Neutron stars and black holes

7.10 Neutron stars and black holes

What remains from this cataclysmic stellar explosion depends on the mass of the collapsing core. When stars, whose total mass is greater than ∼8 solar masses but less than ∼12 solar masses, collapse the result is a neutron star – the core being supported by neutron degeneracy pressure as described above. The typical mass of such a neutron star would be ∼1.4 solar masses so that it is, in effect, a giant nucleus containing ∼10 57 neutrons. It will have a radius between 10 km and 15 km – the theoretical models are not all that precise. Assuming a radius of

10 km, the average density would be 6.65 ⫻ 10 14 g cm ⫺3 – more than that of an atomic nucleus!

Gravity at the surface would be intense; for a 1.4 solar mass star with a radius of 10 km, the acceleration due to gravity at the surface would be 190 billion times that on the surface of the Earth and the speed of an object having fallen from a height of 1 m onto the surface would be 6.88 million km h ⫺1 ! A simple Newtonian calculation of the escape velocity from the surface gives a value of 0.643c. This implies that both special and general relativity need to be invoked when consider- ing neutron stars. The structure of a neutron star is very complex; part may even

be in the form of a superfl uid sea of neutrons which will thus have no viscosity.

Stellar Evolution – The Life and Death of Stars

Figure 7.11 Cross-section of a neutron star. Outer (solid) crust: nuclei of iron and nickel; inner crust: nuclei, superfl uid electrons and electrons; outer core: superfl uid neutrons, superconducting protons and electrons; inner core: condensed pions, kaons and quark matter?

A neutron star may have an outer crust of heavy nuclei, the majority being of iron and nickel. Within this is an inner crust containing elements such as krypton, superfl uid neutrons and relativistic degenerate electrons. The inner crust overlays an interior of superfl uid neutrons intermixed with superconducting

protons and relativistic degenerate electrons. Finally there may be a core of pions or other elementary particles (Figure 7.11).

Like white dwarfs, neutron stars become smaller and denser with increasing mass, but there will become a point when the neutron degeneracy pressure can no longer support the mass of the star. So, in an analogous manner to the

Chandrasekhar Limit for the maximum mass of a white dwarf, there is a limit, believed to be about 3 solar masses, beyond which the collapse continues to form

a black hole as will be discussed in Section 7.13. Stars rotate as, for example, our Sun which rotates once every ∼25 days at its equator. The core of a star will thus have angular momentum. As the core collapses, much of this must be conserved (some is transferred to the surrounding material), so the neutron star that results will be spinning rapidly with rotational periods of perhaps a few milliseconds. The neutron star will also be expected to have a very intense magnetic fi eld. This rotating fi eld has observational consequences that have allowed us to discover neutron stars and investigate their properties.

When the neutron star is fi rst born its surface temperature may approach

10 11 K. It initially cools by emitting neutrinos and antineutrinos – an interest- ing process that lasts about a day. A neutron decays to a proton, electron and an antineutrino. The proton then combines with an electron to give a neutron and

a neutrino – a sort of merry-go-round during which the neutrinos carry away energy and cool the star down to about 10 9 K. Neutrinos carry away much of the star’s energy for about 1000 years whilst the surface temperature falls to a few

Introduction to Astronomy and Cosmology

surface which stays close to 1 million K for the next thousand years. Its luminosity will then be comparable with that of our Sun.

This explains why the Crab Nebula could be still visible. It was known that a star close to the centre of the nebula had a very strange spectrum. If this were the neu- tron star associated with the supernova explosion, its energy output would have kept the gas thrown out into the interstellar medium excited, so remaining visible. The way in which this was confi rmed and how, to date, nearly 2000 neutron stars have been discovered is one of the most interesting stories of modern astronomy.