Over 1000 pulsars have been discovered, all with periods between 0.0016 and 4 s.
The best known pulsar, which is at the center of the Crab nebula, has a period of
0.033 s that is increasing at a rate of 10^5 s per year as the pulsar loses angular
momentum.Black HolesAn old star whose mass is less than 1.4Msunbecomes a white dwarf and one whose
mass is between 1.4 and 3 Msunbecomes a neutron star. What about still heavier old
stars? Neither a degenerate electron gas nor a degenerate neutron gas can resist gravi-
tational collapse when M 3 Msun. Does such a star end up as a point in space? This
does not seem likely. One argument comes from the uncertainty principle, x p
2. This principle prevents a hydrogen atom from collapsing beyond a certain size
under the inward pull of the proton’s electric field. The same principle ought to pre-
vent a massive old star from collapsing beyond a certain size under an inward gravi-
tational pull. Or perhaps the quarks of which neutrons and protons are composed
(Chap. 13) have special properties that stabilize such a star when it reaches a certain
density.
Whatever its final nature, as an old star of M
3 Msuncontracts it passes the Schwarz-
schild radius of Eq. (2.30) and from then on is a black hole (Sec. 2.9). We can receive
no further information from the star because its gravitational field is too intense to per-
mit anything, even photons, to escape past its event horizon.
Not only heavy stars end up as black holes. As time goes on, both white dwarfs and
neutron stars attract more and more cosmic dust and gas. When they have gathered
up enough additional mass, they too will become black holes. If the universe lasts long
enough, then everything in it may be in the form of black holes.Statistical Mechanics 331
The pulsar at the center of the Crab nebula flashes 30 times per second and is throught to
be a rotating neutron star. These photographs were taken at maximum and minimum emis-
sion. The nebula itself is shown in the photograph at the start of this chapter; it is now
about 10 light-years across and is still expanding.bei48482_Ch09.qxd 1/22/02 8:46 PM Page 331