; more recent calculations, with improvements in the expression of the nuclear forces, give 1.5-3 M . (We will use 2 M  in this course.)

7. 16 October 2001Astronomy 102, Fall 20017 Circumference of Rochester (outer loop) Maximum mass 2 M  Oppenheimer’s theory of neutron stars (cont’d) Updated calculation using 1990s-vintage inputs for the strong nuclear force; otherwise the same as Oppenheimer and Volkoff. Circumference (km)

8. 16 October 2001Astronomy 102, Fall 20018 White dwarfs, neutron stars and black hole horizons Rochester Earth WD NS BH Circumference (cm)

9. 16 October 2001Astronomy 102, Fall 20019 Implications of neutron stars: (Type II) supernovae  After the electron degeneracy pressure is overpowered, and the electrons and protons combine to form neutrons, the star is free to collapse under its weight. Nothing can slow down this collapse until the neutrons are close enough together for degeneracy to set in. Requires confinement to space a factor of order 1000 smaller than for electron degeneracy pressure.  This collapse takes very little time, and the collapsing material is moving very fast when neutron degeneracy pressure takes over.  A neutron-degeneracy-pressure supported core can form from the inner part of the collapsing material.  The outer, collapsing material that didn’t make it into the neutron core proceeds to bounce off this core, rebounding into the rest of the star and exploding with great violence.

10. 16 October 2001Astronomy 102, Fall 200110 A supernova forms from a dead, massive star (not drawn to scale) Star: 6 M , 10 7 km circumference Core: 1.4 M , 10 5 km circumference Core: 10 4 km circum- ference. Electrons and protons begin combining to form neutrons. 2 years

11. 16 October 2001Astronomy 102, Fall 200111 A supernova forms from a dead, massive star (continued) Core: 70 km circumference, neutron degeneracy pressure sets in. Core: 10 4 km circumference. Electrons and protons begin combining to form neutrons. 1.2 seconds

12. 16 October 2001Astronomy 102, Fall 200112 A supernova forms from a dead, massive star (continued) Core: 70 km circumference, neutron degeneracy pressure sets in. This makes the core very stiff. Outside of core: still collapsing, moving inwards at about 10 10 cm/s. (Near light speed!) Bounces off stiff core.

13. 16 October 2001Astronomy 102, Fall 200113 A supernova forms from a dead, massive star (continued) Core: Still 70 km circumference, it is now stable. Outside of core: the rebounding outer-star material explodes the rest of the star. Energy comes from bounce, and from gravitational energy of core. A few seconds

14. 16 October 2001Astronomy 102, Fall 200114 A supernova forms from a dead, massive star (continued) Neutron star About a day Expanding supernova shell. Very, very bright for about a month after explosion (can outshine rest of galaxy!).

15. 16 October 2001Astronomy 102, Fall 200115 Mid-lecture break  Be on the lookout, on your email, for a notice of the availability of Homework Set #4 on WeBWorK. Image of Supernova 1994D in the galaxy NGC 4526, taken a few weeks after it was first discovered in March 1994, by the High-z Supernova Search Team, with the NASA Hubble Space Telescope. Supernova

16. 16 October 2001Astronomy 102, Fall 200116 Supernova 1987A Before : the Tarantula Nebula in the Large Magellanic Cloud, in 1984. The star that exploded is indicated by the white arrow. After: the same field, two weeks after the supernova went off. It was still easily visible to the naked eye. Images by David Malin, Anglo-Australian Observatory.

17. 16 October 2001Astronomy 102, Fall 200117 The appearance of a supernova as time passes Here is an animated view of the first month after the explosion of a supernova, courtesy of UC Berkeley’s Supernova Cosmology Project (Perlmutter, Nugent, Conley, Nugent). Click on image to see movie.

18. 16 October 2001Astronomy 102, Fall 200118 Neutron stars, supernovae and pulsars Many hundreds of neutron stars are known today; they appear mostly as pulsars : pulsating, starlike sources of radio and visible light, discovered in 1967 by Jocelyn Bell.  The Oppenheimer-Volkoff theory of neutron stars, and their maximum mass, has been confirmed in all essentials.  Theory and experiment on nuclear matter at high density done largely through the US and USSR nuclear weapons development programs.  Astronomers have only been able to measure the masses of a handful of neutron stars; they all turn out to be around 1.4-1.5 M , comfortably less than 2 M .

19. 16 October 2001Astronomy 102, Fall 200119 Neutron stars, supernovae and pulsars (continued)  The Zwicky theory of supernova explosion by neutron- star formation has basically been confirmed.  Many pulsars are seen to be associated with supernova remnants. Notably the Crab pulsar and nebula, in Taurus, remnants of Supernova 1054.  Not all live stars in the neutron-star mass range will become neutron stars; many eject a large fraction of their mass in their final stages of life and make the white dwarf cutoff. In their final “mass loss” stage, light from the stellar core lights up the ejected material, producing a planetary nebula.

20. 16 October 2001Astronomy 102, Fall 200120 Pulsar

21. 16 October 2001Astronomy 102, Fall 200121 A neutron star observed directly The neutron star at the center of the Crab Nebula, the remnant of the supernova visible in the year 1054. It is seen as a pulsar in these images taken 0.03 second apart. (This image’s orientation is rotated counterclockwise about 100 o from the previous one.) On Off

22. 16 October 2001Astronomy 102, Fall 200122 Final collapse of burned-out stars: white dwarf, neutron star, or black hole? If these stars do not eject mass while in their death throes, their fates are as follows: the Sun will become a white dwarf, Procyon will become a neutron star, and Sirius A will become a black hole. Sun Procyon Sirius A Circumference (cm) WD NS BH

23. 16 October 2001Astronomy 102, Fall 200123 Summary: status of the Schwarzschild singularity and black holes  Electron and neutron degeneracy pressure can prevent the formation of black holes from dead stars, but only for masses below about 2 M .  Stars with masses in excess of this must eject material during their final stages of life if they are to become white dwarfs or neutron stars. ( Most do.)  For masses larger than this, no force known to science exists that would prevent the collapse from proceeding to the formation of a black hole. For very heavy stars, black hole formation is probably compulsory. (Einstein’s objections are overruled.)