White Dwarfs and Neutron Stars
This chapter on the physics of compact objects begins with a section on white dwarfs. It will be shown that the famous Chandrasekhar equation is just the relativistic Thomas–Fermi equation. For white dwarfs the Thomas–Fermi approximation is ideally justif
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White Dwarfs and Neutron Stars
With all reserve we suggest the view that supernovae represent the transitions from ordinary stars to neutron stars, which in their final stages consist of extremely closely packet neutrons. —W. Baade and F. Zwicky (1934)
7.1 Introduction The bewildering variety of normal stars covers the mass range 0.07M M 60 to 100M . Masses smaller than the lower limit cannot become sufficiently hot to ignite nuclear burning and stars more massive than 60 to 100 solar masses would be unstable. The many different and sometimes brilliant evolutionary paths lead to the following few end-products of stellar evolution (see Fig. 7.1). 1. Low-mass stars with masses M 4M evolve into white dwarfs. White dwarf’s progenitor stars often undergo relatively gentle mass ejection (forming “planetary nebulae”) at the end of their evolutionary lifetimes and thereby reduce their mass below the Chandrasekhar limit for white dwarfs of about 1.4M . The slowly cooling white dwarf has a size approximately equal to that of the Earth. The Sun will become a white dwarf in about 5 × 109 years. We understand the structure of these objects in great detail. 2. It is possible that some stars in the range 4 to 8M ignite carbon under very degenerate conditions and are completely disrupted in some sort of supernova. (This is a very delicate problem for numerical simulations.) 3. For stars with masses larger than about 11M nuclear fusion proceeds all the way up to iron. At this point the central core runs into an instability and collapses catastrophically. This comes about as follows: In the last stages of nuclear energy generation an “iron core” of burned out elements is formed, which has the structure of a white dwarf. Around this core of iron peak elements an onion N. Straumann, General Relativity, Graduate Texts in Physics, DOI 10.1007/978-94-007-5410-2_7, © Springer Science+Business Media Dordrecht 2013
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White Dwarfs and Neutron Stars
Fig. 7.1 Mass-radius diagram for some astrophysical objects
structure is built up as a result of shell burning in various shells. The central white dwarf-like region finally becomes unstable due to electron capture and/or photo-disintegration of the iron-peak elements into α-particles. At this point the core starts to collapse in practically free fall. There are now two possibilities. (a) For some mass range, neutron star residues with increasing masses of 1.4– 2.0M , say, will be left behind a prompt or delayed supernova explosion. (b) For sufficiently massive stars, the core will, however, most likely accrete too much mass to be stable and will then collapse very quickly to a black hole. In this picture we do not expect a collapse directly to a black hole. A protoneutron star is formed first, which accretes sufficient mass through a stalled shock until it becomes unstable and undergoes a general relativistic collapse. It is difficult to say for which mass range of stars this is going to happen, but we do expect the formation of black holes for some very massive star
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